Determine the approximate value that should replace the question mark (?) in the mathematical expression below.

$1248.01+?{}^3=96.01\%\text{of}1525.01$

The correct option is 6.

To find the approximate value that should replace the question mark (?), we can round off the numbers in the given expression to their nearest whole numbers to make calculations simpler.

Given equation:

$1248.01+{?}^3=96.01\%\text{of}1525.01$

Let us approximate the values:

1248.01 can be approximated as 1248.
96.01% can be approximated as 96%.
1525.01 can be approximated as 1525.

Now, substitute these approximate values into the equation:

$1248+{?}^3=96\%\text{of}1525$

First, calculate 96% of 1525:

$96\%\text{of}1525=\frac{96}{100}\times 1525$

$=0.96\times 1525=1464$

Now substitute 1464 back into the equation:

$1248+{?}^3=1464$

Subtract 1248 from both sides to isolate ${?}^3$:

${?}^3=1464-1248$

${?}^3=216$

Take the cube root of both sides to find the value of (?):

$?=\sqrt[3]{216}$

$?=6$

Thus, the approximate value that replaces the question mark is 6.