Answer:
93.63
Therefore, she need to get a minimum of 93.63 out of 100 in the final exam
Step-by-step explanation:
Given;
Each midterm exam = 15% of total grade
Final exam = 40% of total grade
Midterm scores = 75, 77, 81 and 84 (out of a possible 100)
Total midterm score = 75+77+81+84 = 317
To determine the grade of the four midterm exams in the total score;
We need to find the 15% of the midterm score;
= 15% of 317
= 0.15×317
= 47.55 %
To get a minimum score of 85 % of the total score, the amount of the total score to be secured in the final exam is;
Final exam = 85% - 47.55% = 37.45%
Since final exam is 40% of the total score;
It means she need to get 37.45% out of 40% of the final exam.
Converting it to a score of 100;
Final exam score = 37.45/40 × 100
Final exam score = 93.63
Therefore, she need to get a minimum of 93.63 out of 100 in the final exam
, where r is a residual. Plugging the pair into the formula, we obtain that 
and r=0.5