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

$\frac{624.01}{?}+{12.98}^2=51.98\%\text{of}400.01$

The correct answer is 16 (Option 1).

To find the approximate value that replaces the question mark (?), we can round each number in the given expression to its nearest whole number or convenient value:

1. $624.01\approx 624$

2. $12.98\approx 13$

3. $51.98\%\approx 52\%$

4. $400.01\approx 400$

Now, substitute these approximate values into the given equation:

$\frac{624}{?}+{13}^2=52\%\text{of}400$

Calculate the right-hand side of the equation:

$52\%\text{of}400=\frac{52}{100}\times 400=52\times 4=208$

Calculate ${13}^2$:

${13}^2=169$

Now substitute back into the equation:

$\frac{624}{?}+169=208$

Subtract 169 from both sides:

$\frac{624}{?}=208-169$

$\frac{624}{?}=39$

Solve for ?:

$?=\frac{624}{39}=16$

Thus, the value that should replace the question mark is 16.