Final answer:
Marlin needs a minimum score of 90 on her final exam to achieve an average of 75 for her AMDM semester grade.
Step-by-step explanation:
To calculate the minimum score Marlin needs on the final exam in her AMDM class to achieve an average of 75 or higher, we first add her current test grades and then factor in the final exam, which counts as three test grades. Her current test grades are 65, 73, 80, 50, 73, and 65. The sum of these grades is 406. To find the needed average, we multiply 75 (the target average) by the total number of test grades, 9 (since the final counts as three), which equals 675. Therefore, the total points needed from all tests including the final is 675. Subtracting Marlin's current total (406) from 675 gives us the total points needed on the final. Since the final counts as three tests, we divide this number by 3 to find the minimum score needed on the final exam.
The calculation goes as follows:
- Sum of current grades: 65 + 73 + 80 + 50 + 73 + 65 = 406
- Total needed for an average of 75: 75 * 9 = 675
- Total points needed on the final: 675 - 406 = 269
- Minimum final exam score: 269 / 3 ≈ 90
Therefore, the minimum score Marlin needs on her final exam to earn a 75 average for the semester is 90 (rounded to the nearest whole number).