Suppose you're on a game show, and you're given the choice of three doors: behind one door is a sports car; behind all of the others is bicycles. you pick a door, say no. 1, and the host, who knows what's behind the doors, opens another door, say no. 2, revealing a bicycle. he then says to you, "do you want to pick door no. 3? " is it to your advantage to switch your choice?

Adriver from the university of florida women’s swimming and diving team is competing in the in ncaa zone b championships

In the polynomial below, what number should replace the question mark to produce a difference of squares? x2 + ? x - 36

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?