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This image presents a math problem in Hebrew. The problem concerns two schools and their students' average grades.

Here’s a translation of the problem:

**Question 12:**  
In two schools, an exam was conducted:
- In the first school, there are 200 students. The average score of the students was 72.
- In the second school, there are 600 students. The average score of the students was 8 points higher than that of the first school.

A. What is the average score for all students in both schools together?

B. After 40 students from the first school joined the second school, their average score was 93. What is the new average score in the second school?

Let me solve this step by step:

### Part A:
We need to find the overall average score of both schools combined.

- First school: 200 students, average score 72.
- Second school: 600 students, average score 72 + 8 = 80.

The combined average score \( M \) is calculated by the formula for weighted averages:

\[
M = \frac{n_1 \cdot M_1 + n_2 \cdot M_2}{n_1 + n_2}
\]

where:
- \( n_1 = 200 \) (number of students in the first school),
- \( M_1 = 72 \) (average score of the first school),
- \( n_2 = 600 \) (number of students in the second school),
- \( M_2 = 80 \) (average score of the second school).

Substituting the values:

\[
M = \frac{200 \cdot 72 + 600 \cdot 80}{200 + 600}
\]

Let me calculate this.The combined average score for all the students in both schools together is **78**.

### Part B:
40 students from the first school, who had an average score of 93, transferred to the second school. We need to find the new average score for the second school after these students joined.

- Original number of students in the second school: 600.
- Average score of the second school before the transfer: 80.
- Number of transferred students: 40.
- Their average score: 93.

The new average score \( M_{\text{new}} \) in the second school is calculated as:

\[
M_{\text{new}} = \frac{n_{\text{old}} \cdot M_{\text{old}} + n_{\text{new}} \cdot M_{\text{new}}}{n_{\text{old}} + n_{\text{new}}}
\]

where:
- \( n_{\text{old}} = 600 \) (number of original students in the second school),
- \( M_{\text{old}} = 80 \) (average score of the second school),
- \( n_{\text{new}} = 40 \) (number of transferred students),
- \( M_{\text{new}} = 93 \) (average score of transferred students).

Let me calculate this.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to walk you through the process for calculating the new average manually, or do you have any other questions?

Here are some related questions:
1. How do weighted averages apply in real-life scenarios?
2. What would happen to the average if more students transferred between schools?
3. Can the average score of a group decrease if new members with higher scores join?
4. How do we calculate the median in a similar situation?
5. What is the difference between the mean and the mode in a data set?

**Tip:** When dealing with averages, remember that each group contributes proportionally to the final result based on its size.

In two schools, an exam was conducted:
- In the first school, there are 200 students. The average score of the students was 72.
- In the second school, there are 600 students. The average score of the students was 8 points higher than that of the first school.

A. What is the average score for all students in both schools together?

B. After 40 students from the first school joined the second school, their average score was 93. What is the new average score in the second school?

Solve a weighted average problem where students transfer between schools, changing the overall average. The problem involves calculating the combined average score and the new average after a transfer of students with different scores.

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