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Today, Madelyn is running a 1010-mile race and using her watch to help with pacing. She will run at a steady pace of 99 minutes per mile, and so she expects to finish the race in 9090 minutes. The function D(m)D(m) represents the distance Madelyn has left to run, in miles, after mm minutes.\newlineWhat is the domain of D(m)D(m)?\newlineChoices:\newline(A)all real numbers from 00 to 1010\newline(B)all whole numbers from 00 to 9090\newline(C)all whole numbers from 00 to 1010\newline(D)all real numbers from 00 to 9090

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Q. Today, Madelyn is running a 1010-mile race and using her watch to help with pacing. She will run at a steady pace of 99 minutes per mile, and so she expects to finish the race in 9090 minutes. The function D(m)D(m) represents the distance Madelyn has left to run, in miles, after mm minutes.\newlineWhat is the domain of D(m)D(m)?\newlineChoices:\newline(A)all real numbers from 00 to 1010\newline(B)all whole numbers from 00 to 9090\newline(C)all whole numbers from 00 to 1010\newline(D)all real numbers from 00 to 9090
  1. Define Domain: Madelyn is running a 1010-mile race at a steady pace of 99 minutes per mile. The function D(m)D(m) represents the distance she has left to run after mm minutes. To find the domain, we need to determine the set of all possible values for mm, which is the time in minutes.
  2. Calculate Expected Finish Time: Since Madelyn runs at a pace of 99 minutes per mile and the race is 1010 miles long, she expects to finish the race in 9090 minutes. Therefore, the minimum time mm can be is 00 minutes (at the start of the race), and the maximum time mm can be is 9090 minutes (at the end of the race).
  3. Determine Domain Range: The domain of D(m)D(m) is the set of all real numbers from 00 to 9090 because time can be measured in fractions of a minute, and Madelyn can be at any point in the race between the start and finish. Therefore, the domain includes all real numbers between 00 and 9090, inclusive.

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