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iris [78.8K]
4 years ago
5

5 points

Mathematics
1 answer:
Flauer [41]4 years ago
4 0

Answer:

<em>The payment for driving 80 miles is $78</em>

Step-by-step explanation:

<u>Mathematical model </u>

Mathematical models are used in disciplines like natural sciences and engineering, among many others.

The data provided in the question allows building a model for the charges of the car rental, knowing there are two fees:

A fixed charge of $50

A variable charge or $0.35 per mile driven.

<em>Part A</em>

Using m as the number of miles driven for the day, the model for the payment for the car rental is:

P(m)=50+0.35m

<em>Part B</em>

Find the payment if the car is driven m=80 miles:

P(80)=50+0.35*80

P(80)=50+28=78

The payment for driving 80 miles is $78

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A company makes pens. They sell each pen for $99.
Sindrei [870]

Answer:

a) Profit = 84000

b) at break even number of pens sold = 46

Step-by-step explanation:

Profit = Selling price - Cost price

Total revenue generated = 99 * 1000

Total revenue generated = 99000

Total cost on making the pen  = 11 * 1000

Total cost on making the pen = 11000

Total cost including the initial cost = 11000 + 4000

Total cost including the initial cost =  15000

Profit = 99000 - 15000

Profit = 84000

Break even is when the cost are equal to Revenue thus no profit or loss

Revenue = total cost (break even)

9x = 1x + 4000

9x - x = 4000

8x = 4000

x = 500

At breakeven Revenue = 9 * 500

At breakeven Revenue =  4500

since one pen is sold at 99 therefore at break even number of pens sold = 4500/99 = 45.45( to 2 decimal place)

at break even number of pens sold = 46

4 0
3 years ago
Convert 491 into binary number
sergij07 [2.7K]

Answer:

111101011 subscript 2

Step-by-step explanation:

491 / 2 = 245 , 1 remainder

245 / 2 = 122 , 1 remainder

122 / 2 = 61 , 0 remainder

61 / 2 = 30 , 1 remainder

30 / 2 = 15 , 0 remainder

15 / 2 = 7 , 1 remainder

7 / 2 = 3 , 1 remainder

3 / 2 = 1 , 1 remainder

1 / 2 = 0 , 1 remainder

Now, we're going to put the remainders together in reverse order to get the final answer.

111101011 ---> this is the final solution

See the image below for how you would write 111101011 subcript 2.

6 0
3 years ago
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frez [133]
1). 2³ x 7
2). 2 x 3²
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Solve the system using elimination.<br> 5x + 8y = –29<br> 7x – 2y = –67
MA_775_DIABLO [31]
First, multiply the second equation by 4 so that 8y can cancel out. Now you have
5x+8y=-29
and
28x-8y=-268
Add these equations to get 
33x=-297
Divide both sides by 33, and you have
x=-9
Now, simply solve for y by plugging it into an equation, and you have
y=2
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3 years ago
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12 × (3 + 2²) ÷ 2 - 10
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Answer:

32

Step-by-step explanation:

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