Suppose that you pick a bit string from the set of all bit strings of length ten. Find the probability that: i. The bit string has the sum of its digits equal to seven.

ii. The bit string has more 0s than 1s.

iii. The bit string has exactly two 1s, given that the string begins with a 1.

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.)

Heather is riding a quadratic function that represents a parabola that touches but does not cross the x-axis at x=-6

If x varies directly as y, and x = 7.5 when y = 10, find x when y = 4