High School

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Lorraine turns on her oven to roast vegetables. The oven warms to the desired temperature in 10 minutes. She turns off the oven about an hour later. The function \(f(t)\) represents the temperature, in degrees, inside the oven \(t\) minutes after turning it on.

Which statements about this situation are most likely true? Choose all that are correct.

A. Given \(f(5)\)
B. Given \(f(0) = f(400)\), this most likely means the highest temperature the oven reached was 400 degrees.
C. Given \(f(5)\)
D. It is unlikely that \(f(30) = f(45)\) since \(30 \neq 45\).
E. It is likely that \(f(30) = f(45)\) since the oven should have stayed at a steady temperature between 30 and 45 minutes.

Answer :

Final answer:

For the oven's temperature function, it is incomplete to assess truth based on Given f(5). It is incorrect that f(0) = f(400) would indicate the highest temperature, and f(30) = f(45) is likely true, suggesting the oven maintains a steady temperature during cooking.

Explanation:

When analyzing the temperature function f(t) of the oven over time, different statements can be made about its behavior:

  • The statement Given f(5) is incomplete and cannot be assessed for truth without additional information.
  • Given f(0) = f(400), it is incorrect because it suggests the temperature of the oven at the beginning and at 400 minutes is the same, which is unlikely given the context. Instead, it may suggest that the initial temperature and the temperature after the oven has been off for while are the same.
  • Given f(5) is again incomplete without further information presented.
  • It is unlikely that f(30) = f(45) because typically, 30 and 45 minutes represent different times and we expect temperature to be stable within that period as the oven maintains its temperature during cooking.
  • It is likely that f(30) = f(45) since once the oven reaches its desired temperature, it should maintain this steady temperature while cooking the food, until turned off.

We can conclude that the oven's temperature function f(t) likely increases to the desired temperature within 10 minutes and remains steady while cooking, which aligns with typical cooking temperatures for ovens.

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