Answer:
Explanation:
To find the number of teachers who can teach all three subjects, we need to use the principle of inclusion-exclusion based on the provided information. Let's break down the given data and use a Venn diagram:
- The total number of vacancies for English language teachers: 24.
- The total number of vacancies for history teachers: 22.
- The total number of vacancies for fine arts teachers: 18.
- The number of vacancies for both English language and history: 13.
- The number of vacancies for both history and fine arts: 70.
- The number of vacancies for both English language and fine arts: 9.
Now we can create a Venn diagram to visualize the information:
__________
| H |
E |____12____| F
| 1│ |
|______│_____|
E: English language
H: History
F: Fine arts
In the diagram:
- The number written inside the English language circle represents the number of vacancies exclusively for English language teachers, which is 24.
- The number written inside the history circle represents the number of vacancies exclusively for history teachers, which is 22.
- The number written inside the fine arts circle represents the number of vacancies exclusively for fine arts teachers, which is 18.
Now, let's fill in the overlapping areas:
- The overlapping area between English language and history represents the vacancies for teachers who can teach both subjects (13).
- The overlapping area between history and fine arts represents the vacancies for teachers who can teach both subjects (70).
- The overlapping area between English language and fine arts represents the vacancies for teachers who can teach both subjects (9).
Finally, we need to find the number of teachers who can teach all three subjects, which is the overlapping area in the center of the Venn diagram.
Looking at the diagram, we can see that this overlapping area is represented by the number 1.
Therefore, the number of teachers who can still teach all three subjects would be 1.