To determine the student's final grade for the semester based on the given categories and their respective weights and grades, we need to follow these steps:
1. Identify the weights and corresponding grades:
- Quiz: [tex]\(30 \%\)[/tex], Grade: [tex]\(75\)[/tex]
- Labs: [tex]\(15 \%\)[/tex], Grade: [tex]\(68\)[/tex]
- Exams: [tex]\(50 \%\)[/tex], Grade: [tex]\(82\)[/tex]
- Attendance: [tex]\(5 \%\)[/tex], Grade: [tex]\(30\)[/tex]
2. Convert the percentage weights to decimal form:
- Quiz: [tex]\(30 \% = 0.30\)[/tex]
- Labs: [tex]\(15 \% = 0.15\)[/tex]
- Exams: [tex]\(50 \% = 0.50\)[/tex]
- Attendance: [tex]\(5 \% = 0.05\)[/tex]
3. Calculate the weighted contribution of each category to the final grade:
- Quiz: [tex]\( \text{Weight} \times \text{Grade} = 0.30 \times 75 = 22.5\)[/tex]
- Labs: [tex]\( \text{Weight} \times \text{Grade} = 0.15 \times 68 = 10.2\)[/tex]
- Exams: [tex]\( \text{Weight} \times \text{Grade} = 0.50 \times 82 = 41.0\)[/tex]
- Attendance: [tex]\( \text{Weight} \times \text{Grade} = 0.05 \times 30 = 1.5\)[/tex]
4. Sum the contributions from all categories:
[tex]\[
22.5 + 10.2 + 41.0 + 1.5 = 75.2
\][/tex]
Therefore, the student's final grade for the semester is [tex]\(75.2\)[/tex].
This matches the answer provided in the options given. Thus, the final grade best represented by the calculations is:
75.2
