For my experiment, I set up a series circuit. I had to use 3 different gauges of copper wires and test them against electrical resistances. My results were:  $$ \begin{array}{rccc} \text{12-gauge wire:} &amp; 0.04 \, \mathrm{A} &amp; 0.004 \, \mathrm{V} &amp; 0.025\, \Omega \\  \text{8-gauge wire:} &amp; 0.04 \, \mathrm{A} &amp; 0.003 \, \mathrm{V} &amp; 0.075\, \Omega \\  \text{4-gauge wire:} &amp; 0.04 \, \mathrm{A} &amp; 0.001 \, \mathrm{V} &amp; 0.1\phantom{00}\, \Omega \\ \end{array} $$  I have to fill out this table:   But I'm not sure how to fill out the average and standard deviation part, nor if i filled out the independent and dependent variable part out right.
So, for my science fair I had to test the gauge of a copper wire vs electrical resistance. What I did was I set up a series circuit involving a 6v battery, a light bulb, a multimeter, and a voltmeter. I would change out three different wires with three different gauges.   For the 4-gauge wire, I got 0.004V and 0.04A. For the 8-gauge wire, I got 0.003V and 0.04A For the 12-gauge wire, I got 0.001V and 0.04A.   In this experiment, what would the independent and dependent variables?  We also have to fill out a table like this:
In  it states that      [xkcd] means calling the Ackermann function with Graham's number as the arguments just to horrify mathematicians.   $A(g_{64},g_{64})$  In  it states that      Even simply making $g_{65}$ dwarfs the number $A( A(g_{64}, g_{64}), A(g_{64}, g_{64}))$ into insignificance.   So:  Is $g_{65}$ greater than $A(g_{64}, g_{64})$?  And is it greater than $A( A(g_{64}, g_{64}), A(g_{64}, g_{64}))$? What can I actually do with a high credit score? I recently checked my credit score via two of my credit card providers. It seems to be hovering between 790 and 815. One service brands the score it provides as a FICO score and the other specifically says its score comes from Transunion.   What can I actually do to leverage this high credit score to my advantage?  The only new debt I might take on would be a small HELOC or car loan. Does a high score give me any negotiating power with the lender to get a better rate? Should I treat the score as a card in my hand or is it something I should show early in negotiations?  Does a high score make me eligible for any discounts on insurance?  Does a high score open up any options for earning more interest on savings accounts?  The typical advice I'm reading suggests refinancing a mortgage. That seems like good advice in general but it does not apply to my personal circumstances. I've got 3.5% on a 15 year note with 9 years left. A casual review of current rates suggest I could maybe scrape 0.5% off of that, hardly seems worth the effort and cost for half a percent. How to add a subclass as a subview so that background of subview is set in front of superview Flag as Broken Link I keep finding broken links in posts, currently I add a comment in the hope someone will return to update it or if I find a link I edit the answer.   I imagine this will only increase over time so I wonder if there could be a standard way to manage this?  My idea is adding a new flagging reason like "contains broken links", then it will go to a review queue where people will be able to have a look and fix the broken links. UV Unwrapping a Modified Model I modified an existing model by removing unwanted vertices, then selecting surrounding vertices and creating faces one triangle at a time (By pressing 'F').  On UV unwrapping the mesh, the faces which were added by me seem to stretch from the very bottom left of the map, shown below.    How do I create a face so it appears on the UV map as expected? resolution is undefined in XeTeX so the following code will produce different values when compiled with pdfTeX and XeTeX.  \documentclass{article} \usepackage{graphicx}  \newsavebox\IBox \savebox\IBox{\includegraphics[scale=1]{koala.jpg}}  \begin{document} \the\wd\IBox \end{document}   How to force pdfTeX and XeTeX to produce the same measurement for the imported image? I simply know that a single free quark does not exist. What is the reason that we can not get a free quark?  If we can't get a free quark then what is single-top-quark? Why is the complex number $z=a+bi$ equivalent to the matrix form $\left(\begin{smallmatrix}a &-b\\b&a\end{smallmatrix}\right)$ Possible Duplicate:          On Wikipedia, it says that:     Matrix representation of complex numbers   Complex numbers $z=a+ib$ can also be represented by $2\times2$ matrices that have the following form: $$\pmatrix{a&amp;-b\\b&amp;a}$$   I don't understand why they can be represented by these matrices or where these matrices come from. Abstract algebra book recommendations for beginners. I am taking abstract algebra in this semester. I find that my lecturer didn't provide enough examples for understanding. So I would like to ask what are the recommended books which has lots of solved problems and exercises? The lecturer said in this semester, he will cover group theory, ring theory and a bit of field theory. Which book contains extensive information in these three fields? How to make the taskbar blink my application like Messenger does when a new message arrive? Is there an API call in .NET or a native DLL that I can use to create similar behaviour as Windows Live Messenger when a response comes from someone I chat with? A sphere of radius R is rolling without slipping with a velocity v and collides inelastically with a step of height h &lt; R. What is the minimum velocity for which the sphere will be over the step?    Relevant equations  Total kinetic energy (maybe): $\frac{1}{2}I\omega^{2}+\frac{1}{2}mv^2$  Gravitational potential energy: $mgh$   Moment of inertia about a point a distance d from the CM from de center of mass: $I=I_{cm}+md^{2}$ Rolling without slliping  $v=\omega R$  A discussion of the problem This problem is confusing to me: I know the collision is inelastic so there is no conservation of kinetic energy, there is torque when the sphere pivots the step so the angular momentum is not conserved either, the linear momentum doesn't give a lot information and even though I tried to see what condition needs the torque about the pivot point (to give a net torque in the direction of rotation and thus passing the step), I'm not able to see which torque can overcome the one from gravity which doesn't let the sphere slide up:    The sphere has an angular velocity, but I'm missing something conceptual because I can't figure out how to formally state that the angular momentum changed the right amount so that the sphere made it past the step.  The attempt at a solution  My (almost certainly wrong) attempt was to say that the sphere lost kinetic energy because of the change on potential energy:  $\frac{1}{2}I\omega^{2}+\frac{1}{2}mv^2 +mgR = mg(R+h)\\ v=\sqrt{\frac{10}{7}gh} $  I hope you can help me :) If I have a dataset with a very rare positive class, and I down-sample the negative class, then perform a logistic regression, do I need to adjust the regression coefficients to reflect the fact that I changed the prevalence of the positive class?  For example, let's say I have a dataset with 4 variables: Y, A, B and C.  Y, A, and B are binary, C is continuous.  For 11,100 observations Y=0, and for 900 Y=1:  set.seed(42) n &lt;- 12000 r &lt;- 1/12 A &lt;- sample(0:1, n, replace=TRUE) B &lt;- sample(0:1, n, replace=TRUE) C &lt;- rnorm(n) Y &lt;- ifelse(10 * A + 0.5 * B + 5 * C + rnorm(n)/10 &gt; -5, 0, 1)   I fit a logistic regression to predict Y, given A, B and C.   dat1 &lt;- data.frame(Y, A, B, C) mod1 &lt;- glm(Y~., dat1, family=binomial)   However, to save time I could remove 10,200 non-Y observations, giving 900 Y=0, and 900 Y=1:  require('caret') dat2 &lt;- downSample(data.frame(A, B, C), factor(Y), list=FALSE) mod2 &lt;- glm(Class~., dat2, family=binomial)   The regression coefficients from the 2 models look very similar:  &gt; coef(summary(mod1))               Estimate Std. Error   z value     Pr(&gt;|z|) (Intercept) -127.67782  20.619858 -6.191983 5.941186e-10 A           -257.20668  41.650386 -6.175373 6.600728e-10 B            -13.20966   2.231606 -5.919353 3.232109e-09 C           -127.73597  20.630541 -6.191596 5.955818e-10 &gt; coef(summary(mod2))               Estimate  Std. Error     z value    Pr(&gt;|z|) (Intercept) -167.90178   59.126511 -2.83970391 0.004515542 A           -246.59975 4059.733845 -0.06074284 0.951564016 B            -16.93093    5.861286 -2.88860377 0.003869563 C           -170.18735   59.516021 -2.85952165 0.004242805   Which leads me to believe that the down-sampling did not affect the coefficients.  However, this is a single, contrived example, and I'd rather know for sure. How to create a bootable USB stick? If I open up many tabs in Chrome, the Tabs start to shrink. This is usually a normal behavior if the tabs would use the whole availible space, BUT in my case the tabs shrink too much. They don't use up the whole availible space anymore, but only go until somwhere at three quarters of the window. The more tabs I open, the larger the availible space gets until it reaches a maximum. This strikes me as somewhat not so normal.  Another funny thing is, if I use a second Monitor to extend my Desktop, Tabs will be smaller on the second Desktop and will only fill half the availible space from the beginning. For example right now I have 6 tabs open, which fill out approximately half the availible space. If I open more tabs, only the tab size reduces. This has not been like that when I first installed the browser.  This is what it looks like:    Is there any solution for this?   I hereby explicitly mean NO extensions. I found enough extensions to handle tabs. I just want them to behave normally without any of those tab-extensions. Re-Installing Chrome does NOT work, I tried that. How to persistently control maximum system resource consumption on Mac? Before Mavericks, I could use /etc/launchd.conf file to change maximum system resource consumption, for example:  limit maxfiles 16384 unlimited limit maxproc 16384 unlimited   It no longer works in Mavericks.  What is the correct way to do it in the recent version of OS X? Conditional Expectation of Bernoulli R.V. Let $X_1, X_2,\ldots, X_n$ be iid bernoulli r.v. with parameter $p$. Let $S=X_1+\cdots+X_n$ and $Y=X_1X_2$. Compute $\mathbb{E}(Y\mid S)$.  I know that $\mathbb{E}(X_1\mid S) = S/n$. So If I could split $\mathbb{E}(Y\mid S)$ into two then I would be done. But I don't think that is allowed. How to proceed? What's wrong with this digital signature scheme? With regards to user authentication...   The server sends Alice a randomly chosen number. Alice signs the number and sends the signature back to the server. The server checks the signature using Alice's public key. If it's valid, the server accepts her connection request.   Suppose that Alice uses the same private key to log in to the server and sign her emails. The authentication mechanism signs the bare challenge without hashing, while Alice signs the hash of the email message.   Apparently, the server can forge emails from Alice under this scheme? If so, how could this be prevented? How to force the evaluation of a lambda term in haskell to the strong normal form One of the new search hints is wrong Cardinality of set of real continuous functions I believe that the set of all $\mathbb{R\to R}$ continuous functions is $\mathfrak c$, the . However, I read in the book &quot;Metric spaces&quot; by Ó Searcóid that set of all $[0, 1]\to\mathbb{R}$ continuous functions is greater than $\mathfrak c$:  &quot;It is demonstrated in many textbooks that $\mathbb{Q}$ is countable, that $\mathbb{R}$ is uncountable, that every non-degenerate interval is uncountable, that the collection of continuous functions deﬁned on  $[0,1]$ is of a greater cardinality than $\mathbb{R}$, and that there are sets of greater and greater cardinality.&quot;  I understand that (via composition with the continuous function $\tan$ or $\arctan$) these sets of continuous functions have the same cardinality. Therefore, which claim is correct, and how do I prove this?