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Problems in Galois Theory
a. Let K be a field of characteristic p > 0, and let c in K. Show that if alpha is a root of f (x) = x^p - x - c, so is alpha + 1. Prove that K(alpha) is Galois over K with group either trivial or cyclic of order p.
b. Find all subfields of Q ( sqrt2, sqrt 3) with proof that you have them all. What is the minimal polynomial of sqrt2+ sqrt3? Which subfields does it generate over Q?
Find the probability that a bag of fertilizer will weigh between 45 and 55 pounds?
The marginal cost function
Compute the mean and variance for binomial distribution. Calculate the mean and standard deviation (by hand) for the binomial distribution with the probability of a success being 1/4, 1/2, 3/4.
Calculate the free end deflection caused by the load using general expression for the internal Elastic Strain Energy.
Write a simplified expression for the weekly revenue and Construct a table of values and graph the function
Differentiating a function using the product rule and finding the tangent line equation at particular point.
An archer has probability 0.3 of hitting a certain target. What is the probability of hitting the target exactly two times in four attempts?
Assuming that there is no cost to enter the .sweepstakes, find the expected value of the amount won for one entry. Round to the nearest tenth.
A sample of 500 travelers who used the internet to book a trip were asked to which travel website they used. There responses are given in the table below. Use this information to construct a circle graph illustrating the percent of people who gave..
Probability problems based on Poisson & Normal distribution
From the sensitivity analysis, which warehouse site should have had more paper allocated to it at the start of the week and by how much per tonne would the overall cost of transport have been reduced?
Evaluate the length and width of the given rectangle using the area and the relation of length and width.
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