\begin{tabular}{l} )) Pam signed up for a new gym. She had \\ to pay a \( \$ 45 \) sign-up fee and will pay dues o \\ \( \$ 30 \) each month for 6 months. \\ Which expression tells you the total cost of \\ m's 6-month gym membership? \\ \hline\( \$ 45+\$ 30) \cdot 6 \) \\ \hline\( \$ 45+(\$ 30 \cdot 6) \)\end{tabular}

To determine the total cost of Pam's 6-month gym membership, we need to analyze the costs involved: 1. **Sign-up Fee**: Pam pays a one-time sign-up fee of \( \$ 45 \). 2. **Monthly Dues**: Pam pays \( \$ 30 \) each month for 6 months. Now, let's break down the two expressions provided: 1. **Expression 1**: \( (\$ 45 + \$ 30) \cdot 6 \) - This expression suggests that we first add the sign-up fee and the monthly dues together, and then multiply the total by 6. This would imply that the sign-up fee is paid every month, which is incorrect. 2. **Expression 2**: \( \$ 45 + (\$ 30 \cdot 6) \) - This expression indicates that we first calculate the total monthly dues for 6 months by multiplying \( \$ 30 \) by 6, and then add the sign-up fee of \( \$ 45 \). This correctly represents the total cost of the membership. Thus, the correct expression that tells you the total cost of Pam's 6-month gym membership is: \[ \$ 45 + (\$ 30 \cdot 6) \] This expression accurately accounts for the one-time sign-up fee and the total of the monthly dues over the 6-month period.