My hard drive is broken on my Mac, I have a new one, but how can I install OS X?
How to install the OS with a new Hard drive?
How do you split a long exact sequence into short exact sequences? How does one split up a long exact sequence into short exact sequences?  Say you have some longs exact sequences of modules $$ 0\longrightarrow M_1\stackrel{\phi_1}{\longrightarrow}M_2\stackrel{\phi_2}{\longrightarrow}M_3\stackrel{\phi_3}{\longrightarrow}M_4\stackrel{\phi_4}{\longrightarrow}\cdots $$ I've read it's possible to split this into short exact sequences. What exactly does that mean? Would it be written as short exact sequences, one appended to another like $$ 0\longrightarrow N_1\longrightarrow M_1\longrightarrow N&#39;_1\longrightarrow 0\longrightarrow N_2\longrightarrow M_2\longrightarrow N&#39;_2\longrightarrow 0 \longrightarrow\cdots? $$ If so, how does this work? Merci. When reading lens reviews on the Internet, I often find subjective statements about the image quality that a lens produces, such as "good contrast" or "sharp". The problem is that I don't think I am capable to actually see these qualities on an image. I don't even think I could tell the difference between a cheap kit lens and a top lens, if not by "this just looks better".  So my question is: without looking at sharpness tests and MTF curves, how do you learn to judge the quality of a lens based only on sample images? What are the characteristics you look for and what constitutes good or bad in each of them? Command to move a file to Trash via Terminal Ohm's law states that  electric current is directly proportional to voltage provided that physical conditions like temperature remain constant i.e. $$V = IR$$  On the other hand,  $$\text{Power = Voltage} \times \text{Current}$$  So here it seems that the higher the voltage, the lower the current, provided that the power remains constant (i.e. current is inversely proportional to the voltage here which is against Ohm's Law.).   Now my question is how do physicists explain this apparent contradiction? Or maybe this not a contradiction because I am analysing things incorrectly?   P.S.: I am a tenth grade student so please refrain from the usage of highly complicated terminologies in your answers. How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$ How to show  $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$ Infinite Series $\sum\limits_{n=1}^{\infty}\frac{1}{4^n\cos^2\frac{x}{2^n}}$ How to prove that  $$\sum_{n=1}^{\infty}\frac{1}{4^n\cos^2\frac{x}{2^n}}=\frac1{\sin^2x}-\frac1{x^2}$$ Linear Discriminant Analysis for $p=1$ Under what conditions will healers switch targets? I've been using healers lately, which I haven't really utilized much before. I've noticed that they will sometimes switch targets, even when their original target still lives.   What conditions are needed for healers to switch targets? Question I use pgfplots with the ultra thick option ans without explicitly giving the domain for the y-axis. It seems that in this case, some part of my graph is &quot;eaten&quot; by the margin: see the picture below to understand what I mean. Is there a way to avoid this? Code \documentclass{article} \usepackage{pgfplots} \begin{document}  \begin{tikzpicture}  \pgfplotsset{every axis/.append style={                     axis x line=middle,    % put the x axis in the middle                     axis y line=middle,    % put the y axis in the middle                     axis line style={-&gt;},  % arrows on the axis                     xlabel={$x$},          % default put x on x-axis                     ylabel={$y$},          % default put y on y-axis                     grid = major                     }}  \begin{axis}[xmin=-5,xmax=5] \addplot[orange,smooth, ultra thick] {sin(deg(x))} ;                  \end{axis} \end{tikzpicture}  \end{document} Evaluate definite interval of normal distribution Let me filter jobs by the employer's Joel Test Scores Assume $\{a_n\}$is a sequence which  satisfies the following recursion formula: $$a_{n+1}=a_n+\frac{2a_{n-1}}{n+1}~(n\geqslant 1).$$ and $a_0=\pi,a_1=\pi^2 $. How to compute $\displaystyle\lim_{n\to \infty}\frac{a_n}{n^2}$? Releasing bound ports on process exit How do I make sure that a socket bound to a port is properly released on process exit such that the port can be reused without bind() failing with EADDRINUSE? I've written a tiny program which just creates a socket, binds it to a fixed port, waits for a connection and then immediately terminates. When I rerun the program, the bind() call fails with EADDRINUSE, but if I wait a few minutes, it succeeds.  Is there a way I can explicitly "unbind" the socket, thereby freeing the port number? I wanted to tweet something on the lines of "Stack&nbsp;Overflow is awesome". When I do this kind of stuff, I usually use a username (for example: ) or a hashtag ()  I found , but it seems it is from someone unrelated with Stack&nbsp;Overflow.  Is there a Twitter account I can reference, or should I use a hash-tag? Should I just point to the site?  Thanks!  (Notice: I've seen lots of questions regarding Twitter and Stack&nbsp;Overflow, but those are mostly about integration/login with Twitter for the users accounts; I'm just asking for a single account for Stack&nbsp;Overflow; probably for announcements and PR, which is different) I'm having some difficulty understanding how to interpret variable importance output from the Random Forest package. Mean decrease in accuracy is usually described as "the decrease in model accuracy from permuting the values in each feature".   Is this a statement about the feature as a whole or about specific values within the feature? In either case, is the Mean Decrease in Accuracy the number or proportion of observations that are incorrectly classified by removing the feature (or values from the feature) in question from the model?   Say we have the following model:  require(randomForest) data(iris) set.seed(1) dat &lt;- iris dat$Species &lt;- factor(ifelse(dat$Species=='virginica','virginica','other')) model.rf &lt;- randomForest(Species~., dat, ntree=25, importance=TRUE, nodesize=5) model.rf varImpPlot(model.rf)     Call:  randomForest(formula = Species ~ ., data = dat, ntree = 25,  proximity = TRUE, importance = TRUE, nodesize = 5)  Type of random forest: classification Number of trees: 25 No. of variables tried at each split: 2          OOB estimate of  error rate: 3.33% Confusion matrix:           other virginica class.error other        97         3        0.03 virginica     2        48        0.04     In this model, the OOB rate is rather low (around 5%). Yet, the Mean Decrease in Accuracy for the predictor (Petal.Length) with the highest value in this measure is only around 8.   Does this mean that removing Petal.Length from the model would only result in an additional misclassification of 8 or so observations on average?   How could the Mean Decrease in Accuracy for Petal.Length be so low, given that it's the highest in this measure, and thus the other variables have even lower values on this measure? My kids are playing Minecraft on 2 PCs, creative mode.  They are connected by the way of one of them starts a single player game on the other one than joins that game over the LAN.  Can I, using Minecraft PE on my iPad, join their game as well? How to prove $a^3 + b^3 +c^3 - 3abc =1 $, If a,b,c are infinite series as given in the description box below? How do I prove that $$ a^3+b^3+c^3−3abc = 1 $$ if   $ a = 1+\frac{x^3}{3!}+\frac{x^6}{6!}......$ , $b=x+\frac{x^4}{4!}+\frac{x^7}{7!}....$ , $c=\frac{x^2}{2!}+\frac{x^5}{5!}+\frac{x^8}{8!}......$ ?  I have tried the following :-  I discovered that $a+b+c=e^x$ and that $a=\frac{d(b)}{dx}$, $b=\frac{d(c)}{dx}$, $c=\frac{d(a)}{dx}$ . But I am unable to proceed further with these information. Unable to lock the administration directory (/var/lib/dpkg/), are you root? I get this error in Lubuntu 12.04 when I try to update in terminal:  $ apt-get update E: Could not open lock file /var/lib/apt/lists/lock - open (13: Permission denied) E: Unable to lock directory /var/lib/apt/lists/ E: Could not open lock file /var/lib/dpkg/lock - open (13: Permission denied) E: Unable to lock the administration directory (/var/lib/dpkg/), are you root? Proving by strong induction that $\forall n \ge 2, \;\forall d \ge 2 : d \mid n(n+1)(n+2)...(n+d-1) $ I have read the thread regarding , but it does not answer my question.  I am confused about the notation for change in Physics. In Mathematics, $\delta$ and $\Delta$ essentially refer to the same thing, i.e., change. This means that $\Delta x = x_1 - x_2 = \delta x$. The difference between $\delta$ and $d$ is also clear and distinct in differential calculus. We know that $\frac{dy}{dx}$ is always an operator and not a fraction, whereas $\frac{\delta y}{\delta x}$ is an infinitesimal change.   In Physics, however, the distinction is not as clear. Can anyone offer a clearer picture?