To find the temperature in Joelle at 3:00 AM given that the temperature at 2:30 AM is [tex]\(-3^{\circ} F\)[/tex] and it drops [tex]\(\frac{3}{4}\)[/tex] of a degree in 30 minutes, follow these steps:
1. Identify the initial temperature:
- The initial temperature at 2:30 AM is [tex]\(-3^{\circ} F\)[/tex].
2. Determine the change in temperature:
- The temperature drops by [tex]\(\frac{3}{4}\)[/tex] of a degree in 30 minutes.
3. Calculate the new temperature:
- Subtract the temperature drop from the initial temperature.
- New temperature = Initial temperature [tex]\(-\)[/tex] Temperature drop
4. Apply the values:
- Initial temperature = [tex]\(-3^{\circ} F\)[/tex]
- Temperature drop = [tex]\(\frac{3}{4}\)[/tex]
New temperature = [tex]\(-3\)[/tex] - [tex]\(\frac{3}{4}\)[/tex]
5. Convert the temperature drop to a decimal for easier subtraction:
- [tex]\(\frac{3}{4} = 0.75\)[/tex]
So, New temperature = [tex]\(-3 - 0.75 = -3.75^{\circ} F\)[/tex]
Thus, the temperature in Joelle at 3:00 AM is [tex]\(-3.75^{\circ} F\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{-3.75^{\circ} F} \][/tex]
