Chris purchased a new mattress for $1,399. He will need to pay $78 each month on his interest-free loan to pay off the total price of the mattress in 18 months. Separately, Chris sets aside $50 each month in a savings account, which currently shows a balance of $250. Create an augmented matrix from a system of equations to help Chris determine when he can use monthly payments and savings to pay off the total purchase price of the mattress.?

Out of five men and five women, we form a committee consisting of four different people. assuming that each committee of size four is equally likely, find the probabilities of the following events: 1. the committee consists of two men and two women 2. the committee has more women than men. 3. the committee has at least one man. for the remainder of the problem assume that alice and bob are among the ten people being considered. 4. both alice and bob are members of the committee.