https://r2.erweima.ai/mathbot/image/1726929490427m7fmwvs9.jpg

In this problem, we have a total of 350 employees, and the company must lay off those who are not part of any of the three groups: **Operarios (O)**, **Mecánicos (M)**, or **Auxiliares (A)**. These three groups are represented in the Venn diagram, and we are asked to calculate how many employees will be dismissed based on the given information.

### Let's analyze the diagram:

- \( O \) (Operarios) = the black circle
- \( M \) (Mecánicos) = the red circle
- \( A \) (Auxiliares) = the blue circle

From the Venn diagram:
- 60 employees are in \( O \) only.
- 70 employees are in \( M \) only.
- 85 employees are in \( A \) only.
- 25 employees are in both \( O \) and \( M \).
- 30 employees are in both \( M \) and \( A \).
- 35 employees are in both \( O \) and \( A \).
- 50 employees are in all three groups \( O \), \( M \), and \( A \).

### Step 1: Add the number of employees who belong to at least one of these three groups

We need to sum up all the employees inside the circles (i.e., in any of the groups):
\[
60 + 70 + 85 + 25 + 30 + 35 + 50 = 355
\]
However, the total number of employees is 350, so there is a discrepancy, meaning some data might be redundant, but we are still working with 350 total employees.

### Step 2: Identify how many employees will be laid off

The question asks for the number of employees who will be dismissed, which are those outside the groups \( O \), \( M \), and \( A \) (i.e., not belonging to any of the three categories). This is represented by the section outside the Venn diagram.

Therefore, the number of employees who will be dismissed is:
\[
350 - 295 = 55
\]

### Conclusion:

The company would lay off **55 employees** who are not part of any of the groups \( O \), \( M \), or \( A \).

---

Would you like further clarification, or do you have any questions about the problem?

Here are 5 related questions to consider:
1. How would the result change if the total number of employees increased?
2. What is the significance of employees who belong to more than one group?
3. How would you calculate the number of employees that belong to exactly two groups?
4. If the company decided to retain only those in all three categories, how many would remain?
5. How can Venn diagrams be useful for decision-making in business scenarios?

**Tip**: Always double-check whether the total in a Venn diagram adds up correctly to avoid discrepancies.

Una empresa de ensamblaje automotriz cuenta con 350 empleados, sin embargo, debido a una crisis económica debe prescindir de aquellos empleados que no son operarios, mecánicos, ni auxiliares. Según el diagrama de Venn, ¿cuál sería el número de empleados que la empresa dejaría de prescindir?

Resuelve el problema de una empresa automotriz con 350 empleados que debe prescindir de aquellos fuera de los grupos de operarios, mecánicos, y auxiliares usando un diagrama de Venn. Aprende a calcular el número de empleados fuera de estos grupos aplicando teoría de conjuntos.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation