Find the first five terms of the sequence defined by each of these recurrence relations and initial conditions. (a) an = 5an−1, a0 = 2 (b) an = a 2 n−1 , a1 = 2 (c) an = 3an−1 + an−2, a0 = 1, a1 = 2 (d) an = nan−1 + a 2 n−2 , a0 = 1, a1 = 1 (e) an = an−1 − an−2 + an−3, a0 = 1, a1 = 2, a2 = 0.

At a lunchron, guests are offered a selection of five different grilled vegetables and four different meats. in how many waya could one choose three vegetables and two meats?

Monthly water bills for a city have a mean of $108.43 and a standard deviation of $32.09. find the probability that a randomly selected bill will have an amount greater than $155, which the city believes might indicate that someone is wasting water. would a bill that size be considered unusual?

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?