Question

The temperature falls from 0 degrees to Negative 12 and one-fourth degrees in 3 and one-half hours. Which expression finds the change in temperature per hour?
Negative StartFraction 7 over 2 EndFraction divided by StartFraction 49 over 4 EndFraction
Negative StartFraction 7 over 2 EndFraction times StartFraction 49 over 4 EndFraction
Negative StartFraction 49 over 4 EndFraction times StartFraction 7 over 2 EndFraction
Negative StartFraction 49 over 4 EndFraction divided by StartFraction 7 over 2 EndFraction

Answer 1

To find the change in temperature per hour, we first need to determine the total change in temperature and the total time in hours.

1. **Calculate the change in temperature**:

The temperature changes from 0 degrees to -12.25 degrees (which is -12 and one-fourth degrees). The change in temperature is calculated as follows:

\[
\text{Change in temperature} = \text{final temperature} - \text{initial temperature} = -12.25 - 0 = -12.25 \text{ degrees}
\]

2. **Calculate the total time**:

The total time given is 3.5 hours.

3. **Calculate the change in temperature per hour**:

We can express the change in temperature per hour as:

\[
\text{Change in temperature per hour} = \frac{\text{Change in temperature}}{\text{Total time}} = \frac{-12.25}{3.5}
\]

To simplify further, we can convert -12.25 and 3.5 into fractions:
\[
-12.25 = -\frac{49}{4} \quad \text{and} \quad 3.5 = \frac{7}{2}
\]

Now we can substitute these values into the expression:
\[
\text{Change in temperature per hour} = \frac{-\frac{49}{4}}{\frac{7}{2}}
\]

To divide fractions, we multiply by the reciprocal:
\[
= -\frac{49}{4} \times \frac{2}{7}
\]

Thus, we need to identify the correct expression from the provided options. The correct expression that is equivalent to our calculation is:

- **Negative StartFraction 49 over 4 EndFraction divided by StartFraction 7 over 2 EndFraction**

So the answer is:
\[
\text{Negative StartFraction 49 over 4 EndFraction divided by StartFraction 7 over 2 EndFraction}
\]