Prove each of the following statements using strong induction. (a) Prove that any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps. (b) Prove that any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps. (c) Prove that any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.\

Let f (x) = x e8x. find a formula for the nth derivative of f, where n is any positive integer. use x and n in your answer if needed. f (n)(x) =

Someone answer this asap rn for ! a discount store’s prices are 25% lower than department store prices. the function c(x) = 0.75x can be used to determine the cost c, in dollars, of an item, where x is the department store price, in dollars. if the item has not sold in one month, the discount store takes an additional 20% off the discounted price and an additional $5 off the total purchase. the function d(y) = 0.80y - 5 can be used to find d, the cost, in dollars, of an item that has not been sold for a month, where y is the discount store price, in dollars. create a function d(c(x)) that represents the final price of an item when a costumer buys an item that has been in the discount store for a month. d(c(x)) =

The graph shows the charges for a health club in a month. make a function table for the input-output values. writes an equation that can be used to find the total charge y for the number of x classes