What approximate value will come in place of the question mark (?) in the following question?
`((3. 0 7)/(4.01))^(2) xx 127.96 + 442.02 = ?`

Options

A. 529
B. 514
C. 503
D. 497

Answer

To solve the equation \(\left(\frac{3.07}{4.01}\right)^2 \times 127.96 + 442.02 = ?\), we will follow these steps:

### Step 1: Approximate the values
We will round the numbers to make calculations easier:
- \(3.07 \approx 3\)
- \(4.01 \approx 4\)
- \(127.96 \approx 128\)
- \(442.02 \approx 442\)

### Step 2: Substitute the approximated values
Now, we substitute the approximated values into the equation:
\[ \left(\frac{3}{4}\right)^2 \times 128 + 442 \]

### Step 3: Calculate \(\left(\frac{3}{4}\right)^2\)
Calculating \(\left(\frac{3}{4}\right)^2\):
\[ \left(\frac{3}{4}\right)^2 = \frac{9}{16} \]

### Step 4: Multiply by 128
Now, we multiply \(\frac{9}{16}\) by 128:
\[ \frac{9}{16} \times 128 = \frac{9 \times 128}{16} = \frac{1152}{16} = 72 \]

### Step 5: Add 442
Finally, we add 442 to the result:
\[ 72 + 442 = 514 \]

### Final Answer
Thus, the approximate value that will come in place of the question mark (?) is:
\[ \boxed{514} \]