A total of n balls, numbered 1 through n, are put into n urns, also numbered 1 through n in such a way that ball i is equally likely to go into any of the urns 1, 2, ..., i. Find (a) the expected number of urns that are empty; (b) the probability that none of the urns is empty.

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?

Larry wants to buy some carpeting for his living room. the length of the room is 4 times the width and the total area of the room is 16 square meters. what is the length of the living room

The graph is supposed to show f(x) = 3 sin (x/4+1) - 1/2. which of the following are correctly represented in the graph? select two of the following that apply.