Estimate the value that should fill in the blank space (represented by ?) in the expression below:

$31.9\times 55.011-?=\left(12.01\right){\mathrm{³}}^{}+7.94\%\text{of}\mathrm{ 250.14}$

The correct option is 12.

To find the estimated value of the unknown quantity (represented by ?), we approximate each decimal number in the given expression to its nearest whole number or convenient value.

The given mathematical expression is:

$31.9\times 55.011-?={\left(12.01\right)}^3+7.94\%\text{of}250.14$

Step 1: Round off each numerical value for easy calculation.

• $31.9\approx 32$

• $55.011\approx 55$

• $12.01\approx 12$

• $7.94\%\approx 8\%$

• $250.14\approx 250$

Step 2: Simplify the Multiplication on the Left-Hand Side (LHS).

$31.9\times 55.011\approx 32\times 55=1760$

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

First, calculate the cube of 12:

${\left(12.01\right)}^3\approx {12}^3=12\times 12\times 12=1728$

Next, calculate the percentage component:

$7.94\%\text{of}250.14\approx 8\%\text{of}250=\frac{8}{100}\times 250=20$

Now, add both results on the RHS:

$\text{RHS}\approx 1728+20=1748$

Step 4: Solve for the missing value (?).

Substitute the approximated values into the main equation:

$1760-?=1748$

Rearrange the terms to find the value of ?:

$?=1760-1748$

$?=12$

Thus, the estimated value that fills in the blank space is 12.