What is the correct form (singular or plural) of the following two sentences:  A particular amount of students has/have access. A particular amount of students was/were selected.  In my opinion, it could be either referred to &quot;amount&quot;, which would be singular (has/was) or to &quot;students&quot;, which would be plural (have/were).
Can anyone please help and tell me if this sentence is correct?  &quot;A significant amount of zombies were detected in your city.&quot;  In my opinion it should be &quot;A significant amount of zombies was detected in your city.&quot; because &quot;amount&quot; should be in agreement with &quot;was&quot; even though amount usually refers to something plural. Are both (was and were) acceptable in this case? Edit1: Yes, &quot;number&quot; would be the correct one in this case. So allow me to ask one more thing.  &quot;A significant amount of purchases were detected...&quot;  Does the use of &quot;number&quot; apply in this case also? As purchase is not exactly a thing/person. And if no, is it correct to say &quot;A significant amount of purchases were detected...&quot;? Edit2: So, please tell me what is the correct phrasing?  &quot;A significant amount of purchases were detected...&quot; &quot;A significant amount of purchases was detected...&quot;  Or, since purchases are countable, is the use of &quot;number&quot; instead of &quot;amount&quot; correct here, as in:  &quot;A significant number of purchases were detected...&quot; &quot;A significant number of purchases was detected...&quot;  Or would amount be correct since a purchase involves money and it refers to the amount of money? Would greatly appreciate an answer, and if possible a detailed explanation.
Removing nodes from graphs such that one is dependent on other - ZIO $2010$, P$1$ Greetings Community! The above problem you see is a combinatorics problem I could not solve. :( This problem is from ZIO $2010$, P$1$.     Here is what I did: Observe that every graph can be divided into "sub-groups" which may help in solving. We first remove the empty set. Then the singleton set. Consider the bigger but smaller than the sub-parts example:    The singleton sets are $\{4,5,6\}$ which are at the least position in the graph.   The dual sets are $\{2,4\}, \{3,5\}, \{3,6\}$, the bottom - two portions in the graph. The triplet sets are $\{2,4,5\}, \{4,5,6\}$ which we may manually count but for the bigger graphs in the sub-part, this may prove to be difficult and this is where I am stuck.   Any help would be appreciated. Thanks. executing web service using postman I am working on an iGoogle-like application. Content from other applications (on other domains) is shown using iframes.   How do I resize the iframes to fit the height of the iframes' content?  I've tried to decipher the javascript Google uses but it's obfuscated, and searching the web has been fruitless so far.  Update: Please note that content is loaded from other domains, so the  applies. Evaluating $\int^\pi_{-\pi} \cos^3(x) \cos(ax)~dx$ I need to evaluate $I = \int^\pi_{-\pi} \cos^3(x) \cos(ax)~dx$ where $a$ is some integer.   I get: $\dfrac{2a(a^2-7)\sin(\pi a)}{a^4 - 10a^2 + 9}$. However $\sin(\pi a)$ is $0$ for all $a$ so $I=0$. But as noted by an answer, there are answers for $a = 1,3,-1,-3$. What is the correct way to install proprietary ATI Catalyst Video Drivers (fglrx) directly from AMD? I am planning on doing a fresh install of Ubuntu and want to know what is the correct way to install ATI Catalyst Video Driver?      There are multiple valid answers for this question spanning over several versions of Ubuntu. For your convenience an index of each below: Alternate moves, first one to roll a 6 wins: what's the probability of winning? Question: Players A and B play a sequence of independent games. Player A starts and throws a fair die and wins on a "six". If she fails then player B throws the same die and wins on a "six" or fails otherwise. If she fails then player A gets the die and throws again, and so on. The first player to throw a "six" wins. Find the probability that player A wins.  Here is what I have done:  A wins right away: $\dfrac{1}{6}$  A fails B wins: $\dfrac{5}{6}\times \dfrac{1}{6}$  A fails B fails A wins: $\dfrac{5}{6}\times \dfrac{5}{6}\times \dfrac{1}{6}$  Unlike another similar question which the player B can win on "five" and "six" after player A fails on the first throw, in this case, the games do not seem to have an endpoint. How should I calculate the probability that player A wins then? Salesforce to Xero integration using Named Credentials by OAuth 2.0 Linux genisoimage Batch How can I hover over icons in Ubuntu Dock to see all windows of one application? I'm using Ubuntu 17.10 with GNOME 3. How can I show all open windows of a certain application using the sidebar (aka Ubuntu Dock)? Right now I have to right-click and select "all windows" to see my other open windows.   Is there a quicker way to do this? Nested cross validation for model selection How can one use nested cross validation for model selection?   From what I read online, nested CV works as follows:   There is the inner CV loop, where we may conduct a grid search (e.g. running K-fold for every available model, e.g. combination of hyperparameters/features) There is the outer CV loop, where we measure the performance of the model that won in the inner fold, on a separate external fold.    At the end of this process we end up with $K$ models ($K$ being the number of folds in the outer loop). These models are the ones that won in the grid search within the inner CV, and they are likely different (e.g. SVMs with different kernels, trained with possibly different features, depending on the grid search).  How do I choose a model from this output? It looks to me that selecting the best model out of those $K$ winning models would not be a fair comparison since each model was trained and tested on different parts of the dataset.  So how can I use nested  CV for model selection?   Also I have read threads discussing how nested model selection is useful for analyzing the learning procedure. What types of analysis /checks can I do with the scores that I get from the outer K folds? "In" and "on": How can I decide which one to use for vehicles? Examples:   In a car, van, etc. On a bus, boat, motorcycle, etc.   How can one decide which preposition to use? Is memorization the only way or is there a better way?  Note: People generally explain this by either distinguishing between open and closed vehicles or between large and small vehicles. However, the examples I've given defeat both explanations. Selecting the size of a System.Drawing.Icon? How are reserved and formal synonyms? In the dictionary reserved means - not revealing emotions and formal means - prim or stiff. I saw they were synonym in the Google dictionary. What makes these two words similar, I wonder? "Has/Have/Had" as a main verb and auxiliary verb I need help regarding the use of has/have/had both as a main verb and as an auxiliary verb.  In the sentence below, the word has acts as the main verb. I would normally follow it with the phrase "so do I."        Kenny has a car, and so do I.      On the other hand, the word has in the following sentence acts as an auxiliary verb. I would normally follow it with the phrase "so have I."        Kenny has bought a car, and so have I.      a) Are sentences 1 &amp; 2 above correct? I'm under the impression that so do I is used when has/have/had is the main verb of a sentence, and so have/had I if it's an auxiliary verb in a sentence.  b) Does the verb has/have always need a supporting "auxiliary verb" (either implied or mentioned)? (e.g., Kenny has a car = Kenny does have a car.) Let $A$ be a $n\times n$ matrix with entries $a_{ij}=i+j $ . Calculate rank of $A$.  My work : I noticed that A is symmetric . Hence all of its eigen vectors are real .. That is all i have got .   Your help will be highly appreciated .Thank you . Does name of sitemap file that Wordpress generates matter? Custom fields not useable in Approve/Reject Approval Request I'm trying to get through my first SalesForce mod and it's definitely been a rocky path. I have one task I'm trying to do, but this section is holding me back.  I have two custom fields.  One a pick list and the other a text box. I have added them to the Approve/Reject Approval Request section in the Opportunity page. I added the fields through the Select Fields to Display on Approval Page Layout and they DO show up on the Approve/Reject Approval Request section. I added them in like ().  However, just the label for the fields show, the field itself is nowhere to be found and can't be used.    You can see and even use the fields when you open the Opportunity page itself, but when you go to use the Approve/Reject, you can't do anything with them or see any values.  I was never a SalesForce user and got this tossed in my lap and really don't know my way around yet. I appreciate any help on this!!  Thanks!!  Kurt How can I vertically align elements in a div? I have a div with two images and an h1. All of them need to be vertically aligned within the div, next to each other. One of the images needs to be absolute positioned within the div. What is the CSS needed for this to work on all common browsers? &lt;div id=&quot;header&quot;&gt;   &lt;img src=&quot;..&quot; &gt;&lt;/img&gt;   &lt;h1&gt;testing...&lt;/h1&gt;   &lt;img src=&quot;...&quot;&gt;&lt;/img&gt; &lt;/div&gt; How to make a table from two lists? Does any particle ever reach any singularity inside the black hole?