Ahybrid car can travel 45 miles on 1 gallon of gas. determine the amount of gas needed for a 500 mile trip

If a fair 6 sided cube is rolled 60 times, theoretically how many times should you expect to roll a 4 or a 5?

How many solutions does the nonlinear system of equations graphed below have?

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?