A new theater is being built for the city ballet. The balcony has 200 seats. The floor has 10 rows with x seats in each row. The number of people in the theater must be under 500 to meet fire safety regulations. What is the solution of this inequality, and what is it's meaning? A. 10x + 200 > 500; the new theater must have more than 30 seats in each row on the floor to meet fire safety regulations. B. 10x + 200 < 500; the new theater must have fewer than 30 seats in each row on the floor to meet fire safety regulations. C. 10x > 500; the new theater must have more than 50 seats in each row on the floor to meet fire safety regulations. D. 10x < 500; the new theater must have fewer than 50 seats in each row on the floor to meet fire safety regulations.

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.