https://file.aiquickdraw.com/mathbot/file/17271903380057i8lsrng.jpg

The image you have uploaded contains a mathematics and statistics question sheet. I'll help break down the questions based on what's visible.

### 1. The first question (1.a) involves:
- A set of students taking both *Statistics* and *Mathematics* exams.
- The problem provides:
  - 170 students passed either Mathematics or Statistics.
  - 60 students failed Statistics.
  - 70 students failed Mathematics.
  - 100 students passed both Mathematics and Statistics.
  
The question asks for the **total number of students** who took the exam.

#### Steps to solve:
- Use the principle of inclusion and exclusion to find the total number of students, based on the given numbers.

---

### 2. The second question (1.b) deals with set operations:
- You are given:
  - \( U = \) Set of natural numbers less than 10
  - \( A = \{1, 3, 5, 6\} \)
  - \( B = \{2, 5, 7, 8\} \)
  - \( C = \{1, 5, 6, 8\} \)

- You need to perform the following operations:
  1. \( (A \cap B)^\prime - C \)
  2. \( B^\prime - (A \cup C)^\prime \)

Also, you're asked to **solve and draw the Venn diagram** for these operations.

---

### 3. The second main question (2) is related to economics, focusing on demand and supply:
- You're given the demand function \( D = -2Q + 250 \) and that the market equilibrium occurs when the price is 160.
- When the price is 170, the number of units supplied is 50.

The sub-questions include:
- Finding the **supply function**.
- Determining **how many units are demanded** at a certain price.
- Calculating the **effect of a government subsidy** of 20 per unit on the supply and the **total amount enjoyed by consumers**.

---

Would you like me to solve any specific part of this question sheet in detail, or provide a full solution to one of the problems? Let me know if you'd prefer details for a specific one.

---

**Follow-up questions:**
1. How would you solve for the total number of students in the first part of question 1?
2. What approach do you take to handle set operations and Venn diagrams in question 1(b)?
3. How would you determine the supply function based on the given data in question 2(a)?
4. How does a subsidy impact the market in terms of supply and demand?
5. Can you identify the relationship between demand and price from the given equation in question 2?

**Tip:** For complex set operations, it's often helpful to list out the elements of each set and work step by step, particularly when performing complement and difference operations.

A problem set involving statistics, set theory, and economics, asking about the number of students passing exams, set operations, and demand/supply functions in market equilibrium.

This problem involves determining the number of students passing Statistics and Mathematics exams using inclusion-exclusion, solving set theory operations with Venn diagrams, and finding the market equilibrium using supply and demand functions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation