A student prepares a mixture by combining \(25.0 \text{ mL}\) of \(4.0 \times 10^{-3} \text{ M AgNO}_3\text{(aq)}\) with \(75.0 \text{ mL}\) of \(8.0 \times 10^{-3} \text{ M NaCl(aq)}\) at \(25^\circ\text{C}\).

\[\text{AgCl(s)} \rightleftharpoons \text{Ag}^+\text{(aq)} + \text{Cl}^-\text{(aq)}\]

What is the value of the reaction quotient, \(Q\), for the dissolution equilibrium above immediately upon mixing these two solutions?