Robert took $50 with him to spend on pizza and games for himself and his friends at chucky cheese. the price for each slice of pizza was $5. the price of each game was half the price of a slice of pizza. (a) sketch the graph that represents the situation and label the intercepts. use one axis to represent the number of slices of pizza and the other axis to represent the number of games. (b) what do the intercepts and the solutions of your graphed function mean in context of the problem?

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.