Which graph shows a proportional relationship between x and y?
a) a
b) b
c) c
d) d

Gretchen is setting up for a banquet. she has 300 chairs and needs to distribute them evenly among t tables. how many chairs should she put at each table? write your answer as an expression.

Scarlet bought three pairs of sunglasses and two shirts for $81 and paula bought one pair of sunglasses and five shirts for $105 what is the cost of one pair of sunglasses and one shirt?

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.