I know how Booster Packs drop, but I am wondering just how often they drop. Is it random? Do they drop when you get achievements in games? Do they drop when you buy a game?
So today I woke up and noticed new item in inventory which was a booster pack containing 3 cards from L4D 2. From what I see on market these booster packs are new (graph only shows up to 19 of June). No matter the game it seems to always contain 3 cards. There are two actions I can do with it: unpack or sell. There is fancy animation when you unpack the booster ;)    I'm not exactly sure why I got it, I have few guesses:   I got new badge, power player - this could give me a booster? Because of new badge I reached level 10 - maybe every couple levels there are gifts? It just dropped randomly for everyone?   Maybe together we could rule out above guesses. It's also interesting from the point of market, to estimate how many boosters are there. With some games they seem to be more valuable than 3 cards separately, but that maybe only initial confusion.
This is a question from the free Harvard online abstract algebra .  I'm posting my solutions here to get some feedback on them.  For a fuller explanation, see  post. This problem is from assignment 5.  a) Prove that the relation $x$ conjugate to $y$ in a group $G$ is an equivalence relation on $G$. b) Describe the elements $a$ whose conjugacy class (= equivalence class) consists of the element $a$ alone.  a) Let $G$ be a group and $R$ be a relation on $G$ defined by $a\sim b$ if $a$ is conjugate to $b$.  Then $a\sim b$ if there is a $g\in G$ such that $a = gbg^{-1}$.  Let $a$ be an element of $G$.  Then $a=eae^{-1}$.  So $a\sim a$ and $R$ is reflexive.  Let $a$ and $b$ be elements of $G$ such that $a\sim b$.  Then there is a $g\in G$ such that $a=gbg^{-1}$.  Then $b=g^{-1}ag$.  Since $g^{-1}\in G$, $b\sim a$.  Hence, $R$ is symmetric.  Let $a,b$, and $c$ be elements of $G$ such that $a\sim b$ and $b\sim c$. Then there are elements $g,g^\prime\in G$ such that $a=gbg^{-1}$ and $b=g^\prime cg^{\prime -1}$.  Then $a=g(g^\prime c g^{\prime -1})g^{-1}=(gg^\prime)c(g^{\prime -1}g^{-1})=(gg^\prime)c(gg^\prime)^{-1}$. Since $gg^\prime\in G$, $a\sim c$.  Hence $R$ is transitive.  Therefore $R$ is an equivalence relation on $G$. b) Let $S$ be the set of elements of $G$ such that, for $s\in S$, $s=gsg^{-1}$ for any $g\in G$.  Then $sg=gs$.  So $S$ is the set of elements that commute with every element of $G$.  In other words, $S$ is the center of $G$. Again, I welcome any critique of my reasoning and/or my style as well as alternative solutions to the problem. Thanks. Adding Image to a Polygon Average distance between two random points in a square drawing at least 90% of colors from urn with large populations I am trying to install  under Wine. The program setup continually requests proxy settings. My broker tells me this shouldn't happen, and is a problem on my end. Here is what I have tried to attempt to solve this error:   I have gone into Network settings and proxy is set to none. I have looked in Wine Regedit and proxy_enable is set to 0. I have checked the firewall settings on my modem. I have tried reinstalling wine. I have installed lib32nss-mdns I can log on to my modem in iexplore using the gateway ip but thats it I've set my DNS to 10.0.0.138 to reflect the gateway I've set up a 32 bit Wine prefix   How should I proceed in solving this? How to disable auto brightening LCD Ice skater increase of energy This may be a very basic question but I am not seeing how it works. Consider the standard example of an ice skate rotating about his/her center of mass and pulling in his/her arms. The torque is zero so we have conservation of angular momentum. This implies that $\omega$ increases to keep $I\omega$ constant, but then $K_{rot}=\frac{1}{2}I\omega^2$ doesn't stay constant, it increases. This implies that there is work done, but what force is doing this work? What can you use Python generator functions for? I'm starting to learn Python and I've come across generator functions, those that have a yield statement in them.  I want to know what types of problems that these functions are really good at solving. What is the difference between "accumulative" and "cumulative"? I'm having a hard time understanding the real distinction between  and .  accumulative     adjective         tending to accumulate or arising from accumulation; cumulative.   tending to accumulate wealth; acquisitive.      cumulative     adjective         increasing or growing by accumulation or successive additions: the cumulative effect of one rejection after another.   formed by or resulting from accumulation or the addition of successive parts or elements.   of or pertaining to interest or dividends that, if not paid when due, become a prior claim for payment in the future: cumulative preferred stocks.      These definitions (and those from other dictionaries as well) say different things but I can't understand how they aren't really meaning the same thing.  Yet, when thinking about it, it seems there are some cases where it is distinctly more correct to use one or the other.  What's the difference, practically? Is there a way to disable the hardware on/off switch for the Wireless interface? Local BLAST Copy Number per Hit I generated a series of local BLAST databases using makeblastdb of metagenomic data and am searching for the presence of a particular gene. While I can do the normal BLAST analysis looking at e-values, % identity, etc. I haven't been able to figure out how to determine how many times a given sequence exists in the database.  So: given a BLAST database of metagenomic data where a particular gene may exist multiple times, how do I determine the copy number of a given BLAST hit?  Thanks in advance. I've heard that you always want the same size of RAM (2x1GB sticks) but does their placement matter? I have four slots on my motherboard but does it matter if the sticks are not adjacent?  This particular question involves the How to prevent water from freezing XPS 15 stuck on 800MHz I'm running Ubuntu 16.04 with CPU: i7-6700.  Even with one of the cores sitting on 100% utilisation cpufreq-info reports.  ... analyzing CPU 7:   driver: intel_pstate   CPUs which run at the same hardware frequency: 7   CPUs which need to have their frequency coordinated by software: 7   maximum transition latency: 0.97 ms.   hardware limits: 800 MHz - 3.50 GHz   available cpufreq governors: performance, powersave   current policy: frequency should be within 800 MHz and 3.50 GHz.                   The governor "performance" may decide which speed to use                   within this range.   current CPU frequency is 800 MHz.   Each CPU shows 800 MHz.  How do I get my CPU frequency to increase under load? How to create a GUID / UUID I'm trying to create globally-unique identifiers in JavaScript.  I'm not sure what routines are available on all browsers, how &quot;random&quot; and seeded the built-in random number generator is, etc. The GUID / UUID should be at least 32 characters and should stay in the ASCII range to avoid trouble when passing them around. So i have this $3\times 3$ matrix  $$     \begin{pmatrix}     -2 &amp; 0 &amp; 0 \\     3 &amp; 1 &amp; -6 \\     0 &amp; 0 &amp; -2 \\     \end{pmatrix} $$  I want to check if the matrix is diagonizable. First thing i do is find the roots : namely $\lambda_1 = −2$ of multiplicity $2,$ and $\lambda_2 = 1$ of multiplicity $1.$  In order to ensure that the matrix is diagonalizable we need to find a basis of $\mathbb{R}^3$ whose elements are eigenvectors for $A.$ In particular, since we have the eigenvalue $\lambda_1=-2$ having multiplicity $2$ we need to check that the dimension of the eigenspace $E(\lambda_1)$ is equal to $2.$ We compute the eigenspaces of $A.$  $\DeclareMathOperator\Nul{Nul}$On the answer sheet is says that we need to find $\Nul(A+2Id)$... but why $2Id?$ Isn't is supposed to be $-2,$ so $\Nul(-2Id-A)$??   I do not understand this $\Nul(A+2Id).$ I always thought that we should compute $\Nul(-2Id-A),$ so what do i need to do ?   $\Nul(-2Id-A)$ gives me a different result from $\Nul(A+2Id).$  Does that mean that since $-2$ has a multiplicity of $2,$ we need to work with $2$ and not $-2$?  Somebody please help with a clear and simple explanation ! Thanks! What is the pronunciation of "the"? I read that the definite article is pronounced differently depending on the word that follows it.  Which is the exact pronunciation of the? Install Nvidia driver instead of nouveau I've installed Ubuntu 14.04 and I'm experiencing a fuzzy/blurry screen and bad support for multiple screens.  I realized that Ubuntu installs nouveau as default, but I need to install nvidia drivers, so I tried this:   sudo apt-add-repository ppa:ubuntu-x-swat/x-updates apt-get update apt-get install nvidia-current apt-get upgrade       Now that nvidia is installed, you need to blacklist the nouveau driver   so it don’t pop out when you will reboot. Create or edit the following   file:  nano /etc/modprobe.d/blacklist-nouveau.conf       …and add these lines at the end:  blacklist nouveau blacklist lbm-nouveau options nouveau modeset=0 alias nouveau off alias lbm-nouveau off    I checked via the software &amp; updates if nvidia driver got installed successfully, and it says the driver installed is nvidia 304.117  I then tried to run:  lshw -c video | grep 'configuration'   and the result is that the driver is still nouveau:  configuration: driver=nouveau latency=0   So how do I install and use the nvidia drivers? Text editor to edit large (4.3 GB) plain text file Is there any text editor, which can edit such file?  I've  tried:   gedit kate nano vim mcedit   without success. Automate Fixed Width Page, length > some minimum length, but only as long as needed I am trying to automate the solution proposed by egreg to  by hooking into \begin{document} and \end{document}.  So, egreg's solution works fine:  \documentclass{article} \def\MinimumPaperHeight{12cm} \usepackage{geometry} \geometry{paperwidth=\MinimumPaperHeight,paperheight=\maxdimen,margin=1cm} \usepackage{lipsum}  \begin{document} \setbox0=\vbox{ \lipsum[1-6] } \dimen0=\dp0 \pdfpageheight=\dimexpr\ht0+2cm\relax \ifdim\pdfpageheight&lt;\MinimumPaperHeight \pdfpageheight=\MinimumPaperHeight \fi \unvbox0\kern-\dimen0 \end{document}   But can't seem to get this to work:  \documentclass{article} \def\MinimumPaperHeight{12cm} \usepackage{geometry} \geometry{paperwidth=\MinimumPaperHeight,paperheight=\maxdimen,margin=1cm} \usepackage{lipsum} \usepackage{environ}  \NewEnviron{MyBox}{     \setbox0=\vbox{\BODY}% }{%     \dimen0=\dp0%     \pdfpageheight=\dimexpr\ht0+2cm\relax%     \ifdim\pdfpageheight&lt;\MinimumPaperHeight \pdfpageheight=\MinimumPaperHeight \fi%     \unvbox0\kern-\dimen0% }  \AtBeginDocument{\begin{MyBox}} \AtEndDocument{\end{MyBox}}  \begin{document} \lipsum[1-6] \end{document}   Hooking into \AtBeginDocument is per this solution on .