To determine the minimum grade required on the final exam to achieve an overall grade of 85% in the class, we need to calculate the contributions of the different grade categories and their weights. Let's go through the steps:
1. Calculate the weighted grade for attendance:
[tex]\[
\text{Weighted Attendance} = \text{Grade Earned} \times \text{Weight by Category}
\][/tex]
[tex]\[
\text{Weighted Attendance} = 100\% \times 0.10 = 10.0
\][/tex]
2. Calculate the weighted grade for tests:
[tex]\[
\text{Weighted Tests} = \text{Grade Earned} \times \text{Weight by Category}
\][/tex]
[tex]\[
\text{Weighted Tests} = 70\% \times 0.30 = 21.0
\][/tex]
3. Calculate the weighted grade for homework:
[tex]\[
\text{Weighted Homework} = \text{Grade Earned} \times \text{Weight by Category}
\][/tex]
[tex]\[
\text{Weighted Homework} = 80\% \times 0.20 = 16.0
\][/tex]
4. Calculate the total current weighted grade excluding the final exam:
[tex]\[
\text{Total Current Weighted Grade} = \text{Weighted Attendance} + \text{Weighted Tests} + \text{Weighted Homework}
\][/tex]
[tex]\[
\text{Total Current Weighted Grade} = 10.0 + 21.0 + 16.0 = 47.0
\][/tex]
5. Determine the overall target grade and the final exam's weight:
[tex]\[
\text{Target Overall Grade} = 85.0
\][/tex]
[tex]\[
\text{Final Exam Weight} = 0.40
\][/tex]
6. Calculate the minimum grade needed on the final exam to achieve the overall target grade:
[tex]\[
\text{Needed Final Exam Grade} = \frac{\text{Target Overall Grade} - \text{Total Current Weighted Grade}}{\text{Final Exam Weight}}
\][/tex]
[tex]\[
\text{Needed Final Exam Grade} = \frac{85.0 - 47.0}{0.40} = \frac{38.0}{0.40} = 95.0
\][/tex]
Therefore, to achieve an overall grade of 85% in the class, the student needs to score a minimum of [tex]\(95\%\)[/tex] on the final exam. Thus, the correct answer is:
[tex]\[
\boxed{95\%}
\][/tex]
