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 answer is 6 (Option 4).

To find the approximate value that replaces the question mark (?), we can round each decimal term in the given equation to its nearest whole number for easier calculation.

Let us analyze the given mathematical expression:

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

Step 1: Approximate the numbers to their nearest integers.

• $1248.01\approx 1248$
• $96.01\%\approx 96\%$
• $1525.01\approx 1525$

Step 2: Rewrite the expression using approximated values.

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

Step 3: Calculate the Right-Hand Side (RHS).

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

Simplifying the fraction:

$\frac{96}{100}\times 1525=0.96\times 1525=1464$

Step 4: Substitute the RHS back into the equation and solve for ?.

$1248+{?}^3=1464$

Subtract 1248 from both sides:

${?}^3=1464-1248$

${?}^3=216$

Take the cube root of both sides:

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

$?=6$

Thus, the approximate value that should replace the question mark is 6.