Marriott Hotels purchased nine iRobot Roomba i7+ for \( \$ 870 \) each. It received a \( 15 \% \) discount for buying more than five and an . additional \( 6 \% \) discount for immediate delivery. Terms of payment were \( \frac{4}{10}, \frac{\mathrm{n}}{30} \). Marriott Hotels pays the bill within the cash discount period. How much should the check be written for? Note: Do not round intermediate calculations. Round your final answer to the nearest cent.

To calculate the total amount that Marriott Hotels should write the check for, we first need to calculate the initial cost before discounts, then apply the discounts, and finally account for the cash discount. 1. **Calculate the initial cost:** \[ \text{Initial cost} = \text{Price per Roomba} \times \text{Quantity} = 870 \times 9 = 7830 \] 2. **Apply the first discount (15%):** \[ \text{First discount} = 7830 \times 0.15 = 1249.50 \] \[ \text{Cost after first discount} = 7830 - 1249.50 = 6580.50 \] 3. **Apply the second discount (6%):** \[ \text{Second discount} = 6580.50 \times 0.06 = 394.83 \] \[ \text{Cost after second discount} = 6580.50 - 394.83 = 6185.67 \] 4. **Finally, apply the cash discount (4%):** \[ \text{Cash discount} = 6185.67 \times 0.04 = 247.43 \] \[ \text{Final amount to pay} = 6185.67 - 247.43 = 5938.24 \] The check should be written for **$5938.24**.