In an experiment, the temperature of the reactants was being carefully monitored. It was observed that the maximum and minimum temperature recorded were `64.7^(@)`Fahrenheit and `72.05^(@)` Fahrenhit . Which of the following inequalities represents all possible temperature values, t, observed during the experiment ?

Options

A. `| t - 72.05| gt 7.35`
B. `|t - 72.05| = 7.35`
C. `|t - 72.05| le 7.35`
D. `|t- 72.05| lt 7.35`

Answer

To solve the problem, we need to determine the inequality that represents all possible temperature values \( t \) observed during the experiment, given the minimum and maximum temperatures recorded.

### Step-by-Step Solution:

1. **Identify the Minimum and Maximum Temperatures:**
- The minimum temperature recorded is \( 64.7^\circ F \).
- The maximum temperature recorded is \( 72.05^\circ F \).

2. **Set Up the Inequality:**
- We want to express that the temperature \( t \) can take any value between the minimum and maximum temperatures, inclusive.
- This means \( t \) can be greater than or equal to the minimum temperature and less than or equal to the maximum temperature.

3. **Write the Inequality:**
- The inequality that represents this situation is:
\[ 64.7 \leq t \leq 72.05 \]

4. **Interpret the Inequality:**
- This inequality indicates that the temperature \( t \) can be any value starting from \( 64.7^\circ F \) up to \( 72.05^\circ F \), including both endpoints.

5. **Check for Correctness:**
- The inequality includes both the minimum and maximum temperatures, which is consistent with the problem statement that both temperatures are recorded.

### Final Answer:
The inequality that represents all possible temperature values \( t \) observed during the experiment is:
\[ 64.7 \leq t \leq 72.05 \]