Question

your course grade is based on one midterm that counts as 20% of your final grade, a set of quizzes that counts as 15% of your final grade, a set of homework assignments that counts as 35% of your final grade, and a final exam that counts as 30% of your final grade. your midterm score is 84, your quiz score is 73, your homework score is 93, and your final exam score is 77. what is your overall final score? options: a. 83.95, b. 81.75, c. 82.85, d. 83.40

Explanation:

Step1: Calculate midterm contribution

Midterm score: 84, weight: 20% = 0.2
Contribution: \( 84 \times 0.2 = 16.8 \)

Step2: Calculate quizzes contribution

Quizzes score: 73, weight: 15% = 0.15
Contribution: \( 73 \times 0.15 = 10.95 \)

Step3: Calculate homework contribution

Homework score: 93, weight: 35% = 0.35
Contribution: \( 93 \times 0.35 = 32.55 \)

Step4: Calculate final exam contribution

Final exam score: 77, weight: 30% = 0.3
Contribution: \( 77 \times 0.3 = 23.1 \)

Step5: Sum all contributions

Total: \( 16.8 + 10.95 + 32.55 + 23.1 \)
First, \( 16.8 + 10.95 = 27.75 \)
Then, \( 27.75 + 32.55 = 60.3 \)
Finally, \( 60.3 + 23.1 = 83.4 \) Wait, but let's check again. Wait, maybe I miscalculated? Wait, no, let's recalculate each step:

Wait, midterm: 84*0.2=16.8

Quizzes:730.15: 730.1=7.3, 73*0.05=3.65, total 10.95

Homework:930.35: 930.3=27.9, 93*0.05=4.65, total 32.55

Final exam:77*0.3=23.1

Now sum: 16.8 + 10.95 = 27.75; 27.75 + 32.55 = 60.3; 60.3 +23.1=83.4. But the options have D as 83.40, which matches. Wait, but maybe I made a mistake in weights? Wait the problem says: midterm 20%, quizzes 15%, homework 35%, final exam 30%. Let's check the total weight: 20+15+35+30=100, correct. So the calculation is:

\( (84 \times 0.2) + (73 \times 0.15) + (93 \times 0.35) + (77 \times 0.3) \)

Calculate each term:

84*0.2 = 16.8

73*0.15 = 10.95

93*0.35 = 32.55

77*0.3 = 23.1

Sum: 16.8 + 10.95 = 27.75; 27.75 + 32.55 = 60.3; 60.3 +23.1=83.4, which is 83.40, option D.

Answer:

D. 83.40