Lucy drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 6 hours. When Lucy drove home, there was no traffic and the trip only took 4 hours. If her average rate was 22 miles per hour faster on the trip home, how far away does Lucy live from the mountains?

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.)