4.) Luc earns \( \$ 1075 \) per hour pouring concrete and usually works \( 4-m]^{44} \) hours per week. He is paid bi-weekly. a) How many hours will Luc work in a 2 -week period? b) Calculate his total earnings for 1 pay period. c) Calculate his monthly earnings for a 2-pay month. d) Calculate his monthly earnings for a 3-pay month.

Certainly! Let's break down each part of the problem step by step. --- **Given:** - **Hourly Rate:** \$1,075 per hour - **Hours Worked Per Week:** \(4 - m]^{44}\) hours (Assuming a typographical error, we'll interpret this as **44 hours per week**) - **Payment Frequency:** Bi-weekly (every 2 weeks) --- ### **a) How many hours will Luc work in a 2-week period?** **Calculation:** \[ \text{Hours per week} \times \text{Number of weeks} = 44 \, \text{hours/week} \times 2 \, \text{weeks} = 88 \, \text{hours} \] **Answer:** Luc will work **88 hours** in a 2-week period. --- ### **b) Calculate his total earnings for 1 pay period.** Since Luc is paid bi-weekly, one pay period is 2 weeks. **Calculation:** \[ \text{Total Hours} \times \text{Hourly Rate} = 88 \, \text{hours} \times \$1,075/\text{hour} = \$94,600 \] **Answer:** Luc's total earnings for one pay period are **\$94,600**. --- ### **c) Calculate his monthly earnings for a 2-pay month.** A **2-pay month** means Luc receives two paychecks in that month. **Calculation:** \[ \text{Earnings per Pay Period} \times \text{Number of Paychecks} = \$94,600 \times 2 = \$189,200 \] **Answer:** Luc's monthly earnings in a 2-pay month are **\$189,200**. --- ### **d) Calculate his monthly earnings for a 3-pay month.** A **3-pay month** means Luc receives three paychecks in that month. **Calculation:** \[ \text{Earnings per Pay Period} \times \text{Number of Paychecks} = \$94,600 \times 3 = \$283,800 \] **Answer:** Luc's monthly earnings in a 3-pay month are **\$283,800**. --- **Summary:** - **a)** 88 hours - **b)** \$94,600 - **c)** \$189,200 - **d)** \$283,800 --- > **Note:** The interpretation of \(4 - m]^{44}\) as **44 hours per week** is based on the assumption that there was a typographical error in the original problem. If this interpretation is incorrect, please provide the correct expression for accurate calculations.