frees \
NATH 136 3. A survey of 10 students a Brookdale produced the following reals
Lab 1.4 61 lke ENGL 121
ere Go S4lke MATH 131
Rael Gree: 57k CHEM 101
3k both ENGL 121 and MATH 131
ee — 15

Question

frees \
NATH 136 3. A survey of 10 students a Brookdale produced the following reals
Lab 1.4 61 lke ENGL 121
ere Go S4lke MATH 131
Rael Gree: 57k CHEM 101
3k both ENGL 121 and MATH 131
ee  — 15 ike bolh MATH 131 and CHEM 101
17 ike bath ENGL 121 nd CHEM 101
ee a Ske al tree courses
; 4. Us the Venn diagram belo 0 show the numbers f peopl who belo in cach
1: Usedhe folloving formation to fd he unter of cess isch ofthe eons  Remeibs 1o siblac any ave hefre ating be umber othe
ih sion mark (0) 3204) 00,8) = 1200 63. ft fi
ENGL 121 MATH 131
Li GE 01
Region 1: Regond Region.
bo. Tow many stents donot ike any of the subjecs?
Region: Region's _ Regond
Reid __ Reins How many stadets donot ike MATH 1317
2. A survey of 800 Brookdale sudens showed that 245 take th rin, 05 tke the bus.
nd 335 do not take ihe he rain or the bus. Use the Venn diagram to help you a How many students ke only ve sbjec?
determine the answers th following questions
2. How many commuters take bth th rin andthe bus? . Tow many students ike MATH 131 or CHEM 101, but not ENGLI21
b. How many commuters ake oly th rain?
© How many students ike MATH 131 only?
& How many students ike ENGLI2! and MATH 1

VIPSolutions · Accepted Answer

Let's break down the questions and provide guidance or answers for each.

---

### **1. Venn Diagram Regions**

Given:
- $ n(U) = 3200 $
- $ n(A) = 400 $
- $ n(B) = 1200 $
- $ n(C) = 650 $

#### Venn Diagram Regions:
The diagram has 8 regions. Let's number them as follows (from left to right, top to bottom):

1. Only $A$
2. Only $B$
3. Only $C$
4. $A \cap B$ (not $C$)
5. $A \cap C$ (not $B$)
6. $B \cap C$ (not $A$)
7. $A \cap B \cap C$
8. Outside all sets

Given in the diagram:
- Center ($A \cap B \cap C$): 75
- $A \cap C$ only: 95
- $B \cap C$ only: 180
- $C$ only: 210

We need to solve for the other regions.

Let:
- Region 1 ($A$ only): $x$
- Region 2 ($B$ only): $y$
- Region 3 ($A \cap B$ only): $z$
- Region 8 (outside all): $w$

Let's write equations from the sets:

- $n(A) = x + 95 + 75 + z$
- $n(B) = y + 180 + 75 + z$
- $n(C) = 210 + 95 + 180 + 75$
- $n(U) = x + y + z + 95 + 75 + 180 + 210 + w$

You can solve for each variable by plugging in the numbers and solving step by step.

---

### **2. Commuter Survey**

Given:
- Total = 800
- Train = 245
- Bus = 305
- Neither = 335

Let $x$ be the number that take both train and bus.

Equation:
$$
245 + 305 - x + 335 = 800
$$
$$
550 - x + 335 = 800
$$
$$
885 - x = 800 \implies x = 85
$$

**a. Both train and bus:** **85**

**b. Only train:** $245 - 85 = 160$

---

### **3. Student Survey**

Given:
- ENGL 121: 61
- MATH 131: 54
- CHEM 101: 57
- ENGL 121 & MATH 131: 9
- ENGL 121 & CHEM 101: 15
- MATH 131 & CHEM 101: 17
- All three: 5

Let’s use inclusion-exclusion to fill in the Venn diagram:

- Only ENGL 121: $61 - 9 - 15 - 5 = 32$
- Only MATH 131: $54 - 9 - 17 - 5 = 23$
- Only CHEM 101: $57 - 15 - 17 - 5 = 20$
- ENGL 121 & MATH 131 only: $9 - 5 = 4$
- ENGL 121 & CHEM 101 only: $15 - 5 = 10$
- MATH 131 & CHEM 101 only: $17 - 5 = 12$
- All three: 5

Now, you can answer the questions:

b. **Do not like any:**  
Total liking at least one = 32 + 23 + 20 + 4 + 10 + 12 + 5 = 106  
So, $150 - 106 = 44$

c. **Do not like MATH 131:**  
Sum regions not including MATH 131: Only ENGL 121 (32), Only CHEM 101 (20), ENGL 121 & CHEM 101 only (10) = **62**

d. **Only one subject:**  
ENGL 121 only (32) + MATH 131 only (23) + CHEM 101 only (20) = **75**

e. **MATH 131 or CHEM 101, but not ENGL 121:**  
MATH 131 only (23) + CHEM 101 only (20) + MATH 131 & CHEM 101 only (12) = **55**

f. **MATH 131 only:** **23**

g. **ENGL 121 and MATH 131 but not science:**  
ENGL 121 & MATH 131 only = **4**

h. **Exactly two subjects:**  
ENGL 121 & MATH 131 only (4), ENGL 121 & CHEM 101 only (10), MATH 131 & CHEM 101 only (12) = **26**

---

If you need more detailed calculations or help filling in the Venn diagrams for #1, let me know!

✨ VIPSolutions

Question:

Final Answer:

📢 Instructions:

Study Help, Fast Answers

✨ VIPSolutions

Question:

Final Answer:

📢 Instructions:

Related Answers

Study Help, Fast Answers