A particular professor is known for his arbitrary  grading policies. Each paper receives a grade  from the set {A, A-, B+, B, B-, C+}, with equal  probability, independently of other papers. How  many papers do you expect to hand in before you  receive each possible grade at least once?
What is the average number of times it would it take to roll a fair 6-sided die and get all numbers on the die?  The order in which the numbers appear does not matter.  I had this questions explained to me by a professor (not math professor), but it was not clear in the explanation.  We were given the answer $(1-(\frac56)^n)^6 = .5$ or $n = 12.152$  Can someone please explain this to me, possibly with a link to a general topic?
How do I install Ubuntu Server (step-by-step)? I'd like to install Ubuntu server on my machine, is there a step-by-step instructions on how to accomplish that or a guide that will just go through the basic steps of installing Ubuntu Server from beginning to end.  Instructions originally for 13.04. What was the galaxy formation Rust saw before confronting Erol Childress in  S01E08?  It was weird like out of the series. I guess it was some sort of hallucination, a product of Rust's madness or addiction. Change border color of \fbox Possible Duplicate:          I'm using an \fbox to have a border around a minipage.  \fbox{ \begin{minipage}{0.25\textwidth} my content \end{minipage} }   Is there any way to set the border color of the \fbox? Set a global policy for floats positioning I have a document with many floats (figures, specifically).  I want to be able to change the global floats positioning policy from htbp to just h (or even H with the floats package).  For my-own reasons, I don't want to do this by appending the [h] argument to each float env.  One option that I can think of is using a macro:  \newcommand{\mypos}{h} % or htbp \begin{figure}[\mypos]...   I also prefer not to do that - It is cumbersome.  Is there a way to set the global float positioning argument globally? Show that if $x$, $y$, $z$ are integers such that $x^2 + y^2 = z^2$, then at least one of them is divisible by $2$, at least one is divisible by $3$, and at least one is divisible by $5$.  I know that $x,y,z$ are sides of a right-angled triangles. If I start putting values, then I can show, but have no clue about mathematical approach.  How do I solve it mathematically, using modular arithmetic? A better proof for $\det(P) = \pm1$ if $P$ is an orthogonal matrix How can I accept the Microsoft EULA agreement for ttf-mscorefonts-installer? After a recent update, ttf-mscorefonts-installer prompted me to accept its license agreement.     ┌─────────────────┤ Configuring ttf-mscorefonts-installer ├─────────────────┐  │                                                                           │   │ TrueType core fonts for the Web EULA                                          │                                                                               │ END-USER LICENSE AGREEMENT FOR MICROSOFT SOFTWARE                             │                                                                               │ IMPORTANT-READ CAREFULLY: This Microsoft End-User License Agreement           │ ("EULA") is a legal agreement between you (either an individual or a          │ single entity) and Microsoft Corporation for the Microsoft software           │ accompanying this EULA, which includes computer software and may include      │ associated media, printed materials, and "on-line" or electronic              │ documentation ("SOFTWARE PRODUCT" or "SOFTWARE"). By exercising your          │ rights to make and use copies of the SOFTWARE PRODUCT, you agree to be        │ bound by the terms of this EULA. If you do not agree to the terms of          │ this EULA, you may not use the SOFTWARE PRODUCT.                              │                                                                               │                                  &lt;Ok&gt;                                         │                                                                           │   └───────────────────────────────────────────────────────────────────────────┘    Screenshot:   For some reason my terminal will not allow me to accept, or for some reason I am pressing the wrong hotkey...  I've tried every letter on the keyboard and Enter among others...  I'm sure there is a very simple and obvious solution to this.  I've also just tried to remove the package completely however the terminal states that due to the package not being correctly installed, I should reinstall the package before removing it.  Very frustrating!  Essentially, because I cannot successfully install this package, I can't really ever upgrade my system because I always have to end up terminating the terminal with the license agreement (thus the upgrade fails). In formal logic, how is it possible for an argument with a contradictory conclusion to be valid? I've recently been trying to introduce myself to formal logic, and I've hit a stumbling point:  In the text I'm reading, a valid argument is defined as "an argument in which it is impossible for the premises to be true and at the same time the conclusion false."  The text then later prompts me to declare whether it's possible for an argument to be valid with a contradiction for a conclusion. The answer key then claims that yes, it is in fact possible, but offers no further explanation. I'm also supposed to create an example.  I just can't wrap my head around this one.  Here's the example I've worked up, is this a valid argument?   If grass is green then it is raining.  If water is wet then it is not raining.  Therefore: It is raining and not raining.   My head hurts. How to get permanent token? I really need to get permanent token or dynamic generator. We set job in the server and this service will come to salesforce and get the data. To provide this, I created connected app, got the token from postman by myself and gave it. After a while (approximately 1 day), we faced with session id problem.   What can I do? This is sort of a follow-up to a feature request that resulted in obscuring spam / offensive content from 10K-visible answers:   Suggest the same to be done for questions. As of now, spam questions (, ) preserve their titles and content. Suggest to revise the titles to something like     This question was marked as spam or offensive and is therefore not shown   And the text to something like:     This question was marked as spam or offensive and is therefore not shown - you can see the revision history for details".   Where "the revision history" links to the question revision history.    For those interested, here is a link to screen shots of how spam shines through my flagging summary page and is displayed to me when I click the link to one of deleted questions: .  For the sake of precision, flagger having less than 10K rep would see only upper screen shot - the one that lists question titles ("Call giRℒs blah blah &lt;phone number&gt;") - in their  page. With regard to the theory that each time a wave function collapses the universe  so that each possible outcome really exists - where does all the energy required to create all the new universes come from? Does $\sum\limits_{k=1}^n 1 / k ^ 2$ converge when $n\rightarrow\infty$? I can prove this sum has a constant upper bound like this: $$\sum_{k=1}^n \frac1{k ^ 2} \lt 1 + \sum_{k=2}^n \frac 1  {k (k - 1)} = 2 - \frac 1 n \lt 2$$ And computer calculation shows that sum seems to converge to 1.6449.  But I still want to know:  Does this sum converge? Is there a name of this sum (or the series $\frac{1}{k^2} $)? Given the Python function:  def a_method(arg1, arg2):     pass   How can I extract the number and names of the arguments. I.e., given that I have a reference to func, I want the func.[something] to return ("arg1", "arg2").  The usage scenario for this is that I have a decorator, and I wish to use the method arguments in the same order that they appear for the actual function as a key. I.e., how would the decorator look that printed "a,b" when I call a_method("a", "b")? I have tried some of the solutions posted elsewhere in the support forum, one seemed like it worked but after a steam update i found myself back at square one  I am a new Linux user and am already at a learning curve :)  Thanks for any help  Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  libgl1-mesa-glx:i386 : Depends: libglapi-mesa:i386 (= 10.1.3-0ubuntu0.3)  unity-control-center : Depends: libcheese-gtk23 (&gt;= 3.4.0) but it is not going to be installed                         Depends: libcheese7 (&gt;= 3.0.1) but it is not going to be installed E: Error, pkgProblemResolver::Resolve generated breaks, this may be caused by held packages. Press return to continue: Suppose we view fluids classically, i.e., as a collection of molecules (with some finite size) interacting via e&amp;m and gravitational forces. Presumably we model fluids as continuous objects that satisfy some differential equation. What mathematical result says that modeling fluids as continuous objects can accurately predict the discrete behavior of the particles? I don't know anything about fluid mechanics, so my initial assumption may in itself be wrong. Who are the 3 men who would have a chance against Jaime Lannister in a sword fight? In Game of Thrones season 2, episode 8, "The Prince of Winterfell" , Jaime Lannister says to Brienne:     There are three men in the kingdoms who might have a chance against me [in a sword fight]   Who are those three people?                                  I don't believe this quote, or any variation, appears in the books. There was this quote from A Storm of Swords when he is fighting Brienne:     She is stronger than I am.      The realization chilled him. Robert had been stronger than him, to be sure. The White Bull Gerold Hightower as well, in his heyday, and Ser Arthur Dayne. Amongst the living, Greatjon Umber was stronger, Strongboar of Crakehall most likely, both Cleganes for a certainty. The Mountain’s strength was like nothing human. It did not matter. With speed and skill, Jaime could beat them all.   So in the books it suggest that Jaime can beat anyone, though he is only referring to people of great strength, not necessarily of great skill (somebody such as Barristan Selmy, who is not considered to be exceptionally strong but is exceptionally skillful, may be able to beat him).  Is there any canon evidence to suggest who these three people may be?  I won't accept any purely speculative answers. However if there is no direct canon quote answering the question (which I believe to be the case) I will consider answers that are strongly inferred from canonical sources (such as a canon quote saying X is the greatest fighter in the kingdom, for example). How to handle calendar TimeZones using Java? I have a Timestamp value that comes from my application. The user can be in any given local TimeZone.  Since this date is used for a WebService that assumes the time given is always in GMT, I have a need to convert the user's parameter from say (EST) to (GMT). Here's the kicker: The user is oblivious to his TZ. He enters the creation date that he wants to send to the WS, so what I need is:  User enters: 5/1/2008 6:12 PM (EST)  The parameter to the WS needs to be: 5/1/2008 6:12 PM (GMT)  I know TimeStamps are always supposed to be in GMT by default, but when sending the parameter, even though I created my Calendar from the TS (which is supposed to be in GMT), the hours are always off unless the user is in GMT. What am I missing?  Timestamp issuedDate = (Timestamp) getACPValue(inputs_, "issuedDate"); Calendar issueDate = convertTimestampToJavaCalendar(issuedDate); ... private static java.util.Calendar convertTimestampToJavaCalendar(Timestamp ts_) {   java.util.Calendar cal = java.util.Calendar.getInstance(       GMT_TIMEZONE, EN_US_LOCALE);   cal.setTimeInMillis(ts_.getTime());   return cal; }   With the previous Code, this is what I get as a result (Short Format for easy reading):  [May 1, 2008 11:12 PM] Remove Actions/Filters added via Anonymous Functions That's a freaking bad practice I must say. Spent last two hours finding a solution to remove actions and filters added via Anonymous functions.    This is the code used on a Parent Theme, and I need to remove it.  /**  * Add custom columns to admin comments grid  *  * Rate that user set.  */ add_filter( 'manage_edit-comments_columns', function( $default ) {     $columns['smr_comment_rate']  = __( 'Rate', 'txtdmn' );      return array_slice( $default, 0, 3, true ) + $columns + array_slice( $default, 2, NULL, true ); });   Got , played with it heavily, but no help. So, is there any other alternative that will remove actions/filters added via anonymous functions?  Thanks Is there a 2D generalization of the coefficient of restitution? The  characterizes a collision in one dimension by relating the initial and final speeds of the particles involved,  $$C_R = -\frac{v_{2f} - v_{1f}}{v_{2i} - v_{1i}}$$   In a 2D collision, the velocity can be split into components parallel and perpendicular to the "plane of collision" (the plane tangent to the two objects' surfaces at their contact point), and the equation above applies to the perpendicular components of the velocities only. One could write  $$\begin{pmatrix}v_{2f\shortparallel} - v_{1f\shortparallel} \\ v_{2f\perp} - v_{1f\perp}\end{pmatrix} = \begin{pmatrix}1 &amp; 0 \\ 0 &amp; -C_R\end{pmatrix}\begin{pmatrix}v_{2i\shortparallel} - v_{1i\shortparallel} \\ v_{2i\perp} - v_{1i\perp}\end{pmatrix}$$   My question is, is it useful (i.e. does it produce a more accurate description of realistic 2D collisions) to generalize that matrix? Perhaps by allowing the top left element to be unequal to 1, or allowing nonzero off-diagonal elements? Or is there some nonlinear relation that works better?  As usual, if you know of any relevant published research, references would be much appreciated. I'm cooking two different dishes in the oven at the same time that each require different temperatures. One is a roasted vegetable dish that says to cook at 475 for 35-40 minutes and the other is parmesan crusted pork chops at 350 for 40-45 minutes. What do you suggest I do?