An architect is considering bidding for the design of a new museum. the cost of drawing plans and submitting a model is $18,000. the probability of being awarded the bid is 0.4, and anticipated profits are $45,000, resulting in a possible gain of this amount minus the $18,000 cost for plans and a model. what is the expected value in this situation?

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.

The number of members f(x) in a local swimming club increased by 30% every year over a period of x years. the function below shows the relationship between f(x) and x: f(x) = 10(1.3)xwhich of the following graphs best represents the function? graph of f of x equals 1.3 multiplied by 10 to the power of x graph of exponential function going up from left to right in quadrant 1 through the point 0, 0 and continuing towards infinity graph of f of x equals 10 multiplied by 1.3 to the power of x graph of f of x equals 1.3 to the power of x

For a function f(x), a) if f(7) = 22 then f^-1(22) = b) f^-1(f(c)) =