Becky read 10 books in 4 days.Sarah reads 50 books in 20 days. Are the two girls reading at the same rate

Before the pandemic cancelled sports, a baseball team played home games in a stadium that holds up to 50,000 spectators. When ti

spayn [35]

Answer:

(a) $D(x)=-2,500x+60,000$

(b) $R(x)=60,000x-2500x^2$

(c) x=12

(d)Optimal ticket price: $12

Maximum Revenue:$360,000

Step-by-step explanation:

The stadium holds up to 50,000 spectators.

When ticket prices were set at $12, the average attendance was 30,000.

When the ticket prices were on sale for $10, the average attendance was 35,000.

(a)The number of people that will buy tickets when they are priced at x dollars per ticket = D(x)

Since D(x) is a linear function of the form y=mx+b, we first find the slope using the points (12,30000) and (10,35000).

$\text{Slope, m}=\dfrac{30000-35000}{12-10}=-2500$

Therefore, we have:

$y=-2500x+b$

At point (12,30000)

$30000=-2500(12)+b\\b=30000+30000\\b=60000$

Therefore:

$D(x)=-2,500x+60,000$

(b)Revenue

$R(x)=x \cdot D(x) \implies R(x)=x(-2,500x+60,000)\\\\R(x)=60,000x-2500x^2$

(c)To find the critical values for R(x), we take the derivative and solve by setting it equal to zero.

$R(x)=60,000x-2500x^2\\R'(x)=60,000-5,000x\\60,000-5,000x=0\\60,000=5,000x\\x=12$

The critical value of R(x) is x=12.

(d)If the possible range of ticket prices (in dollars) is given by the interval [1,24]

Using the closed interval method, we evaluate R(x) at x=1, 12 and 24.

$R(x)=60,000x-2500x^2\\R(1)=60,000(1)-2500(1)^2=\$57,500\\R(12)=60,000(12)-2500(12)^2=\$360,000\\R(24)=60,000(24)-2500(24)^2=\$0$

Therefore:

Optimal ticket price:$12
Maximum Revenue:$360,000

3 0

3 years ago

PLEASE HELP!!!!! its Friday children uwu<br> this question isn't really math but yall smart !

Vesna [10]

Answer:

Mercury is smaller than Mars

8 0

3 years ago

Read 2 more answers

huma has 4 bags of square inch tiles with 6 in each bag she uses them to meaure the area of a rectangle on her homework. ahter c

poizon [28]

Answer:

20 square inches

Step-by-step explanation:

No. of bags Huma has : 4

No. of tiles in one bag: 6

Total no . of tiles in 4 bag = 4 * No. of tiles in one bag

= 4*6 = 24

No of tiles left with huma = 4

Let x be the no of tiles used to cover rectangle

Hence,

sum of no. of tiles left with huma and no of tiles used to cover rectangle should be equal to Total no . of tiles in 4 bag

mathematically

no. of tiles left with huma(4) + no of tiles used to cover rectangle (x) = Total no . of tiles in 4 bag (24)

4 + x = 24

subtracting 4 from both sides

4 + x -4 = 24 - 4

=> x = 20

Thus, 20 square inches tiles are used to cover the rectangle.

This means that area of rectangle is 20 square inches .

6 0

3 years ago

explain how mid-nineteenth-century American values and social trends are conveyed in The Voyage of Life paintings by Thomas Cole

Thepotemich [5.8K]

Answer:

Step-by-step explanation:

American values and social trends are conveyed in The Voyage of Life paintings by Thomas Cole. how did society influence the art

8 0

2 years ago

Find the value of x.

LUCKY_DIMON [66]

Answer:

25

Step-by-step explanation:

8 0

3 years ago