I get American football in Brazil. I try to watch the game, but, honestly, can't understand a thing. One thing that made me curious was the numbers on the ground. For instance, there's a &quot;1st &amp; 10&quot; beside a team.  But I thought I saw a &quot;3rd &amp; 8&quot; beside the other team.  What does that mean?
One thing that made me curious while watching a football game on TV was the numbers that appear on the ground. For instance, there's a "1st &amp; 10" beside one team, but there was a "3rd &amp; 6" a few minutes prior (and I think it was beside the other team). What do these numbers mean?
Linear regression prediction interval If the best linear approximation (using least squares) of my data points is the line $y=mx+b$, how can I calculate the approximation error? If I compute standard deviation of differences between observations and predictions $e_i=real(x_i)-(mx_i+b)$, can I later say that a real (but not observed) value $y_r=real(x_0)$ belongs to the interval $[y_p-\sigma, y_p+\sigma]$ ($y_p=mx_0+b$) with probability ~68%, assuming normal distribution?  To clarify:  I made observations regarding a function $f(x)$ by evaluating it a some points $x_i$. I fit these observations to a line $l(x)=mx+b$. For $x_0$ that I did not observe, I'd like to know how big can $f(x_0)-l(x_0)$  be. Using the method above, is it correct to say that $f(x_0) \in [l(x_0)-\sigma, l(x_0)+\sigma]$ with prob. ~68%? What I am looking for is to have system wide implementation of sound enhancements like bass boosts, echoes, Fidelity, Stereo enhancement and so on.  Audio Video players have their own equalizer but they enhance only the audio / video files they are playing.  So to enhance sounds playing such as: YouTube, Spotify, System Sound, etc. I need a enhancer software. Back in Windows, I used to use SRS HD audio lab to do the same.  P.S. I have a horrible Speaker set. If $\mathbf A$ and $\mathbf B$ are Hermitian, when does $\det(\mathbf A-\lambda\mathbf B)=0$ have only real roots? Let $\mathbf A, \mathbf B$ be Hermitian matrices of the same size. What is the characterization of $\mathbf A, \mathbf B$ such that $p(\lambda)=\det(\mathbf A-\lambda\mathbf B)=0$ has only real roots?   If $\mathbf B$ is positive definite (I corrected this), it is easy to see $p(\lambda)$ has only real roots. Does $\exp(2ir\pi)$ equal $1$? What's wrong? 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NOTE: Information represented is from Spain. Correct projection is 4326, but client use Google rasters, so I am storing data in 900913 to avoid reprojections and increase performance. Using Zorn's lemma show that $\mathbb R^+$ is the disjoint union of two sets closed under addition. Let $\Bbb R^+$ be the set of positive real numbers. Use Zorn's Lemma to show that $\Bbb R^+$ is the union of two disjoint, non-empty subsets, each closed under addition. Matrix of Linear Transformation by right multiplication I am trying to solve the following problem:   Let $A$ be an $n\times n$ matrix, and let $V$ denote the space of $n$-dimensional row vectors. What is the matrix of the linear operator ‘‘right multiplication by $A$’’ with respect to the standard basis of $V$?  I am not sure where to begin with this problem. All chromium extensions throw errors since update to 13.10 I read a story once about a man who escapes from his pursuers by doing an uncontrolled jump into hyperspace. If I'm not mixing my stories up he was blind but could see through the eyes of other sighted people/animals nearby. He was able to see through his pet but it dies and he thinks he's finished - he's blind and lost in hyperspace but there's a rat on board which he eventually catches by turning off gravity and then he can see through the rat's eyes. He works out how hyperspace operates and can hop back to where he came from.   Can anyone remember the name of the story and the author? I enjoyed it when I was a kid and would like to read it again. So the stories of the Hunger Games are set in , a post-apocalyptic society situated in North America. Is there anything to explain what caused the Apocalypse? Whether from the main books, any extra material or interviews? (No fanfic please.)  As well as the cause, is there any indication of when the apocalypse happened? And how long after the apocalypse are the events of the Hunger Games? 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