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In one common system for finding a grade-point average, or GPA, the grades are assigned the following points:

[tex]\[ A=4, \, B=3, \, C=2, \, D=1, \, F=0 \][/tex]

[tex]\[
\begin{tabular}{|c|c|}
\hline
Grades & \# of Credit Hours \\
\hline
B & 5 \\
B & 4 \\
B & 2 \\
C & 3 \\
\hline
\end{tabular}
\][/tex]

The GPA is calculated by multiplying the number of credit hours for a course by the number assigned to each grade, and then adding these products. Then divide this sum by the total number of credit hours. Because each course grade is weighted according to the number of credits of the course, GPA is called a weighted mean.

Calculate the GPA for this transcript:

The grade point average is 2.79. (Round to the nearest hundredth as needed.)

Sagot :

GinnyAnsweridn
To calculate the GPA (Grade Point Average) for the given transcript, we need to follow a systematic step-by-step process. Here is how it's done:

1. List the Grades and Corresponding Credit Hours:
[tex]\[ \begin{array}{|c|c|} \hline \text{Grade} & \text{Credit Hours} \\ \hline B & 5 \\ B & 4 \\ B & 2 \\ C & 3 \\ \hline \end{array} \][/tex]

2. Determine the Grade Points for Each Grade:
Using the given system:
[tex]\[ \begin{align*} A &= 4 \\ B &= 3 \\ C &= 2 \\ D &= 1 \\ F &= 0 \\ \end{align*} \][/tex]

3. Calculate the Weighted Grade Points for Each Course:
Multiply each grade's point value by the number of credit hours for that course.
[tex]\[ \begin{align*} \text{For Grade B (3 points) and 5 credit hours:} & \quad 3 \times 5 = 15 \\ \text{For Grade B (3 points) and 4 credit hours:} & \quad 3 \times 4 = 12 \\ \text{For Grade B (3 points) and 2 credit hours:} & \quad 3 \times 2 = 6 \\ \text{For Grade C (2 points) and 3 credit hours:} & \quad 2 \times 3 = 6 \\ \end{align*} \][/tex]

4. Sum the Weighted Grade Points:
Add all the products from the previous step.
[tex]\[ 15 + 12 + 6 + 6 = 39 \][/tex]

5. Calculate the Total Number of Credit Hours:
Sum all the credit hours.
[tex]\[ 5 + 4 + 2 + 3 = 14 \][/tex]

6. Compute the GPA:
Divide the total sum of the weighted grade points by the total number of credit hours.
[tex]\[ \text{GPA} = \frac{39}{14} \approx 2.7857142857142856 \][/tex]

7. Round the GPA to the Nearest Hundredth:
To match typical GPA reporting conventions, round the result to two decimal places.
[tex]\[ \text{GPA Rounded} \approx 2.79 \][/tex]

Therefore, the GPA for this transcript, rounded to the nearest hundredth, is 2.79.
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