A community theater uses the function p(d)=−4d2+200d−100 to model the profit (in dollars) expected in a weekend when the tickets to a comedy show are priced at d dollars each. Write and solve an equation to find out the prices at which the theater would earn $1,500 in profit from the comedy show each weekend. Show your reasoning. At what price would the theater make the maximum profit, and what is that maximum profit. Show your reasoning.

price = $25

maximum profit is $2400

Step-by-step explanation:

Given the function modeled by the community theatre as

p(d)=−4d^2+200d−100

The maximum profit will be ,ade at dP/dd = 0

dP/dd = -8d + 200

0 = -8d + 200

8d = 200

d = 200/8

d = 25

hence he theatre will make maximum profit at a price of $25

Substitute d = 25 to get the maximum profit

p(25)=−4(25)^2+200(25)−100

p(25) = -2500+5000-100

p(25) = 2400

Hence the maximum profit is $2400

all three statements are true

step-by-step explanation:

a shipping fee of 5% is charged online with every item purchased online

first let's just take each option and calculate them based on this, to see if the answers matched

keith buys a 40 dollar book

40 x 0.05 = 2

therefore there will be a two dollar fee on keith's book

40 + 2 =42

the first statement is true

a chair costs $80

80 x 0.05 = 4

80 + 4 = 84

the second statement is true

george buys a 20 dollar calculator

20 x 0.05 = 1

20 + 1 = 21

the third statements are true

all three statements are true

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)