Ireally need with this last problem the students in the freshman class plan to use the profits from selling hats for a class trip. the cost to have 200 hats made is $1500. they will be sold for $12 each. a. write an equation to represent the profit, p, earned from selling x hats. b. use the equation you wrote in part a to find the minimum number of hats that must be sold for the class to recover the cost of making the 200 hats. show your work or explain how you found your answer. c. suppose the class decides to charge $15 per hat instead of $12. at this selling price, how many fewer hats must be sold to recover the cost of making the 200 hats? show your work or explain how you found your answer.

Step-by-step explanation:

a. Profit, p, earned from selling x hats when hat will be sold for $12 each:

p = 12x

b. To recover the cost of making the 200 hats which is $1500, profit, p >= cost:

p = 12x >= 1500

x >= 1500/12 = 12.5

So the minimum number of hats that must be sold = 13

c. New hat price = $15 so p = 15x

p = 15x >= 1500

x >= 1500/15 = 10

So the new minimum = 10 which is 3 fewer.

-232

step-by-step explanation:

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.