Determine the greatest common factor of the given expressions.

the rain caused the river to rise a total of 6 2/3 inches. the river was was rising a an average of 2/3 of an inch each hour. ho

Tasya [4]

2 1/2 you divide 6 2/3 by 2/3

8 0

3 years ago

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

Convert these unlike fractions to equivalent like fractions and add them. You must use the LCD to get the answer correct. If pos

Kamila [148]

Answer:

3

Step-by-step explanation:

The fractions are: $\frac{1}{5}$ and $\frac{2}{3}$ . Let's take a look at the denominators: 5 and 3. The LCD of 5 and 3 is 15. 5x3=15, 3x5=15. So now we would multiply the denominators to make them the same number like this: $\frac{5}{15}$ and $\frac{10}{15}$ . Remember that if you multiply the denominator by a certain number, you must multiply the numerator by the same number as well. For example, in $\frac{2}{3}$ , we multiply 3 by 5 and 2 by 5. Same number. Now with that out of the way, let's work on the equation: $\frac{1}{5}$ + $\frac{2}{3}$ . We know it is the same as $\frac{5}{15}$ and $\frac{10}{15}$ . So now all we do is add the numerators together: 5+10=15 or $\frac{15}{15}$ . Now we have to reduce the fraction. $\frac{15}{15}$ can be reduced to 3 by dividing 15 by 5=3. The final fraction is $\frac{3}{3}$ or can be simply put as 3 since 3/3 is a whole number. That's it - you're done!