Vote: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ( \( \$ 2,354.67 \) ). All percentage values in the answers need to include a percentage sign (\%). For all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06). Salespersons at the Kings Park Auto Giant are paid a commission, \( c(p) \), based on the profit, \( p \). The following piecewise function gives the commission rules. \[ c(p)=\left\{\begin{array}{ll} 0.20 p & \text { when } 0 \leq p<900 \\ 0.23 p & \text { when } 900 \leq p<1,500 \\ 0.25 p & \text { when } p \geq 1,500 \end{array}\right. \] a. If the profit is \( \$ 1,500 \), what is the percent commission rate? \( \square \) b. If the profit is \( \$ 900 \), what is the percent commission rate? \( \square \) c. What is the commission on a car sold for a \( \$ 970 \) profit? \( \square \) d. Kings Park Auto Giant purchases a car for \( \$ 32,090 \) and sells it for \( \$ 33,200 \). What commission is paid to the salesperson? \( \square \)

To find the commission rate for each profit amount, we need to use the given piecewise function \( c(p) \) and calculate the commission for each profit amount. a. If the profit is $1,500, we need to find the commission rate using the piecewise function. b. If the profit is $900, we need to find the commission rate using the piecewise function. c. To find the commission on a car sold for a $970 profit, we need to use the piecewise function and calculate the commission. d. To find the commission paid to the salesperson when Kings Park Auto Giant purchases a car for $32,090 and sells it for $33,200, we need to calculate the profit and then use the piecewise function to find the commission. Let's calculate the commission for each profit amount. Calculate the value by following steps: - step0: Calculate: \(0.25\times 1500\) - step1: Multiply the numbers: \(375\) a. If the profit is $1,500, the commission rate is 0.25, which is 25%. b. If the profit is $900, the commission rate is 0.23, which is 23%. c. To find the commission on a car sold for a $970 profit, we need to use the piecewise function. Since the profit is between 900 and 1500, the commission rate is 0.23. Therefore, the commission on a car sold for a $970 profit is 0.23 * 970 = $223.10. d. To find the commission paid to the salesperson when Kings Park Auto Giant purchases a car for $32,090 and sells it for $33,200, we need to calculate the profit first. The profit is $33,200 - $32,090 = $1,110. Then, we can use the piecewise function to find the commission. Since the profit is between 900 and 1500, the commission rate is 0.23. Therefore, the commission paid to the salesperson is 0.23 * 1,110 = $255.30.