For one child, a childcare facility charges $350 per month for preschool and $5.00 per hour for each additional hour for after-school care. The function below can be used to determine f(h), the monthly fee for after-school care and preschool, where h represents the number of hours spent in after-school care. f(h) = 350 + 5h If the total monthly bill for one child was $750, what was the total number of hours the child spent in after-school care? A. 100 B. 90 C. 88 D. 80

Given that y varies directly to the square root of (x + 1), and that y = 1 when x = 8,(a)express y in terms of .x,(b)find the value of y when x = 3,(c)find the value of x when y = 5.

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.

What are the measures of angles a, b, and c? show your work and explain your answers. 25 points