Prove the following $\neg((A\cap B)\cup (\neg A \cap C)) = (A\cap\neg B)\cup (\neg A\cap \neg C)$

How can I prove the following statements are equivalent using laws of set theory?  $\neg((A\cap B)\cup (\neg A \cap C)) = (A\cap\neg B)\cup (\neg A\cap \neg C)$  Using De Morgans laws to simplify the first statement:  $(\neg A\cup\neg B)\cap (A \cup \neg C)$ but I have no idea where to go from here.


Ubuntu 14.04.2 partition installing help!

I'm trying to install Ubuntu to a partition. Will this allow me to save my changes that i make on the system? I'm really concerned if this would or could mess my laptop up.


OS X El Capitan and older not available on App Store?

So it turns out I can not install Sierra because I have a Mid2009 Macbook Pro. I wanted to update to El Capitan, but it turns out its no longer available on the app store?  Any ideas, how to get El Capitan?


I have a class, Tile, that has a constructor with parameters of a Color object:  class Tile { public:     static const int size = 32;      Tile();     Tile(Color &color);      void render(int x, int y);      Color getColor();      ~Tile(); private:     Color _color; };   Then I have a subclass, TileGrass, which inherits Tile:  class TileGrass : public Tile { public:     TileGrass();     ~TileGrass(); };   Now the issue is that the TileGrass needs to inherit the Tile constructor with the Color parameters. But, the TileGrass object already knows what color it needs to give to the superclass, so I don't want to have to pass in a Color object when creating a new TileGrass object. In Java I can do something like this:  public class TileGrass extends Tile {  public TileGrass() {     super(color object); } }   How can I do something like this in C++?


recount to the other vs recount to each other

They recounted to the other what  had happened to them. They  recounted to each other what had happened to them. They recounted  each other what had happened to them.   Which sentence is more correct?


I need help with the following exercise:  determining the value of the next sum:  $$\sum _{ m=1 }^{ \infty  }{ \sum _{ n=1 }^{ \infty  }{ \frac { { m }^{ 2 }n }{ { 3 }^{ m }(n{ 3 }^{ m }+m{ 3 }^{ n }) }  }  } $$ First time I face a double sum. I have not the slightest idea how to begin to work it


Does anybody know of any software which will allow me to compress an ISO. file?


What is the purpose of a PCB with no copper tracks, but only unconnected copper rings?

I have a PCB which has the perfect size for a project of mine, so I would like to use it if possible. However, the copper plating on the back side of PCB only surrounds the individual holes (that is, no holes are interconnected). See picture right here:    I find this strange. How can this be useful? I would definitely need some copper tracks with interconnected holes in there because some components need to be connected to each other. Am I supposed to make my own tracks somehow?  I saw some stuff online about people who would insert multiple wires in the same hole to make interconnections, but this seems undesirable. I'd rather avoid that if there is some way to make tracks.


"Undefined reference" to declared C++ static member variable

I have started programming with Java, I just achieved which I consider as a "good" level in matter of language knowledge.  For fun I decided to start programming using C++, I'm fairly new to this language but I'm a fast learner and I think it's not that far from Java.  I've created a test class which has a value and a name as attributes, and an objects counter as a global variable.    #include<iostream>   /* local variable is same as a member's name */ class Test {     private:        double x;        std::string name;        static int nb;     public:         Test(double x, std::string n)         {             this->x=x;             this->name=n;             nb=nb+1;         }        void setX (double x)        {            // The 'this' pointer is used to retrieve the object's x            // hidden by the local variable 'x'            this->x = x;        }        double getX()        {            return this->x;        }        std::string getName()        {            return this->name;        }         static int getNb()        {            return nb;        }  };   int main() {    Test obj(3.141618, "Pi");    std::cout<<obj.getX()<<" "<<obj.getName()<<" "<<Test::getNb()<<std::endl;    return 0; }   When executed the programm outputs this error :  In function `Test::Test(double, std::string)':  (.text._ZN4TestC2EdSs[_ZN4TestC5EdSs]+0x4a): undefined reference to `Test::nb'  (.text._ZN4TestC2EdSs[_ZN4TestC5EdSs]+0x53): undefined reference to `Test::nb' In function `Test::getNb()':  (.text._ZN4Test5getNbEv[_ZN4Test5getNbEv]+0x6): undefined reference to `Test::nb' error: ld returned 1 exit status   some chinese to me.  I don't get it.


An intuitive reasoning for 1+2+3+4+5..... + ∞ = -1/12?

I was just watching this video:   In it, a professor working at the Nottingham University( Dr. Ed Copeland I think) shows how 1+2+3+4+5....+ ∞ = -1/12 Is this a joke? Or does it contain somewhere within it a flaw?  Now, I know that this channel and the people running it are by profession researchers so it does make me think whether this is true.  but at the same time, you are adding positive numbers on one hand and getting a negative sum?  The video also shows how 1-1+1-1+1-1.... =1/2 and that is counter intuitive too, how can you get a fraction when you are only adding together integers? I do however, painfully accept this as the truth because this is an infinite G.P. with r= -1. and I can get the answer using the formula.  what I am asking is:   Is this actually true or altogether false, or a limitation to the current system of mathematics and accepted as true only because otherwise, mathematics would be proven wrong? Is there any intuitive explanation to this (both the series that are mentioned), or can I only see it using mathematics? The video mentions that their are actual uses in physics for this. What are they?   I have read other answers and the opinions in them are conflicting, some say it is false and some say that it is true. Also, other questions don't seem to answer all hree of the questions posed.


Cheapest option to exchange money in Japan

I will be travelling from Europe to Japan and considering what's the best way to get Japanese yen:   Bring EUR from home country and exchange in Japan - airport or other place? Use ATM in Japan - how much does it charge? Pay by credit card - availability to use such option? Additional fees?


I was playing around with some integrals and noticed that some integrals of the form:  $$I(a,b,c)=\int_a^\infty \frac{\arctan(x+b)}{x^2+c}dx$$ Does have a closed form. I am trying to find for what constant $c$ will this work. In case you wonder why only $c$ is problematic, I will try to show by an example.  $$I=I(1,3,16)=\int_1^\infty \frac{\arctan(x+3)}{x^2+16}dx$$ Let's start by letting $x-1=t\,$ thus: $$I=\int_0^\infty \frac{{\arctan(\color{blue}{t+4})}}{t^2+2t+17}dt$$ With $\displaystyle{t=\frac{17}{y}\rightarrow dt=-\frac{17}{y^2}dy}$ $$I=\int_0^\infty \frac{{\arctan\left(\color{red}{\frac{17}{y}+4}\right)}}{\left(\frac{17}{y}\right)^2 +\frac{34}{y}+17 }\frac{17}{y^2}dy\overset{y=t}=\int_0^\infty \frac{{\arctan\left(\color{red}{\frac{17}{t}+4}\right)}}{t^2+2t+17}dt$$ $$2I=\int_0^\infty \frac{{\arctan(\color{blue}{t+4})+{\arctan\left(\color{red}{\frac{17}{t}+4}\right)}}}{t^2+2t+17}dt$$ $${\arctan(\color{blue}{t+4})+{\arctan\left(\color{red}{\frac{17}{t}+4}\right)}}=\arctan\left(\frac{\color{blue}{t+4}+\color{red}{\frac{17}{t}+4}}{1-(\color{blue}{t+4})\left(\color{red}{\frac{17}{t}+4}\right)}\right)$$ $$=\arctan\left(\frac{x^2+8x+17}{x}\frac{x}{-4(x^2+8x+17}\right)=\pi-\arctan\left(\frac14\right)$$ Above follows since the original integral is positive so we take $\arctan(-x)$ as $\pi-\arctan x $ and therefore getting a negative answer will not be an issue. $$I=\frac12 \left(\pi -\arctan\left(\frac14\right)\right)\int_0^\infty \frac{1}{t^2+2t+17}dt$$ Well, now the inner integral is not hard to compute and the final answer happens to be: $$I=\frac12 \left(\pi -\arctan\left(\frac14\right)\right)\frac14\arctan\left(\frac{t+1}{4}\right)\bigg|_0^\infty =\frac{\pi^2}{16}-\frac{3\pi}{16}\arctan\left(\frac14\right)+\frac18\arctan^2\left(\frac14\right) $$ There are more examples that I found by checking and try such as:  $$I(1,2,9)=\int_1^\infty \frac{\arctan(x+2)}{x^2+9}dx$$ $$I(2,1,6)=\int_2^\infty \frac{\arctan(x+1)}{x^2+6}dx$$ $$I(2,2,13)=\int_2^\infty \frac{\arctan(x+2)}{x^2+13}dx$$ And so on... All those can be solved by the same method: First substitute $x-a=t$, then let $t=\frac{\alpha}{y}$, where $\alpha$ is the "free of x" coefficient from the denominator.   The problem is that I tried more than $100$ combinations to get those integrals which is not that nice. How can we "smartly" find $c$ so that $I(a,b,c)$ is evaluable by symmetry? Or put in other word what should be $c$ if one wants to compute by symmetry $I(7,13,c)$?


I am using Ubuntu 14.04 Trusty Tahr with kernel (3.13.29). A couple of days ago the login screen doesn’t allow me to login. In the error log there is a   gnome-session error Segmentation fault on LibX11.so.6.3 error 4   This line occurs every time I try to log in. I have a Lenovo W530 and I am using the nouveau display driver.  I installed the gnome desktop environment, so at login I can choose the environment I want but this hasn't solved the problem. I re-installed Ubuntu and this error cropped up when I did a distribution upgrade on the system.


Display Monthly Attendance Report in MySql

I am doing a School Management System in php using Mysql DB. I am stuck in my Project. Please anybody suggest what I am doing wrong.  I have two tables in my database; one is to store Students records another one is to store their attendance day wise  Now I want to display a report of all students in particular class for the current month whether they were present or absent. But I am capturing only Absent students details only in attendance table.  I have written sql query to display the result here is:  SELECT tab.class, attend, DATE, ta.rollno, ta.StdNm  FROM tbl_absentees tab, tbl_admission ta WHERE ta.Cls = class   AND ta.rollno = tab.rollno   AND class =22   AND attend =  'A'   AND DATE =  '2013-06-07';   The result is:  Class Attend RollNo StudentName   But I want to display in 31 days table manner by taking only Date in attendance table if attend=A display A for absent Days otherwise Display 'P' for remaining days  How can I do this in mysql? Can anyone suggest/give me an idea to achieve this.  Sorry for misclarification in my question. Actually I want to display an attendance report for a particular month where data comes from two tables:   the first table consists of StudentName, RollNo, Class the second table consists of Date, Status, RollNo, Class   Now I want to display report like .


Is there any tutorial to install CUDA on Ubuntu 18.04?  The instructions on the Nvidia website for 17.04 and 16.04 do not work for 18.04.  I get a message telling me to reboot then re-run the installer.  However when I do this I get that same message again.


Proving the limit $\lim_{n\rightarrow\infty}(1+\frac{1}{n})^n=e$

I want to prove that $\lim_{n\rightarrow\infty}(1+\frac{1}{n})^n=e$  There is a solution of the sum provided in my text book. There the expansion of $(1+\frac{1}{n})^n$ is like below:  $(1+\frac{1}{n})^n= 1+{n\choose 1}\frac{1}{n}+{n\choose 2}\frac{1}{n^2}+{n\choose 3}\frac{1}{n^3}+.....$  But how can they write it as an infinite expansion? Does not the expansion end in the term $\frac{1}{n^n}$? But then we cannot prove that its limit is $e$, since $e$ has an infinite expansion.   Please help me clear this doubt. Thanks in advance.


Pronoun + "would rather" + (pro)noun + verb: what is a grammatical structure of such phrases?

In George R. R. Martin's A Game Of Thrones, there is a moment when one character says the following words:     “So the slaver has become a spy. I would rather he become a corpse.”   Now, I understand the general meaning of it: that the speaker would prefer that person to be dead rather than spying around. What I don't understand is the exact grammar behind the second sentence of the example below.  From what I know, rather is an adverb, so the main clause doesn't have a predicate and technically is incomplete. And since there is a common language structure "pronoun + would rather + verb1 (+ than + verb2)", like I would rather die (than do it), I assume that in my example is used some specific shortened form of a more verbose construction, like it's the case with would that i could. Am I correct? If so, then what is the full form of it?  Also, I'm not entirely sure in what tense become is used in the second sentence. Is it a subjunctive present form, or some shortened form of present perfect that was used in the first sentence, or maybe something else entirely?  And one more thing. When "would rather" is used like in the example above, does it imply some, I don't know how to say it, temporal reference, i.e. when the action described by the verb that follows it should happen or should have happened? In other words, in my example, does the speaker express a wish to see that person dead already or simply want him to die at any time in the future?  Thank you!


Please help me with this limit without using L'Hôpital's rule. I would by happy if you use simple solving. Thank you as much as I can ;).   $$\lim_{x\to0}{{\frac{\ln(\cos(-5x))}{\ln(\cos(-3x))}}}$$


Convergence test for: $\sum\limits_{n = 1}^{\infty} \frac{n}{e^n}$

I know, for example, that the series:  $$\sum\limits_{n= 1}^{\infty} \frac{1}{e^n}$$  is a geometric series of the form $\sum\limits_{n = 1}^{\infty} k x^n$, where $k = 1$ and $x = \frac{1}{e}$ and it is convergent1. But when I have, as in my case:  $$\sum\limits_{n = 1}^{\infty} \frac{n}{e^n}$$  a ratio of functions I'm struggling to find a method to find whether the series is convergent/ divergent and to find a value in the former case. Thus the following question arises:  What series convergence method to use in case of ratio of functions?    1. And its value is: $\frac{k}{1 - x} - 0^{th}term$


Get RD user client hostname in Server 2012 R2 RD deployment

There is currently nowhere in the server manager GUI that I can see, that shows me the hostname of the machine a user is using to log onto our remote desktop deployment.  I have had a quick look through the powershell commandlets included with 2012 R2, but cannot find anyway to get the hostname for each connection.  Is it possible to retrieve this information?


Unable to uninstall apps for secondary account

I have a Nexus 10 on which I have a master account, and a secondary  (restricted) account for my kids.  Recently, one of them got hold of it while it was logged in and installed a bunch of games. I removed them again — or so I thought. I just found out that, while they don't show up in the list of apps tray, they do show up among the app permissions for the secondary account, as well as in the list of apps available via settings -> apps.  I can't uninstall them from either location. While I suspect I can I uninstall them from the secondary account, how do I know they're really gone if I do so?  Shouldn't I be able to uninstall them from the master account?


Prove the zero in the complex number system is unique.  I have an idea but i don't know how start this proof.   The idea:  I think start out with the assumption that there exist two different unities, say, $a$ and $b$, and then proceeds to show that this assumption leads to some contradiction.  But i'm a little stuck. Can someone help me?


Resize Move Partitions on Dual Boot System

I would like to be able to adjust the partitions shown below. Specifically, I want to add an additional 10GB from the unallocated space to /dev/sda5 (Ubuntu install). I will then format the remaining unallocated space as NTFS so it can be shared data between Windows and Ubuntu.   I am unable to increase the size of /dev/sda5 - I am only able to shrink it.  Any assistance would be greately appreciated.


How to get an enum value from a string value in Java?

Say I have an enum which is just public enum Blah {     A, B, C, D }  and I would like to find the enum value of a string, for example "A" which would be Blah.A. How would it be possible to do this? Is the  the method I need? If so, how would I use this?


How to show $u \in R^{x} \implies u \in R[X]^{x}$ for integral domain $(R,+, \times)$

I am studying ring theory and have come across polynomial rings. There is an exercise to show that $$u \in R^{x} \implies u \in R[X]^{x}$$ where $(R,+, \times)$ is an integral domain. I know that $R^{x}$ is the set of all units in R, which is the set of all elements of $R$ with a multiplicative inverse, and similarly for $R[X]^{x}$. But I am stuck with proving the above statement.


Changing the qedsymbol to a personal icon

When I write out my own proofs by hand on paper, I use my own personal variant of Q.E.D. / square to finish out the proofs (its a cursive version of my initials).   I've doodled up this icon on paint and want to insert it into my proof environments in the end as its Q.E.D. symbol.   I know how to change the symbol to whatever using   \renewcommand{\qedsymbol}{text here}   But I don't know how to extend this to use an image file rather than text. Any advice appreciated!


How do I resolve a connection issue I'm having between my laptop and my Brother printer?

Brother HL-L2305w Laser Printer for CUPS OS: Ubuntu 20.04.2 LTS, 64 bit GNOME: 3.36.8 Used linux-brprinter-installer-2.2.2-2 to install drivers. Printer and laptop are connected to the same WiFi SSID network. Test prints can be made directly from the printer but not from the laptop. Note: This printer was previously connected to a Windows machine and one test print indicates that the Windows drivers are still installed. $ avahi-discover Browsing domain 'local' on -1.-1 ... Browsing for services of type '_http._tcp' in domain 'local' on 3.0 ... Browsing for services of type '_ipp._tcp' in domain 'local' on 3.0 ... Browsing for services of type '_printer._tcp' in domain 'local' on 3.0 ... Browsing for services of type '_pdl-datastream._tcp' in domain 'local' on 3.0 ... Found service 'Brother HL-L2305 series' of type '_http._tcp' in domain 'local' on 3.0. Found service 'Brother HL-L2305 series' of type '_ipp._tcp' in domain 'local' on 3.0. Found service 'Brother HL-L2305 series' of type '_printer._tcp' in domain 'local' on 3.0. Found service 'Brother HL-L2305 series' of type '_pdl-datastream._tcp' in domain 'local' on 3.0.  $ avahi-browse -rt _ipp._tcp +   wlo1 IPv4 Brother HL-L2305 series                       Internet Printer     local Failed to resolve service 'Brother HL-L2305 series' of type '_ipp._tcp' in domain 'local': Timeout reached  Recent dmesg:   are the results of running the various commands suggested in  troubleshooting guide. It seems that the laptop and printer cannot "see" each other so printing from the laptop is not possible. Solutions?


List of related tags on 'Tag top users' page should not include the tag itself

If not a bug, this at least is inconsistent behavior.   Go to any  or  page, say for 'bug'. Check the list of related tags, note 'bug' itself is not present. The  page, however, has 'bug' at the top of the list of related tags.     Similarly, any tag is listed at the top of the 'Related tags' list on the 'Top users' page, but not elsewhere.


I have just installed 12.04 LTS on my laptop and I'm kinda new in this. I am required to write some program in Fortran 77 and I need a Fortran 77 compiler. I have tried installing g77 as described in the Ubuntu website but was unable to do so. I have typed in the following in terminal:  sudo apt-get install g77   and get the following:  Reading package lists... Done Building dependency tree        Reading state information... Done Package g77 is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source  E: Package 'g77' has no installation candidate   May I know what is the problem? I have tried searching g77 in the software center but apparently it is not there. Does this mean it is not available for 12.04?  I'm currently using an Asus K43S laptop with Intel Core i5-2450M processor and my Ubuntu is installed alongside Windows.


The 'grub-efi-amd64-signed' package failed to install target/

I am unable to install Ubuntu 18.04.  To start things off, I see a black screen instead of installation instruction after booting the liveusb using BIOS boot (not UEFI). Not sure why this black screen but I am guessing its a graphics driver issue. I am using a newly bought amd rx560 card.  But I did however gain access to the OS by setting 'nomodeset'. Unfortunately at the end of the installation process, it failed to install the GRUB, giving me the error message shown in the title of this question.  I usually have two partitions for any linux distro: swap and root. I also leave the "Device for bootloader installation" option untouched. Which is by default /dev/sda  Please feel free to ask me any information regarding this. I really need help on this. I don't want to go back to windows after 9 years of ubuntuship.


One material with different color per mesh?

I just started a project width a lot of colored pencils in it.  As I want to have all of them have the same Material, but a different color, i came up with the question:  Is there a way to create a single Material und assign different colors to meshes that all have this one material assigned?  Or:  Is it possible to link the materials of the pencils, so if I tweak one of them, the rest will have the changes applied, too?


Are the implications of an infinite universe necessarily so unsettling

I have often heard it said (by professional cosmologists) that if the universe is infinite, then there necessarily exist infinitely many copies of me repeated throughout.  The reasoning seems to be that any finite volume of space can contain at most finitely many fundamental particles existing in finitely many configurations.  From here it is implied that all possible (permissible) configurations must both exist and occur infinitely often.  This does not sound like a sound argument to me, so I have to believe that I have misunderstood the argument.    Is this unsettling implication true in an infinite universe, and if so how is it justified.


Is the universe immediately dependent upon the past?

Given complete knowledge of the precise state of every property of every particle and energy phenomenon existing in our universe for a given infinitely small frame of time, is it possible to completely determine the status of every property of every particle and energy phenomenon existing in the succeeding time frame?  This situation assumes that there are no restrictions towards the access of any information, particularly particle states, existing in the universe.  How can this situation be mathematically modeled?


I have downloaded ubuntu iso on windows 10.  I have tried double click on iso file but windows asks for application to use. how do I start the iso?   Is it secure to run ubuntu under windows 10?


Installing Ubuntu over Mint in a dual boot configuration

I'm attempting to replace an existing Mint installation with Ubuntu on a UEFI system. The complication is that I'm dual-booting with Windows, and I'm very wary of messing that up in the process.  In the installer, I'm choosing to do "something else" as the installation type. I am then presented with the following (I've stitched multiple screens together to make this a bit easier to understand):    I'm unsure on exactly what I need to do here to ensure my Ubuntu replaces my Mint. I'm particularly concerned about the following:   Will Grub show me only Ubuntu and remove the current Mint entry? The "Device for boot loader installation" has me concerned. Should I leave this as /dev/sda? Do I need to manually delete the partitions currently used for Mint?   Can anyone tell me the exact procedure I should follow here?


Should I use "a" or "an" when I abbreviate a word?

Taking notes, I was going to write this:     therefore p′ is a shortest path.   But the topic is APSP which stands for "all pairs shortest paths" so I decided to just write SP instead and...  Is it written with a like this     therefore p′ is a SP   or with an like this (because in my head I would "read" the S)     therefore p′ is an SP


I am working on a custom carrier board using a TI microcontroller as the master and an ADC IC as the slave. It appears that sometimes SCL will stay high when it shouldn't, almost like the master releases it. We only get this fault condition on a reset of the MCU (or total system power cycle) but it does not happen every time, maybe one out of ten on average.   Data transfer will be fine most of the time, until one of the unlucky resets causes the issues. You can see in the image below that after the address byte is sent SCL just goes high after a few clock pulses. Any ideas?


How does capacitor block DC when an AC signal is superimposed on top of it?

This question has been in my head for so many days. When I was studying BJT amplifiers, capacitors were used for blocking DC. It is called a coupling capacitor. When the AC signal is superimposed on DC and is applied to the circuit shown, what would be output across R(Vo)? My professor told that we will get a sine wave(5sinWt) with reference to ground and DC(10) would be eliminated. But I am not able to visualize the waveforms across C and R. I want to know how capacitor charges and discharges and blocks dc. Please help me with the waveforms.


Is there any size limit to the amount of information a human (or other) brain can hold

Im not sure how this would ever be tested but is there a limit to how much the brain can 'hold' before it reaches capacity ?  I guess this could also be interpreted in terms of memory, as how well some one remember something before reaching capacity / forgetting 'old' memories to make way / space for new ones.


How can I see my full character without idling?

Is there a way I can see my full character without having to tilt the camera down at him? The only way that works is having my character idle and rotating the camera around him.


How can I upgrade the Ubuntu 18.04.3 kernel to 5.0

I'm using Ubuntu 18.04.3 LTS with kernel version 4.15.0-55-generic.  How can I upgrade the kernel to 5.0? I have run the update-manager -d command already.


I am matching whole words in a sentence using preg_match in PHP. This works fine. But it happens that sometimes a word is not matched due to one typo. For instance the official word is "Prader Willi syndrome". But then a biologist types "Prader-Willi syndrome" (the extra hyphen).   Is it possible to match words where you allow one typo using a regex?


Alias accepting variables from the result of evaluation

I was trying to define an alias that helps me to cd to the directory that is created most recently, and I'm using the following in my .bashrc:  alias cdlatest="latestdir=$(ls -td -- */|head -n 1); cd $latestdir"   But this alias only works once. If I change to a new directoy, it still tries to cd to the last directory. It seems becaue the variable $(ls -td -- */|head -n 1) is only evaluated once from the start. How to fix this?


I used the sklearn.metric roc_auc_score,it gave me a value 0.91.  What is the does this number mean?   I am interested to learn how this is calculated,could someone please direct me to some information on this?


The symbol for the first person pronoun used to have a different and peculiar shape before the onset of computers. Now we simply use "I". How may I access this symbol?


How to solve this probability problem analytically (instead of using simulation)? Probability of Bill wins the game if he goes first

Here is the problem setup:  Two people play a game of throwing balls at a pin. Sally hits the pin 70% of the times she throws, and Bill hits the pin 40% of the times he throws. The game is won by the person who hits the target first. If Bill throws first each time, find the probability he will win.  With simulation, I get Bill's probability of winning to be around 0.52 (rounding to two decimal places). How to solve this problem analytically?


Short story: man rescues alien from cruel hanging ceremony, but alien turns into a shrub

I am seeking a short story where a man rescues an alien from a cruel hanging ceremony, but the alien turns into a shrub. It turns out the hanging ceremony was a way the aliens,of humanoid form, had developed to prevent themselves turning into a non-motile   mature form and to retain their humanoid form.The young ones were muscular and agile, but after the ceremony the older ones were emaciated and weak. By saving the young alien, the man is horrified when the rain starts and the young alien turns into a shrub ! The joke at the end is that the spaceman telling the story recounts how the unfortunate kind  man carts the shrub around the universe with him from job to job, and doesn't know he has the wrong shrub. He had grabbed it in the rain storm as they hurried to take off in their space ship while the angry aliens approached to rescue their young one. This was probably written in the late 1950's. One phrase in the story describes the spaceman doing maintenance, tightening bolts in rotation as per the service manual.


If statement to tell if a file is in a directory

I am writing a bash script and want it to tell me if the names of the files in a directory appear in a text file and if not, remove them.  Something like this:  counter = 1 numFiles = ls -1 TestDir/ | wc -l  while [$counter -lt $numFiles] do      if [file in TestDir/ not in fileNames.txt]      then           rm file      fi      ((counter++)) done


How do you cook a steak like those found in fine steakhouses?

I went to a 5* restaurant once, the steak was unbelievable.  You could cut it with a butter knife, it was fat and juicy, pink in the middle, great stuff.  When I cook it at home, I seem to just slice the beef thick, shallow fry it in olive oil with some garlic and  that is all.  It tastes pretty good, but is so far off what I had in that restaurant.  Anyone know how to cook the best steak?  Better cuts of meat?  Fry in butter?  Also any tips in general on how to cook good steak.  All appreciated!


Prove that $\cos x +\cos 2x + \cos 3x + ...+ \cos nx =\cos \left(\dfrac{n+1}{2}x\right) \sin \left(\dfrac{nx}{2}\right)\csc \dfrac{x}{2}$   Attempt:   Clearly, $P(1)$ is true.   Assume $P(m)$ is true.   Thus,  $P(m+1) = (\cos x +\cos 2x + \cos 3x + ...+ \cos mx)+ \cos((m+1)x)$  $= \cos \left(\dfrac{m+1}{2}x\right) \sin \left(\dfrac{mx}{2}\right)\csc \dfrac{x}{2} + \cos((m+1)x)  \\= \csc (\dfrac x 2)\left(\cos \left(\dfrac{m+1}{2}x\right) \sin \left(\dfrac{mx}{2}\right)+ (\cos(m+1)x)\sin (\dfrac x 2)\right)$  What do I do next?


Loops around 0 of polynomial restricted to the unit circle

Given a polynomial with coefficients in C, consider the image of the polynomial restricted to the unit circle (That is plugging in only things with absolute value one). How many loops around 0 can this image do? I'm thinking that at most the degree of the polynomial but I haven't been able to come up with a reason.


Where do the Transformers get their ammunition from?

In the Transformers films, Autobots have been shown to use ammunition for their weapons. In the fourth film, one of the Autobots claimed that he ran out of ammo during the battle with Galvatron and his army of transformers created by humans.  So where exactly do the Transformers get the ammo to reload their weapons? I don't think the humans make the ammo because that wouldn't explain where Decepticons who live on Earth get theirs - since the military would never work for them (the 3rd film showed that some people worked for the Decepticons, but I don't know if they had the resources).


Is the equation $y=\sqrt{x}$ a function?  A function has one only one $y$ value for a $x$ value.  An equation is an expression.  For the equation $y=\sqrt{x}$, $y=\pm\sqrt{x}$ Therefore, for a given $x$, there are 2 $y$ values.  However when I plot this equation in the calculator it only shows me the top half.  Please explain.   Thanks!


I'm trying to use natbib in a manuscript draft using the document class nature. If I use the bibliography style naturemag, any citation I try to use with \citet{something} does not turn up correctly, and is given a missing author.  Is there any way to solve this, or is the naturemag bibliography style incompatible with \citet citations?


I know that color comes from things not absorbing a certain wavelength of light, but what property gives something color? Like what property of copper atoms makes copper as a whole brown, or cobalt blue? Is there a solid states physics explanation for where color arises from microscopically in different materials?


Defining a variable after inner function is a bad practice?

I was thinking that variable can be only accessed after its declaration.  But apparently, Python's name resolution starts to look for from inside to outer.  My question is that this is bad practice in terms of readability? I was wondering that this might be a common knowledge for Pythonista so that I can write this kind of code from now on.  def outer():     def inner():         print x     x = ‘foo’     inner()   >>> outer() >>> ‘foo’


Is there an easy algorithm that outputs a random element of $SO(3)$ distributed according to Haar measure on $SO(3)$?  Or more generally, replace $SO(3)$ with any compact matrix Lie group. Note: I'm looking for something that assumes you can sample real numbers from "standard" distributions, e.g. uniform, normal, etc. (basically anything that's pre-implemented in a modern computer language)


I was wondering if we need to check the multicollinearity between variables when we run the stepwise regression, If yes, why? Also, If we have several IV, how we should know which interaction we should include in the model?


If $c >0$, $c≠ 1$, $z_1≠z_2$, prove that $\frac{|z-z_1 |}{|z-z_2 | }=c$ represents a circle. Find its center and radius.

I am studying complex analysis, and I was solving some questions regarding the subject when I stumbled upon this question. The equation above represents a circle, where $c$ is an arbitrary complex number. I don't get how it represents a circle, I tried proving it but I failed. Any help in finding the radius and center and proving the equation?


Within the Star Wars timeline, we first see Chewbacca in Episode III: The Revenge of the Sith. In it he appears as a full grown adult and seems to have a high status within his community. Then, of course, he appears in the "middle 3" episodes, where he pretty much looks the same.  Now he has appeared in Episode VII: The Force Awakens, still looking as if he hasn't aged. That is a period of over 50 years. How long do Wookiees live, and how do they change as they age?  Canon answers preferred, if possible.


change or deactivate iOS 9 newsfeed on the search screen

I have an iPhone 5 and just updated to iOS 9 (all german).   What I really do not like is the content of the newsfeed that is presented to me on the search screen. How can I change what content is presented to me (no more news from spiegel.de or focus.de please!) or if that is not possible, how can I completely disable news on that search screen but keep all the rest of the proactive search features on that search screen?   It appears in the US locale, the  but this app (and the switch for it) does not exist in iOS 9 that detects a german locale.


Showing $Z(D_n) \cong \Bbb Z_2$ when $n$ is even

Let $n \geq 3.$ Show that $Z(D_n) \cong \Bbb Z_2$ if $n$ is even, and $Z(D_n)=\{e\}$ when $n$ is odd.  First, let $n$ be odd. Assume for the contrary that there exists $\sigma \in D_n$ such that $e \neq \sigma$ and $\sigma \tau=\tau \sigma$ for all $\tau \in D_n$, where $e$ denotes the identity in $D_n.$ Since $\sigma \neq e$, there exists $i,j$ positive distinct integers such that $\sigma(i)=j.$ Let $k \neq i,j$ and let  $\tau=(i k)$\ (such a $k$ exists since $n \geq 3$). By our assumption, we should have $\sigma \tau=\tau \sigma$, so $$\sigma(\tau(i))=\sigma(k)\neq j=\tau(j)=\tau(\sigma (i))$$ a contradiction, so $\sigma$ must equals $e$. Hence, $Z(D_n)=\{e\}$ i.e the $Z(D_n)$ is trivial, for $n$ odd.  I feel i am ok with the part when $n$ is odd, but i am getting stuck when the case $n$ is even. So I would really appreciate any help or thoughts about that.  An alternative proof:  assume that $e \neq g \in Z(D_n)$. Then, $g=a^ib^j$ where $1 \leq i \leq n,\ \ j \in \{0,1\}$, so we have two cases:\ case (i) $g=a^i$. By the assumption that $ g \in Z(D_n)$ and the relation between $a,b$, we have $a^ib=ba^i=a^{-i}b$, therefore $a^i=a^{-i}$ which implies that $e^{2i}=1$. So $e^{2i}=1=e^n$ which means $i=\frac{n}{2}.$\ case(ii) $g=a^ib$. By assumption and the relation between $a,b$,$$a^i=(a^ib)b=b(a^ib)=(ba^i)b=a^{-i}bb=a^{-i}$$ so $a^{i}=a^{-i}$, which implies $i=\frac{n}{2}$. Also, for $a$ we have $$(a^ib)a=a^i(ba)=a^{i-1}b=a(a^ib)=a^{i+1}b$$ i.e $a^{i-1}=a^{i+1}$ here we have $a^2=1$, so what does that mean? and how to show $D_n \cong Z_2$ when $n=2k.$  Thank you.


Prove an inequality using complex analysis

If $f:\mathbb{D}\rightarrow\mathbb{D}$ is holomorphic then prove that   $$\frac{|f(0)|-|z|}{1 + |f(0)||z|} \leq|f(z)| \leq\frac{|f(0)| + |z|}{1 - |f(0)||z|} $$   I have been wracking my brain for hours and am out of ideas.  The hypothesis seems to suggest an application of the Schwarz lemma but I cannot find a suitable function - I've tried functions of the form $$\frac{f(z) - f(0)}{\mbox{scale factor}}$$ and none have worked.  I also tried working backwards to obtain an inequality and got $$-|z|\leq|f(z)||1\pm f(0)z| - |f(0)|\leq |z|\;\;\;\mbox{(*) }$$ If I could prove $$|f(z)[1\pm f(0)z] - f(0)|\leq 1$$ then I could obtain (*), but with so few conditions on $f$ I have no idea how to proceed.


How to sync iPhone HEIC / HEIF photos to MacBook Photos v1.5 (El Capitan)

My iPhone (iOS 12.3.1) takes pictures in HEIC / HEIF format.  I have an older Macbook (13" mid-2009) with MacOS El Capitan, which includes Photos v1.5.  When my iPhone photos get synced via iCloud to the Macbook, the thumbnails show up fine, but when I click on the photo, a large grey exclamation mark is shown.  What settings should I change to ensure they're also viewable in El Capitan Photos 1.5?  Please note that I'm not looking for another tool to run manually prior to each sync, as suggested in the "Duplication Question" suggestion.  I'm just looking for a set of configuration settings that others are using successfully, to take pictures on the iPhone using HEIC / HEIF, and view automatically (i.e. without using another tool manually) on my Macbook El Capitan.


Got Ubuntu 20.04 LTS for development needs, but In Jetbrains Rider i am not able to use  CTRL+ALT+SHIFT+[RIGHT|LEFT] shortcut for code rearranging. Tried to find the shortcut in settings -> keyboard shorcuts but failed. Any advice to work it out?


Show that $\sin(z) = z$ has infinitely many solutions in complex numbers. Little Picard theorem should help, but using big Picard theorem is undesirable. Thanks a lot!


Regular expression for parsing name and email from text

This is the regular expression I have formed so far:  /(?:("?(?:.*)"?)\s*)?\s<(.*@.*)>|(?:mailto:(.*@.*))|(.*@.*)/gi     I'm trying to extract 'Name' & 'Email' from the following:  John Smith <john.smith@gmail.com> John Smith <johnsmith@gmail.com> "John Smith" <johnsmith@gmail.com> "John" <johnsmith@gmail.com> John Smith<johnsmith@gmail.com> <johnsmith@gmail.com> johnsmith@gmail.com mailto:johnsmith@gmail.com "John"<johnsmith@gmail.com>  To: John Smith <john.smith@gmail.com> From: John Smith <john.smith@gmail.com> Reply-to: john.smith@gmail.com Return-path: <john.smith@gmail.com> Message-id: <john.smith@gmail.com> References: <john.smith@gmail.com> Original-recipient: rfc822;john.smith@gmail.com for john.smith@gmail.com ESMTPSA id <john.smith@gmail.com> domain of john.smith@gmail.com envelope-from=john.smith@gmail.com (ORCPT john.smith@gmail.com)   Having started from scratch, I feel as if I'm almost there - but having trouble with 3 things:   Stripping double quotes from the first capturing group Dealing with the whitespace missing variant: John Smith<johnsmith@gmail.com> False positives in the 'Name' field for the latter block, so I need a way of excluding these (perhaps using the preceding :, :, =, for, id, of?)   As a complete regular expression novice, I would appreciate a little direction from someone knowledgeable on how I might overcome these issues.  For the curious, I've unfortunately lost my CardDAV and thus all contacts, so in true Linux fashion, I'm going to rebuild a list of emails by manually parsing my entire raw MBOX, sorting by most common, and go from there.  I will be using bash grep, or perl sed.  Thank you for you time!


When will "apt-get install" does not asking for Y or N

When I run sudo apt-get install <whatever> it returns the choice to Y or N. Is there any exception to this behavior?     Because recently when I ran similar commands (without -y ) it didn't ask for Y or N. I used  Ctrl + C to interupt the process.


How to upgrade a 3rd generation iPad to IOS 7?

I have a family member with a 3rd Gen iPad (a1416) currently running iOS 6. They need to install an app that requires iOS 7. When looking at the system upgrade page in settings, it shows iOS 9 which I believe isn't compatible and also would probably run pretty slow anyway.   Is it possible to upgrade this 3rd Gen iPad to iOS 7? How can we do that? Thanks!  PS: I've already looked at  but the site mentioned in the answer there doesn't offer a signed iOS 7 image.


After installing NVIDIA drivers, I boot into a black screen [13.10]

Edit: Trying solution after solution found on these forums with the bootloader has apparently corrupted the bootloader. I missed pressing shift twice in a row and on the third attempt, the bios does not recognize a bootloader anymore. So it looks like I'm starting from scratch.  I am new to Ubuntu and I am using a 1440p & 1080p multi-monitor display setup. Using the default drivers (neuveau?), I am unable to get my display working because when I change my 1080p screen to be in portrait mode instead of the default landscape mode, my 1440p monitor goes black (It's a Crossover 27").  As a result, I assumed that the neuveau drivers won't cut it for my setup. So, I installed NVIDIA drivers for my GTX 680 using this guide:   After installation and reboot, both of my monitors are now black. I can hear the Ubuntu jingle at the log-in screen. Pressing CTRL+ALT+F1 results in a black screen with a flashing white underscore.   Using just one monitor procures the same results.   I am at a loss of where to go next.   Thanks for your help.  Edit: I decided to try running the following command (In recovery mode):  sudo apt-get purge nvidia-current   This did not resolve my issue. I still boot into a black screen.  2nd Edit: Things are getting stranger now. After attempting to uninstall the video drivers, I booted into recovery mode to try to update my system and reinstall them. After trying the networking option, Ubuntu froze there. So I did Cntrl+C and Ubuntu booted. My primary monitor was still black, but my secondary somehow worked. After logging in, my driver now says GTX 680.  So, I rebooted, and now I'm still back at the black screen on both monitors.


as you can see the flowers are not focused, I cannot focus everything, I have to chose the squirrel or the flowers, is it normal?  THANK you  D750 28-300


The genus of an algebraic curve is invariant under isomorphisms

I would like to know how to prove (or even better to see a full proof) of the following "fact".          Let $C_1$ and $C_2$ be two smooth curves and let $\phi : C_1 \rightarrow C_2$ be an isomorphism. Then     $$ \text{genus}(C_1) = \text{genus}(C_2) $$      I am not completely sure this is true since I haven't seen this result explicitly stated, but I Imagine it has to be true.   The motivation for this comes from an exercise from Silverman's book The Arithmetic of Elliptic Curves. I was doing the following exercise and I found that I needed the above mentioned fact in order for my argument for $(i) \implies (ii)$ to work.          2.5 Let $C$ be a smooth curve. Prove that the following are equivalent (over $\bar{K}$):          (i) $C$ is isomorphic to $\mathbb{P}^1$.          (ii) $C$ has genus $0$.          (iii) There exist distinct points $P, Q \in C$ satisfying $(P) \sim (Q)$      I've thought about it but unfortunately I don't really see how to easily relate the dimensions of the Riemann Roch spaces associated to each curve.   I would really appreciate some help with this.   Thank you.


Why does a wireless network give a more accurate location than a wired network?

I build a simple HTML5 website that takes my location (in latitude-longitude), and simply shows my location in Google maps.  I opened the HTML document with my laptop Asus K53E-B1 and I found that when I connected to a wireless network, it showed almost my precise location (about 100 meter of inaccuracy),  while when I plug in the network cable, and test again, it's a bit Inaccurate. (showed a street 12KM away from me).  Can you explain me why is a wireless network gives more accurate location?  Tested with Google Chrome.


Cannot install QGIS 3 on Ubuntu 18.04 (From ubuntu repo. Not ubuntugis-unstable )

When I want to install QGIS latest ver 3.3.4 to ubuntu 18.04 it rises error bellow :  Setting up qgis-providers (1:3.4.4+28bionic) ... /usr/lib/qgis/crssync: error while loading shared libraries: libQt5Core.so.5: cannot open shared object file: No such file or directory  dpkg: error processing package qgis-providers (--configure):  installed qgis-providers package post-installation script subprocess returned error exit status 127  dpkg: dependency problems prevent configuration of qgis:  qgis depends on qgis-providers (= 1:3.4.4+28bionic); however:   Package qgis-providers is not configured yet.  dpkg: error processing package qgis (--configure):  dependency problems - leaving unconfigured dpkg: dependency problems prevent configuration of qgis-plugin-grass:  qgis-plugin-grass depends on qgis (= 1:3.4.4+28bionic); however:   Package qgis is not configured yet.  dpkg: error processing package qgis-plugin-grass (--configure):  dependency problems - leaving unconfigured No apport report written because the error message indicates its a followup error from a previous failure.                           No apport report written because the error message indicates its a followup error from a previous failure.                                                     Errors were encountered while processing:  qgis-providers  qgis  qgis-plugin-grass  E: Sub-process /usr/bin/dpkg returned an error code (1)  I have removed it several times and install again but the problem still remains.  I use repository :  bionic main


How to intersect objects and delete leftover internal planes?

I'm trying to find a simple way to create vertices where two objects intersect and delete the leftover internal planes + then join the meshes so that I have one hollow mesh to sculpt. The reason I need to know this is that on my first sculpt I just joined the meshes, but it didn't create vertices at the intersecting points so when I went to sculpt it just overlapped the meshes as you can see here in the neck.  Here is what I am working on now, it needs to be 1 hollow mesh


As I have started on learning rings, I saw the notation $\mathbb{Z}[i]$ was used in the context of '$\mathbb{Z}[i]$ is a commutative ring'. What does this notation mean? Is it complex numbers where the coefficients are integer values?


What's the simplest way to call Http GET url using Delphi?

There's a web services I want to call in my application, I can use it with importing the WSDL or by just use "HTTP GET" with the URL and parameters, so I prefer the later because it's simple thing.  I know I can use indy idhttp.get, to do the job, but this is very simple thing and I don't want to add complex indy code to my application.  UPDATE: sorry if I was not clear, I meant by "not to add complex indy code", that I don't want add indy components for just this simple task, and prefer more lighter way for that.


I just deleted a file in Nautilus with Shift+Delete, which warned me that "If you delete an item, it will be permanently lost." I wonder if there is no way to recover the file?  My OS is Ubuntu 10.10.


How to refresh AD security group on Sql Server permissions

I am using Sql Server 2008 on Small Business Server 2003; client is using WinXP.   I added a user to my Active Directory Security Group; Why can't this user immediately access the database? It seems there is a delay before the user is recognized in Sql Server.   I am using AD Security Groups for permissions expressly so that I don't need to add individual users in Sql Server. So effectively I don't need to do anything but add the user to the AD Security Group in order to grant access.  But for some reason Sql Server doesn't immediately recognize the addition. I've seen this a number of times. I add the user to the group but that user can't access data until the next day. It seems that it doesn't query the Active Directory in real time. Can you confirm that is so?  What do I need to do so that Sql Server "refreshes" the list of users from Active Directory?


Return to an already open application when a user tries to open a new instance

This has been a problem that I haven't been able to figure out for sometime.  Preventing the second instance is trivial and has many methods, however, bringing back the already running process isn't.  I would like to:   Minimized: Undo the minimize and bring the running instance to the front. Behind other windows: Bring the application to the front.   The language I am using this in is VB.NET and C#.


A while ago, the following question was posted by the OP, who requested for help in proving the following inequality: Let $a,b,c,d$ be positive reals such that $a+b+c+d=1$. Prove that: $$\frac{a^3}{b+c}+\frac{b^3}{c+d}+\frac{c^3}{a+d}+\frac{d^3}{a+b} \ge \frac{1}{8}.$$  I have added the extra condition that $a,b,c,d$ must all be positive reals, since the given inequality by itself would not hold otherwise, as another user has pointed out in the comments. Since the original post has been closed (in all fairness to the OP, the condition of positive reals could be implied, especially if this was a competition math problem), I decided to open a new post in order to provide a possible solution for the OP, as well as inquire if there are other possible means to prove this inequality. My solution involves AM-GM, so it would be nice to see other methods that work as well.


To prove that the dimension of $V$ is $d_1^2 + \ldots + d_k^2$

Let $A$ be an $n \times n$ diagonal matrix with characteristic polynomial   $$(x - c_1)^{d_1} \cdots (x - c_k)^{d_k} , $$   where $c_1,\ldots,c_k$ are distinct. Let $V$ be the space of $n \times n$ matrices $B$ such that $AB = BA$. Prove that the dimension of $V$ is $d_1^2 + \cdots + d_k^2$.   I am completely stuck on it. Can someone help me please? Thanks for your help.


I would like to know why the menu button has been removed from Android in Android 6 and 7 mobile phones, hosting an apps button instead. Thanks.  (I remember long pressing the home button on Android 4 to get to the apps list.)


I've downloaded the file to install Ubuntu 14.04.1 LTS but I can't open it. Some advice?

The file is 'ubuntu-14.04.1-desktop-amd64.iso' and there is another one with the same name. I couldn't open it so I neither could install the new version. I'm really new into updates and ubuntu world, please help! Thanks! FJC


I'm having trouble in proving the following:  If $U$ is a neighborhood of $e$, there exists $V$ neighborhood of $e$ such that $V^{-1}V \subseteq U$  Can someone please verify if what I wrote makes sense? And if possible show the way to go further, because I'm stucked.  My attempt:   Let $G$ a topological group.  (Definition: A topological group $G$ is a topological space with a group structure such that the applications $m: G \times G \to G$ and $r:G \to G$, defined by $m(x,y) = x.y$ and $r(x) = x^{-1}$ are continuous.)  $V^{-1}V = \{ x^{-1}y ; x,y \in V\}$   $U$ is a neighborhood of $e$, then is $V^{-1}V$ a neighborhood of $e$?  Since $r$ is homeomorphism and the right-translation $\delta_y:G \to G, \delta_y(x)=x.y$ is homeomorphism, the application $\delta_y \circ r :G \to G$ is homeomorphism. Let $x \in U$. Then $\delta_y \circ r(x) = x^{-1}y$ is in an open set, because of continuity. Why is it a neighborhood of $e$?


Single Markers Used For Punctuation of Plurals

May I punctuate letters-as-letters and words-as-words in this manner (in lieu of italics)?  The professor said that Joel used too many 'why's, 'like's, and 'whereas's in his essay.  If we're using single markers (quotes) for this purpose, would the word 'whereas' be pluralized as 'whereas's or 'whereas'es? My vote is for 'whereas's (without the 'es' ending. Do you agree)?   And for letters and numbers (using this same method), are the following correct?  His 'y's look like '4's. His 'j's look like 't's.  I don't like this: 4s or 4's  I want to give strong emphasis to the individual letters and individual words (for the plurals) by using this method. Is it a viable alternative? I think the British might employ this technique.  Thanks for your continued support and guidance.


At a party $n$ people toss their hats into a pile in a closet.$\dots$

Question: At a party $n$ people toss their hats into a pile in a closet. The hats are mixed up, and each person selects one at random. What is the expected number of people who select their own hats?  My Attempt: Note, $$E(X) = \sum_{s\in S} p(s)X(s)$$   $E(x)$ is the expected value. $p(s)$ is the probability of event $s$. $S$ is the sample space. $X(s)$ is the random variable.   The probability of one person picking his/her hat is $\dfrac{1}{n}$, two person picking their hat is $\dfrac{1}{n}\dfrac{1}{n-1}$. Let $n$ be the number of people, let $P(n, r)$ be number of $r-permutation$ in $elements$. to generalize,  $$p(s) = \dfrac{1}{P(n, s)}$$ where $s$, the sample is the number of people who picked their own hat.  Before I plug it all in to the $E(X)$ equation, the random variable is $X(s) = s$, or simply an identity function. My expected value formula is,  $$E(X) = \sum_{s\in S} \dfrac{1}{P(n, s)}*s$$  $$E(X) = \sum_{s=1}^{n} \dfrac{1}{P(n, s)}*s$$  Is this anywhere right? If I'm on track, how do I show what it equals to? The answer key said it should equal to one, but I'm lost from here.


Is the process of accumulating reputation on this site exponential?

Does it become easier to accumulate reputation on this site the more reputation that you have? Is that somehow exponential?


How can lens cause consistent front or back focus?

I can understand body focusing problems, but I can't imagine why lens might cause front or back focus. I have two third party manufacturer lenses for my Nikon: one is front-focusing, the other is back-focusing. The body works fine on five other lenses, 4 of those from Nikon.  Correct me if I'm wrong: the phase detection focus sensor gathers light from different angles and steers the motor back or forth, so that images on focus point (be it stripe or cross) align. Given that everything is right with the body, the system of mirrors creates the same image on the autofocus sensor as it does on the film or digital sensor.  Now, assuming body mirrors are calibrated, either the camera algorithm didn't move the motor, when its focus sensor still detected misalignment or the lens moved between mirror going up and shutter firing.  I can understand that some motors might not be precise, but that would give inconsistent focus depending on the direction of the last correction. I can understand poor quality lens, that would blur parts of the image, give chromatic abberations etc. I can understand non-planar focus shape, but it still doesn't explain why the image on the focus point would not be in focus. I can understand moire effects, but that is not the case I observed.  I see no way that the lens can create a consistent focus shift other than body doing this on purpose. How can lens cause front or back focus?


Whatsapp Profile Pictures folder missing

I have a peculiar scenario with the Whatsapp Profile Pictures folder. Previously the Profile Pictures of contacts which I view used to get stored inside Whatsapp Profile Pictures folder. One day an error message (I presume) got popped up and I pressed OK without reading the message. From then the folder went missing but I am able to view the pictures even if the mobile is offline. Don't know where it is now saving the images. I have also checked if the folder was hidden. Even if I recreate the folder it is not storing the images in that folder. I have also reinstalled the application. Does whatsapp store the images in any other format or location other than storing in the default folder.


Can the "Vote to close" button be placed more conveniently in the popup in the mobile layout?

When a question received close votes for being a duplicate and one also casts a close vote for that reason, previously suggested duplicates can be selected.  That's convenient. The preview of the duplicate is expanded to show the entire question and all answers, which helps reviewing this possible duplicate.  The big amount of additionally displayed content pushes the submit button very far down. It's often sufficient to read the other question or a few answers to decide if it is indeed a duplicate.  All the convenience of being able to click on a previous suggestion is eliminated by the need to scroll all the way down to the bottom of the pop-up in order to click on the submit button.  Some possible solutions I could think of:   position the button near the top create multiple buttons and place one below the question and every answer move the button along when scrolling the window keep the height of the popup constant and let the content of the question expand in its own scrollable environment


Multiple regression - Interpreting the plots

I used the inbuilt dataset stackloss here. I used following R code for creating the multiple regression model.  > head(stackloss)   Air.Flow Water.Temp Acid.Conc. stack.loss   1        80         27         89         42   2        80         27         88         37   3        75         25         90         37   4        62         24         87         28   5        62         22         87         18   6        62         23         87         18  > fit <- lm(stack.loss ~ .,data=stackloss) > plot(fit)   And when I plot the model, the four following graphs are displayed.      How to interpret these graphs? What are the significance of these graphs? How to use these graphs?


Evaluate $$ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots$$  All i could do was to see that $$\frac{1}{3}=\frac{1}{2.1+1},\frac{1}{5}=\frac{1}{2.2+1},\frac{1}{7}=\frac{1}{2.3+1},\dots$$  SO, we should be able to write   $$ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots=1+\sum_{n=1}^{\infty}\frac{1}{2n+1}.\frac{1}{4^n}$$  This is what i could simplify the given question to...   But, this is doing me no good.. I could not go any further..  I would be thankful if some one can help me to clear this.  I would request users who are trying to help me to just give necessary hints but not post it as answer.  Thank You.


I am using Ubuntu 18.04. I tried installing Wine. Afterwards following error showed. E:Type 'cleadeb' is not known on line 1 in source list /etc/apt/sources.list, E:The list of sources could not be read.  Now I cannot install any other app. How do I solve this error?


Voltage rating vs. power rating of a resistor

My question may sound very basic, but I am very confused by the difference between the voltage and power ratings of a resistor.   says:     Rated Power      The maximum amount of power that can be continuously loaded to a resistor at    a rated ambient temperature. Network    and array products have both rated power per package as well as per element.      Rated Voltage      The maximum value of DC voltage or AC voltage (rms) capable of being applied continuously to resistors at the rated        ambient temperature.   I read  for a . Page 3 of the datasheet shows this formula:  \$ RCWV = \sqrt{P\times R}\$     Where RCWV = Rated DC or RMS AC continous working voltage at   commercial-line frequency and waveform(volt)      P = power rating (watt)      R = nominal resistance (ohm)   The above 27Ω resistor on the link has 50V voltage rating and 0.2W power rating, then I place the values into the provided formula  \$ RCWV = \sqrt{0.2\text{W} \times 27\Omega}=2.32V\$  Could anyone explain me why the voltage rating is 50V, not 2.32V?  When I want to calculate the maximum current that the resistor can stand using the power rating of the resistor (0.2W):  \$ P=I^2 \times R \$  \$ I = \sqrt{\dfrac{P}{R}} = \sqrt{\dfrac{0.2\text{W}}{27\Omega}} = 86\text{mA}\$  If I use the voltage rating:  \$ I = \dfrac{V}{R} = \dfrac{50\text{V}}{27\Omega} = 1.85\text{A}\$  By looking at these results, I should use the power rating, right?


Check a constraint after adding a Foreign Key

If I add a foreign key constraint with the following command:  ALTER TABLE [abc]  WITH CHECK ADD  CONSTRAINT [fk_some_col]    FOREIGN KEY([some_col_id]) REFERENCES [xyz] ([some_col_id])   Is there any reason or advantage to follow it with this line?  ALTER TABLE [abc] CHECK CONSTRAINT [fk_some_col]


I'm using the glossaries package. I have an acronym (eg. API) that should be explained in the Glossary. It should be linked to the Glossary at occurrence but should be written out at first occurrence. How can I do that?  Explanation: I want something like that:  This is a test of Application Programming Interface (API). And this is the second occurrence of API.  Acronyms API Application Programming Interface Glossary API An Application Programming Interface (API) is a particular set of rules and specifications that a software program can follow to access and make use of the services and resources provided by another particular software program that implements that API


Is it possible for someone to do their masters in Maths once they've earned their degree in Computer Science?

I was wondering. Is it possible for someone to major in Maths as in do their masters in Maths once they've earned their degree in Computer Science?


Convergence of $\sum \limits_{n=1}^{\infty}\sqrt{n^3+1}-\sqrt{n^3-1}$

Hello I am a high school student from germany and I am starting to study math this october. I am trying to prepare myself for the analysis class which I will attend so I got some analysis problems from my older cousin who also studied maths. But I am stuck on this problem. Check the following series for convergence/divergence $$\sum \limits_{n=1}^{\infty}\sqrt{n^3+1}-\sqrt{n^3-1}$$ I tried to prove the convergence by comparison test  $$\sqrt{n^3+1}-\sqrt{n^3-1}= \frac{2}{\sqrt{n^3+1}+\sqrt{n^3-1}}=\frac{1}{n^2} \cdot \frac{2\sqrt{n}}{\sqrt{1+\frac{1}{n^3}}+\sqrt{1-\frac{1}{n^3}}}$$ and then compare it with $$\sum \limits_{n=1}^{\infty}\frac{1}{n^2}$$  But in order to do that, I need to prove that $$\frac{2\sqrt{n}}{\sqrt{1+\frac{1}{n^3}}+\sqrt{1-\frac{1}{n^3}}} \leq 1$$ But I am having problems to prove that. Does anyone have tip how to solve this problem?


Is there any consensus as to whether a Tenser's Floating Disk floats over water?   asks a related question, but the water thing isn't asked nor answered there.  So, would you have it float above the water's surface, or above the ground below the water/liquid?


Combination problem: retrieve four kinds of objects with restriction

How many ways are there to select (combinations) $n$ objects from $a$ identical  objects of first kind, $b$ identical  objects of second kind, $c$ identical  objects of third kind and  $d$ identical objects of fourth kind? P.S. : Since the maximum number of any kind is restricted it is different from the original stars and bars problem where there is no restriction.


Finding the distribution of $\|X-\mu \|_\Sigma^2$ with $X \sim N(\mu,\Sigma)$

Let $\Sigma$ be positive definite and symmetric and let $\| x \|_\Sigma := \sqrt{x^t\Sigma^{-1}x}$ be the Mahalanobis norm. Let further $X \sim N(\mu,\Sigma)$ be a $p-$variat normally distributed random vector. Find the distribution of $\| X-\mu \|_\Sigma^2$.   I do not kow how I could do that. Could you help me?


Creating Offline Maps using QGIS and OpenStreetMap?

I am working with QGIS 2.10.1, having only little knowledge with the software so far.  I am mapping certain findspots in northern Bavaria and use the OCMlandscape map as basemap. Everything works fine as long as I am in the internet, but I need the whole thing offline.  The Offline plugin Database->offline editing->convert into an offline project doesn't work. The program tells me "unable to open database file".  Afterwards I tried to download the part via Vektor->Open Street Map -> Download Data, but the download gets always interrupted.  I then downloaded the Northern Bavaria map from geofabric (file: .osm). With Vektor -> Open Street Map -> topology imported from XML and afterwards ->topology export to spatial line I get a huge set of data and a blue points or lines or polygons that has the shape of northern bavaria but doesn't look like a topographic card :)  How do I know which tags I have to export?  Or do you have any idea how to get this ground map offline?


Getting NullPointerException while uploading file(s) using p:fileUpload

I'm having issues with <p:fileUpload> constantly receiving java.lang.NullPointerException.  Here's my code:  XHTML:  <h:form enctype="multipart/form-data">     <p:growl id="messages" showDetail="true" />     <p:fileUpload value="#{fileUploadView.file}" mode="simple"/>     <p:commandButton value="Submit" ajax="false" actionListener="#{fileUploadView.upload}"/> </h:form>   fileUploadView.java  public class FileUploadView {      public String[] inFileString;     private UploadedFile file;      public UploadedFile getFile() {         return file;     }      public void setFile(UploadedFile file) {         this.file = file;     }      public void upload() throws IOException {         if (file != null) {             InputStream strumyk = file.getInputstream();             InputStreamReader is = new InputStreamReader(strumyk);             BufferedReader reader = new BufferedReader(is);             inFileString[0] = reader.readLine();             FacesMessage readStream = new FacesMessage(inFileString[0]);              FacesMessage message = new FacesMessage("Succesful", file.getFileName() + " is uploaded.");             FacesContext.getCurrentInstance().addMessage(null, message);         }     } }   Am I doing something wrong here?


How to know when it's possible to solve a modular equation?

In my professor's notes there's the following example:  $$21x \equiv 15 \pmod{39} \Leftrightarrow 21x - 39y = 15$$  It reads:      Because $\gcd(21,-39) = 3$ and $3\mid15$, this equation has a solution.   This confuses me because just earlier, and on articles I've read on the internet what it always says is that these equations are only possible if gcd(21,39) (in this case) equals 1, or that they are relatively prime. Now I am just confused. Which one is it?


Can I use $V-E+F=k$ when dealing with spheres and great circles?

A great circle is a circle drawn on a sphere that is an "equator," i.e., its center is also the center of the sphere. There are $n$ great circles on a sphere, no three of which meet at any point. They divide the sphere into how many regions?      (The Art and Craft of Problem Solving, Page $37$, Problem $2.2.14$)   $2.2.12$ asks about the relation between vertices, edges and faces on a $3\text{-d}$ polyhedron, which is simply $V-E+F=2$.  $2.2.13$ asks about the number of regions an infinite plane can be split into using $n$ non-parallel lines, no three of which meet at any point. Here I checked a few cases, determined that $k=1$ and used $V-E+F=1$ to find that $f(n)=\frac 12 (n^2+n+2)$ where $f(n)$ is the number of regions.  For $2.2.14$, I am once again attempting to find $k$ such that I can use $V-E+F=k$. However, I am unsure how to define vertices or edges here. The few things I attempted all suggested different values of $k$ for different values of $n$.   I am unsure as to how I can determine $k$, as well as defining how vertices and edges are counted.  Additionally, it would be really helpful if there was a simple way to manually count the number of edges, vertices and faces, especially since making $4$ great circle on a sphere and reading the number of faces, vertices and edges using Geogebra $3\text{-d}$ was very difficult.


Prove altered version of Eisenstein's criterion

Let $f(x)=a_0 +a_1x+\dots +a_nx^m \in\mathbb Z[x]$.  Suppose $\exists p$ prime: $p\mid a_1$, $p\mid a_2$, $\dots$, $p\mid a_n$, but $p^2 \nmid a_n$ and $p\nmid a_0$.   Prove $f(x)$ is irreducible in $\mathbb{Q}[x]$.  Note that this is not Eisentein's criterion, but it is very close.    "Proof"  (by contradiction)    We assume $f(x)=a_0 +a_1x+\dots +a_nx^m \in\mathbb Z[x]$, $\exists p$ prime: $p\mid a_1$, $p\mid a_2$, $\dots$, $p\mid a_n$, but $p^2 \nmid a_n$ and $p\nmid a_0$,  and $f(x)$ is reducible in $\mathbb{Q}[x]$.  if $f(x) $ is red. over $\mathbb{Q}$ we know it will be red in $\mathbb{Z}[x]$ so $\exists g(x),h(x)\in\mathbb Z[x]$ s.t. $$ f(x)=g(x)b(x) \text{ where } 1 \leq \deg g(x),\deg h(x) <n$$  Say $g(x)=b_rx^n+\dots+ b_0$ and $h(x)=c_sx^s+\dots +c_0$ now, $$                    p\nmid a_0 \equiv \neg (p\mid c_0 t_0)\equiv \neg  (p\mid c_0 \vee p\mid t_0)\equiv p\nmid c_0 \wedge p\nmid t_0                          $$   $$p^2 \nmid a_n\equiv p^2 \nmid c_s t_r \equiv p^2 \nmid c_s \wedge p^2 \nmid c_r$$  also, $p\mid a_n$ so $p\neq 0,\pm1 $ so $p\mid c_r r_s $  $\vdots$  Contradiction somewhere  $\vdots$


If you trigger Tree of Perdition's ability, then give the tree -13/-13, does the player go to 0 life?

If you activate 's ability, "Exchange target opponent's life total with Tree of Perdition's toughness", then play a spell before the ability resolves that brings the tree's toughness to 0, does the opponent's life total become 0?


What are pros and cons of using single page with anchors vs section with subpages in menu? I'm asking in context of "About us" section where we have such information as: basic facts, offices, team and values.


Display of Publications for Personal Website

I've seen a number of sites and web controls for presenting a list of papers (e.g., in BibTex format) on one's personal website.  Some sites also allow you to manage your citation list, then link to a list of publications.  I was wondering about people's experiences with these different tools and the pros/cons.  While I've historically just manually dumped my refs in HTML format for my site, I'm looking to use something a bit more elegant and maintable these days.  Ideally, I would like it to have the following characteristics:   Easy to add/edit papers (e.g., generate from BibTex, Mendeley, online storage, etc.) Splitting papers into groups (e.g., journal papers, conference papers, etc.) Decent fallback display for users with JS disabled.  Ideally, no change at all. Papers sortable by year Can specify links or upload pre-print PDF's that users can download   Does anyone know how well existing solutions stack up on these?


Remove gaps between polygons of a shapefile

I have extracted a polygon shapefile using raster to vector tool from TIFF image, and it has produced polygons from the Raster, but it has also generated the gaps between the polygons as attached in below image. What is best way to remove those gaps between polygons?


Determine remainder of the product of two numbers, when we know the remainder of each individually?

I want to confirm some of my logic with remainders.  If I know the remainder of $\frac{x}{y}$ is $n$, and the remainder of $ \frac{z}{y}$ is $m$, then can I say that the remainder of $ \frac{xz}{y}$ is $n*m$?  I don't have a formal proof, but I can't find a counter-example.


Installing Ubuntu server create problem in my Dell R540

My problem is that when i started install ubuntu server in my server machine(Dell R540), it starts showing me the problem that "there was a problem completing the installation" and it restart with same language prompt again. so I detect the problem and it is not with my hardware machine but it is because of the ISO fie I downloaded from the ubuntu official website. I firstly downloaded the iso from here :   so this iso file is responding with "there was a problem completing the installation" after that I downloaded another ISO from here :   It smoothly worked so the question is why these two are behaving differently.


Visual Studio IntelliSense & syntax highlighting not recognizing Unity types

Frequently when I open a Unity C# script in Visual Studio, the built-in Unity Engine types aren't recognized, so I don't get syntax highlighting or code completion hints for things like MonoBehaviour.    Sometimes if I delete the script and create a new one it works, but lately nothing I do solves the problem.  Is there something I can do?


Understanding the Mathematics of Wigner function

I fully understand that  provides the complete information of a state of a quantum system, i.e. quantum phase space, while not violating Uncertainty principle. But can anyone tell me how this is derived and why it could work at the first place?  To me the mathematics isn't very simple to visualise. It looks like some convolution and fourier transform in place at the same time. It would be helpful if anyone can motivate the origin of the terms in the function?


What's the reason using Map class for instantiate of HashMap class?

Why Map class is used in the case below? I've been stuck to this question for long time... Map<Integer, String> m = new HashMap<>();  Instead of just using HashMap class like this.  HashMap<Integer, String> m = new HashMap<>();


How do I block myself from time-eating websites?

I want to block my Mac (running Snow Leopard) at work from accessing sites like Facebook and reddit.  there are browser extensions, but I'm worried about security – I get nervous allowing them to "access my data on all websites".  Is there a simple direct way to do it?  My main browser is Google Chrome.


How to copy and paste a file through the command-line?

I want to copy and paste a file to /usr folder but I guess I need root access to do so so I need to learn how to copy and paste a file from one location to another through the terminal.


How does adding more Pokèmon to gyms work now?

It used to be that you could train on your own gyms by attacking them, then once you got the points high enough from doing that, you could put a Pokèmon of your own in it. Obviously this mechanic has changed, but I can't figure out what it's been replaced with. The only thing I can figure out how to do is feed berries to any demotivated Pokèmon, but there's no indication that doing so opens up new slots. The little tutorial you can view when at a gym doesn't mention how to do it either.   How do I open up a slot to put my Pokèmon in a gym? (Or are the slots always open, and all the gyms I see just happen to be full?)


How to tip housekeeping in hotels if leaving tips daily?

I just read a question and answer about tipping housekeeping daily (). But how should I physically give them the money? Obviously if I see them I can hand them the money but if I'm out for the day?   I guess I leave cash somewhere obvious, should I leave a note as well? What if it's a non-English speaking country (I'm not sure if you'd be expected to tip there, but maybe you want to). Is there some customary place to leave the tip?   As someone brought up in a generally non-tipping country I often have to work out how to tip, but in general you can just keep an eye on what everyone else does. Not in this case.


This is an archery probability question...What is the methodology to solve this??  [1]:


Something happened to my Chrome on mobile, and now Stack Overflow looks weird

Something happened to my Chrome on mobile (my phone was in my pocket, so maybe something got pressed), and now Stack Overflow looks weird. What happened? This is how it should look (this screenshot is from Chrome DevTools on desktop, using Samsung S5 option):  And this is how it actually looks on my mobile (note that this is the standard view, not Desktop Site view):


How do i show that if every continuous function on $X$ is bounded, then $X$ is compact?

Let $(X,d)$ be a metric space. Assume every continuous function on $X$ is bounded. Prove that $X$ is compact.  Well, i don't know which continuous function should i fix to start an argument. I tried to fix a function $f(x)=d(x,x_0)$, but i think it doesn't work. How do i prove this?


Finding every $n$ such that there exists a $n$-th degree polynomial which satisfies $f(x^2+1)={f(x)}^2+1$

I'm interested in functional equation. I've been thinking about the following functional equation: $$f(x^2+1)={f(x)}^2+1\ \ \ \cdots(\star).$$  I found several functions such as $f(x)=x, x^2+1, (x^2+1)^2+1,\cdots$. Then, I got interested the following question:  Find every natural number $n$ such that there exists a $n$-th polynomial which satisfies $(\star).$  Then, I got the following fact:  Fact: There exists a $2^k$-th polynomial which satisfies $(\star)$ for any non-negative integer $k$.  Proof: Let us define $\{f_k(x)\}$ as the following: $$f_0(x)=x, f_{k+1}(x)={f_k(x)}^2+1\ \ \ \cdots(\star\star).$$  Supposing that both $f_0(x)$ and $f_k(x)$ satisfy $(\star)$, then $f_{k+1}(x)$ also satisfies $(\star)$ because  $$f_{k+1}(x^2+1)=\{f_k(x^2+1)\}^2+1=\{{f_k(x)}^2+1\}^2+1={f_{k+1}(x)}^2+1.$$  Hence, $\{f_k(x)\}$ satisfy $(\star)$. Since we know that the degree of $f_k(x)$ is $2^k$ inductively from $(\star\star)$, now the proof is completed.  However, I can't prove that there is no other $n$ such that there exists a $n$-th polynomial which satisfies $(\star)$.  Then, here is my question.  Question: Could you show me how to solve the above question?


After you've typed in a question, you get suggested tags that appear that look like this:        It appears that you need a minimum amount of characters ():     you must have entered a title (any length) and a minimum body length of 220 characters.   But other than that, how are the tags chosen? Is it:   A match of the title/body with other questions (taking the tags from those questions) A match of the title/body with tag excerpts (taking tags with overlap) A match of the title/body with tag wikis (taking tags with overlap) All of the Above None of the Above Other (please explain)   Some additional info from :  The suggested tags seem to only pop up on meta.so (they do not work on regular Stack Overflow, or on other SE sites).  While we're on the topic, why isn't this feature implemented network-wide?


What we cannot know, mathematical version

with a similar title, where he covers a few aspects of the boundaries of human knowledge, in short "things we know we will never know". It sounds a little bit spooky to know of such limitations. Although Marcus is a mathematician, his book doesn't cover mathematical topics only. So, I am more interested in mathematical "things we know we will never know".  Thus, my question is:     What are some interesting mathematical examples, with solid proofs (desirably), revealing "things we know we will never know"?   I will provide few examples, to begin with:   , we know it's in between $0$ and $1$, but we will never be able to compute it. And generally, the fact that not all  can . . Further to the definable numbers, . Or with more details from the author  Also stated as


Regular expression for complicated email

I want an regex for email that starts with numbers and letters.  My regex is   /^[a-zA-Z0-9._-]+@[a-zA-Z0-9.-]+\.[a-zA-Z]{2,4}$/   What is wrong in this? It allows ._- from start and in between. But I don't want this  Valid emails = s@gmail.com, s.p@y.com, s_p123@g.com   Invalid emails = ....s@g.com, s---g@g.com, s...@g.com, 44s..p@g.com, ----s@g.com  Does anyone know how this can be done?


I know the syntax for <? ?> is not always allowed, and will spark notices if you have them enabled... but I haven't seen many people use <?=$var?> to echo a variable... is this illegal syntax or completely accepted in all versions of PHP?  <?php echo $var; ?>   vs  <?=$var?>


Example of Group that is not Internal direct product under weaker condition

I know definition of internal direct which is stronger that is      $G$ is internal direct product of normal subgroup $N_i$ where $i$ is indexing upto $n$. Then         $G=N_1N_2N_3N_4N_5......N_n$   $N_i \cap (N_1....N_{i-1}N_{i+1}......N_n)=(e)$      It is clear that internal direct product is not possible in case of weaker condition of $N_i \cap N_j=(e)$. But I couldn't able to find counterexample to justify above.  Any help in this regard will be appreciated.


My son is in 2nd grade.  His math teacher gave the class a quiz, and one question was this:     If a triangle has 3 sides, and a rectangle has 4 sides,    how many sides does a circle have?   My first reaction was "0" or "undefined".  But my son wrote "$\infty$" which I think is a reasonable answer.  However, it was marked wrong with the comment, "the answer is 1".  Is there an accepted correct answer in geometry?  edit: I ran into this teacher recently and mentioned this quiz problem.  She said she thought my son had written "8." She didn't know that a sideways "8" means infinity.


The rules for mounted combat (PHB p.198) state:  While you're mounted, you have two options. You can either control the mount or allow it to act independently. Intelligent creatures, such as dragons, act independently. You can control a mount only if it has been trained to accept a rider.  The first two sentences seem to always give you the choice but the next two appear to limit this choice. What is the correct interpretation?


Which is more preferable to use: lambda functions or nested functions ('def')?

I mostly use lambda functions but sometimes use nested functions that seem to provide the same behavior. Here are some trivial examples where they functionally do the same thing if either were found within another function: Lambda function >>> a = lambda x : 1 + x >>> a(5) 6  Nested function >>> def b(x): return 1 + x  >>> b(5) 6  Are there advantages to using one over the other? (Performance? Readability? Limitations? Consistency? etc.) Does it even matter? If it doesn't then does that violate the Pythonic principle:  .


In a car model, I have a tire object that is using a very simple BSDF where the only value that's not left default is the base color, set to grey. I would like to ask someone more experienced how I could modify the cycles shader to add a white stripe to the tire like the ones old cars had. I tried playing with the ColorRamp node, but without success.


I wanted to search an old post of mine that contained the word "router". So I went to the stackexchange main page and looked for "user:me router". I got many results, but none of them is a post of mine:  What am I doing wrong?


Can Animals in Animal Crossing New leaf return to town and live there once again?

my favorite animal, Tom, moved away 3 years ago, how do I get Him back!


Maximum limit for flags waiting for review

So many flags with status "Waiting for review" in my profile .    How many maximum flag exists with this status.  Any option to delete or modify option to existing pending review. How long days flag waiting for review


What is the difference between I was there, and I have been there?

I was there twice last year. I have been there twice in the last year.


How to overwrite a !important css property

function chBody() { var color = prompt("Enter colour"); document.body.style.background = color; }   For learning purposes...   I'm trying to add an !important property after color to overwrite my css.  these are what I tried. I think the first one worked and then stopped working in codePen. maybe  color !important; color + " !important"; color + "!important";   Any help or a point in the right direction would be much appreciated.   If this method is wrong could I just use setAttribute() instead?  -- Thanks  ** The question marked as a duplicate of this isn't really a duplicate and didn't actually give what I was looking for whereas the comment in this answer did. Seems salty af


Prove that $5\cos A+3\cos\left(A+\frac{\pi}{3}\right)+3$ lies between $-4$ and $10$

After much of solving, I arrive at the expression $$\frac{1}{2}\left[13 \cos A-3\sqrt{3}\sin A +6\right].$$     I can't conclude anything from this. Please help. Hints are welcome.


explicit formula for recurrence relation $a_{n+1}=2a_n+\frac{1}{a_n}$

For $n\in\mathbb N$, $$a_{n+1}=2a_n+\frac{1}{a_n},\quad a_1=1. $$ Can any one give an explicit formula for all $a_n$? If such an explicit general formula doesn't exist, please explain it. I've tried to figure out the $n$-iterated function $f^{(n)}$ where $f(x)=2x+1/x$ or even $f(\tan(t))$. But in either cases, I failed.Since the recurrence isn't linear nor homogeneous,the generating function method doesn't apply here.


Use differentiation to find a power series representation for $f(x)=\frac{1}{(1+x)^2}$

Need help on all steps. Use differentiation to find a power series representation for $$ f(x)=\frac{1}{(1+x)^2} $$


prove that there exists a perfect cube that divides 135 consecutive integers

how would you prove that for 135 consecutive integers $a_1,a_2,...,a_{135}$ such that for all integers $k$, $1 \leq k \geq 135$ there exists a perfect cube $z_k > 1$ such that $z_k$ divides $a_k$?  Im stuck on this question and don't even know how to start. All I know is that if $z_k$ divides $a_k$ then $a_k = mod (z_k)$


How to install Android OS and Android Apps on PC?

How to install Android OS and Android Apps on PC ? If possible , android 4.0.3 .


Entering Canary Islands with Multi Schengen Visa issued by The Netherlands

We live in Amsterdam and i am married to a Russian that also has a dutch paspoort. We applied for a Multi Schengen visa for her parents. The  both got it for 4 and mom for 5 years.  They traveled to The Netherlands 4 times on that visa already. All ok.  Now we booked a trip for them direct to Canary Island Tenerife from Moskou.   Can they enter the Island without problems ? As they have a Visa issued by The Netherlands and they fly direct to Spain from Moskou.  I think there i no probelm but are a little worried. There first 4 visits where in The Netherlands so the visa is used for it main Destination.  I read the other topic but its not a Visa issued by The Netherlands to a Russian passport holder. The other topic didnt clearly answered my question. and also this "If you have a multi-entry visa for the Schengen area, you must first enter the country that issued the visa; after this you can enter any Schengen country. If you have a single-entry visa, you can only enter the country that issued the visa. Note to multi-entry visa holders: if your period of stay in Schengen countries within any 180 day period exceeds the allowed period (usually 90 days) as specified in your visa, you may be refused entry" is on aeroflot website. I think they mean the first time you use the visa....   I hope you guys can help me. Thanks a million!


Update iPad 3 iOS 5.1.1 to 7.0.4 not 7.1?

I have iPad 3 iOS 5.1.1 Jailbroken.  I now want to update to 7.0.4 or 7.0.6 but can NOT figure out how. (7.1.1 is currently the official update)  Manual updates thru iTunes to a 7.0.6 restore file always result in "This device isn't eligible" error despite hosts editing. I've tried on multiple computers.  Am I hosed?


On work done by motion of objects in elliptic orbits

In uniform circular motion, the force is perpendicular to the instantaneous direction of motion. So work done is zero. But if an object is in elliptical orbit such as a planet, I find it hard to understand how the force is perpendicular to direction of motion. And if it is not, some work is done which also doesn't seem to make sense.


Disable "open with" option on Firefox downloads (force Firefox to always save all files)

The symptoms   Users open their web mail accounts, click on some attachment, and click "Open with Word". Users edit their precious documents for hours. Users save word doc and exit.  Users can't find file.  Users grab torches and pitchforks (last step optional).     The cause of the problem  The download dialog for Firefox shows two options: "Save file" and "Open with".     By choosing "open with", Firefox downloads the file to a temp folder and opens the associated application. I want to prevent this behavior.   What I tried  I made my homework and searched the , and the Knowledge Base (like ,  or ) and if I understood correctly, the download dialog box will depend not on the file's extension, but rather on its mime type.  I know I can set the behavior by going to Preferences > Applications, like this:    However:    Firefox relies on the mime type informed by the server. But it can be itself incorrect, omitted, or redundant (one file type can have multiple mime types, or vice-versa).  Firefox remembers the "Do this automatically for files like this from now on" check-box on a per-mimetype  basis. If I want to enforce a certain behavior, I have to manually set it for each mime type. I can not create new entries in the applications list. It is populated only when a new download is made from an unregistered mime type. Only then I can change the behavior in the list. I can edit the  file, forcing the "save file" behavior, but I couldn't find a way to enforce this to all files.   What I need is a way to (preferably) make it impossible to open with an external application, or at least to force the file to be saved.  I know I can set browser.altClickSave in about:config to have it save the file when I click pressing ALT, but I need some solution that does not require user interaction.


Problem with citing in biblatex, document just shows the citation key

I'm having quite a lot of trouble with correct citation in my document. Everything compiles fine, but it just shows the citation key in bold letter instead of the actual citation. Also, nothing shows up in the bibliography, even with \nocite{*}. Here is the relevant code:  \usepackage[backend=biber, autocite=footnote, style=authortitle]{biblatex} \addbibresource{REFS.bib}  \begin{document} \cite{Rouse2019} \printbibliography[type=online, title={Online}] \end{document}   I'm kind of at a loss. When my friend compiles my document, the citation shows up for him. If nothing works, I'll just have him compile it and send that to my teacher lol.  Thank you all for your help


I am trying to find a motor to use to spin a cardboard wheel to drop balls through a hole. I want this to happen pretty slowly, around 10rpm. It also needs almost no torque, as it is spinning cardboard. However, when trying to find a motor, all I can find is extremely fast motors with low torque  or slow motors with high torque. Both options are expensive. Does a very low cost, DC, low speed, low torque motor even exist? Thanks


Why are positive rational numbers countable but real numbers are not?

If we can say that any positive rational number is countable or listable by showing that every positive rational number is the quotient of p/q of two positive integers, and then listing those in an array like this:   1/1 2/1 3/1 4/1 ... 1/2 2/2 3/2 4/2 ... 1/3 2/3 3/3 4/3 ... ....   We know that each row can go on for infinity, so instead we can draw a diagonal lines through the array to ensure that every fraction is counted, right?   But if we take all real numbers and try and list or count them, allegedly we can't, but why?   For example, if we wanted to list or make countable all numbers between 0 and 1, why can't we say that all possible permutations of decimal number combinations could be listed or counted the same way that all fractions are countable or listable for positive rational numbers?   If we're unable to list or count all possible combinations of decimal numbers between 0 and 1, why are we not saying that all the infinite combinations of fractions used to make up all positive rational numbers isn't countable as well?   I realize that a very erudite and technical explanation of the Cantor Diagonalization Argument was provided , however I'm not specifically asking for an explanation of this argument and moreover the very thorough explanation provided by Arturo Magidin for the OP in the post is slightly beyond my understanding as I'm very new to set theory and discrete mathematics.


short story I read in grade school in the mid 1970s - scientifically curious boy reads the ingredient list on his breakfast cereal box,

Trying to track down a short story that I read in grade school in the mid 1970s -probably written in the late 60s-early 70s - might be considered YA lit today.   A scientifically curious boy reads the ingredient list on his breakfast cereal box and then discovers that the ingredient is in all food products except those food that are organic, those who eat organic are suspect as being non-conformist. The boy investigates the substance in a Library and finds out that it was used in population control experiments following rioting and social unrest by the Government in the past and is a banned substance. At home he has been allowed to have some lab rats (considered a "clean" animal) and he begins experimenting with feeding the rats some of the common foods found in the house. When he goes back to the Library he finds that all references to the substance are gone both books and from the computer database. At home his experiment with the rats has led to the ones that were fed food becoming very docile. He also goes to the store and discovers that the substance no longer appears in the ingredients list. He begs his father to get him food from the organic market which he does despite his fears of being labeled as a non-conformist by the authorities That night while watching a broadcast TV special that is about a boy who resembles him greatly who becomes more and more non-conformist and questioning of the authorities except the character is exaggerated - he has a horse that he experiments on instead of rats and attack the food market and librarian - eventually the TV character runs to the roof of the tower he lives in and throws himself off as doctors and the police and his parents try to save him.   He tries to tell people about the substance in the food and is chased by the police and the tenants of the tower to the top of the tower he lives in and is forced off the edge by the mob.  The population live in towers and go back and forth through underground tunnels - The world outside is pristine groomed parkland-The outside is considered "unsanitary" The boy also finds out that there are doors that open on the ground level to the outside.  He begins traveling back and forth on the surface despite the protests of his mother about it being unsanitary "out there" - This alone draws people to first consider him deviant.


What temperature should I set my water heater to?

When adjusting my water heater, what temperature should I set it to? Is the answer different if you have:   Concerns about diseases A dishwasher Young children or elderly that can be easily burned Electric vs Gas heat Type of plumbing (e.g. PEX or Copper)   Also, is there a preferred technique to check the temperature of the water after adjusting it?


Java String not storing same value when assigned to Scanner NextLine()

I have come across a problem with the console handler of my code. I don't know if reading in after assigning it to s.nextLine(); discards the current value of in. Not sure if anything else could affect the String from being read correctly in one line, and incorrectly in the next.  Thanks in advance!  while (loop == true) {         Scanner s = new Scanner(System.in);         String a = s.nextLine();         String in = a;         info("User input: " + in, "DEBUG", 0);         if (in == "kill") {             info("Are you sure you would like to kill the running instance? [Y/N]", "CONSOLE", 0);             if (in == "Y" || in == "y") {                 info("Starting KILL method.", "CONSOLE", 0);                 s.close();                 loop = false             } else if (in == "N" || in == "n") {                 info("Cancelled.", "CONSOLE", 0);             } else {                 info("Illegal arguements given. Cancelled.", "CONSOLE", 0);             }          } else {             info("Illegal Arguements given.", "CONSOLE", 0);         }      }   When I typed kill in the console, it gave me this:  [info @ DEBUG/0]> User input: kill [info @ CONSOLE/0]> Illegal Arguements given.


How do I find out whether my system has USB 3.0 ports?

I want to buy an external USB 3.0 drive and I wonder how to figure out whether my laptop has such a port (or only 2.0).   Neither , nor /proc/bus/input/devices offers any obvious hints, although the former says a lot of 2.0 root hub which might imply v2 and not v3. Right?