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Please explain how to prove the following. As much explanation as possible would be great
Let p(x) = Ax^2 + Bx + C. Prove that for any interval [a,b], the value c guaranteed by the Mean Value Theorem is the midpoint of the interval.
Basic probability problems
Mary is taking courses in both Reading and English. She estimates her probability of passing Reading of 0.4 and English at 0.6 and she estimates her probability of passing at least one of them at 0.8.
A drawer contains n=5 different and distinguishable pairs of socks (a total of 10 socks). If a person randomly selects 4 socks, what is the probability that there is no matching pair in the sample?
Apply DeMoivre's Theorem to solve the following: any angles that are multiples of pi/6, pi/4, pi/3, pi/2 or pi must be converted back into regular complex form!
A sample of 100 provided a sample mean of 75.7. The population standard deviation is known to be 12. At 0.01 level of significance, what is your conclusion? Use either the p-value approach on the critical value of approach.
Binomial Probability Distribution : explained. Thirty percent of women are basketball fans . Four women are randomly selected . Find the probability distribution of the random variable X,
The book value of a machine is $21,000 at the end of its fourth year of life and $14,000 at the end of its sixth year of life. What was the purchase value of the machine, assuming that "straight line depreciation" is being used.
Escher style tessellation
Determine the kernel and range of each of the following linear transformations from R3 into R3. (a) L(x) = (x3, x2, x1)^T
Graph by hand the curve whose parametric equations are given and show its orientation. Find the two different parametric equations for the rectangular equation
Probability - poker fullhouse. A game of poker is played with an ordinary deck of 52 cards, and each player is dealt a hand of 5 cards chosen at random
illustrtes the impact of diversification. ignores the probability distribution of cash flows. can only measure one outcome at a time
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