Find the sum of the infinite series 0.9 + 0.09 + 0.009 +…if it exists.

Nell has a sales clerk job that pays $12 per hour for regular gas work hours. she gets double time for any hours over 40 that she works in a week. how many hours did nell work if her weekly pay was $744

Write the rational number in lowest terms 99/-15

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?