"A total of five players is selected at random from four sporting teams. Each of the teams consists of twelve players numbered from 1 to 12 ... What is the probability that the five selected players contain at least four players from the same team?"
[This current version of FAIL](http://chat.stackexchange.com/transcript/message/36474020#36474020) fails, thus I need to include one last rule: $F a \# 0 \# \dots \# 0 \# 0 \# b \# \dots \# c = F a \# 0 \# \dots \# 0 \# a \# b - 1 \# \dots \# c$
The answer I got was 11*10*9*44/(48C5), but the answer given is 4653/107019, which was simplified from 74448/(48C5), which could be further simplified to 1/23
So @MATHASKER, I haven't read everything you guys have said, but you set it up correctly. So the angular speed is 1100 radians/sec. If you want to convert to revolutions per second, then you divide by $2\pi$.
This is going around everywhere, it seems. But my doctor says it's almost always viral. Just have to take care of yourself. I recommend Mucinex DM for cough/throat.
Zach, what you described is exactly how people used to attempt to model planetary motion on when they realized that standard motion wasn't working. So the planet would stack on epicycles until they realized that if you just make things circle the sun it all checked out
The manufacturer of Zbars estimates that 300 units per month can be sold if the unit price is $230 and that sales will increase by 10 units for each $5 decrease in price. Write an expression for the price p(n) and the revenue R(n) if n units are sold in one month, n≥300.
So if I have to chose five players from four teams of twelve players each given at least four are from the same team there are $4 \times {12 \choose 4} \times 44$ possible choices right?
I am verifying the correctness of my recursive definition for a set. But I have no idea how can I verify it, please take a look at math.stackexchange.com/questions/2216115/…
@WillNjundong: You are told that $p(230)=300$ and that if $p$ goes down $5$, then $n$ goes up $10$. This says that the slope of the linear function $p(n)$ is $-1/2$. So use point-slope.
@Daminark I'm modeling a network protocol design as a differential equation, and trying to find a good stable regime to let it optimize on the conditions I want it to work well on
What we did in class was Banach-Tarski, which proved that if you have a finitely additive measure which was invariant under isometries, you couldn't define it on all subsets of $\mathbb{R}^3$, now we're no longer assuming that
this article is not a little misleading. What it is talking about is Gromov-Witten theory and curve counting.
The counts produced this way are often virtual counts and needs to be adjusted to be the real number of curves on the variety.... and although Gromov-Witten theory is motivated by physicists, algebraic geometers can certainly produce these numbers without knowing any physics. On the other hand, it is indeed impressive that physicists, long before the intersection theory was properly developed, could predict counts that are verified to be true. All these are still quite olds results though.
sounds like a good idea. I sometimes came across interesting abstract algebraic structures in arxiv but I have not checked other branches of maths there yet
Semi philosophical question: Why is the thought process and the actual writing of $\epsilon-\delta$ proofs ran in opposite directions?
e.g. thought process is we try to find the form of the epsilon given some delta, but when writing out the proof, we say what we need to pick in order for a given epsilon to give the required delta
Well, in a proof, you need to demonstrate that there exists the correct delta
But to see how small of a delta you need, you'd need to ask yourself how much leeway you get with a given delta
Anonymous
6:48 AM
Hello people. Anyone good at 3D Geometry here? I wanted to know how to find the incentre, circumcentre and orthocentre of an irregular tetrahedron. Suppose the position vectors of the vertices are $\vec{a},\vec{b},\vec{c},\vec{d}$.
@Balarka Do you try to understand things via trying to understand a picture or do you use being able to understand a picture as a test to confirm that you have understood something?
For a given field $\Bbb F$ and an extension $X$, what exactly is the difference between $\Bbb F[X]$ and $\Bbb F(X)$? For all I'm aware, they're interchangeable (never delved too far into group theory)
Then again, the fact that I'm even asking this question probably means that I have no idea what I'm doing
At one point at MathCamp this summer, a bunch of us were seated around a table and with a few teachers, learning about the Vitali set. We were asked to show why it was non-measurable. Our construction quickly became confusing, so I offered to draw the situation.
Which quickly elicited replies of (I don't remember exactly but something like) "How are you going to draw a Vitali set??" and a sarcastic "Yes, Akiva, draw a Vitali set"
It was like, a bunch of horizontal lines (representing $\Bbb R)$, each containing a translated version of the Vitali set (drawn like a long thin cloud of unit width)
The translations were like an enumeration of $\Bbb Q$ (the first was translated by $0$, the second by $1$, the third by $-1$, etc.)
I think the idea was that the union of all of these was supposed to be $\Bbb R$?
I think you also needed to take the fractional part of each element of each set, or something, so that the union (which is still a disjoint union) becomes $[0,1]$.
Whatever, I don't remember, but it made sense at the time
@AkivaW Suppose I have a smooth map $g : \Bbb R \to \Bbb R$. I want a $C^1$ map $f : \Bbb R \to \Bbb R$ which agrees with $g$ outside $\bigcup I_n$ where $I_n$ are intervals around the $n$-th rational (give $\Bbb Q$ whatever enumeration you want) such that $\sum_n I_n < \infty$. Can see why this can be done?
For $C^0$ it is more or less obvious by a uniform limit argument (modify it at each step with$\bigcup_{k < N} I_k$ and put some height conditions) I guess.
I don't know how to make this $C^1$. Initially what comes to mind is fitting in small bump functions at each $I_k$, but what's counterintuitive is this doesn't work for $C^2$ (by a theorem). So I have no idea.
@Secret This might be relevant. It's partial fractions, but generalized; you essentially write meromorphic functions in terms of things of the form $\frac1{(x-p_i)^k}$, which can be thought of as describing the function's poles/singularities
I was thinking: Given a real $x$, $0$, complex subtraction and exponentiation, and the principal complex logarithm, would it be possible to determine $|x|$?
Wait, no, I'm silly, it would just be $|x|=\exp(\exp(\ln(\exp(\ln(\ln(x))-(0-\ln(\exp(0)-(0-\exp(0))))))-\ln(\exp(0)-(0-\exp(0)))))$
