Find the volume of the pyramid. Round your answer to the nearest hundredth.

You have just opened a new dance club, Swing Haven, but are unsure of how high to set the cover charge (entrance fee). One week

bonufazy [111]

Answer:

a) The demand function is

$q(p) = -4 p + 107$

b) The nightly revenue is

$R(p) = -4 p^2 + 107 p$

c) The profit function is

$P(p) = -4 p^2 + 133.75 p - 939$

d) The entrance fees that allow Swing Haven to break even are between 10.03 and 23.41 dollars per guest.

Step-by-step explanation:

a) Lets find the slope s of the demand:

$s = \frac{79-43}{7-16} = \frac{36}{-9} = -4$

Since the demand takes the value 79 in 7, then

$q(p) = -4 (p-7) + 79 = -4 p + 107$

b) The nightly revenue can be found by multiplying q by p

$R(p) = p*q(p) = p*( -4 p + 107) = -4 p^2 + 107 p$

c) The profit function is obtained from substracting the const function C(p) from the revenue function R(p)

$P(p) = R(p) - C(p) = p*q(p) = -4 p^2 + 107 p - (-26.75p + 939) = \\\\-4 p^2 + 133.75 p - 939$

d) Lets find out the zeros and positive interval of P. Since P is a quadratic function with negative main coefficient, then it should have a maximum at the vertex, and between the roots (if any), the function should be positive. Therefore, we just need to find the zeros of P

$r_1, r_2 = \frac{-133.75 \,^+_-\, \sqrt{133.75^2-4*(-4)*(-939)} }{-8} = \frac{-133.75 \,^+_-\, 53.526}{-8} \\r_1 = 10.03\\r_2 = 23.41$

Therefore, the entrance fees that allow Swing Haven to break even are between 10.03 and 23.41 dollars per guest.

7 0

3 years ago

HELP giving brainlest and more points

cupoosta [38]

Answer:

4,000,000,000 meters

Step-by-step explanation:

4 x 10,000,000,000,000 x 0.0001 = 4,000,000,000 meters

4 0

3 years ago

Read 2 more answers

The table below shows the price for different numbers of notebook:

levacccp [35]

So if 2 notebooks cost 12 divide that
12/2 =6 $ each
So to check if its true the 3notebooksx $6 dollars each should =$18 for 3 notebooks
5 notebooks at $6 each = $30 for 5 notebooks
so What is 4notebooks x$6 each ? =4x6 = $24 for 4 notebooks

8 0

3 years ago

A survey showed that 30% of students bring their lunch to school. The survey polled 300 students. How many of the 300 students d

Karolina [17]

Let's first find how many students bring their lunch to school. This is 30% of 300. To find this value, convert the percentage to a fraction (or decimal) and multiply:

$30\% \,\, \textrm{of} \,\,300 = \dfrac{3}{10} \cdot 300 = \dfrac{900}{10} = 90$

Since 90 students bring their lunch to school, we can say 210 students do not bring their lunch to school. (300 - 90 = 210)

8 0

3 years ago

Mr. See weights his grades. Tests are worth 60%, quizzes are worth 25% and homework is 15%. Joey's test average is an 82, his qu

goldenfox [79]

Answer:

83.15

Step-by-step explanation:

Joey's current grade can be determined by weighting his scores with the weights given and adding the results

Tests = 0.6 x 82 = 49.2

Quizzes = 0.25 x 77 = 19.25

homework = 0.15 x 98 = 14.7

49.2 + 19.25 + 14.7 = 83.15

4 0

3 years ago