Haven't got or haven't gotten?
Difference between "I have got" and "I have gotten"
Change Recycling Bin Location I have a SSD as a primary hard drive, and one HDD for storage. I want the recycling bin to be on the HDD. I want is so that even if I delete files from the SSD the end up on the HDD's recycling bin. What is the proper way of going about this? var functionName = function() {} vs function functionName() {} Why does Stack Overflow allow duplicate display names? What is the reasoning behind the design decision to allow users to create a display name which matches another existing users exactly?    This is opposed to the common practice of enforcing unique user names, and I'd really like to learn something. Suppose $f$ is a differentiable function over $\mathbb{R}$ satisfying $f(0) = 0$. Show that if $f'$ is strictly increasing, then $\frac{f(x)}{x}$ is increasing over $(0,\infty)$.   Attempt:  Since $f'$ is increasing we know that $f'' &gt; 0$ for all $x$. Now let $g(x) = \frac{f(x)}{x}$ and thus $f(x) = xg(x)$. Then we wish to show that $g'(x) &gt; 0$ on $(0,\infty)$ and so since $f'(x) = xg'(x)+g(x)$ and $f''(x) = xg''(x)+2g'(x) &gt; 0$, we have $g''(x) &gt; \frac{-2g'(x)}{x}$. I am not sure how to use this though to prove the statement. What bike+equipment for a long daily urban commute? In the (distant) past I commuted 6 km (more than half an hour) each way, on a cheap bike with big knobbly tyres.  Soon I'll have a new commute: 18 km each way, daily. That's much further than I've done in the past, and I don't want it to take 2 hours each way; but  suggests that it's feasible:      Most people who reside 10 to 20 kilometres away will also find it quite easy to cycle to work, although the distance in the high end of this range will become a little more demanding.   If I can do it in 80 minutes or even less each way, that would be ideal. I'm 49 years old, 6 foot tall, and weigh 170lb, and I want to commute by bike because otherwise I'd be getting no exercise in my week at all.  I've never bought or ridden anything but a cheap bike.  What equipment should I buy then, to commute 11 miles each way through a city (Toronto) on  flat, paved roads, shared with cars:   Wheels? Tyres? Clipless pedals and shoes? Gears? Handlebars (e.g. flat or dropped)? Frame (size, shape, material)? Mud-guard/fender? What can be considered as "Home ties" for a UK Standard Visitor visa (PLAB)? I am an Indian national who recently cleared his PLAB1 examination and has booked to sit PLAB2 in UK (which can be given only in UK). Before applying for a visa, I would like to know about the how one can prove home ties. Of course, I have read about the Family, Job, Property being used as ties but...  I haven't worked since my graduation (two years now) as I wasted a lot of precious time on USMLE. After that IELTS and then PLAB1. So can't show job as tie.  I don't have any property in my name but my father does have residential plots and agricultural lands worth a few crores on his name.    Does an affidavit that I am his only son and heir to all that bla bla bla, serve the purpose?  I do have few life insurance policies in my name.  Can they be used as an indicator of some kind of active Indian society member thingy?  I am unmarried but do intend to show my parents as family ties.   I did my medical studies in China (6-7 years). I have also traveled to a few countries like Russia, Thailand, Philippines, HK, Macau etc etc (though not a single Western country).    Can that be used in my favour in home ties that I have always obeyed country's laws and returned to India upon completion of the purpose of the trip? Program to create EMF that conserves transparency What open source tools allow for the creation of EMFs that conserve transparency in ArcMap?  I tried VeryPDF and Any DWG to Image Converter, neither on actually gave me a vector file that provided transparency.  Adobe Illustrator is a bit pricey when all I want to do is convert CAD blocks to vector symbols to use as ArcMap markers.  Anyone know of a good software for this purpose? How to draw open-close interval in LaTeX I am using the following commands to have half-open interval in a real line:   \begin{tikzpicture}[scale=7] \draw[-&gt;, thick] (-0.1,0) -- (1.7,0); \foreach \x/\xtext in {0/8,0.2/$S_1$,0.4/$T_4$,0.6/$S_3$,0.8/$T_2$,1/$S_3$,1.2/14,1.4/$S_3$,1.6/16}     \draw[thick] (\x,0.5pt) -- (\x,-0.5pt) node[below] {\xtext}; \draw (0.2,0.5pt) node[above] {$c$}; \draw[[-), ultra thick, blue] (0.2,.01) -- (.4,0.01); \draw[(-, ultra thick, green] (0.6,.02) -- (1,0.02); \end{tikzpicture}   Now, I need to have an open-close interval, but I am not able to have that close interval at the end, using the following command:  \begin{tikzpicture}[scale=7] \draw[-&gt;, thick] (-0.1,0) -- (1.7,0); \foreach \x/\xtext in {0/8,0.2/$S_1$,0.4/$T_4$,0.6/$S_3$,0.8/$T_2$,1/$S_3$,1.2/14,1.4/$S_3$,1.6/16}     \draw[thick] (\x,0.5pt) -- (\x,-0.5pt) node[below] {\xtext}; \draw (0.2,0.5pt) node[above] {$c$}; \draw[(-], ultra thick, green] (0.6,.02) -- (1,0.02); \end{tikzpicture}   May I ask for anybody help? Suppose you have a physical . It is true that as amplitude increases, the period increases. Can we demonstrate this fact without explicitly finding the period (which is pretty involved and pretty messy) in:    an intuitive fashion,  rigorously? How to create a new object instance from a Type How do I run .sh scripts? Whenever I open a .sh file, it opens it in gedit instead of the terminal. I can't find any option similar to Right Click → Open With → Other Application... → Terminal.  How do I open this file in the terminal? What is the default password of the sudo? I visit some forums, it tells that the default password is password, but it doesn't work, how can I determine the password? Compute $E(X\mid X+Y)$ for independent random variables $X$ and $Y$ with standard exponential distributions Being $X$ and $Y$ independent random variables distributed as $\mathrm{Exponential}(1)$ and let $T=X+Y$ Calculate $E(X|T)$.  This is my attempt at solving this:  Being $Z=\sum_{i=1}^{n}P_{i}$ where $P_{i}$~$\mathrm{Exp}(\lambda)$ then using it's MFG you have that $$M_{P_i}(t)=\frac{\lambda}{\lambda-t}$$ then $$M_{Z}(t)=M_{\sum{P_{i}}}(t)=(M_{P_{1}})...(M_{P_{n}})=(\frac{\lambda}{\lambda-t})^n$$ with this being the MFG of a $\mathrm{Gamma}$ distribution with parameters $(n,\lambda)$  With this result is easy to see that $T$~$\mathrm{Gamma}(2,1)$  Now $E[X|T]=\int xf_{X|T}(x|t)dx$  Then using Bayes' theorem we can make $$f_{X|T}(x|t)=\frac{f_{T|X}(t|x)f_{X}(x)}{f_{T}(t)}$$ then $$f_{T|X}(t|x)=Pr(T=t|X=x)$$ $$=Pr(X+Y=t|X=x)$$ $$=Pr(x+Y=t|X=x)$$ $$=Pr(Y=t-x)=f_{Y}(t-x)$$  Using this result we can now rearrenge $$f_{X|T}(x|t)=\frac{f_{Y}(t-x)f_{X}(x)}{f_{T}(t)}$$ $$=\frac{e^{-(t-x)}.e^{-x}}{\frac{te^{-t}}{\Gamma(2)}}$$ $$=\frac{1}{t}$$ then $$E[X|T]=\int (x)(\frac{1}{t})dx$$  And this where I got stuck because $1_{x\epsilon(0,\infty})$, I made this explanation step-by-step hoping that someone can se easily check where I went wrong. I would aprecciate a step-by-step answer, thanks. Why use sucrose rather than glucose in an injectable vaccine? An elementary question regarding a multiplicative character over finite fields Reading Chapter 2 of Koblitz's Introduction to Elliptic Curves and Modular Forms, I got stuck on the following question. I would like to proceed my reading, so I would appreciate any hint to this. I have no background in Algebraic Number Theory, but if someone explains in that language, I would like to see it and learn it as much as I can at this moment. References will also be appreciated!  Let $q$ be a power of prime $p$ such that $q \equiv 1 \mod 4$ and $p \nmid 2n$.  Question. Let $\chi_{4} : \mathbb{F}_{q}^{*} \rightarrow S^{1}$ be the character of order $4$, show that $\chi_{4}(-4) = 1$.  The hint in the book says we may show that $\chi_{4}(4) = \chi_{4}(-1) = 1$ for $q \equiv 1 \mod 8$ and $\chi_{4}(4) = \chi_{4}(-1) = -1$ for $q \equiv 5 \mod 8$.  If $q \equiv 1 \mod 8$, then $\chi_{4}(4) = \chi_{4}(2)^{2} = \chi_{2}(2) = \pm 1$, where $\chi_{j}$ denotes the character of order $j$. So I think $2$ must be quadratic residue in this case, but I cannot figure out why. Is the set of polynomials of degree less than or equal to $n$ closed? This question is in relation to the space $C(I)$, $I = [a, b]$. Define $P_n =\{ a_0+\dots+a_nx^n \mid a_i \in \mathbb{R}\}$ (any or all $a_i$ could be zero); clearly $P_n \subset C(I)$. The norm I'm using is $\lVert f\rVert_I = \sup_I |f(x)|$. Is $P_n$ closed under $\lVert\cdot\rVert_I$?   I am almost sure the answer is "yes", but I can't seem to prove it. My first instinct was to biject  $P_n$ to $\mathbb{R}^{n+1}$, using coefficients as coordinates, and prove that sequences of degree-$n$ polynomials converge to degree-$n$ polynomials, but I can't prove that the metric $\lVert\cdot\rVert_I$ is equivalent to the standard metric on $\mathbb{R}^{n+1}$. Next, intuitively given a function $f \in C(I), \notin P_n$ I should be able to find some $\epsilon &gt; 0$ such that there are no low-degree polynomials "nearby", then that function was not a limit point of $P_n$ so $P_n$ is closed. Again I have no idea how to prove this. What should I do? Find the limit: $\lim_\limits{x\to 0}{\frac{\left(1+x\right)^{1/x}-e}{x}}$ Monotonicity in argmin function I have the following equation $$f(a)=\text{argmin}_{t\in\mathbb{R}} \sum_{i=1}^n\frac{1}{2}(1-a)(b_i-t)^2+a| b_i-t |, a\in[0,1]$$  How does one prove that the function is monotone in a? I've just installed Mir and I'm wondering if I'm actually running it or if it fell back to X. How can I tell if Mir is running? How do we know for certain that space is expanding?