Questions: Homework Question 1, 1.4.55-BE HW Score: 0%, 0 of 6 points Points: 0 of 1 Save The cost C of producing x thousand calculators is given by the equation below. C = -15.2x^2 + 14,790x + 540,000 (x ≤ 150) The average cost per calculator is the total cost C divided by the number of calculators produced. Write a rational expression that gives the average cost per calculator when x thousand are produced. The rational expression for the average cost is

Homework Question 1, 1.4.55-BE HW Score: 0%, 0 of 6 points Points: 0 of 1 Save The cost C of producing x thousand calculators is given by the equation below. C = -15.2x^2 + 14,790x + 540,000 (x ≤ 150) The average cost per calculator is the total cost C divided by the number of calculators produced. Write a rational expression that gives the average cost per calculator when x thousand are produced. The rational expression for the average cost is
Transcript text: Homework Question 1, 1.4.55-BE HW Score: $0 \%, 0$ of 6 points Points: 0 of 1 Save The cost $C$ of producing $x$ thousand calculators is given by the equation below. \[ C=-15.2 x^{2}+14,790 x+540,000(x \leq 150) \] The average cost per calculator is the total cost C divided by the number of calculators produced. Write a rational expression that gives the average cost per calculator when $x$ thousand are produced. The rational expression for the average cost is $\square$ (Do not simplify.)
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Solution

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Solution Steps

To find the average cost per calculator, we need to divide the total cost \( C \) by the number of calculators produced. Since \( x \) is given in thousands, the number of calculators produced is \( 1000x \). Therefore, the average cost per calculator is given by the rational expression \( \frac{C}{1000x} \).

Step 1: Define the Cost Function

The cost \( C \) of producing \( x \) thousand calculators is given by the equation: \[ C = -15.2x^2 + 14790x + 540000 \]

Step 2: Define the Number of Calculators Produced

Since \( x \) is in thousands, the number of calculators produced is \( 1000x \).

Step 3: Calculate the Average Cost per Calculator

The average cost per calculator is the total cost \( C \) divided by the number of calculators produced: \[ \text{Average Cost} = \frac{C}{1000x} \]

Step 4: Substitute the Cost Function into the Average Cost Formula

Substitute \( C = -15.2x^2 + 14790x + 540000 \) into the average cost formula: \[ \text{Average Cost} = \frac{-15.2x^2 + 14790x + 540000}{1000x} \]

Final Answer

\[ \boxed{\frac{-15.2x^2 + 14790x + 540000}{1000x}} \]

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