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The problem from the image is asking to calculate the mean score of five additional students, given the mean score of a group of 30 students and the combined mean when these five students are added. Here's a breakdown of how to approach it:

### Problem Setup:

- The mean score of 30 students is 7.7.
- When the scores of 5 additional students are added, the new mean becomes 8.0.
- We need to find the mean score of these 5 additional students.

### Let:
- \( n_1 = 30 \) be the number of students in the first group.
- \( \text{mean}_1 = 7.7 \) be the mean of the first group of 30 students.
- \( n_2 = 5 \) be the number of students in the second group (the additional students).
- \( \text{mean}_2 \) is the unknown mean score of the second group (what we're solving for).
- The combined group has \( n_1 + n_2 = 35 \) students, and the combined mean is 8.0.

### Equation Setup:

We know that the total score of each group is the number of students multiplied by their respective means.

1. Total score of the first group = \( 30 \times 7.7 = 231 \).
2. Total score of the second group = \( 5 \times \text{mean}_2 \).
3. Combined total score = \( 35 \times 8.0 = 280 \).

Now, setting up the equation for the combined group:

\[
231 + 5 \times \text{mean}_2 = 280
\]

### Solving for \( \text{mean}_2 \):

\[
5 \times \text{mean}_2 = 280 - 231 = 49
\]

\[
\text{mean}_2 = \frac{49}{5} = 9.8
\]

So, the mean score of the additional 5 students is **9.8**, which corresponds to option **a**.

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Would you like further clarification or details on this solution?

Here are 5 related questions for further exploration:
1. How is the combined mean of two groups calculated in general?
2. What happens to the overall mean when the second group's mean is lower than the first?
3. Can you derive the same result using a weighted average formula?
4. How does the size of the groups affect the combined mean?
5. What if there were more than two groups? How would the calculation change?

**Tip:** Always check if you can break down the problem into smaller parts (like totals) when dealing with means and averages.

Mean ulangan Matematika dari 30 siswa adalah 7.7. Jika nilai ulangan Matematika dari 5 orang siswa lainnya digabungkan, mean ulangan Matematika dari sekelompok siswa itu menjadi 8.0. Nilai mean ulangan Matematika dari 5 siswa yang digabungkan itu adalah ....

Learn how to calculate the mean score of 5 additional students when the combined mean score of 30 students changes from 7.7 to 8.0. This problem explores key concepts such as algebraic mean calculation and equation solving, suitable for Grades 8-9.

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