Suppose a nonnegative random variable X has mean 50. a) Suppose that we know Var(X) = 25. Find a bound for P(X≥95P(X≥95 or X≤5)X≤5). P(X≥95P(X≥95 or X≤5)X≤5) ≤≤ b) Suppose that we also know that X is binomially distributed. Calculate the precise probability P(X≥95P(X≥95 or X≤5)X≤5). The precise probability P(X≥95P(X≥95 or X≤5)X≤5) is c) Compare the upper bound from (a) with the precise value of P(X≥95P(X≥95 or X≤5)X≤5) from (b). Type "IS" if the precise value is consistant with the bound and "IS NOT" if it is not. Then type "GREATER" if the precise value is greater than the upper bound and "LESS" if it is less. The exact value consistant with the bound from Chebyshev's Theorem estimated above. However, the exact value is much than the upper bound.

Express the following as a function of a single angle, cos(60) cos(-20) - sin(60) sin(-20)

Which two undefined geometric terms always describe figures with no beginning or end?

Acaterer knows he will need 60, 50, 80, 40 and 50 dinner napkins on five successive evenings. he can purchase new napkins initially at 25 cents each, after which he can have dirty napkins laundered by a fast one-day laundry service (i.e., dirty napkins given at the end of the day will be ready for use the following day) at 15 cents each, or by a slow two-day service at 8 cents each or both. the caterer wants to know how many napkins he should purchase initially and how many dirty napkins should be laundered by fast and slow service on each of the days in order to minimize his total costs. formulate the caterer’s problem as a linear program as follows (you must state any assumptions you make): a. define all variables clearly. how many are there? b. write out the constraints that must be satisfied, briefly explaining each. (do not simplify.) write out the objective function to be minimized. (do not simplify.)