Let's solve the expression step by step.
The expression is:
\[ 44 + \left( \frac{10.302}{(32 + 19) - 36 \cdot 5} \right) : (29 \cdot 3 - 76) \]
Step 1: Simplify the Parentheses
First, calculate the values within the parentheses.
Calculate \(32 + 19\): \[ 32 + 19 = 51 \]
Calculate \(36 \cdot 5\): \[ 36 \cdot 5 = 180 \]
Now, calculate \((32 + 19) - 36 \cdot 5\): \[ 51 - 180 = -129 \]
Step 2: Calculate \(29 \cdot 3 - 76\)
Calculate \(29 \cdot 3\): \[ 29 \cdot 3 = 87 \]
Now calculate \(87 - 76\): \[ 87 - 76 = 11 \]
Step 3: Substitute Back
Now substitute back into the original expression:
\[ 44 + \left( \frac{10.302}{-129} \right) : 11 \]
Step 4: Division
Calculate \(\frac{10.302}{-129}\):
\[ \frac{10.302}{-129} \approx -0.0798721 \]
Step 5: Now calculate \(-0.0798721 : 11\)
This is equivalent to:
\[ \frac{-0.0798721}{11} \approx -0.00725101 \]
Step 6: Final Calculation
Combine this with \(44\):
\[ 44 - 0.00725101 \approx 43.99274899 \]
Final Result
Thus, the final result of the expression is approximately:
\[ \boxed{43.9927} \]
(rounded to four decimal places).
