The cost Cof producing x thousand calculators is given by the equation below. \[ C=-6.8 x^{2}+7795 x+230,000(x \leqslant 150) \] 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.

To find the average cost per calculator when \( x \) thousand calculators are produced, we need to divide the total cost \( C \) by the number of calculators produced. 1. **Identify the total cost \( C \)**: \[ C = -6.8 x^{2} + 7795 x + 230,000 \] 2. **Determine the number of calculators produced**: Since \( x \) is in thousands, the number of calculators produced is \( 1000x \). 3. **Write the expression for average cost per calculator**: The average cost \( A \) can be expressed as: \[ A = \frac{C}{\text{number of calculators}} = \frac{C}{1000x} \] 4. **Substituting \( C \) into the average cost formula**: \[ A = \frac{-6.8 x^{2} + 7795 x + 230,000}{1000x} \] 5. **Simplifying the expression**: We can simplify this expression by dividing each term in the numerator by \( 1000x \): \[ A = \frac{-6.8 x^{2}}{1000x} + \frac{7795 x}{1000x} + \frac{230,000}{1000x} \] This simplifies to: \[ A = -\frac{6.8 x}{1000} + \frac{7795}{1000} + \frac{230,000}{1000x} \] 6. **Final rational expression for average cost**: Thus, the average cost per calculator when \( x \) thousand calculators are produced is: \[ A = -\frac{6.8 x}{1000} + \frac{7795}{1000} + \frac{230}{x} \] This is the rational expression that gives the average cost per calculator.