Alice and Billy each separately apply for and receive loans worth $8,000 apiece. Alice has a very good credit score, so her loan has an APR of 5.61%, compounded monthly. Billy’s credit score is rather low, so his loan has an APR of 10.57% interest, compounded monthly. If both of them repay their loans over a five year period, making equal monthly payments based on their own loan, how much more will Billy have paid than Alice?

The center of the circumscribed circle lies on line segment and the longest side of the triangle is equal to the of the circle.

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?

In trapezoid abcd, ac is a diagonal and ∠abc≅∠acd. find ac if the lengths of the bases bc and ad are 12m and 27m respectively.