2,88:35/72+(1,0625-5/12)•16

To solve the expression \( 2.88 : \frac{35}{72} + (1.0625 - \frac{5}{12}) \cdot 16 \), we will follow the order of operations (parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right).

1. Solve the division and fractions:

   • \( 2.88 : \frac{35}{72} \) can be rewritten as \( 2.88 \cdot \frac{72}{35} \).
   • Calculating \( \frac{72}{35} \): \[ \frac{72}{35} \approx 2.0571 \]
   • Now, \( 2.88 \cdot 2.0571 \approx 5.925 \).

2. Calculate \( 1.0625 - \frac{5}{12} \):

   • Convert \( \frac{5}{12} \) to a decimal: \[ \frac{5}{12} \approx 0.4167. \]
   • Now calculate the subtraction: \[ 1.0625 - 0.4167 \approx 0.6458. \]

3. Multiply by 16:

   • Now compute \( 0.6458 \cdot 16 \): \[ 0.6458 \cdot 16 \approx 10.3328. \]

4. Final Calculation:

   • Now combine all parts: \[ 5.925 + 10.3328 \approx 16.2578. \]

Thus, the final result of the expression is approximately \( 16.2578 \).