The article cited in exercise 20 also gave the following values of the variables y = number of culs-de-sac and z = number of intersections: y 1 0 1 0 0 2 0 1 1 1 2 1 0 0 1 1 0 1 1 z 1 8 6 1 1 5 3 0 0 4 4 0 0 1 2 1 4 0 4 y 1 1 0 0 0 1 1 2 0 1 2 2 1 1 0 2 1 1 0 z 0 3 0 1 1 0 1 3 2 4 6 6 0 1 1 8 3 3 5 y 1 5 0 3 0 1 1 0 0 z 0 5 2 3 1 0 0 0 3 a. construct a histogram for the y data. what proportion of these subdivisions had no culs-de-sac? at least one cul-de-sac? b. construct a histogram for the z data. what proportion of these subdivisions had at most five intersections? fewer than five intersections?

(a) compute the maclaurin polynomial m2(x) for f(x) = cos x. (b) use the polynomial of part (a) to estimate cos π 12. (c) use a calculator to compute the error made using the estimate from part (b) for the value of cos π 12. remember that the error is defined to be the absolute value of the difference between the true value and the estimate.

Lines b and c are parallel. what is the measure of 2? m2 = 31° m2 = 50° m2 = 120° m2 = 130°

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.)