Which one is correct? The "80% of [it]" part is what has me confused.  a. 80% of what I listen to is K-pop groups.  b. 80% of what I listen to are K-pop groups.  Should I perhaps just say "K-pop groups are 80% of what I listen to"?
Does a percentage require a singular or plural verb, for example, do we say ten percent "go" or "goes"?
If I have a $2\times 2$ or $3\times 3$ matrix, how should I go about computing the eigenvalues and eigenvectors of the matrix?  NB: I am making this question to provide a unified answer to questions about eigenvalues of small matrices so that all of the specific examples that come up can be marked as duplicates of this post. See . What are "good men that do nothing" called? "The only thing necessary for the triumph of evil is for good men to do nothing." -Edmund Burke  Is there an idiom, phrase or preferably a single word that we can call people that could have helped but didn't? Bystanders don't necessarily have help to give. Cowards aren't particularly helpful either.    Addendum:  For example, once EMS has arrived on scene, bystanders are encouraged not to try to help, unless they're a nurse and therefore have the necessary skills to, and sometimes even then so. If in The Service, I would not want a coward (a liability) next me holding the line. Not to take anything away from these great answers, or to insist on a non-militaristic point of view, I would like to veer into the commercial or civilian realm in which I find this quote most often alluded to, E.G., "If we all gave 5 cents we could cure cancer tomorrow." Pretend most of us did give 5 cents and we did cure cancer, but you didn't give. You are now a(n) ____?... yes, I know what we call them, but what is their proper designation? What is the meaning of "algebraically indistinguishable" I heard the term couple of times (in Field theory class and book), for example: The different roots of $p(x)=x^3-2$ are "algebraically indistinguishable".  I understand the meaning intuitively, but what does it really mean ? .NET DateTime.Now returns incorrect time when time zone is changed How to Preload Tabs/Set Multiple Websites as Default in Firefox, IE, etc Any website can set as the homepage of Firefox which loads spontaneously. Is this for multiple tabs? Then BBC Health, CNN, Yahoo Health, msn.com would all extemporarily materialise (in four separate tabs); I then wouldn't have to open each website manually. How to fix 'Android is starting' optimization on every boot? I recently updated to Lollipop on a Moto G (1st Gen).   It was running a bit slow, so I wiped by cache then performed a factory reset as recommended.  I now receive the 'Android is starting optimising app xx of xx' every time I boot.   Obviously not life and death, but it's annoying to have to wait 10 minutes for every reboot.   Is this a known issue and is there any way to fix this? How do I root my Android device? This is a common question asked by those who want to root their phones. How exactly do I root my Android device? Are there risks involved? Recently upgraded to a Samsung S10e and Android 10, but all Q&amp;A in the Stack Exchange app v1.0.95 are blank.  The title and comments are visible, but question/answer posts are just white space. Accessing the About page in the app is also blank.  I tried clearing data, cache and re-installing the app, but I still get the same behaviour. How did the transdimensional Edo god (Edo lord) come to be the overseer of the Edo? Why not always present logistic regression estimates in the response scale (probablity)? There's a lot of discussion in epidemiology around the relative merits of odds ratios vs risk ratios. Proponents of the former cite the mathematical qualities of odds (not constrained to be between 0 and 1) and their suitability for examining common outcomes. Proponents of the latter believe that RR's are often more interpretable, and match how clinicians and the public tend to think. Some have suggested methods to model risk ratios directly (in multivariable models). For instance, the log binomial model and poisson regression with robust standard errors. What I don't understand is - why don't we just fit the model using standard logistic regression and perform the inverse logit transformation on the fitted estimates? For instance, lets say we are trying to predict coronary heart disease using BMI (exposure) and age (confounder). We could fit the model and estimate the odds of CHD across the range of values of BMI (adjusted for age), according to the model. We then take the inverse-logit of those fitted odds to transform them onto the probability scale. Seemingly this way we now have an idea of the risk of the outcome across all values of the exposure, which we can plot or otherwise describe. But i've never seen this method recommended. Which makes me think there must be a conceptual issue with it?? p.s. lets assume we are performing a cross-sectional or cohort study (not a case-control study). The responsiveness is really bad on a newly installed Ubuntu 14.04 LTS.  Here's the specs of my laptop:  Quadcore Intel i7-4600U CPU @ 2.10GHz 12GB Ram 1TB Samsung EVO SSD   And when gradle is compiling, my entire system slows to a crawl, videos begin stuttering, browser scrolling lags... etc.  The same goes when a page refresh occurs in another window in Chrome, and while it refreshes, the HTML5 video in another tab begins stuttering.  How can I fix this?  Here are some logs:  $ vmstat -a 1 5 -   $ iostat -x 1 5 -   $ top -b - jQuery attribute selector variable How can I parse dates and convert time zones in Perl? Compute the mean of $(1 + X)^{-1}$ where $X$ is Poisson$(\lambda)$ Question  Let $X$ be Poisson with parameter $\lambda$.  Compute the mean of $(1 + X)^{-1}$. (Introduction to Probability Theory, Hoel, pp. 104)  Answer Key  The answer key shows that the mean is $\lambda^{-1}(1 - e^{-\lambda})$  My Solution  $$E(1 + X)^{-1} = \sum\limits_{j = 1}^\infty (1 + j)^{-1} \dfrac{\lambda^{(1 + j)^{-1}}e^{-\lambda}}{(1 + j)^{-1}!}$$ $$= e^{-\lambda} \sum\limits_{j = 1}^\infty \dfrac{\lambda^{(1 + j)^{-1}}}{((1 + j)^{-1} - 1)!}$$ $$= \lambda^{-1} e^{-\lambda} \sum\limits_{j = 1}^\infty \dfrac{\lambda^{(1 + j)^{-1} - 1}}{((1 + j)^{-1} - 1)!}$$ $$= \lambda^{-1} e^{-\lambda}(e^{\lambda} - 1)$$ $$= \lambda^{-1}(1 - e^{-\lambda})$$  EDIT: I found why I got the answer incorrect.  Thanks for those who answer the question! :) It is will known that increasing cooling of a metal casting will lead to finer micro-structure which mean higher mechanical properties. If I have 2 molds one is thick copper die ,&amp; second is just thin-walled copper cup or mold cooled by water. which one of them excepted to cool the molten metal i.e. aluminium faster ?   by calculation it seems that copper die have higher cooling power as it has higher thermal diffusivity , but in real life it seems water have more cooling power. I am so confused. An increasing number of funding organizations require publications on the research that they fund to be open access, i.e. available to the public without having to subscribe to a journal or pay a fee. Does anybody know where I can find a list of journals/publishers that do not allow material that they publish to be published this way? Count number of increasing functions, nondecreasing functions $f: \{1, 2, 3, \ldots, n\} \to \{1, 2, 3, \ldots, m\}$, with $m \geq n$. I stumbled upon a question given like:  Let $m$ and $n$ be two integers such that $m \geq n \geq 1$.   Count the number of functions $$f: \{1, 2, · · · , n\} \to \{1, 2, · · · , m\}$$ of the following two types:  (a) strictly increasing; i.e., whenever $x &lt; y, f(x) &lt; f(y)$, and  (b) non-decreasing; i.e., whenever $x &lt; y, f(x) \leq f(y)$.  I tried in the following way.  For (a). We can say $f(n)&gt;f(n-1)$ AND $f(n)&gt;f(n-2) \ldots f(n)&gt;f(1)$ (total $n-1$ elements)  Similarly for $f(n-1)&gt;f(n-2), f(n-1)&gt;f(n-3) \ldots f(n-1)&gt;f(1)$ (total $n-2$ elements)...  and $f(2)&gt;1$  Like this $$(n-1) + (n-2) + \ldots + (1) = \frac{n(n-1)}{2}$$  Is this correct?  For (b). Since there's equality, it will be $$n + (n-1) + ... (1) = \frac{n(n+1)}{2}$$  Is my approach correct? Any help is appreciated. Thanks in advance. Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros Evaluating the double limit $\lim_{m \to \infty} \lim_{n \to \infty} \cos^{2m}(n! \pi x)$ I have to find out the following limit $$\lim_{m\to\infty}\lim_{n\to\infty}[\cos(n!πx)^{2m}]$$ for $x$ rational and irrational. for $x$ rational $x$ can be written as $\frac{p}{q}$ and as $n!$ will have $q$ as its factor the limit should be equal to 1. the second part of irrational is giving me problems. I first thought that limit should be zero as absolute value of cosine term is less than 1 and power it to infinity you should get $0$. But then I realised that it was wrong. I brought the limit down to this form. $$e^{-\sin^2(n!πx)m}$$ after this I find the question quite ambiguous as they have just said $x$ is irrational. If I take $x$ as $\frac{1}{n!π\sqrt{m}}$ I get the limit as $\frac{1}{e}$ but if I take  $x$ as $\frac{2}{n!π\sqrt{m}}$ I get the limit as $\frac{1}{e^4}$. please help me and tell me where have I gone wrong? How did Luke know where to land on Dagobah?