A grocery store is offering a promotion where a customer receives a $0.20 discount per item on selected sale items, and Paulo has a coupon where he receives $0.10 off regularly priced items.

Before applying the discounts, the cost of Paulo's sale items was $61.96 and the cost of Paulo's regularly priced items was $43.30. After applying the discounts, Paulo spent $97.66 on both the sale items and regularly priced items.

If Paulo bought 11 more sale items than regular items, how many items did he buy in all?

A. 18

B. 29

C. 40

D. 47

Two different linear functions are shown below with two points given from each function. use slope-intercept form or point-slope form to find the equation of each. linear function a points: (–5, –2), (–5, 7) linear function b points: (7, –5), (–2, –5) function a has: the equation of line a is: function b has: the equation of line b is:

About 9% of th population is hopelessly romantic. if 2 people are randomly selected from the population, what is the probability that at least 1 person is hopelessly romantic?

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.