May I know which sentence is grammatical?     Given n services in sequential composition, where each of them having   l candidates, the total number of combination is l^n.      Given n services in sequential composition, where each of them having   l candidates, the total number of combination are l^n.      Given n services in sequential composition, where each of them having   l candidates, the total number of combinations is l^n.      Given n services in sequential composition, where each of them having   l candidates, the total number of combinations are l^n.
This hurts my eyes to read it and my ears to say it, but the writer stands by          About the same number of people was awarded bachelor's degrees in 2010 as filed for personal bankruptcy (1.6 million).   Is the subject in this sentence singular or plural?
How do you remove the ability for a user to make a comment or post on a page? I am building a new website on Wordpress, and all my pages have the add comment box at the bottom. I wish fo rthis to be removed from pages such as Home, Contact Us, About etc etc, but want it to remain on the blogs and galleries.  I have read  but do not really understand what this means to do. is there an easier way to do it. I do not have  under Settings -> Discussions. Dealing with a whole bunch of two-line config files, I'd like a way to exclude any files that have a different number of lines.  So, something like:  mv * destdir only if file contains exactly two lines   Or:  wc -l * | grep '^ *2' | xargs mv {} destdir   Except that neither of those is actual working code.  While writing this I realized I do have a way to do this, which is ugly as heck, and I've included it below as an answer.  Is there an easy/clean way to do this? Is it possible to run commands from spotlight? I run commands in terminal a lot and i'm wondering if it is possible to run the commands from spotlight. For example in spotlight  would like to run the command(because i have a lot of network issues):   ping google.com   And then spotlight to load terminal and execute the command instead of having to load terminal because it takes so long to load. So is this possible? Test for convergence  $$\sum_{n=1}^{\infty} \frac{1}{n^n}$$  I'm at a loss on what to do, is this a geometric series $\frac{1^n}{n^n}$? Difference between shutdown and shutdownNow of Executor Service Subset of a countable set is itself countable How is it proved that if $$A \subset B\ \text{with}\ B\ \text{countable} $$ then $A$ is either countable, finite, or empty? I think the proof involves a $1-1$ correspondence between $\mathbb{N}$ and $A$ but other than that I do not know how to proceed.  EDIT: I have checked the solution and it advises me to proceed as follows. " As a start to a definition of $$g: \mathbb{N} \rightarrow A$$ set $$g(1)=f(n_1) $$ Then show how to inductively continue this process to produce a $1-1$ function $g$ from $\mathbb{N}$ onto $A$."  So the proof according to my book involves induction. Finding Maximum value of consecutive positive integers with constraints Let, $x,y,z$ be consecutive positive integers such that $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} &gt; \frac{1}{10}$ I need to find the maximum value of $x+y+z$ ?  My attempt:  I tried guessing first, To maximise $x+y+z$ it is necessary to have high value for $x$, But not too high which will contradict the constrain of the problem. As we can roughly split the $0.1$ into three parts so I started with numbers closer to $30$ with trial an error I got that for $x=29$ we get the optimum and final result would be 90 (=max. value of $x+y+z$).   Is there any way to arrive at this conclusion with using inequalities? Any hints will be appreciated... wrong positioning of figure with tabular in xelatex Draw power from a portable mobile charger to power circuits I usually power my beginner prototype circuits using mb102 power supply board, but it needs an external elimeter to draw power and then regulate it.  I was looking for a portable solution for my 5 volt and 3.3 volt circuit needs and came up with using a portable battery charger for mobile phones.  I tried powering up a simple transistor and LED circuit with it but it wouldn't power-up.   I feel that there is some load sensing circuit in the portable charger which doesn't detect these low power circuits.  I also tried connecting different resistors to the charger, the charger outputs 5 Volts for a few seconds and then again shuts down and doesn't stay ON continuously.  It would be really comfortable to use a portable charger since it could be charged using a phone charger and would be very handy.  What can I do to make the charger output power on low loads? How does remittance work? How does it differ from direct money transfer? I have a bank account in Germany in which I receive my salary in Euros. I want to deposit a part of it in my Indian bank account for personal savings. My Indian bank account is in INR. As I see it, I have two options:   To use a remittance service that converts my Euros into INR and deposits in my account. I am not sure how it works. The service (which I know is reliable) I signed up for asks me to deposit Euros in a certain account ("funding") which will be converted to INR and deposited in my account. How does that work exactly? Use my bank's service to make a international bank transfer to my account. Is that even possible, given that my Indian account is in INR? Will I incur higher conversion fees and lower exchange rate?   In general, what are the pros and cons of each of the above methods? And are there any other methods? "A flea hops randomly on the vertices of a triangle with vertices labeled 1,2 and 3, hopping to each of the other vertices with equal probability. If the flea starts at vertex 1, find the probability that after n hops the flea is back to vertex 1."  Could someone provide a hint to help me start this? What are instructions on how to download videos from YouTube?    Notice: Terms of Service Violation  Please be aware that by following any of the answers below, you will be violating YouTube's . In particular, from Section 5.B.:     Content is provided to you AS IS. You may access Content for your information and personal use solely as intended through the provided functionality of the Service and as permitted under these Terms of Service. You shall not download any Content unless you see a “download” or similar link displayed by YouTube on the Service for that Content. You shall not copy, reproduce, distribute, transmit, broadcast, display, sell, license, or otherwise exploit any Content for any other purposes without the prior written consent of YouTube or the respective licensors of the Content. YouTube and its licensors reserve all rights not expressly granted in and to the Service and the Content. I currently have a masters degree in an engineering field and I don't currently have any PhD degrees (I may study for a doctorate degree in future). It happens that when I go to conferences or scientific occasions, even in the emails I receive from people; they use a doctor prefix for my name; but I do not have a PhD degree.  What is a good etiquette to deal with such thing? Should I directly tell them that I do not have a doctorate degree? Or should I neglect such a mistake by them and don't do anything?  I think it is unethical not to correct such thing, because the person may still think that I have a PhD degree; and such wrong usage of title should be corrected some way. Once a person used doctor title for my name in an email and I just added a line in my reply to his email, stating that I have a masters degree. Why is "the set of all sets" a paradox, in Layman's terms? I've heard of some other paradoxes involving sets (i.e., &quot;the set of all sets that do not contain themselves&quot;) and I understand how paradoxes arise from them.  But this one I do not understand. Why is &quot;the set of all sets&quot; a paradox?  It seems like it would be fine, to me.  There is nothing paradoxical about a set containing itself. Is it something that arises from the &quot;rules of sets&quot; that are involved in more rigorous set theory? I'm thinking about installing Ubuntu Desktop, but I don't know what flavor is the best for my system. What are the minimum and recommended hardware requirements? What kind of CPU? How much memory? Should I have Hardware Acceleration? What flavor should I use?  This is an attempt of a canonical answer. My answers have the &quot;official  requirements&quot;, the recommended are a mix of official sources and opinion based (along with the answer it's told the source). You can comment or edit if you feel that the information is obsolete or incomplete. It is a good rule of thumb that any system capable of running Windows Vista, 7, 8, x86 (Intel) OS X will almost always be a lot faster with any Ubuntu flavor even if they are lower-spec than described below. $\int_{\frac{1}{3}\pi}^{\frac{2}{3}\pi} {\sin(x)\;dx}$ using Riemann sums? Option clash when using graphicx and tikz packages The following code fails Option clash for package graphicx, it seems to be an incompatibility between the package graphicx (when the option pdftex is used) and the package tikz.  \documentclass[a4paper,10pt]{book} \usepackage[T1]{fontenc} \usepackage[utf8x]{inputenc} \usepackage{tikz} \usepackage[pdftex]{graphicx}  \begin{document}      The lazy dog...  \end{document}   I am currently working with Debian wheezy (updated as of 10th November 2012), and the latest TeXLive LaTeX distribution included.  Any ideas? How to change the name of an iOS app? I began an iPhone project the other day with a silly development code name, and now I want to change the name of the project since it's nearly finished.   But I'm not sure how to do this with Xcode, trying the obvious of changing the application's name in the info.plist file, causes the signing process to go wrong (I think...) and my app won't launch giving me a Launcher error.  I guess I could make a new project and copy paste everything over, but it seems so primitive that I'm hoping for a more civilized solution. Update from 14.04 to 16.04 failed with GPG error Seasonal Loan Amortization