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Need help for this question please help!

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First let me paste the question.

**This problem is based on an (almost) true story. A child, who shall remain nameless, has a large pile of clean socks. This pile contains m pairs of socks with pictures and patterns and n
pure white socks. Each pair of socks consists of two identical socks and every pair is unique — no two pairs look the same. All pure white socks are identical. Each day, the child randomly selects two socks from the pile, puts them on, and heads for school.
But today is a picture day and the child needs to wear two identical socks. So the child randomly selects two socks and if both socks are identical, the child puts them on and heads out the door. If the two socks are not identical, the child throws the socks into the laundry basket (they are now dirty — don’t ask why) and continues the same process of randomly selecting two socks from the pile of remaining clean socks. As this process continues, the parents are starting to get worried: Will this child ever make it to school today? Please help them to compute the probability that the child will not find a pair of identical socks using this process.
This problem is based on an (almost) true story. A child, who shall remain nameless, has a large pile of clean socks. This pile contains m pairs of socks with pictures and patterns and n
pure white socks. Each pair of socks consists of two identical socks and every pair is unique — no two pairs look the same. All pure white socks are identical. Each day, the child randomly selects two socks from the pile, puts them on, and heads for school.
But today is a picture day and the child needs to wear two identical socks. So the child randomly selects two socks and if both socks are identical, the child puts them on and heads out the door. If the two socks are not identical, the child throws the socks into the laundry basket (they are now dirty — don’t ask why) and continues the same process of randomly selecting two socks from the pile of remaining clean socks. As this process continues, the parents are starting to get worried: Will this child ever make it to school today? Please help them to compute the probability that the child will not find a pair of identical socks using this process.**

First of all, the limitations are n<=500 pairs of socks, and m<=200 white socks. I’ve really tried to solve question every way i can. I used permutation of 7! and then count the paired socks. At test problem, there are 3 white and 2 paired socks. I could only solve this by counting all paired socks in 7! permutations. Can you help me how i can solve this question? I used python by the way, and this is a competitive programming question.

At initial test answer, there are 3 white socks and 2 paired socks (total of 7 socks). And the answer is:0.457142857142857

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The Farkas Lemma: Let $A$ be an $mtimes n$ matrix, $binmathcal{R}^m$. Then exactly one of the following two assertions is true:

(1) There exists an $xin mathcal{R}^n$ such that $Ax=b$ and $xge0$.

(2) There exists a $yin mathcal{R}^m$ such that $A^Tyge0$ and $b^Ty<0$.

I want to check which assertion is true for a given $b$. So I constructed the linear programming problem according to the second statement:

begin{equation}

min b^Ty\

s.t. -A^Tyle0

end{equation}

The idea is simple. if the solution $b^Ty$ is great than or equal to $0$, then the first assertion is true; otherwise the second one is true.

But the following matlab implementation always gives me the result $y=0$ or “the problem is unbounded”. Something is wrong, but i have no idea. I would be thankful for any help or references.

```
m = 2;
n = 4;
A = rand(m,n);
b = rand(m,1);
f = b;
A = -A';
y = linprog(f,A,zeros(n,1),(),(),(),());
```

Marissa can paint a garage door in 3 h .When Marissa works with roger,they paint the same door in 1 hour. How long would it take roger to pain the door on his own(answer to the nearest tenth)

My work

so marissa pains in 3 hr

mariisa +roger=1 h

how long will it take roger=x

x+3/x+1+x/x=

it takes roger 3.3 hours

Domainers may laugh but I just registered six domains today that I can’t believe were available. I want to wait at least 24 hours before I d… | Read the rest of https://www.webhostingtalk.com/showthread.php?t=1822117&goto=newpost

So I’m runng a VPN server and a apache web service on this ubuntu server.

So if you connect to a VPN network, your remote host, in my ca… | Read the rest of https://www.webhostingtalk.com/showthread.php?t=1822119&goto=newpost

I’m not exactly sure how to categorize this question so sorry if it’s in the wrong place. I’m trying to understand one part of a lemma given in a paper on invariant sets for PDEs and I’m getting hung up on signs. I think it might just be me not understanding notation or forgetting some analysis. Anyway it looks like:

Let $G:mathbb{R}^n rightarrow mathbb{R}$ be a smooth function, and let $dG$ and $d^2G$ denote the first and second derivatives of $G$. They note here that “the $v$ dependence of $dG$ and $d^2G$ is being suppressed.” $v$ being a function of $x$ and $t$ that satisfies a generic form PDE:

$frac{partial v}{partial t}=epsilon D Delta v +Sigma M^i frac{partial v}{partial x^i}+f,$ $epsilon>0$

And satisfies some boundary conditions. Continuing, with $gammaleft(tright)$ being a smooth curve in $mathbb{R}^n$ and with dots denoting time derivatives, they note that:

$dot{left(Gcirc v right)}=dGleft(dot{gamma}left(tright) right) $

$ddot{left(Gcirc v right)}=dG^2left(dot{gamma}left(tright) right) +dGleft(ddot{gamma}left(tright) right)$

Finally, suppose $v:mathbb{R}^m rightarrow mathbb{R}^n$ is a smooth function with range in the set $Sigma={v:Gleft(vright)leq 0}$ and that $Gcirc vleft(x_0right)=0$. Then for $xiinmathbb{R}^m$ and $hinmathbb{R}$, $Gcirc vleft(x_0+hxi right)leq Gcirc vleft(x_0right)$. After this they make use of a Taylor expansion to show $dGleft(dvleft(xiright) right)=0$ as $h$ goes to $0$.

I’m not sure if the information above the last paragraph is helpful, but I figured I’d include just in case. They use some of it later with a convexity argument to reach more conclusions. What’s mixing me up here is how the range of $v$ is defined. I understand it to mean that $v$ maps points in $mathbb{R^m}$ to points in $mathbb{R^n}$ that, when $G$ is applied to them, give positive real numbers. So, if the value of $Gcirc vleft(x_0right)=0$ and I move in some direction $xi$ and distance $h$ away from $x_0$, I would expect that that value is also going to be $geq 0$ given the restrictions on the range of $v$. However, the inequality they give suggests that the quantity is $leq 0$. Can you clarify?

Sorry for the long post.

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I have created a word document on my computer, or any other file. I then take that file and move it to an external device, would that file leave a trace on the computer? Is it recoverable on the computer? If it is, how do I recover it?

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