Posting and answering questions you have already found the answer to
Can I answer my own questions, even if I knew the answer before asking?
IS or ARE? "The only thing that I want you to hit right now IS/ARE the books" In this sentence, which is the right word?     The only thing that I want you to hit right now is/are the books. How to create a good glass reflection with Principled BSDF Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$ Let $A,B$ be matrices $m\times n$ $(A, B \in M_{m\times n}(R))$. How can we prove that $$\operatorname{rank}(A+ B) \le \operatorname{rank}(A) + \operatorname{rank}(B)\ ?$$ Wikipedia says that the name of concept comes from physics, but I cannot find any similarity between these two concepts. Maximum Likelihood Estimation (MLE) in layman terms Could anyone explain to me in detail about maximum likelihood estimation (MLE) in layman's terms? I would like to know the underlying concept before going into mathematical derivation or equation. Why does chmod +w not give write permission to other(o) When I run chmod +w filename it doesn't give write permission to other, it just gives write permission to user and group.  After executing this command  chmod +w testfile.txt   running ls -l testfile.txt prints  -rw-rw-r-- 1 ravi ravi 20 Mar 10 18:09 testfile.txt   but in case of +r and +x it works properly.  I don't want to use chmod ugo+w filename. unblock slime presta valve My Son's bike has slime inner tubes.  The bike has been sitting in the garage since last summer and the front tyres valve now seems blocked.  Its has what feels like 15-20 psi in it but I can not get the valve to let any air out or take any more in.  I have no idea at this point how to get it to unblock the valve so I can use it again.  For that matter I don't know how I could get the tire off as it has a reasonable (not ridable) amount of air in it without slashing the tyres (nice kings 2.2 which are pretty new).  I have tried putting the pump on it and putting a bit of air into it to try and clear the blockage but that didn't do anything.  Any ideas please? Given a Java InputStream, how can I determine the current offset in the stream? I'd like something like a generic, re-usable getPosition() method that will tell me the number of bytes read from the starting point of the stream.  Ideally, I would prefer this to work with all InputStreams, so that I don't have to wrap each and every one of them as I get them from disparate sources.  Does such a beast exist?  If not, can anyone recommend an existing implementation of a counting InputStream? Area enclosed between the curves $y=x^2$ and $y=60-7x$ Find the area enclosed between the curves $y=x^2$ and $y=60-7x$.  I am completely new at this but I have tried and I believe that it should be between the numbers $0$ and $60$ is this right? How does the new Tie-Breaker work? In Clash of Clans there was an update on 9/16 adding a Tie-breaker into the wars, can anybody explain in detail how this mechanism works? How to downgrade a package via apt-get? How can I downgrade a package to an older version via apt-get?  Other tools are also acceptable but apt-get is preferred. Regular expression to match a line that doesn't contain a word I know it's possible to match a word and then reverse the matches using other tools (e.g. grep -v). However, is it possible to match lines that do not contain a specific word, e.g. hede, using a regular expression?   Input:  hoho hihi haha hede   Code:  grep "&lt;Regex for 'doesn't contain hede'&gt;" input   Desired output:  hoho hihi haha Removing intercept from GLM for multiple factorial predictors only works for first factor in model I am running a binomial logistic regression with a logit link function in R. My response is factorial [0/1] and I have two multilevel factorial predictors - let's call them $a$ and $b$ where $a$ has 4 factor levels  $(a_1,a_2,a_3,a_4)$ and $b$ has 9 factor levels $(b_1,b_2,\dotsc,b_9)$. Therefore:  mod &lt;- glm(y ~ a + b, family = binomial(logit), data=pretend) summary(mod)   The model output would then show all the information about the model as well as the coefficients.  There is a factor level for both a and b missing (a1 and b1) from the summary output. I understand that it is constrained in the "intercept" of the model. I have read that if I want to remove the intercept term and see the estimates for those factor levels I can just add -1 to the model formula, i.e.:  mod2 &lt;- glm(y ~ a + b - 1, family=binomial(logit), data=pretend) summary(mod2)   In the new model (mod2) the intercept term is then gone and variable a's factor-level a1 is given amongst the list of coefficients. But, variable b's factor-level b1 is still missing and given that there is no intercept term anymore, how can I interpret the odds-ratio for that factor level then?  Could someone please explain to me how to get the coefficient for b1 too and why this is happening? How should I print types like off_t and size_t? The close dialog says there are two off-topic votes, but none of the off-topic reasons have votes next to them I've found strange behavior when closing this  - I definitely see that there are 3 closing votes and 2 of them are at "Off-topic" section:   -but there are no explanations on section itself:   -while, normally, it's expected that it will appear. In custom comments section there are also no closing-votes displayed.   Perhaps it's just my browser (which is FF 26 x64 under Win) - so marking this as a "possible bug". Thank you for your attention. My HDRI doesn't appear on Cycles Render I have 6 images, and I want to align them in this way  (a)image1 (c)image3 (e)image5  (b)image2 (d)image4 (f)image6  Any one know how to do that?  The problem for me is how to make (a), (b),..., (f) in vertical direction. How to compute the size of the allocated memory for a general type Cannot remove JDK – /usr/sbin/alternatives: No such file or directory When I try to remove Java with sudo apt-get remove jdk1.8.0-40 I get this:    Reading package lists... Done Building dependency tree        Reading state information... Done The following packages will be REMOVED:   jdk1.8.0-40 0 upgraded, 0 newly installed, 1 to remove and 0 not upgraded. 1 not fully installed or removed. After this operation, 245 MB disk space will be freed. Do you want to continue? [Y/n] y (Reading database ... 231488 files and directories currently installed.) Removing jdk1.8.0-40 (1.8.040-1) ... find: `/usr/java/*': No such file or directory /var/lib/dpkg/info/jdk1.8.0-40.postrm: line 586: /usr/sbin/alternatives: No such file or directory /var/lib/dpkg/info/jdk1.8.0-40.postrm: line 598: /usr/sbin/alternatives: No such file or directory dpkg: error processing package jdk1.8.0-40 (--remove):  subprocess installed post-removal script returned error exit status 127 Errors were encountered while processing:  jdk1.8.0-40 E: Sub-process /usr/bin/dpkg returned an error code (1)   Output of  ls -1 /var/cache/apt/archives/*jdk*:  openjdk-7-jre_7u75-2.5.4-1~trusty1_amd64.deb openjdk-7-jre-headless_7u75-2.5.4-1~trusty1_amd64.deb   Output of sudo dpkg --purge --force-all jdk1.8.0-40:  (Reading database ... 231488 files and directories currently installed.) removing jdk1.8.0-40 (1.8.040-1) ... /var/lib/dpkg/info/jdk1.8.0-40.postrm: line 586: /usr/sbin/alternatives: No such file or directory /var/lib/dpkg/info/jdk1.8.0-40.postrm: line 598: /usr/sbin/alternatives: No such file or directory dpkg: error processing package jdk1.8.0-40 (--purge): subprocess installed post-removal script returned error exit status 127 Errors were encountered while processing:  jdk1.8.0-40   When trying the edit I get this:  (Reading database ... 231488 files and directories currently installed.) Removing jdk1.8.0-40 (1.8.040-1) ... /var/lib/dpkg/info/jdk1.8.0-40.postrm: line 586: /usr/sbin/alternatives: Permission denied /var/lib/dpkg/info/jdk1.8.0-40.postrm: line 598: /usr/sbin/alternatives: Permission denied dpkg: error processing package jdk1.8.0-40 (--remove):  subprocess installed post-removal script returned error exit status 126 Errors were encountered while processing:  jdk1.8.0-40 E: Sub-process /usr/bin/dpkg returned an error code (1) What are bitwise operators? I'm someone who writes code just for fun and haven't really delved into it in either an academic or professional setting, so stuff like these bitwise operators really escapes me.  I was reading an article about JavaScript, which apparently supports bitwise operations. I keep seeing this operation mentioned in places, and I've tried reading about to figure out what exactly it is, but I just don't seem to get it at all. So what are they? Clear examples would be great! :D  Just a few more questions - what are some practical applications of bitwise operations? When might you use them?