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Part 1
A​ student's course grade is based on one midterm that counts as 2020​% of his final​ grade, one class project that counts as 1010​% of his final​ grade, a set of homework assignments that counts as 3535​% of his final​ grade, and a final exam that counts as 3535​% of his final grade. His midterm score is 7272​, his project score is 8787​, his homework score is 7575​, and his final exam score is 8080. What is his overall final​ score? What letter grade did he earn​ (A, B,​ C, D, or​ F)? Assume that a mean of 90 or above is an​ A, a mean of at least 80 but less than 90 is a​ B, and so on.
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Part 1
His overall final score is enter your response here.

We can calculate the student's overall final score by taking the weighted average of each component based on the percentage it contributes to the final grade. Let's break it down:

### Components:
1. **Midterm**: 20% of final grade
2. **Project**: 10% of final grade
3. **Homework assignments**: 35% of final grade
4. **Final exam**: 35% of final grade

### Scores:
- Midterm: 72
- Project: 87
- Homework: 75
- Final exam: 80

### Weighted Final Score Calculation:
To find the weighted final score, we multiply each score by its corresponding weight and then sum the results:

\[
\text{Overall Score} = (72 \times 0.20) + (87 \times 0.10) + (75 \times 0.35) + (80 \times 0.35)
\]

Now let's calculate:

\[
72 \times 0.20 = 14.4
\]
\[
87 \times 0.10 = 8.7
\]
\[
75 \times 0.35 = 26.25
\]
\[
80 \times 0.35 = 28
\]

Adding them together:

\[
14.4 + 8.7 + 26.25 + 28 = 77.35
\]

### Final Score:
The overall final score is **77.35**.

### Letter Grade:
According to the grading scale provided:
- A: 90 or above
- B: 80 to less than 90
- C: 70 to less than 80
- D: 60 to less than 70
- F: below 60

Since the overall score is 77.35, the student earns a **C**.

Would you like more details or have any further questions?

### Related Questions:
1. How would the final score change if the homework weight was reduced?
2. What would the overall score be if the student scored higher on the midterm?
3. How does changing the weight of the final exam affect the overall score?
4. What score would the student need on the final exam to earn a B?
5. How would the letter grade change if the grading scale used plus/minus grading?

### Tip:
Weighted averages are crucial when different components of a score have unequal importance, so always ensure to use the correct weight for each component.

A student's course grade is based on one midterm that counts as 20% of his final grade, one class project that counts as 10% of his final grade, a set of homework assignments that counts as 35% of his final grade, and a final exam that counts as 35% of his final grade. His midterm score is 72, his project score is 87, his homework score is 75, and his final exam score is 80. What is his overall final score? What letter grade did he earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of at least 80 but less than 90 is a B, and so on.

Learn how to calculate a student's overall final score and letter grade based on weighted averages. This problem involves midterm, project, homework, and final exam scores, and demonstrates the use of the weighted average formula. Suitable for students in Grades 9-12.

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