30. Which matrix multiplication can be used to find a store's cost of buying 30 pairs of pants for \$5 each and selling 12 pairs of pants for \( \$ 34 \) each? F. \( \left[\begin{array}{ll}30 & 12\end{array}\right]\left[\begin{array}{r}-5 \\ 34\end{array}\right] \) H. \( \left[\begin{array}{r}-5 \\ 34\end{array}\right]\left[\begin{array}{ll}30 & 12\end{array}\right] \) G. \( \left[\begin{array}{ll}30 & 12\end{array}\right]\left[\begin{array}{r}5 \\ -34\end{array}\right] \quad \) J. \( \left[\begin{array}{r}5 \\ -34\end{array}\right]\left[\begin{array}{ll}30 & 12\end{array}\right] \)

To find the store's cost of buying 30 pairs of pants for \$5 each and selling 12 pairs of pants for \$34 each, we can set up a matrix multiplication that represents these transactions. 1. **Buying Cost**: The cost of buying 30 pairs of pants at \$5 each can be represented as: - Quantity: 30 pairs - Cost per pair: -5 (negative because it's an expense) 2. **Selling Revenue**: The revenue from selling 12 pairs of pants at \$34 each can be represented as: - Quantity: 12 pairs - Revenue per pair: 34 We can represent these transactions in matrix form: - Let \( \mathbf{q} = \begin{bmatrix} 30 \\ 12 \end{bmatrix} \) be the quantity matrix. - Let \( \mathbf{p} = \begin{bmatrix} -5 \\ 34 \end{bmatrix} \) be the price matrix (with the cost as negative). The multiplication we want to perform is: \[ \mathbf{q} \cdot \mathbf{p} = \begin{bmatrix} 30 & 12 \end{bmatrix} \begin{bmatrix} -5 \\ 34 \end{bmatrix} \] This multiplication will yield a single value that represents the total cost of buying and selling the pants. Thus, the correct answer is: **F. \( \left[\begin{array}{ll}30 & 12\end{array}\right]\left[\begin{array}{r}-5 \\ 34\end{array}\right] \)**