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Mnenie [13.5K]
3 years ago
15

5. Write the quotient of 7 less than a number and 6' as an expression. Use x as the variable.​

Mathematics
1 answer:
marissa [1.9K]3 years ago
5 0

Answer:

\frac{x-7}{6}

quotient means the problem will be a fraction

7 less than a number x-7

and 6 (6)

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Construct a mathematical model for the following real-life situations(make a table)
zhenek [66]

The mathematical model representing the scenarios described can be expressed as follows :

  • If n ≤ 8 ; A(n) = 31.25n
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1.)

Amount paid per 8 hours at summer job = 250

Additional hours beyond, 8 hours = 1.5 × hourly rate

Let:

  • hourly rate = p
  • Number of hours worked = n
  • Amount earned as a function of n, A(n)

Hourly rate, p = (250 ÷ 8) = 31.25

Therefore, the hourly rate, p at the summer job = $31.25

Overtime pay = 1.5 × 31.25 = $46.875

Therefore,

If n ≤ 8 ; A(n) = 31.25n

If n > 8 ; A(n) = 31.25 + 46.875(n - 8)

2.)

Let :

  • Number of playing hours = n
  • Total amount charged as a function of n ; T(n)

Therefore,

T(n) = First hour fee + (charge per additional hour × number of additional hours)

T(n) = 15 + 5(n - 1)

Therefore, the models can be used to calculate the total earning and amount charged for any given hour value.

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6 0
2 years ago
you are shopping for disposable cameras to hand out at a party. the daytime cameras costs 2.75 dollars and the flash camera cost
LenKa [72]

The solutions that involve whole numbers of cameras are (7, 13), (8, 12), (9, 11), (10, 10), (11, 9), (12, 8) and (13, 7)

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The given parameters are:

  • Daytime cameras = $2.75
  • Flash camera = $4.25
  • Number of cameras = 20 cameras
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Represent the daytime camera with x and the flash camera with y.

So, we have:

x + y = 20

65 <=2.75x + 4.25y <= 75

Make y the subject in x + y = 20

y = 20 - x

Substitute y = 20 - x in 65 <=2.75x + 4.25y <= 75

65 <=2.75x + 4.25(20 - x) <= 75

Expand

65 <=2.75x + 85 - 4.25x <= 75

This gives

65 <=-1.5x+ 85  <= 75

Subtract 85 from the inequality

-20 <=-1.5x <= -10

Split the inequality

-1.5x >= -20 and -1.5x <= -10

Divide by -1.5

x <= 13.33 and x >= 6.67

Combine the inequality

6.67 <= x <= 13.33

<h3>List all of the solutions that involve whole numbers of cameras.</h3>

In (a), we have:

6.67 <= x <= 13.33

This means that:

x = 7, 8, 9, 10, 11, 12, 13

Recall that:

y = 20 - x

So, we have:

y = 13, 12, 11, 10, 9, 8, 7

So, the solutions that involve whole numbers of cameras are (7, 13), (8, 12), (9, 11), (10, 10), (11, 9), (12, 8) and (13, 7)

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