A movie theater has been charging $10.00 per person and selling about 500 tickets on a typical weeknight. After surveying their customers, the theater management estimates that for every 50 cents that they lower the price, the number of moviegoers will increase by 50 per night. Find the demand function. (Let x represent the number of tickets sold and p represent the price.)

Answer:

[tex]p(x) = -0.01x + 15[/tex]

Step-by-step explanation:

Given

Let x represent the number of tickets, and p the charges

[tex](x_1,p_1) = (500,10)[/tex]

A reduction of 50c gives an increment of 50 tickets.

This gives:

[tex](x_2,p_2) = (500+50,10-0,5)[/tex] ---- [tex]50c = \$0.5[/tex]

[tex](x_2,p_2) = (550,9.5)[/tex]

Required

Determine the demand function

First, calculate the slope:

[tex]m = \frac{p_2 - p_1}{x_2 - x_1}[/tex]

[tex]m = \frac{9.5 - 10}{550-500}[/tex]

[tex]m = \frac{-0.5}{50}[/tex]

[tex]m = -0.01[/tex]

So, the equation is:

[tex]p = m(x - x_1) + y_1[/tex]

[tex]p = -0.01(x - 500) +10[/tex]

[tex]p = -0.01x + 5 +10[/tex]

[tex]p = -0.01x + 15[/tex]

Hence, the function is:

[tex]p(x) = -0.01x + 15[/tex]

the percent change from 50 to 43

SOME ONE HELP PLEASE

For what value of m is the expression x4+mx2+64 a perfect square?

The total cost of an electronic photo
display comes to $100. The price
y plus the tax of $6 equals $100.
Write an equation to find the price
of the electronic photo display.

The table below shows the favorite color of all the students at Wolff Elementary school.

Solve for x Enter the solutions from least to greatest . (x - 4)(- 5x + 1) = 0 lesser x = greater x =

If you are saving 60% which is $54, what will the sale price of the Printer be?

A $60

B $54

C $36

D $90​

Which of the following statements are true? (Select all that apply)

Correlation coefficients are negative when the relationship is weak and positive when they are strong.

Correlation coefficients show the relationship of the x and y values.

Correlation coefficients can be any value less than 1 or greater than −1.

Correlation coefficients show the x and y intercepts of the best fit line.

Correlation coefficients can be represented by the variable r.

A frustum of height 4 is part of a larger pyramid of height 6. What is the ratio of the volume of the frustum to the volume of the pyramid?

can someone help find me? i need to answer!!!!

Solve for x using cross multiplication 3x - 3 5 = 2x – 2 4 x = [?]​

If the graph of the second equation in the system passes through the points (-12, 20) and
(4, 12), which statement is true?

PLEASE ITS URGENT I NEED HELP ..
PLEEEAASEEE !!!
I BEG YOU GUYS ...

Thanks for the help...

i actually put the answer AT RANDOM so pay no attention to it​

Choose two statements that are true for this expression.

6x^3-8x^2-40/y+21

A. The entire expression
B. There are three terms
C. There are four terms
D. The term -40/y is a ratio

Which is a true statement about angles 1 and 2? O the two angles are supplementary
the two angles are complementary
the two angles are neither complementary nor supplementary
the two angles are vertical angles​

What is the area of ​​a rectangle that is 6 inches long by 1/12 inch wide?

Dima’s mom went to the bakery and bought 18 donuts. 1/2 of the donuts were chocolate. Dima‛s family ate 1/3 of the chocolate donuts but didn‛t eat any other kind. What fraction of the donuts did they eat?

Use distributive property to write the expression in standard form 7 (4x - 5y - 2) Use the distributive property and collect like terms to create an equivalent expression 4x - 3 (x - 2y ) + (1/2) (6x - 8y)

NEED HELP ASAP!!!!!!!!!

For each geometric sequence, write a recursive rupe by finding the common ratio by calculating the ratio of consecutive terms. Write an explicit rule for the sequence by writing each term as the product of the first term and a power of the common ratio.​

A plate is considered a major plate if it covers an area of more than _____________ kilometres.



A. 200,000,000 km2



B. 40,000,000 km2



C. 2,000 km2



D. 20,000,000 km2

96 pencils come in a box. If 4 teachers share 3 boxes equally, how many pencils does each teacher receive-

work out m and c for the line y= 2x+1​

10
TIME REMAINING
50:51
What are the solutions of x squared + 6 x minus 6 = 10?

How many integers satisfy each inequality?
-102

I will give out 40 points for the four answers but if you just take the points and don't answer properly I will report you

Test the claim that the mean GPA of night students is significantly different than the mean GPA of day students at the 0.02 significance level.
GPA-Night GPA-Day 3.15 3.47 3.68 3.49 3.34 3.07 3.07 3.31 3.31 3.28 3.2 3.05 3.07 3.12 2.8 3.5 3.04 3.04 3.13 3.19 3.54 3.26 3.24 3.31 3.02 3.45 3.44 2.9 2.79 2.76 3.18 2.69 2.99 3.46 3.28 3.09 3.16 2.72 3.08 3.14 2.47 3.08 3.03 2.99 3.02 3.11 2.58 2.84 3.36 2.99 3.04 2.99
(1) The null and alternative hypothesis would be:
a.H0:μN≥μD
H1:μN>μD.
b.H0:μN=μD
H1:μN≠μD.
c.H0:pN≥pD
H1:pN d.H0:pN=pD
H1:pN≠pD.
e.H0:μN≤μD
H1:μN<μD
f.H0:pN≤pD
H1:pN>pD.
(2) The test is:_______.
a. right-tailed.
b. two-tailed.
c. left-tailed.
(3) The sample consisted of 70 night students, with a sample mean GPA of 2.12 and a standard deviation of 0.08, and 70 day students, with a sample mean GPA of 2.08 and a standard deviation of 0.02

HELP PLSSSSSSSSSSSSS Carin is going to paint walls of her room green. The green paint is too dark so she mixes it with white paint. She tries different mixtures. Which of the following will give the darkest green color?
A. 1 part green + 3 parts white
B. 2 parts green + 6 parts white
C. 3 parts green + 9 parts white
D. 4 parts green + 12 parts white
E. They will all be equally dark.

help .........thanks

SOMEONE PLEASE HELP IM STUCK AND ITS MY LAST QUESTION