Confidence interval for single observation from Poisson
Determining confidence interval with one observation (for Poisson distribution)
About the point $P$ inside a square $ABCD$ satisfying $BP = BC$ and $\angle APD = 90^\circ$ There is a problem I'm trying to solve from the Polish XI Olimpiada Matematyczna Gimnazjalistów. It is question 2 from . (The deadline of 12 October 2015 has passed.)    So far I found $x^2$ and $y^2$ (that are $|AP|^2$ and $|PD|^2$).  In order to prove, that AP=2PD, can I just divide $$ \sqrt{\frac{x^2}{y^2}} $$ and show, that it equals $2$? Show: $ f(a) = a,\ f(b) = b \implies \int_a^b \left[ f(x) + f^{-1}(x) \right] \, \mathrm{d}x = b^2 - a^2 $ Get value of R, G, B by color Unwanted faint lines connecting dashed double line Building on the answer  by wrtlprnft, I have the following code     \documentclass[tikz,margin=1cm]{standalone}    \usetikzlibrary{decorations.markings}    \begin{document}    \begin{tikzpicture}         \tikzstyle{arrowed double line}=[             dashed, double distance between line centers=3pt,             postaction=decorate,             decoration={                 markings,                 mark=between positions 10pt and -10pt step 20pt with {                     \arrow[thin,yshift= 1.5pt,xshift=.8pt]{&gt;}                     \arrow[thin,yshift=-1.5pt,xshift=.8pt]{&lt;}                 },             },         ]         \draw[arrowed double line] (0,0) --  (1,2);     \end{tikzpicture} \end{document}   which produces this:    I am unhappy with the faint transverse lines between the dashes. I don't even know why tikz decides to draw them.  Is there a way to get rid of them?  Thanks in advance to all replies.  PS the same thing occurs at the caps of double solid lines Can the Telekinesis spell be used to manipulate liquids? There is (there's) vs.There are What are the roots of the creeping usage of "there's" for both singular and plural predicates? (This seems to be more common in spoken English.) I have 2 theories.  Perhaps it is because spoken communication our society is becoming less formal by the day. Or perhaps it is a reflection of speakers of other languages having increasing contact with native English speakers.  I am aware of German  "es gibt" and Spanish  "hay" constructions. Please comment.  3/06/14 I ran a couple of Google Ngrams and was surprised to find a greater rise in the use of "there's" in English fiction than in general English language books, since the turn of the century.  This would seem to support my contention that informality is behind the shift. Making adult decisions "is" or "are" really not fun: Which is correct? Making adult decisions are/is really not fun.     What is the proper answer and why? My gut says "is" but I can't explain why. Server 2008 Net Send or Msg? I have a Windows 2008 server running as a domain controller. The details are as follows:  Domain: corp Server Name: oxygen   The workstations are all running Windows XP SP3 and have fixed IP addresses.  I am trying to use the net send functionality to be able to send simple messages to either individual machines/users and also to all machines. This is so I can send a message to a user to alert them about something, or likewise alert everyone of something such as the server being rebooted.  Is this possible using Windows Server 2008? If so, what would the command be? What is an observer in quantum mechanics? What is the "last" data that get's backed up, when running pg_dump on a live server? I'm wondering: If I start doing a pg_dump of a very large database (it would take hours), that is still running actively receiving writes, what is then the last data that goes into the backup? Is it:   The data as-it-was, at the point in time where the pg_dump command was initiated. The last changes that it encountered at some point where it was dumping that individual record. Something else.   Bonus question: If I'm trying to dump a database as part of trying to rescue it from corrupt data, will it then make any difference whether I use the directory format or the custom format? Is the XP for an encounter split among the party members or not? At this point, I am unclear as to how to handle encounter XP. Does each surviving party member receive a proportional share, or the full amount? That is, assume a 4-character party had completed an encounter worth 400 XP. Would each party member receive 100 XP, or 400 XP? Number of monomials of certain degree Least rank of a matrix Let $A$ be a $7\times 7$ matrix such that it has rank $3$ and $a$ be $7\times 1$ column vector.  Then least possible rank of $A+(a a^T)$ is? ($a^T$ is transpose of the vector)  Intuitively I think it's $2$ as $a a^T$ has rank $1$, and the most it could affect is one row of $A$. Likelihood Ratio Test for Exponential Distribution with a Limited Parameter Space I want an editor that is as good as TextPad (for Windows) for compiling and running Java programs on Ubuntu 12.04. Please suggest one. I know that for any nonzero $x,y\in\mathbf{R}$,  $$ax^2+by^2+cxy &gt; 0,$$  where $a,b,c\in\mathbf{R}$. What can I deduce about $a$, $b$, and $c$?    For example, letting $x=1$ and $y=0$, I know that $\boxed{a&gt;0}$. Letting $x=0$ and $y=1$, I know that $\boxed{b&gt;0}$. Letting $x=y=1$, I know that $\boxed{c&gt;-(a+b)}$.  What else can I deduce about $a$, $b$, and $c$? How will I know when it's time to stop looking? (Is that last question even answerable?) The search parameter isanswered ignores acceptances Defend against flag spam in chat We have incidents where we get 10+ flags from the same room in rapid succession. This happens on multiple occasions and we have reason to believe it's a single user doing this.  I don't think it's of value to allow a single user to flag more then n messages in a small time period.  If we could have some anti-flag spam measures put in place, then that would be great. Is "there're" (similar to "there's") a correct contraction? Q: "Do you have any juice?"   A: "Yes, there's some in the fridge."   Sounds perfectly fine to me, but:     Q: "Do you have any towels?"   A: "Yes, there's some in the closet."   Does not.  I asked for towels - plural - so wouldn't "Yes, there're some in the closet," in which there are is turned into a contraction be the correct way to say it?  Spellcheck, however, doesn't like "there're", and I think I'm the only person I've ever heard use the word "there're".  Even folks who I know say "there are" shorten it to "there's" when possible.  Am I saying it wrong, or are both forms acceptable? How to set default style for arrow tips in TikZ?