The cost of fuel to propel a boat through the water (in dollars per hour) is proportional to the cube of the speed. A certain ferry boat uses worth of fuel per hour when cruising at miles per hour. Apart from fuel, the cost of running this ferry (labor, maintenance, and so on) is per hour. At what speed should it travel so as to minimize the cost per mile traveled?

An oil exploration company currently has two active projects, one in asia and the other in europe. let a be the event that the asian project is successful and b be the event that the european project is successful. suppose that a and b are independent events with p(a) = 0.2 and p(b) = 0.8. (a) if the asian project is not successful, what is the probability that the european project is also not successful? (b) what is the probability that at least one of the two projects will be successful? (c) given that at least one of the two projects is successful, what is the probability that only the asian project is successful? (round your answer to three decimal places.)