To solve the expression \( 44 + \left( \frac{10.302}{(32 + 19) - 36 \cdot 5} \right) : (29 \cdot 3 - 76) \), let's follow the order of operations step by step:
Calculate the parentheses:
- \( 32 + 19 = 51 \)
- \( 36 \cdot 5 = 180 \)
- So, \( (32 + 19) - 36 \cdot 5 = 51 - 180 = -129 \)
Next calculation:
- \( 29 \cdot 3 = 87 \)
- Then, \( 87 - 76 = 11 \)
Replace the values back into the expression: The expression now looks like: \[ 44 + \left( \frac{10.302}{-129} \right) : 11 \]
Divide \( 10.302 \) by \( -129 \):
- \( \frac{10.302}{-129} \approx -0.07989 \)
Then divide by \( 11 \):
- \( -0.07989 : 11 \equiv -0.07989 \div 11 \approx -0.00726 \)
Now, finalize the expression: Replace back into the overall equation: \[ 44 + (-0.00726) \approx 43.99274 \]
Therefore, the final result of the expression is approximately: \[ \boxed{43.99274} \]