First, let's evaluate the sums in both columns:
Column A: \[ 0.5 + \frac{3}{4} \] We can convert \(0.5\) to a fraction: \[ 0.5 = \frac{1}{2} \] Now we can add \(\frac{1}{2} + \frac{3}{4}\). To add these fractions, we need a common denominator, which is \(4\): \[ \frac{1}{2} = \frac{2}{4} \] Now we can add: \[ \frac{2}{4} + \frac{3}{4} = \frac{5}{4} \] This is a rational number.
Column B: \[ \sqrt{3} + \frac{2}{5} \] The term \(\sqrt{3}\) is an irrational number, and \(\frac{2}{5}\) is a rational number. The sum of a rational and an irrational number is always irrational: \[ \sqrt{3} + \frac{2}{5} \text{ is irrational.} \]
Now we have determined the nature of the sums:
- Column A: \( \frac{5}{4} \) is rational.
- Column B: \( \sqrt{3} + \frac{2}{5} \) is irrational.
Now let's evaluate the statements:
- Statement #1: Only Column A has a rational sum. (True)
- Statement #2: Only Column B has a rational sum. (False)
- Statement #3: Column A and Column B both have rational sums. (False)
Thus, the correct statement is Statement #1.
The response is: 1.