Baseball fans can buy tickets for seats in the lower deck or upper deck of the stadium. tickets for the lower deck cost $42 each. ticket prices for the upper deck are 75% of the cost of tickets for the lower deck. which inequality represents all possible combinations of x, the number of tickets for the lower deck, and y, the number of tickets for the upper deck, that someone can buy for no more than $800? a) 42x + 56y ≤ 800 b) 42x + 31.5y ≤ 800 c) 42x + 56y > 800 d) 42x + 31.5y > 800

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.