To determine which of the given sums results in a rational number according to the Closure Property, let's analyze each option:
1. **0.643892553… + 34**:
- 0.643892553... is a rational number (as it can be expressed as a fraction).
- 34 is also a rational number.
- The sum of two rational numbers is rational, so this expression results in a rational number.
2. **0.6̅ + 9/10**:
- 0.6̅ (which is 0.666...) is a rational number (it can be expressed as 2/3).
- 9/10 is clearly a rational number.
- Thus, this sum also results in a rational number.
3. **√36 + √221**:
- √36 = 6 (which is rational).
- √221 is not a rational number (as 221 is not a perfect square).
- The sum of a rational number (6) and an irrational number (√221) is irrational, so this doesn't satisfy the closure property.
4. **π + 4–√**:
- π is irrational, and 4–√ (which is 2) is rational.
- The sum of an irrational number (π) and a rational number (2) is irrational.
In conclusion, the sum of **0.643892553… + 34** and **0.6̅ + 9/10** results in rational numbers.
So, the correct responses that produce sums resulting in rational numbers are:
- **0.643892553… + 34**
- **0.6̅ + 9/10**
Both of these options are valid according to the Closure Property.