To calculate the expression \(0.0961 + 4.873 \cdot \sqrt{0.8345}\), we first need to calculate the square root of \(0.8345\):
\[ \sqrt{0.8345} \approx 0.9157 \quad (\text{using a calculator}) \]
Next, we multiply \(4.873\) by \(0.9157\):
\[ 4.873 \cdot 0.9157 \approx 4.46 \quad (\text{using a calculator}) \]
Now we add \(0.0961\) to this result:
\[ 0.0961 + 4.46 \approx 4.5561 \]
So, the final result of the expression \(0.0961 + 4.873 \cdot \sqrt{0.8345}\) is approximately:
\[ \boxed{4.5561} \]