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Softa [21]
3 years ago
12

One health club charges a $44 sign-up fee and $30 per month. Another health club charges a $99 sign-up fee and $25 per month. Fo

r what number of months is the cost the same?
Mathematics
1 answer:
Nina [5.8K]3 years ago
6 0
The answer is 11 because there is a $55 dollar difference starting out and the monthly fees are $5 apart, 55 divided by 5 is 11
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Given the Production Function Q = 72X + 15X 2 - X 3 , where Q =Output and X=Input (5 marks) a) What is the Marginal Product (MP)
rusak2 [61]

Answer:

a.) Marginal Product (MP) = 120

b.) Average Product = 126

c.) At x = 12, the output is maximum.

d.) After 5 levels of inputs diminishing returns set in.

Step-by-step explanation:

Given that,

Q = 72x + 15x² - x³

a.)

Marginal Product is equal to

\frac{dQ}{dx} = 72 + 30x - 3x^{2}

At x = 8

MP = 72 + 30(8) - 3(8)²

     = 72 + 240 - 192

     = 120

∴ we get

Marginal Product (MP) = 120

b.)

Average Product is equals to

= \frac{Q}{x}

= 72 + 15x - x²

At x = 6

Average Product = 72 + 15(6) - 6²

                             = 72 + 90 - 36

                             = 126

∴ we get

Average Product = 126

c.)

For Maximizing Q,

Put \frac{dQ}{dx} = 0

⇒72 + 30x - 3x² = 0

⇒24 + 10x - x² = 0

⇒x² - 10x - 24 = 0

⇒x² - 12x + 2x - 24 = 0

⇒x(x - 12) + 2(x - 12) = 0

⇒(x + 2)(x - 12) = 0

⇒x = -2, 12

As items can not be negative

∴ we get

At x = 12, the output is maximum.

d.)

Now,

For Diminishing Return

\frac{d(MP)}{dx} = \frac{d^{2}Q}{dx^{2} }   < 0

⇒30 - 6x < 0

⇒-6x < -30

⇒6x > 30

⇒x > 5

∴ we get

For x > 5, the diminishing returns set in

i.e.

After 5 levels of inputs diminishing returns set in.

3 0
3 years ago
Segment PQ has a midpoint of E. If PE=4x-3 and 6x+2, what is the value of x ?
topjm [15]

Answer:

P

Step-by-step explanation:

7 0
4 years ago
The cost of 5 pounds of apples is $6.45. Which statements can be used to solve for a, the cost of each pound of apples? Check al
natka813 [3]

Answer:

B) To solve, find the cost of 1 pound of apples; write a division equation.

C) The correct equation for this problem is 5a = $6.45. Solve this problem by dividing both sides by 5.

F) Each pound of apples costs $1.29.

5 0
3 years ago
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Any cookie jar 1/4 of the cookies or chocolate chip and 2/3 of the rest are peanut butter what fraction of all the cookies peanu
CaHeK987 [17]

Answer:

3/12

Step-by-step explanation:

5 0
3 years ago
How does the relationship between multiplication and division help you divide rational numbers?
Kisachek [45]
A rational number is one which can be represented using fractions. The opposite of division is multiplication and vice versa. Knowing this information, you can easily go about turning a division of two fractions into the multiplication of two fractions.
Ex.
(1/2) / (3/4) = ?
multiply the denominator of your fraction by the reciprocal of the denominator.
(1/2)*(4/3) / (3/4)*(4/3)
(4/6) / 1 = 4/6
So when dividing rational numbers, you can multiply the denominator by its reciprocal. This would be an example of converting a division problem into a multiplication one
3 0
4 years ago
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