To determine the minimum grade needed on the final exam to achieve an overall grade of 85%, we need to calculate the contributions of the existing grades and find out what is required from the final exam.
1. Attendance Grade Contribution:
- Grade: [tex]\(100 \%\)[/tex]
- Weight: [tex]\(10 \%\)[/tex]
- Contribution: [tex]\[
100 \% \times 10 \% = 10.0 \%
\][/tex]
2. Tests Grade Contribution:
- Grade: [tex]\(70 \%\)[/tex]
- Weight: [tex]\(30 \%\)[/tex]
- Contribution: [tex]\[
70 \% \times 30 \% = 21.0 \%
\][/tex]
3. Homework Grade Contribution:
- Grade: [tex]\(80 \%\)[/tex]
- Weight: [tex]\(20 \%\)[/tex]
- Contribution: [tex]\[
80 \% \times 20 \% = 16.0 \%
\][/tex]
4. Total Contribution from Attendance, Tests, and Homework:
[tex]\[
10.0 \% + 21.0 \% + 16.0 \% = 47.0 \%
\][/tex]
5. Required Contribution from Final Exam:
- Target Overall Grade: [tex]\(85 \%\)[/tex]
- Required Contribution: [tex]\[
85 \% - 47.0 \% = 38.0 \%
\][/tex]
6. Minimum Grade Needed on the Final Exam:
- Weight of Final Exam: [tex]\(40 \%\)[/tex]
- Minimum Grade: [tex]\[
\frac{38.0 \%}{40 \%} = 95 \%
\][/tex]
Therefore, the minimum grade needed on the final exam to earn an overall grade of 85% in the class is [tex]\(95\%\)[/tex]. The correct answer is:
[tex]\[
\boxed{95 \%}
\][/tex]
