A student received the grades for a class with the weighted categories below. Which of the following best represents their final grade for the semester?

\begin{tabular}{|l|l|l|}
\hline
Category & Weight & Grade \\
\hline
Quiz & [tex]$30 \%$[/tex] & 75 \\
\hline
Labs & [tex]$15 \%$[/tex] & 68 \\
\hline
Exams & [tex]$50 \%$[/tex] & 82 \\
\hline
Attendance & [tex]$5 \%$[/tex] & 30 \\
\hline
\end{tabular}

A. 88.7
B. 63.75
C. 75.2
D. 18.8



Answer :

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