Mary has had five unit tests in math so far this semester.
she has achieved scores of 86, 82, 93, 88, and 89 out of 100.
she knows there are only two unit tests left, and would like to achieve an overall average of 90 on the seven tests.
a) can she achieve her desired average? if so, what average would she need to achieve on the last two tests?
b) what is the minimum score she could get on either of the last two tests, and still achieve an overall average of 90?

1- 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.2- 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 the first question?

Dots sells a total of 279 t-shirts ($2) and shorts ($4). in april total sales were $670. how many t-shirts and shorts did dots sell?

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false. 1^2 + 4^2 + 7^2 + + (3n - 2)^2 = [n(6n^2-3n-1)/2]