Estimate the approximate value that should replace the question mark (?) in the mathematical expression below. (Note: Precise calculation of the exact value is not required.)

$59.90\%\text{of}1020.11-9.88\%\text{of}79.91=?{}^3+92.01$

The correct option is 8.

To estimate the value of the question mark (?), we round off the given numbers to their nearest simple whole numbers:

$59.90\%\approx 60\%$

$1020.11\approx 1020$

$9.88\%\approx 10\%$

$79.91\approx 80$

$92.01\approx 92$

Now, substitute these approximate values into the given expression:

$(60\%\text{ of }1020)-(10\%\text{ of }80)={?}^3+92$

Step 1: Calculate 60% of 1020.

$\frac{60}{100}\times 1020=6\times 102=612$

Step 2: Calculate 10% of 80.

$\frac{10}{100}\times 80=8$

Step 3: Simplify the left side of the equation.

$612-8=604$

Step 4: Solve for ?³.

$604={?}^3+92$

${?}^3=604-92$

${?}^3=512$

Step 5: Find the cube root of 512.

$?=\sqrt[3]{512}$

Since 8³ = 8 × 8 × 8 = 512, we get:

$?=8$

Thus, the approximate value that replaces the question mark is 8.