Use the binomial theorem to expand (2a + 2b)5.
a. 32a5 + 80a4b + 320a3b2 + 320a2b3 + 80ab4 + 10b5
b. 32a5 + 160a4b + 320a3b2 + 320a2b3 + 160ab4 + 32b5
c. 32a5 + 160a4b + 640a3b2 + 160ab4 + 32b5
d. 32a5 + 160a4b + 320a3b2 + 320a2b3 + 160ab4 + 20b5

Diane owes $387 to her brother. if she debits her bank account $161.25 a month to pay him back, how many months will it take her to pay off the debt?

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?

Carl's candies has determined that a candy bar measuring 3 inches long has a z-score of +1 and a candy bar measuring 3.75 inches long has a z-score of +2. what is the standard deviation of the length of candy bars produced at carl's candies?