To find the change in temperature per hour, we first need to determine the total change in temperature and the total time in hours.
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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:
\[ \text{Change in temperature} = \text{final temperature} - \text{initial temperature} = -12.25 - 0 = -12.25 \text{ degrees} \]
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Calculate the total time:
The total time given is 3.5 hours.
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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: \[ \text{Negative StartFraction 49 over 4 EndFraction divided by StartFraction 7 over 2 EndFraction} \]