What is grammatically correct:      saying “4% of people was classified as introverts”.   Or saying     4% of people were identified as introverts.   The context is that I’m reporting the results of a survey.
Should you use a plural verb if you refer to a fraction?     Nine tenths of the pillar have rotted away.   I think has should be used here, but I'm not sure.
How to correct for small p-value due to very large sample size I have an iPhone 6 (with proper iTunes backup) where all of my contacts where, but I bought a new iPhone 7 and had to initialize it as new iPhone, due to several time-related constraints, so now I have a few but new contacts on my new phone, but none of the older ones, but would be the best practice oriented, for just recovering the old contacts from the iTunes backups?  PS: I still have the old iPhone 6, so it could be used as "temporary storage" if needed. We are supposed to prove that the zero vector is unique with the additive identity $x+O=x$ and then by creating another additive identity with $O'$, then $x+O'=x$.  We set them equal $x+O=x+O'$ and use the vector cancelling theorem to get $O=O'$, but how does this prove that the zero vector is unique? Evaluation of $\displaystyle \int_{0}^{1}\frac{x\ln (x)}{\sqrt{1-x^2}}dx$   $\bf{My\; Try::}$ Let $\displaystyle I = \int_{0}^{1}\frac{x\ln x}{\sqrt{1-x^2}}dx\;,$ Put $x=\cos \phi\;,$ Then $dx = -\sin \phi d\phi$  and Changing Limit, We get  $$\displaystyle I = -\int_{\frac{\pi}{2}}^{0}\cos \phi \cdot \ln(\cos \phi )d\phi = \int_{0}^{\frac{\pi}{2}} \ln(\cos \phi)\cdot \cos \phi d\phi$$  Now Using Integration by parts, We get  $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\int_{0}^{\frac{\pi}{2}}\frac{\sin^2 \phi}{\cos \phi}d\phi$$  So $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\int_{0}^{\frac{\pi}{2}}\frac{(1-\cos^2 \phi)}{\cos \phi}d\phi$$  So $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\int_{0}^{\frac{\pi}{2}}\sec \phi d\phi-\int_{0}^{\frac{\pi}{2}}\cos \phi d\phi$$  So $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\left[\ln\left|\sec \phi+\tan \phi\right|\right]_{0}^{\frac{\pi}{2}}-\left[\sin \phi\right]_{0}^{\frac{\pi}{2}}$$  So $$\displaystyle I = \left[\ln(\cos \phi)\cdot \sin \phi\right]_{0}^{\frac{\pi}{2}}+\left[\ln\left|\sec \phi+\tan \phi\right|\right]_{0}^{\frac{\pi}{2}}-1$$  Now How can I solve after that, Help Required, Thanks Terminal prompt not wrapping correctly I have an issue where if I type in very long commands in bash the terminal will not render what I'm typing correctly. I'd expect that if I had a command like the following:  username@someserver ~/somepath $ ssh -i /path/to/private/key myusername@something.someserver.com  The command should render on two lines. Instead it will often wrap around and start writing over the top of my prompt, somewhat like this:  myreallylongusername@something.somelongserver.comh -i /path/to/private/key  If I decide to go back and change some argument there's no telling where the cursor will show up, sometimes in the middle of the prompt, but usually on the line above where I'm typing.   Additional fun happens when when I Up to a previous command. I've tried this in both gnome-terminal and terminator and on i3 and Cinnamon. Someone suggested it was my prompt, so here that is:  \[\033[01;32m\]\u:\[\033[01;34m\] \W\033[01;34m \$\[\033[00m\]  Ctrll, reset, and clear all do what they say, but when I type the command back in or Up the same things happens.  I checked and checkwinsize is enabled in bash. This happens on 80x24 and other window sizes.  Is this just something I learn to live with? Is there some piece of magic which I should know? I've settled for just using a really short prompt, but that doesn't fix the issue. Proving that the given set has at most $2^{n-1}$ elements Windows 10 100% Disk Usage after Startup After startup for 5 minutes my system is very slow. The Task Manager shows that the disk usage is at 100%. (Later this number is around 2-4 %, but sometimes for 1-2 minutes go up again at 100%.)  I searched a lot on Google. For example I read , and also other pages. I opened two topic on Microsoft answer.  and one in Hungarian.  But I didn't found the solution yet. So I would like to ask Community's help. :)  Here the steps I already done:   I disabled everything at startups (including services) and the issue is the same.  I disabled Prefetch and Superfetch, the Baground Intellingent Transmission, Windows Search and Windows Defender but the issue is still persists. I made a health check on HDD, I made defrag and file system error check, but there are no errors. Also I tried to reinstall the HDD's driver. I made a full hardware check up, with no errors. The Windows and all the drivers are up-to-date. I tried a clean start. The issue is the same. I deleted Dropbox and all antivirus. I turned of the MSI mode.      I using also Linux, where this error is not occurs. Good to know, that Windows had 4 partitions, but I deleted 2 of them for the Linux. I don't know what partitions was these but both was only 10 - 20 MB.  I using a Dell Inspiron 15R SE 7520 with Windows 10 Home.  Personally I think it can be the Intel Rapid Store Technology "driver", because the problem started around when I installed it. (However I'm not sure.) And my hardware not supported yet by Intel, so I have no the newest driver. However I deleted Intel's software and driver and the issue is the same.    Thank you in advance for your assistance! Can the relative pronoun "whose" be used for animals, things and countries? When I was a student of English as a foreign language, more years ago than I care to count, I was taught that the relative pronoun “whose” could only be used for human beings, i.e., when someone possesses something.   My teachers were native speakers from England, then.   Since that time, I’ve seen “whose”, as a relative pronoun, used in several contexts where no human beings are mentioned, e.g. with animals, objects, countries, abstract nouns, etc, in American newspapers and magazines. Unfortunately, I can’t remember any of the sentences and cannot give examples.  What is acceptable in written and spoken English, and what isn’t, concerning the use of “whose” ? In his lectures on String Theory (), Tong gives a proof of the Weyl anomaly, using equation $(4.36)$. It seems wrong to me.  Here he uses the OPE between the stress-energy tensors $T_{zz}T_{ww}$  obtained when trace vanishes, i.e. $T_{z \bar{z}} = 0$: this implies that they are holomorphic functions $T_{zz} = T_{zz}(z)$. But in this proof he starts from the fact that $T_{z \bar{z}} \neq 0$ (we want to proof this thing after all) and so $T_{zz}$ is not a holomorphic function anymore! In the OPE $(4.36)$ I should have also terms with $(\bar{z}- \bar{w})$.  I can't also understand why he uses in the rest of the proof only the singular term $(z-w)^{-4}$, neglecting the other ones $(z-w)^{-2}$, $(z-w)^{-1}$.  (The same proof is given in these lectures  on conformal field theory, equation $(6.9)$).  I'll be really thankful if someone could explain me this proof :) Let $|A|=\alpha, |B|=\beta, |C|= \gamma$ be cardinals and $\beta \leq \gamma$. Prove $\alpha ^{\beta}\le \alpha ^{\gamma}$.  So from the given we know that there's an injection $f:B\to C$ and some functions $h:B\to A, g: C\to A$. We want to prove there's an injection $l_1:A\to C$. It appears that $f$ doesn't help here.  Trying to take representatives from $A$ and show they're in $C$ and there's an injection doesn't work so maybe the function should be $l_2: h \to g$ but I don't know how to work with it. Why are all snaps being mounted and listed as block devices or partitions for Ubuntu 18.04? As of Ubuntu 18.04 running lsblk shows 16 snap loops (2-3 times for each snap). The question is, why are they being listed as results for lsblk, fdisf-l, and blkid?    It creates a lot of clutter from the actual disks drive partitions I need to see, namely /dev/ partitions. I know a purported duplicate of this question exists, but it only asks why three loops are being listed per snap. I want to know why these snaps are being listed in the first place, and the purported duplicate does not answer this (perhaps those marking this as duplicate could help me by explaining why it is a duplicate). Technically, they qualify as file systems (which I neither created nor asked for), but they are getting in the way of the information output for the /dev/ partitions I am interested in. This becomes a problem when fdisk -l outputs a three page+ list filled mainly with snaps.  The output of a recent (1 week old) Ubuntu install and I have not installed any snaps:    $ lsblk   NAME   MAJ:MIN RM   SIZE RO TYPE MOUNTPOINT   loop0    7:0    0  14.5M  1 loop /snap/gnome-logs/37   loop1    7:1    0   2.3M  1 loop /snap/gnome-calculator/170   loop2    7:2    0  86.6M  1 loop /snap/core/4486   loop3    7:3    0  86.6M  1 loop /snap/core/4650   loop4    7:4    0   1.6M  1 loop /snap/gnome-calculator/154   loop5    7:5    0  14.5M  1 loop /snap/gnome-logs/34   loop6    7:6    0   3.3M  1 loop /snap/gnome-system-monitor/36   loop7    7:7    0   2.3M  1 loop /snap/gnome-calculator/178   loop8    7:8    0    13M  1 loop /snap/gnome-characters/101   loop9    7:9    0   3.7M  1 loop /snap/gnome-system-monitor/45   loop10   7:10   0 139.5M  1 loop /snap/gnome-3-26-1604/64   loop11   7:11   0   140M  1 loop /snap/gnome-3-26-1604/59    loop12   7:12   0   3.7M  1 loop /snap/gnome-system-monitor/41   loop13   7:13   0    21M  1 loop /snap/gnome-logs/25   loop14   7:14   0  12.2M  1 loop /snap/gnome-characters/69   loop15   7:15   0    13M  1 loop /snap/gnome-characters/96   sda      8:0    0 298.1G  0 disk   ├─sda1   8:1    0   512M  0 part /boot/efi   └─sda2   8:2    0 297.6G  0 part /   sr0     11:0    1  1024M  0 rom     (supplemental screen capture of above text):     My snap list shows 6 results:       core   gnome-3-26-1604   gnome-calculator   gnome-characters   gnome-logs   gnome-system-monitor     Meanwhile, gnome-disk-utility shows nothing at all for snaps, only showing my HDD and optical drive.    It won't be very efficient if every installed snap gets listed as a block device (2-3 times each to add). Should I expect future updates to deal with this?  Edit: fdisk-l also dumps out a very long list with 16 instances of these "disk loops" (Disk /dev/loop0, Disk /dev/loop1, etc., each with details which I won't show here because it's too long). This can't be intended behaviour, can it? blkid also lists 16 loops, as TYPE="squashfs". At least parted -l works as expected, only outing my actual disk partitions.    I just tested this, and installing more snaps does add more to the lsblk output. Therefore, fdisk, lsblk, blkid could have potentially huge output lists, according to the number of snaps available, and installed. I need a little hint in a proof on convergence of a sequence. The problem I have is: Suppose $(x_n)$ is a monotone decreasing sequence of real numbers such that $\sum x_n$ converges, prove that:  $$\lim_{n \to \infty} nx_n=0$$  My idea is: proving this fact aims to prove that given $\epsilon &gt;0$ there's some natural $n_0 \in \mathbb{N}$ such that if $n &gt;n_0$ we have $|nx_n|&lt;\epsilon$.  Now, I know that $\sum x_n$ converges, so that given $\epsilon'&gt;0$ there's some $k_0 \in \mathbb{N}$ such that if $k &gt; k_0$ we have:  $$\left|\sum_{i=1}^{k}x_i - S\right|&lt;\epsilon'$$  Where $S = \sum x_n$. Now, since $(x_n)$ is monotone decreasing we know that we must have $x_1 &gt; \cdots &gt; x_k$ so that the sum of all $x_i$ should be less or equal to $k x_k$. So I know that I have:  $$\left|\sum_{i=1}^{k}x_i - S\right|\leq\left|\sum_{i=1}^{k}x_i\right|+|S|\leq|kx_k|+|S|$$  I feel that the proof will come from this, however I'm stuck at this point. Can someone give just a little hint on how to proceed from here?  Thanks very much in advance for your help. What happens if 2 separate abilities require you to sacrifice a creature? If i have two cards that force opponents to sacrifice every upkeep like for example  "At the beginning of each opponent’s upkeep, Mogis deals 2 damage to that player unless he or she sacrifices a creature."  And  "At the beginning of your upkeep, draw a card unless target opponent sacrifices a creature or pays 3 life."  Does the oppenent have to sacrifice twice? Or if they sacrifice Mogis's ability have they not allowed me to draw from indulgent tormentor? Associativity of symmetric difference of sets By $A\oplus B$ we denote the symmectric difference of two sets. The definition is $A\oplus B =(A\setminus B) \cup (B\setminus A)$. Now I hope to show that $A\oplus (B\oplus C) = (A\oplus B)\oplus C$. I remember that there's an elegant proof, but I forget its detail. (The first step is to show $A\oplus (A\oplus B) = B$, and maybe applying this formula, we can obtain associativity.) I added a user account to the admin group and discovered I added wrong user. So I now have to remove the account from the admin group.   How can I remove an account from a group without deleting the user? If a permanent turns into a(nother) creature, has it entered the battlefield? I was playing a game last night with a guy who was playing a new Simic Gatecrash deck, and he claimed that if he made a land into a creature, it counted as entering the battlefield, thus triggering evolve (or other "enters the battlefield" abilities).  I thought this was incorrect, being that the creature didn't actually enter the battlefield, it was just created.  Which of us was right? How do I change my username? How to check if jQuery.ajax() request header Status is "304 Not Modified"? Why teach linear algebra before abstract algebra? Is there a reason why most undergraduate curriculums put linear algebra before abstract algebra?  I'm asking this because personally it seems to be much easier to understand the architecture behind linear algebra as supposed to simply solving problems after a course in abstract algebra. Please use UK pre-uni methods only (at least at first). Thank you.