A natural history museum borrows $2,000,000 at simple annual interest to purchase new exhibits. Some of the money is borrowed at 5%, some at 6.5%, and some at 7.5%. Use a system of linear equations to determine how much is borrowed at each rate given that the total annual interest is $117,000 and the amount borrowed at 6.5% is four times the amount borrowed at 7.5%. Solve the system of linear equations using matrices.

This exercise illustrates that poor quality can affect schedules and costs. a manufacturing process has 130 customer orders to fill. each order requires one component part that is purchased from a supplier. however, typically, 3% of the components are identified as defective, and the components can be assumed to be independent. (a) if the manufacturer stocks 130 components, what is the probability that the 130 orders can be filled without reordering components? (b) if the manufacturer stocks 132 components, what is the probability that the 130 orders can be filled without reordering components? (c) if the manufacturer stocks 135 components, what is the probability that the 130 orders can be filled without reordering components?