At a local grocery store, the deli counter has bologna on sale for \( \$ 4.66 \) per pound with a limit of 1.82 pounds per customer. If \( y \) represents the total cost for buying \( x \) pounds of bologna, then which set of compound inequalities below represents the domain and range of this situation? \[ 0 \leq x \leq 8.48 \text { and } 0 \leq y \leq 1.82 \] \( 0 \leq x \leq 1.8 \) and \( 0 \leq y \leq 4.66 \) \( 0 \leq x \leq 4.66 \) and \( 0 \leq y \leq 1.82 \) \( 0 \leq x \leq 1.82 \) and \( 0 \leq y \leq 8.48 \)

To determine the correct set of compound inequalities representing the domain and range for this situation, let's break down the information: 1. **Domain (\( x \)):** - **Definition:** The domain represents the possible values of \( x \), which in this case is the number of pounds of bologna a customer can buy. - **Given:** There is a limit of **1.82 pounds** per customer. - **Inequality:** \( 0 \leq x \leq 1.82 \) 2. **Range (\( y \)):** - **Definition:** The range represents the possible total costs \( y \) associated with buying \( x \) pounds of bologna. - **Calculation:** Since the price is **\$4.66 per pound**, the total cost \( y \) is calculated as: \[ y = 4.66x \] - **Maximum Cost:** When \( x = 1.82 \): \[ y = 4.66 \times 1.82 \approx 8.48 \] - **Inequality:** \( 0 \leq y \leq 8.48 \) Combining both, the correct set of compound inequalities is: \[ 0 \leq x \leq 1.82 \quad \text{and} \quad 0 \leq y \leq 8.48 \] **Correct Answer:** \( 0 \leq x \leq 1.82 \) and \( 0 \leq y \leq 8.48 \)