Why is $(\mathbb{Z}\oplus\mathbb{Z})/\langle(3,6)\rangle$ not isomorphic to $\mathbb{Z}$?
Find $|(\mathbb{Z} \oplus \mathbb{Z}) / \langle(3,6)\rangle|$ and determine if its cyclic
I am currently studying in class 10 and I am unable to do this problem. $$\tan 70 ° -\tan 20° -2 \tan 40° =4\tan 10°$$ Can anybody please help me.  Thanks! This is a  about securing public DNS resolvers   Open DNS servers seem pretty neat and convenient, as they provide IP addresses that we can use consistently across our company regardless of where they are located. Google and OpenDNS provide this functionality, but I'm not sure that I want these companies to have access to our DNS queries.  I want to set up something like this for use by our company, but I hear a lot about this being dangerous practice (particularly in regards to ) and I want to make sure that we do this right. What things do I need to keep in mind when building this type of environment? How do I get Power Armor training in Fallout New Vegas? I've found some power armor, but I can't use it yet without training. I assumed that the Brotherhood of Steel would train me, if they like me enough.  I've completed the Brotherhood of Steel quest series for the overseer (the original one, I did not overthrow him), but I did not get any Power Armor training. What do I have to do to be able to wear Power Armor? Using the same variable as a fixed and random effect in Mixed Effect Models Can we move "Start a bounty" to a more intuitive location? I have created new partition by selecting free space option and now I can't merge it or recreate it.  I have tried to use iPartition to create a new partition on free space but it said I have no permission.  How can I fix it? 101 positive integers placed on a circle A Pigeonhole Principle problem:     101 positive integers are placed on a circle whose sum is 300. Prove   that it is possible to choose from these numbers some consecutive   numbers whose sum is equal to 200.   (I don't know if the word 'consecutive' is appropriate in this case ,I mean that these numbers follow each other on that circle) Why can't photons have a mass? Why can't photons have a mass? Could you explain this to me in a short and mathematical way? Extending a Homotopy from $X \times [0,1]$ to $X \times \mathbb{R}$ I’ve had a good look and can’t seem to find out how to select all elements matching certain classes in one jQuery selector statement such as this:  $('.myClass', '.myOtherClass').removeClass('theclass');   Any ideas on how to achieve this? The only other option is to do  $('.myClass').removeClass('theclass'); $('.myOtherClass').removeClass('theclass');   But I’m doing this with quite a few classes, so it requires much code. How to create two partitions? How can I iterate over an enum? Using Custom Labels in a Class I have the below If statements using some hard coded strings and I want to make them use as custom labels. I have created custom labels with the same String names as given below. So how can I make these statements to use the Custom Labels I created ?  if(monitoringFrequency == 'daily'){             return dateValue.addDays(1);         }else if(monitoringFrequency == 'weekly'){             return dateValue.addDays(7);         }else if(monitoringFrequency == 'monthly'){             return dateValue.addMonths(1); I loved the keyboard shortcuts in Windows 7 (i.e. Win + &larr; moves a window to the left side of the screen), but I'm not sure on what some of the new ones might be for Windows 8.  What are all of the NEW keyboard shortcuts that I can use while working in Windows 8? Python string prints as [u'String'] This will surely be an easy one but it is really bugging me.   I have a script that reads in a webpage and uses  to parse it. From the soup I extract all the links as my final goal is to print out the link.contents.  All of the text that I am parsing is ASCII. I know that Python treats strings as unicode, and I am sure this is very handy, just of no use in my wee script.   Every time I go to print out a variable that holds 'String' I get [u'String'] printed to the screen. Is there a simple way of getting this back into just ascii or should I write a regex to strip it? Typesetting linguistic rewrite rule I'm trying to (more or less) replicate this phonological rewrite rule:    I'm using the package , and what I manage to accomplish is this:  \documentclass{article} \usepackage{phonrule} \begin{document}  \phonc     {\phonfeat{$-$cnt\\ +hi}}     {[$\alpha$grv]}     {\oneof{%         \phonfeat{$-$cnt\\ $\alpha$grv}\phold\\         \phold\phonfeat{$-$cnt\\ $\alpha$vce}%     }}  \end{document}     My main problem here is what appears after the "when" slash:  (1) The package only provides a left curly bracket - how can I add a right one as well?  (2) The two options within the curly brackets are not well aligned. I think comparing the two pictures themselves says it better than what I could do with words. I have two different list. In the first list are some people picker columns.  Is it possible to create a lookup column for list 2 to add the user from the first list? I know it isn't supported in Sharepoint, but i hope someone have an idea to solve my problem. Animated textures don't work in Blender viewport playback Simple property of a valuation on a field Combinatorial proofs: having a difficult time understanding how to write them out Can someone explain how combinatorial proofs work?  I've included an example questions that's been giving me a hard time.  Any insight on the topic would be great.  $$\sum_{k=1}^{n}k{n \choose k} = n2^{n-1}$$  Another one:  $${2n \choose 2} = 2{n \choose 2} + n^2$$  The solution says:  LHS: Pick two people from a pool of n men and n women. RHS: Pick two women, pick two men, and pick one of each.  But I don't see how this applies.  How does $n^2$ show that we're picking "one of each?"  Thanks for the help :)