Part A: Do you agree with Sally's computation? Explain your reasoning.
Let's first break down the problem into smaller parts and solve it step-by-step to verify if Sally's computations and reasoning are correct.
### Step-by-step Solution:
1. Initial Temperature:
- Sally starts with an initial temperature of [tex]\(-5^{\circ} F\)[/tex].
2. Temperature Rise During the Day:
- The temperature rose by [tex]\(20^{\circ} F\)[/tex] during the day.
- We calculate the new temperature after the rise:
[tex]\[
-5^{\circ} F + 20^{\circ} F = 15^{\circ} F
\][/tex]
- This shows that after the rise, the temperature is [tex]\(15^{\circ} F\)[/tex].
3. Temperature Fall During the Night:
- The temperature then fell by [tex]\(25^{\circ} F\)[/tex] during the night.
- We calculate the final temperature after the fall:
[tex]\[
15^{\circ} F - 25^{\circ} F = -10^{\circ} F
\][/tex]
- This shows that by the end of the night, the temperature is [tex]\(-10^{\circ} F\)[/tex].
4. Total Change in Temperature:
- To find the total change in temperature, we compare the final temperature of [tex]\(-10^{\circ} F\)[/tex] with the initial temperature of [tex]\(-5^{\circ} F\)[/tex].
- The change in temperature is:
[tex]\[
-10^{\circ} F - (-5^{\circ} F) = -10^{\circ} F + 5^{\circ} F = -5^{\circ} F
\][/tex]
- This shows that the total change in temperature is [tex]\(-5^{\circ} F\)[/tex].
### Conclusion:
- Sally's computation is correct.
- She correctly calculated the temperature rise and fall, and her final temperature calculations are accurate.
- The total change in temperature ([tex]\(-5^{\circ} F\)[/tex]) aligns with our step-by-step computations.
Therefore, I agree with Sally's computation. The reasoning is accurate, and the final answers are consistent with the necessary arithmetic operations.
### Final Results:
- Intermediate temperature after the rise: [tex]\(15^{\circ} F\)[/tex]
- Final temperature after the fall: [tex]\(-10^{\circ} F\)[/tex]
- Total change in temperature: [tex]\(-5^{\circ} F\)[/tex]
