The Rao family won a raffle of $1,000 to spend at Dixie Amusement Park. They want to use it for a group tour and for meals. A tour can have at most 8 people in the group, and if there are children on the tour there must be at least one adult. The tour cost $250 plus $100 for each adult and $50 for each child. The meal plan for the park is $15 per person.

A) Write a system of inequalities to model this scenario, and graph the system.

B) What is the maximum number of people who could be in the group, and how much would it cost? Justify your answer

C) Suppose that only adults are going to go on the tour. How many can there be? Explain your answer.

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.)