In the Pirates of the Aegean video game, you may have to investigate o, 1, 2, 3. 4, or 5 grottoes without success before you finally locate a treasure chest. You conclude that the probability you will have to investigate at most x grottoes without success is F(x) P(x s x) l ij and F5) 1. (Remember that n'" (n-1)(n-2)...(n-k+ 1) is the number of permutations (ordered lists without replacement) of k items from n possibilities.) a) What is the probability you will have to investigate exactly 3 grottoes without success? b) What is the expected number ECM) of grottoes you will investigate without success?c) What is the variance Var(M) of the number of grottoes you will investigate without success?

Need solving this second acceleration problem.

Haruka hiked several kilometers in the morning. she hiked only 66 kilometers in the afternoon, which was 25% less than she had hiked in the morning. how many kilometers did haruka hike in all?

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?