3) $9-\frac{4}{3} \div\left(\frac{1}{2}\right)^{-2}+10$

Step 1 ：First, we need to solve the expression inside the parentheses, which is \(\left(\frac{1}{2}\right)^{-2}\). The negative exponent means that we take the reciprocal of the base and then raise it to the power of 2.

Step 2 ：Next, we perform the division operation, which is \(\frac{4}{3} \div\left(\frac{1}{2}\right)^{-2}\).

Step 3 ：Finally, we perform the subtraction and addition operations from left to right.

Step 4 ：The result of the calculation is approximately 18.67. However, this is a floating point number and it may not be exactly accurate due to the limitations of floating point arithmetic in computers. To get the exact result, we can perform the calculation symbolically.

Step 5 ：Final Answer: The result of the mathematical expression \(9-\frac{4}{3} \div\left(\frac{1}{2}\right)^{-2}+10\) is approximately \(\boxed{18.67}\).