Google Chrome has installed in Dutch language (using Windows 10)
How do I change my Chrome language back to English?
I was asked to prove the following:  If $\{ E_1,E_2,\ldots,E_n\}$ is a fully independent set of events, prove that:  $$ P\left(\bigcup_{i = 1}^n E_i \right) = 1 - \prod_{i = 1}^n \left[ 1 - P(E_i) \right]  $$  (Hint: use complements)  I got the following:  Let $\alpha = E_1\cup E_2 \cup \cdots \cup E_n = \{E^C_1 \cap E^C_2 \cap \cdots\cap E_n^C\}^C$. Then, $\alpha^C = \{ E^C_1 \cap E^C_2 \cap \cdots \cap E^C\} $.  Assuming that the set of complements of each ${E_i}$ is also fully independent, we have:  \begin{align} &amp; P(\alpha^C) = \prod_{i = 1}^n P(E_i^C)  = \prod_{i = 1}^n \left[ 1 - P(E_i) \right] \\ &amp; P(\alpha) = 1 - P(\alpha^C) = 1 - \prod_{i = 1}^n \left[ 1 - P(E_i) \right] \\ &amp; P(\bigcup_{i = 1}^n E_i) = 1 - \prod_{i = 1}^n \left[ 1 - P(E_i) \right] \end{align}  However, even though I know (by Googling it) that my assumption is true, I'm unable to prove it so I could validly use it as a lemma. Is there another way to prove this equality? Importing QGIS3 processing tools in standalone script Inspired by , but for QGIS 3 (and therefore Python 3), I would like to use the QGIS processing algorithms in a standalone Python script without a GUI, with a standard installation of Ubuntu Linux. A simple import processing is insufficient: import processing processing.run(    &quot;qgis:rasterlayerstatistics&quot;,    {        'INPUT': .'/somefile.tif',        'BAND': 1,        'OUTPUT_HTML_FILE': './result.html'    } )  Results in: Traceback (most recent call last):   File &quot;&lt;stdin&gt;&quot;, line 1, in &lt;module&gt; ModuleNotFoundError: No module named 'processing'  How do you get access to the QGIS processing module to use the QGIS processing algorithms in a standalone Python script (not the QGIS interpreter)? In response to  question, I started to think about what it means when a Wild Magic Surge results in a "You cast spell-X".  So, "specific beats general" gives:   You can cast a second spell when you would not normally be allowed to You can cast a spell you don't know If the surge forces you to cast a concentration spell you would lose any concentration spell that you currently had active Subject to what the specific entry says you can target it how you like Unless the specific entry prohibits it you could use metamagic on the spell   I am pretty confident in all of the above but if anyone disagrees please address in an answer.  Here comes the question.  How does this impact on your available spell slots?  "You cast ..." to me suggests that if you have an applicable slot available then you have to use it to cast the spell because that is the general rule for casting spells but if you don't then "specific beats general" and it is cast anyway.  Specific examples:     You cast fireball as a 3rd-level spell centered on   yourself   This must be a 3rd level spell:   if you have a 3rd level slot available you have to use it? if you don't, if you have 5 sorcery points and a bonus action available must you use these to get that slot? if you don't have any of that then the spell goes off anyway?      You cast confusion centered on yourself.   No level specified and confusion is a 4th level spell:   if you have a 4th level slot available you have to use it? if you have a 4th, a 6th and an 8th level slot you can choose which one to use? if you have only a 5th level slot but also 6 sorcery points and a bonus action, you could choose to use the 5th level slot or use the points to create a 4th level slot? if you don't have any 4th level or higher slots but you have 6 sorcery points and a bonus action available must you use these to get that slot? if you don't have any of that then the spell goes off anyway?   And so on ... How do I specify unique constraint for multiple columns in MySQL? I have a table:  table votes (     id,     user,     email,     address,     primary key(id), );   Now I want to make the columns user, email, address unique (together).  How do I do this in MySql?  Of course the example is just... an example. So please don't worry about the semantics. given the 2 PDE  $$ \Delta u-au_{tt}+u_{t}=0$$  and $$ \Delta u + Du*Df=0 $$  here $ \Delta u $ is the Laplacian $ Du= grad(u) $ is the gradient and * means scalar product $u_{t} = \frac{\partial u}{\partial t}$  my doubt is what term should i include to get the linear part of the equations $ u_{t} $ and $Du*Df $ from the Euler Lagrange equations in $ R^{n} $ thanks Decomposition of the tensor product $\mathbb{Q}_p \otimes_{\mathbb{Q}} \mathbb{Q}[i]$ into a product of fields I am trying to solve the following problem:     For each rational prime $p$, describe the decomposition of the tensor product $\mathbb{Q}_p \otimes_{\mathbb{Q}} \mathbb{Q}[i]$ into a product of fields, where $\mathbb{Q}_p$ is the field of $p$-adic numbers.    I know that the tensor product of $2$ extensions of a field one of which is finite is Artinian and is therefore a product of Artinian local rings, but I do not know how to compute these Artinian local rings. Please if you can help me with this, I'll really appreciate it. We know Euler formula:  $$ e^{ix}=\cos(x)+i\sin(x). $$  Does this formula work if we replace real number $x$ with complex number $z$? Printer not recognized on Ubuntu Libre Office I am running 14.04 and have a HP Deskjet 2545 wireless printer which is supported by Ubuntu. I have run HpLIP, the latest version and installed the printer.  The printer is recognised by Ubuntu, printer and network, but LibreOffice do not see the printer. Only a Generic printer.  I don't know what to do anymore and would like to get some good advice Add folder name to beginning of filename Same gravatar is displayed for different users in stackexchange.com filters Same gravatar is displayed for different users in the stackexchange.com , under the Top Network Askers in the right side bar.   The red circled image's source (&lt;img src=) are from   https://www.gravatar.com/avatar/?s=18&amp;d=identicon&amp;r=PG&amp;s=30                                ^   Seems the gravatar id is missing here in the image source.  For an example from the list, the user  gravatar id should be    https://www.gravatar.com/avatar/66c66c4d97a7bc3859a85253f003e1fb?s=18&amp;d=identicon&amp;r=PG&amp;s=30   but it is mapped with   https://www.gravatar.com/avatar/?s=18&amp;d=identicon&amp;r=PG&amp;s=30   which caused the display issue. Getting certain columns in bash Does using an extender actually change the aperture of the lens? I just bought a Canon 2X extender and I always believed that it would only result in 2 stops' loss of light and not change the aperture.    However, when I tested this extender on a Canon 135mm f/2 lens, the maximum aperture I could set went down to F/4.  So it kind of confused me, because if I step down the aperture to f/5.6, is it actually setting the aperture to f/5.6 or f/2.8 (i.e., 1 stop below f/2)? How to kill all process with given name? Proving the Cauchy-Schwarz inequality by induction I ran across this problem in some old notes, and I frustratingly can't figure out how to do it   Let $a_i$ and $b_i$ be sequences of natural numbers, use induction to show  $\sum_{i=1}^n (a_ib_i)^{1/2} \le (\sum_{i=1}^n a_i)^{1/2}(\sum_{i=1}^n b_i)^{1/2} $  Obviously this is trivial to show for n=1. I can't make much progress on n+1. I've tried various tactics, squaring both sides etc.   Any hint or help would be appreciated. Thanks. Make a table span multiple pages I have a table that takes up a full page, but I want it to start on a page that already has some text and then continue onto the next page (i.e. it's ok if the table gets broken up and spans two pages). It is a simple two column table:  \begin{table}[h] \centering \begin{tabular}{| p{.20\textwidth} | p{.80\textwidth} |}  \hline foo &amp; bar \\ \hline  foo &amp; bar \\ \hline  ... \end{tabular} \end{table}   I guess I need longtable? How do I use it? Prevent execution of parent event handler I want to change the default timeout in Chrome. In Firefox I can set the value of network.http.connection-timeout in about:config - but how can I do that in Chrome? How did Google find my unlinked newly created pages? I am building a new site, but creating the content using a subdirectory on an existing site. I have never posted a link to this subdirectory anywhere, yet searching Google reveals that Google has found these pages on my site and indexed them.  Further, I updated the site with a robots.txt file that WMT reports as being read, and testing the blocked pages using the WMT test tool indicates that the pages will not be indexed. Apparently this does not remove the pages from existing results, though I submitted a request to do so.  How did Google find these pages to begin with? Is it because I used a common subdirectory name and Google guesses at common subdirectories? I've been trying to play with a rigid body simulations.  I prepared a project of a building made of domino tails. I've placed all objects very tight, but as soon as I start animation it looks like there was some tiny gap between objects, so they all fall down a little bit. For a high building it leads to a construction disaster as the whole building colapses.  Here is an example:  (I'd suggest to use 0.25x speed).  How can I fix it? I've been doing some practice questions in the textbook for an upcoming predicate calculus lecture and I think I've managed to get A and B (possibly C) correct but I am clueless on how I can manage D and E.   For A I got: ∃x(R(x)∧¬B)  For B I got: ∀x(¬R(x)∧B)  For C I got: ∃x(R(x)∧(x=y))   - Not sure if this is even remotely correct    R(X) : ”X is rich”  X = Y : ”X equals Y”  B : ”Bill Gates”  a) Someone besides Bill Gates is rich.  b) Bill Gates alone is rich.  c) At least two people are rich.  d) Exactly one person is rich.  e) Exactly two persons are rich.  The universe of discourse is the set of all people.