Suppose a certain variable star has a period of 10 days. The average brightness of the star is 3.9 magnitudes, and the maximum variation from the average is 0.4 magnitude. Assuming that the variation in brightness is simple harmonic, find an equation that gives the brightness of the star as a function of time. (Let y be the brightness in magnitudes and let t be the time in days. Suppose that when t = 0 the brightness is 3.4 magnitudes and increasing.)

Abig remake 100 loaves of bread in one day how many loaves does the bakery make in 6 days

The function p(x) = –2(x – 9)2 + 100 is used to determine the profit on t-shirts sold for x dollars. what would the profit from sales be if the price of the t-shirts were $15 apiece?

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.)