To determine the minimum grade needed on the final exam to achieve an overall grade of 83% in the class, we need to use the weighted average formula. Let's breakdown the calculations step-by-step:
### Step 1: Calculate the weighted contributions from Attendance, Tests, and Homework
1. Attendance:
- Grade Earned: 100%
- Weight: 10%
[tex]\[
\text{Weighted Attendance} = 100 \times 0.10 = 10.0
\][/tex]
2. Tests:
- Grade Earned: 80%
- Weight: 30%
[tex]\[
\text{Weighted Tests} = 80 \times 0.30 = 24.0
\][/tex]
3. Homework:
- Grade Earned: 95%
- Weight: 20%
[tex]\[
\text{Weighted Homework} = 95 \times 0.20 = 19.0
\][/tex]
### Step 2: Sum of the current weighted grades
[tex]\[
\text{Total Weighted Grades} = \text{Weighted Attendance} + \text{Weighted Tests} + \text{Weighted Homework} = 10.0 + 24.0 + 19.0 = 53.0
\][/tex]
### Step 3: Determine the total needed to reach the overall target
[tex]\[
\text{Overall Target} = 83
\][/tex]
[tex]\[
\text{Remaining Needed} = \text{Overall Target} - \text{Total Weighted Grades} = 83.0 - 53.0 = 30.0
\][/tex]
### Step 4: Calculate the required grade on the Final Exam
Since the final exam weight is 40%, we use the remaining needed divided by this weight:
[tex]\[
\text{Final Exam Grade Required} = \frac{\text{Remaining Needed}}{\text{Final Exam Weight}} = \frac{30.0}{0.40} = 75.0
\][/tex]
Thus, the minimum grade needed on the final exam to earn an overall grade of 83% in the class is [tex]\(75 \%\)[/tex].
### Answer:
[tex]\[
\boxed{75 \%}
\][/tex]
