To determine what effect the salespeople had on purchases, a department store polled 700 shoppers as to whether or not they had made a purchase and whether or not they were pleased with the service. Of those who had made a purchase, 130 were happy with the service and 119 were not. Of those who had made no purchase, 142 were happy with the service and 309 were not. Find the probability that a shopper who was happy with the service had made a purchase (round off to the nearest hundredth).

Consider the polynomials given below. p(x) = x4 + 3x3 + 2x2 – x + 2 q(x) = (x3 + 2x2 + 3)(x2 – 2) determine the operation that results in the simplified expression below. 35 + x4 – 573 - 3x2 + x - 8 a. p+q b. pq c. q-p d. p-q

Iwill give brainliest. suppose tommy walks from his home at (0, 0) to the mall at (0, 5), and then walks to a movie theater at (6, 5). after leaving the theater tommy walks to the store at (6, 0) before returning home. if each grid square represents one block, how many blocks does he walk?

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.