Final answer:
The initial temperature was -11.5°F and it changed by 2/3 of that value, resulting in a final temperature of -3.83°F. This does not match any provided choices exactly but is closest to option (a) -5°F, suggesting an error in the question or options.
Step-by-step explanation:
The subject of this question is Mathematics, and it appears to be suitable for a middle school level. The question asks to calculate the final temperature after a change occurred to the initial temperature, which makes it a problem of basic algebra and understanding temperature change.
The initial temperature in Badger, Minnesota, at 10 pm is -11.5°F. The temperature changed by 2/3 of the current value at 4 pm, meaning the temperature increased by 2/3 times -11.5°F. The temperature increase can be calculated by multiplying -11.5 by 2/3, which results in a change of -7.67°F. To get the final temperature at 4 pm, we add this change to the initial temperature: -11.5°F + (-7.67°F) equals -19.17°F. However, this result does not match any of the provided answer choices. Since this problem might have been misinterpreted, let's consider the other possibility where the temperature instead goes up by 2/3, meaning it would go from -11.5°F to -11.5°F + (11.5°F * 2/3) which equals -11.5°F + 7.67°F, resulting in a final temperature of -3.83°F. This result also does not match any of the provided options exactly, but it is closest to option (a) -5°F, which might suggest a rounding or interpretation error in the question or options provided.