To center or not to center?
Why could centering independent variables change the main effects with moderation?
Can I fly back to Italy if my Italian residency card has expired and is being renewed? I was working on a problem that resulted in the calculation: $20 \equiv 10x \pmod{11}$.  I got the answer $x \equiv 2 \pmod{11}$ with the thought process: Since $10$ is a factor of $20$ I can rewrite $20 \pmod{11}$ as $10x \pmod{11}$ with $x=2$. But isn't this basically the same as using division, which we aren't supposed to do in modular spaces?  If I solve by multiplying $20$ by the multiplicative inverse of $10 \pmod{11}$ which is $10$, I get $200 \pmod{11}$ which simplifies to $2 \pmod{11}$ anyway. Did these numbers just happen to be the same or is my original method valid? How to evaluate environment variables into a string in Python? I have a string representing a path.  Because this application is used on Windows, OSX and Linux, we've defined environment variables to properly map volumes from the different file systems.  The result is:  "$C/test/testing"   What I want to do is evaluate the environment variables in the string so that they're replaced by their respective volume names.  Is there a specific command I'm missing, or do I have to take os.environ.keys() and manually replace the strings? It seems that a number of the statistical packages that I use wrap these two concepts together. However, I'm wondering if there are different assumptions or data 'formalities' that must be true to use one over the other. A real example would be incredibly useful. Is the claim that functions of independent random variables are themselves independent, true?   I have seen that result often used implicitly in some proofs, for example in the proof of independence between the sample mean and the sample variance of a normal distribution, but I have not been able to find justification for it. It seems that some authors take it as given but I am not certain that this is always the case. 24% tax on first pay in the UK? Quite a similar thread to others I've seen here - hope I'm not repeating the same questions again!   I just got my first payslip after arriving in the UK and noticed that the tax is far higher than the HMRC rate for my salary bracket.     I did some research but couldn't find any reason why I would be taxed at 24.23% of my gross this month AND then an additional amount for NI.    I have about £640 back pay from April that is only being paid now,but even so, it doesn't explain the rather large discrepancy between the HMRC rate and what I'm seeing here.   Any ideas? SD card partitioning? why? how? Years ago I read short story about a man sitting in his room. Suddenly appears the same man but from the future and gives him an advice about the future. Original man seems to agree to follow that advice. Man from the future goes away. Then another version of that man from another future comes and gives a completely opposite advice and begs original man to follow it. Then this second version of this man from future also left. Original man stays alone not knowing which advice from future he must follow. My Ubuntu is running fsck on every bootup Steam Install Error on 14.04 Ubuntu 64bit Can't specify the 'async' modifier on the 'Main' method of a console app How to install Internet Explorer (multiple versions)? I am developing one site which has chat feature in Rails. I am using Ubuntu 12.04 LTS. I need to check that the site is IE9 because the chat feature using socket io of HTML5. I want to know that how to install IE9 in Ubuntu. I have looked at Chrome and Firefox extensions but if any standalone is available then please give me suggestion. How many different/unique $4$-letter arrangements are there of the letters in the word Mississauga?  I'm thinking we need permutations? I already tried finding each letter and still don't get it... any help?   So far I've broken it off to:-  $M=1$  $I=2$  $S=4$  $A=2$  $U=1$  $G=1$  However, I don't really know what to do next. Finding total after percentage has been used? Tried my best with the title. Ok, earlier while I was on break from work (I have low level math, and want to be more fond of mathematics)  I work retail, and 20% of taxes are taken out, and I am wanting to find out how much I made before 20% is taken out.  So I did some scribbling, and this is without googling so please be gentle. but lets say I make 2000 dollars per paycheck, so to see how much money I get after taxes I do 2000 * .8 which gives me 1600. I can also do 2000 * .2 which gives me 400 and then do 2000 - 400 (imo I don't like this way since I have a extra unnecessary step)  Anyways, I was pondering how to reverse that to have the answer be 2000, and what I did was 1600 * 1.20 (120%) which gave me 1920, and I thought that is odd so I did 1600 * 1.25 and answer was 2000 exact.  My question is why did I have to add extra 5% (25%) to get my answer? I am sure I did something wrong, and I fairly confident the formula I am using is a big no no.  edit; wow thank you all for your detailed answers. I am starting to like mathematics more and more. I read a novel where several enemy alien species were stranded together on an interdicted planet.  They had to recycle everything and keep hidden. By "keep hidden" I mean make sure there is no evidence of their presence visible from space. They recycled everything and lived in camouflaged dwellings.  The younger generation was building a mixed culture community until the older home species showed up.  One of the alien races had a body made of rings or donuts of gases that mixed to express itself. Members of this species could be taken over and controlled by rings transferred from another member of the species.  The book may be 20 years old or more. Prove that the expression is a perfect square Let $m$ be a natural number. Define $f(m) = m + \lfloor\sqrt{m}\rfloor$. Prove that at least one of the number among $m, f(m), f^2(m), \ldots$ is a perfect square. Here $f^k(m)$ denotes the composition of $f$ over itself $k$ times.  I tried the question, but the greatest integer along with square root is creating trouble. Redirecting from http to https in Apache This is a  about redirecting from http to https in Apache Related:     I have an Appache web server which serves both http://example.com/ and https://example.com/. I want to redirect all http requests to https. Currently I'm using this .htaccess rule to redirect http requests to https. RewriteEngine On RewriteBase / RewriteCond %{HTTPS} off RewriteRule (.*) https://%{HTTP_HOST}%{REQUEST_URI}   It's working as expected for example.com but the same rule is not working for sub links, when I access existing links, like example.com/about it will still load in http, no redirection happens for existing links. How can I make Apache redirect all http requests to https? Is there a word that contains all the vowels? "Jealousy" contains most of the vowels but lacks 'i'. Is there a word in the English language that contains every vowel (and preferably 'y')? For every matrix $A\in M_{2}( \mathbb{C}) $ there's  $X\in M_{2}( \mathbb{C})$ such that $X^2=A$? In what order do multiple readied actions with the same trigger resolve? My players have been scheming with rapid entry tactics for the megadungeon I've recently started running. Unfortunately, the monsters are aware of the adventurers, and this has lead to a weird question of priority. Given the following situation (which I'm pretty sure is going to happen next session in some form or another) what happens?     Alice the adventurer readies an action; if her teammate Carlos opens   the door, she's going to throw the alchemists fire through the door,   which should do enough damage to kill any goblins hiding there.      Meanwhile, on the other side of the door, Bob the goblin is lying in   wait. He readies an action; if the door opens, he's going to hit the   switch to open the trapdoor in the next room, which should drop any    pesky adventurers into a pit with spikes at the bottom.      Carlos opens the door.   I know what happens when , but what happens when multiple readied actions get triggered at the same time? My guess would be an opposed reflex save or initiative check of some kind to see who goes first, but that's entirely just intuition speaking. The rulebook doesn't seem to speak to the issue.