You love nuts. You go to the store to buy almonds and cashews. Cashews cost $2 per pound and Almonds cost $5 per pound. You end up spending $450 on 150 pounds of nuts (you really love nuts). How many pounds of each type of nut did you get? How many pounds of cashews? How many pounds of Almonds?

they will manufacture 8496 cars

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.