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m_a_m_a [10]
2 years ago
12

The bus fare in a city is $1.75. People who use the bus had the option of purchasing a monthly coupon book for $21 . With the co

upon book the fair is reduced to .75 determine the number of times in a month the bus must be used so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book.
Mathematics
1 answer:
Phantasy [73]2 years ago
4 0

Answer:

The bus must be used 21 times a month so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book.

Step-by-step explanation:

This problem can be modeled by two first order functions. One function is the monthly cost without the coupon book, and the other function is the monthly cost with the coupon book.

Monthly cost without the coupon book:

The only thing that the person will spend is the bus fare, that is $1.75. So the cost is:

C_{1}(n) = 1.75n

where n is the number of times that the person rode the bus.

Monthly cost with the coupon book:

The person will spend $21 for the book plus the bus fare, that will be $.75. So the cost is:

C_{2}(n) = 21 + .75n

The total monthly cost without the coupon book is the same as the total monthly cost with the coupon book when C1 = C2. So:

C_{1}(n) = C_{2}(n)

1.75n = 21 + .75n

1.75n - .75n = 21

n = 21

The bus must be used 21 times a month so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon book.

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A manager needs to order company shirts for each employee. She was quoted the following rates. If she orders 75 shirts and passe
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The answer is B.$7.47.

Let's first calculate how much in total 75 shirts cost:
- first 19 (less than 20) cost $10:         19 * $10 = $190
- the next 30 cost $8:                         30 *  $8 = $240
- the rest (26 = 75 - 19 - 30) cost $5: 26 *  $5 = $130

So, in total 75 shirts cost $560:
19 * $10 + 30 * $8 + 21 * $5 = $190 + $240 + $130 = $560

Since 75 shirts are ordered, there must be 75 employees, so each employee must pay $7.47:
$565 ÷ 75 = $7.47
7 0
3 years ago
Read 2 more answers
Perform the following operation
Cerrena [4.2K]

Answer:

When you multiply an odd number of negatives you get a negative result. When you multiply an even number of negatives you get a positive result.

First, multiply normally.

25x10x5

1100

Then determine whether the sign is positive or negative. Since there is an odd number of negatives, the sign is negative.

So, the answer is -1100.

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7 0
2 years ago
A carpenter can make at most 20 tables and at most 30 chairs per day. Each
baherus [9]

Answer:Its B

Step-by-step explanation:

6 0
2 years ago
A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the number of cakes sold per
HACTEHA [7]

Answer:

A) Revenue function = R(x) = (580x - 10x²)

Marginal Revenue function = (580 - 20x)

B) Fixed Cost = 900

Marginal Cost function = (300 + 50x)

C) Profit function = P(x) = (-35x² + 280x - 900)

D) The quantity that maximizes profit = 4

Step-by-step explanation:

Given,

The Price function for the cake = p = 580 - 10x

where x = number of cakes sold per day.

The total cost function is given as

C = (30 + 5x)² = (900 + 300x + 25x²)

where x = number of cakes sold per day.

Please note that all the calculations and functions obtained are done on a per day basis.

A) Find the revenue and marginal revenue functions [Hint: revenue is price multiplied by quantity i.e. revenue = price × quantity]

Revenue = R(x) = price × quantity = p × x

= (580 - 10x) × x = (580x - 10x²)

Marginal Revenue = (dR/dx)

= (d/dx) (580x - 10x²)

= (580 - 20x)

B) Find the fixed cost and marginal cost function [Hint: fixed cost does not change with quantity produced]

The total cost function is given as

C = (30 + 5x)² = (900 + 300x + 25x²)

The total cost function is a sum of the fixed cost and the variable cost.

The fixed cost is the unchanging part of the total cost function with changing levels of production (quantity produced), which is the term independent of x.

C(x) = 900 + 300x + 25x²

The only term independent of x is 900.

Hence, the fixed cost = 900

Marginal Cost function = (dC/dx)

= (d/dx) (900 + 300x + 25x²)

= (300 + 50x)

C) Find the profit function [Hint: profit is revenue minus total cost]

Profit = Revenue - Total Cost

Revenue = (580x - 10x²)

Total Cost = (900 + 300x + 25x²)

Profit = P(x)

= (580x - 10x²) - (900 + 300x + 25x²)

= 580x - 10x² - 900 - 300x - 25x²

= 280x - 35x² - 900

= (-35x² + 280x - 900)

D) Find the quantity that maximizes profit

To obtain this, we use differentiation analysis to obtain the maximum point of the Profit function.

At maximum point, (dP/dx) = 0 and (d²P/dx²) < 0

P(x) = (-35x² + 280x - 900)

(dP/dx) = -70x + 280 = 0

70x = 280

x = (280/70) = 4

(d²P/dx²) = -70 < 0

Hence, the point obtained truly corresponds to a maximum point of the profit function, P(x).

This quantity demanded obtained, is the quantity demanded that maximises the Profit function.

Hope this Helps!!!

8 0
2 years ago
Answer the question about the image.
Anton [14]

Answer:

4

Step-by-step explanation:

hope this helps and have a great day

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