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 answer is 12.

We are given the following mathematical expression to estimate the value of the missing term represented by ?:

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

To solve for ? easily, let us round off each value to its nearest integer or simple manageable figure:

$31.9\approx 32$

$55.011\approx 55$

$12.01\approx 12$

$7.94\%\approx 8\%$

$250.14\approx 250$

Now, substitute these approximate values into the equation:

$32\times 55-?={\left(12\right)}^3+8\%\text{of}250$

Next, evaluate each component of the expression step-by-step:

1. Calculate the product on the left side:

$32\times 55=1760$

2. Calculate the cube of 12:

${12}^3=1728$

3. Calculate 8% of 250:

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

Substitute these calculated values back into our equation:

$1760-?=1728+20$

$1760-?=1748$

Finally, solve for ?:

$?=1760-1748$

$?=12$

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