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Many colleges assign numerical points to grades as [tex]$A-4$[/tex], [tex]$B-3$[/tex], [tex]$C-2$[/tex], [tex]$D-1$[/tex], and [tex]$F-0$[/tex]. Find the grade point average for the following semester grade report.

\begin{tabular}{c|c|c}
Course & Credits & Grade \\
\hline
Math & 5 & A \\
English & 5 & B \\
Physics & 4 & F \\
German & 4 & D \\
History & 4 & F \\
\end{tabular}

The grade point average is [tex]$\square$[/tex] (Round to the nearest hundredth.)



Answer :

GinnyAnswer
To find the grade point average (GPA), we follow these steps:

1. Identify the grade points associated with each grade:
- [tex]\(A = 4\)[/tex]
- [tex]\(B = 3\)[/tex]
- [tex]\(C = 2\)[/tex]
- [tex]\(D = 1\)[/tex]
- [tex]\(F = 0\)[/tex]

2. Determine the total number of credits and the total grade points earned:
- Math:
- Credits: 5
- Grade: A
- Grade Points: [tex]\(5 \times 4 = 20\)[/tex]
- English:
- Credits: 5
- Grade: B
- Grade Points: [tex]\(5 \times 3 = 15\)[/tex]
- Physics:
- Credits: 4
- Grade: F
- Grade Points: [tex]\(4 \times 0 = 0\)[/tex]
- German:
- Credits: 4
- Grade: D
- Grade Points: [tex]\(4 \times 1 = 4\)[/tex]
- History:
- Credits: 4
- Grade: F
- Grade Points: [tex]\(4 \times 0 = 0\)[/tex]

3. Calculate the total credits and the total grade points:
- Total Credits: [tex]\(5 + 5 + 4 + 4 + 4 = 22\)[/tex]
- Total Grade Points: [tex]\(20 + 15 + 0 + 4 + 0 = 39\)[/tex]

4. Compute the GPA:
- GPA [tex]\(= \frac{\text{Total Grade Points}}{\text{Total Credits}}\)[/tex]
- GPA [tex]\(= \frac{39}{22}\)[/tex]
- GPA [tex]\( \approx 1.77\)[/tex] (rounded to the nearest hundredth)

Thus, the grade point average (GPA) is [tex]\(1.77\)[/tex].

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