A business journal investigation of the performance and timing of corporate acquisitions discovered that in a random sample of 2 comma 5502,550 firms, 615615 announced one or more acquisitions during the year 2000. does the sample provide sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 2727%? use alphaαequals=0.010.01 to make your decision.

Find the value of x in each case. give reasons to justify your solutions! d q ∈ pr

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.)

Rose and andrew are financing $128,000 to purchase a condominium. they obtained a 15-year, fixed-rate loan with a rate of 5.05%. they have been given the option of purchasing up to four points to lower their rate to 4.81%. how much will the four points cost them?