Dennis can walk about 2 5/6 miles each hour. About how far can he walk in 3 hours 15 minutes?

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

today only, a sofa is being sold at a 36% discount. The sale price is $560. what was the price yesterday?

pashok25 [27]

Answer:

Step-by-step explanation:

Let yesterday's price be x

Discount percentage = 36%

Sale price = $ 560

(100-36)% of x = 560

64 % *x = 560

$\frac{64}{100}*x=560\\\\x=560*\frac{100}{64}\\\\x=875$

Yesterday's price = $ 875

8 0

4 years ago

There are two sources that serve as the foundation for conducting research on learning. The first source addresses characteristi

Leviafan [203]

Answer:

There are two sources that serve as the foundation for conducting research on learning. The first source addresses characteristics of knowledge itself and the different ways in which we learn things. The second source focuses on what goes on in our minds and how that is theoretically represented.

Step-by-step explanation:

The investigations on the process of how we learn have led to two main sources:

- Acquisition of knowledge which involves assimilation or understanding, storage and retrieval

- The second source belongs to a modern learning cognitive psychology, neuroscience, and cognitive science theories on mental representation, which concerns about the build up of an internal symbol or cognitive representation to hypothetically figure out, external reality.

8 0

3 years ago

Need help checking my answers

kifflom [539]

Answer:

Step-by-step explanation:

_______

Good evening ,

______________

Look at the photo below for the answer,

:)

6 0

3 years ago

36A^4+16Y^2<br> Can someone help me

Alenkasestr [34]

Answer:

4(9a^4+4y^2)

Step-by-step explanation:

factor out common term

6 0

3 years ago

Dennis can walk about 2 5/6 miles each hour. About how far can he walk in 3 hours 15 ​minutes?

Dennis can walk about 2 5/6 miles each hour. About how far can he walk in 3 hours 15 minutes?