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Suppose K is a conjugacy class of S_n (the symmetric group), with K consisting of even permutations. Suppose that x in K. Show that K splits into two conjugacy classes in A_n (the alternating group) iff x commutes with no odd permutation in S_n
A farmer wants to fence o a rectangular ?eld and then divide the ?eld in half with a fence down the middle (see diagram below). If he can only a ord 240 ft. of fencing material, what is the width y which gives the maximum area of the ?eld?
Decision Analysis with Decision Tree, Jack Nimble, an employee of Daniel Construction Company, claims to have injured his back as a result of a fall while repairing the roof at one of the Eastview apartment buildings
Explaining how to derive the formula for the distance between two points -Prepare an essay of 1,000 words explaining how to derive the formula for the distance between two points in analytic geometry 3-space.
Assume that f(z) is analytic at the origin and f(0) = first derivative of f at 0 = 0. Prove that f(z) can be written in the form f(z) = [z^2]g(z), where g(z) is analytic at z = 0.
Write out the probability distribution for of sales during a five-day week. What is the mean and variance of this distribution? Assume that the profit from each sale is $750 for the situation in additional problem. What is the expected weekly profi..
To make a conjecture about the tangent lines and the graph with the proof of the conjecture - Find the distance between the functions is greatest, and prove your conjecture.
What is the probability that two cards drawn from a deck are both aces?. Two cards are drawn at random from an ordinary deck of playing cards. The first is not replaced before the second is drawn. What is the probability that:
Conditions for Linear transformation. This chapter starts as follows rotations about the origin and all reflections in lines through the origin can be expressed as functions with rules of the form
Solve each linear equation. Show your work and check. Solve each equation by first eliminating the decimal numbers.
Rational and Jordan Canonical Forms, Find the rational canonical form and the Jordan canonical form(if possible) for the linear tansformations f: R^3->R^3 given by the matrix
Please prove the following theorem: A system of linear equations has zero, one or infinitely many solutions; there are no other possibilities.
Let f be a surjection. Then f is an isomorphism iff the order of the element f(a) is equal to the order of the element a , for all a belong to G.
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