Find the approximate value of (?) in the following questions.
`(3.011)/(4.99) xx (9.021)/(19.03) xx ? xx 64.99 = (11.023)^(3) + 72.989`

Options

A. 76
B. 85
C. 82
D. 71

Answer

To find the approximate value of the question mark (?) in the equation

\[ \frac{3.011}{4.99} \times \frac{9.021}{19.03} \times ? \times 64.99 = (11.023)^3 + 72.989 \]

we will simplify the equation step by step using approximations.

### Step 1: Approximate the values
First, we will approximate the numbers involved in the equation:

- \(3.011 \approx 3\)
- \(4.99 \approx 5\)
- \(9.021 \approx 9\)
- \(19.03 \approx 19\)
- \(64.99 \approx 65\)
- \(11.023 \approx 11\)
- \(72.989 \approx 73\)

So, we can rewrite the equation as:

\[ \frac{3}{5} \times \frac{9}{19} \times ? \times 65 = 11^3 + 73 \]

### Step 2: Calculate \(11^3 + 73\)
Now, we calculate \(11^3\):

\[ 11^3 = 11 \times 11 \times 11 = 121 \times 11 = 1331 \]

Adding 73 to this gives:

\[ 1331 + 73 = 1404 \]

So, the right-hand side of the equation becomes 1404.

### Step 3: Set up the equation
Now, we can set up the equation:

\[ \frac{3}{5} \times \frac{9}{19} \times ? \times 65 = 1404 \]

### Step 4: Simplify the left-hand side
Now, we simplify the left-hand side:

\[ \frac{3 \times 9 \times 65}{5 \times 19} \times ? = 1404 \]

Calculating \(3 \times 9 = 27\) and \(27 \times 65\):

\[ 27 \times 65 = 1755 \]

So we have:

\[ \frac{1755}{5 \times 19} \times ? = 1404 \]

Calculating \(5 \times 19 = 95\):

\[ \frac{1755}{95} \times ? = 1404 \]

### Step 5: Calculate \(\frac{1755}{95}\)
Now we calculate \(\frac{1755}{95}\):

\[ \frac{1755}{95} = 18.5 \quad (\text{approximately}) \]

### Step 6: Substitute and solve for ?
Now we substitute this back into the equation:

\[ 18.5 \times ? = 1404 \]

To find \(?\), we divide both sides by 18.5:

\[ ? = \frac{1404}{18.5} \]

Calculating this gives:

\[ ? \approx 76 \]

### Final Answer
Thus, the approximate value of \(?\) is:

\[ \boxed{76} \]