Gasoline is to be stocked in a bulk tank once at the beginning of each week and then sold to individual customers. Let Y1 denote the proportion of the capacity of the bulk tank that is available after the tank is stocked at the beginning of the week. Because of the limited supplies, Y1 varies from week to week. Let Y2 denote the proportion of the capacity of the bulk tank that is sold during the week. Because Y1 and Y2 are both proportions, both variables take values between 0 and 1. Further, the amount sold, y2, cannot exceed the amount available, y1. Suppose that a model for the joint probability of Y1 and Y2 is fy1y2(y,1y2) = { 3y1 0<= y2 <= y1 <= 1 and 0 otherwise

a) what is the probability that more than half a tank is sold given that three-fourths of a tank is stocked?

(show work please)

Runners run around the school's football field. the cross country coach determines that the width of the field is seventy yards shorter than the length. part a write an expression that represents the perimeter of the football field. let x represent the length of the football field. include parentheses in your expression. next, write an equivalent expression that does not include parentheses. what property or properties did you use to simplify? explain. part b the cross country coach later determines that the length of the football field is 120 yards. all students must run five laps. using your answer from part a, determine the actual number of yards that each athlete must run in the tryouts. in order to make the team, students must complete the laps in 6 minutes. how quickly must they run each lap?