1. **Stating the problem:** We are given the number of students in each grade category and the corresponding sector angles in a pie chart. We need to identify which grade's sector angle is incorrectly labeled. 2. **Data given:** - Cemerlang (Distinction): 15 students, angle labeled 120° - Kepujian (Credit): 10 students, angle labeled 80° - Lulus (Pass): 12 students, angle labeled 96° - Gagal (Fail): 8 students, angle labeled 64° 3. **Formula for sector angle:** The angle of a sector in a pie chart is given by: $$\text{Angle} = \frac{\text{Number of students in category}}{\text{Total number of students}} \times 360^\circ$$ 4. **Calculate total number of students:** $$15 + 10 + 12 + 8 = 45$$ 5. **Calculate expected angles:** - Cemerlang: $$\frac{15}{45} \times 360 = 120^\circ$$ - Kepujian: $$\frac{10}{45} \times 360 = 80^\circ$$ - Lulus: $$\frac{12}{45} \times 360 = 96^\circ$$ - Gagal: $$\frac{8}{45} \times 360 = 64^\circ$$ 6. **Compare calculated angles with labeled angles:** All labeled angles match the calculated angles exactly. 7. **Conclusion:** None of the sector angles are incorrectly labeled based on the data provided. --- **Next problem:** 1. **Problem:** Given sets \( \xi = \{x: x \text{ is an integer and } 4 \leq x \leq 14\} \), \( P = \{\text{two-digit numbers}\} \), and \( Q = \{\text{multiples of 2}\} \), find \( n(P \cap Q)' \). 2. **Interpretation:** - \( P \) is the set of two-digit numbers in \( \xi \). - \( Q \) is the set of even numbers in \( \xi \). - \( P \cap Q \) is the set of numbers that are two-digit and even. - \( n(P \cap Q)' \) is the number of elements not in \( P \cap Q \) but in \( \xi \). 3. **List elements of \( \xi \):** $$\{4,5,6,7,8,9,10,11,12,13,14\}$$ 4. **Identify two-digit numbers in \( \xi \):** Two-digit numbers are from 10 to 14: $$P = \{10,11,12,13,14\}$$ 5. **Identify multiples of 2 in \( \xi \):** $$Q = \{4,6,8,10,12,14\}$$ 6. **Find \( P \cap Q \):** Numbers that are two-digit and even: $$P \cap Q = \{10,12,14\}$$ 7. **Find complement \( (P \cap Q)' \) in \( \xi \):** Elements in \( \xi \) but not in \( P \cap Q \): $$\{4,5,6,7,8,9,11,13\}$$ 8. **Count elements in \( (P \cap Q)' \):** $$n(P \cap Q)' = 8$$ --- **Next problem:** 1. **Problem:** Steven invests 1000 units each month from March to July in shares with given unit prices. Calculate the average cost per unit of shares purchased. 2. **Data:** | Month | March | April | May | June | July | |-------|-------|-------|-----|------|------| | Price | 2.60 | 2.40 | 2.14| 2.32 | 2.45 | 3. **Calculate units bought each month:** Units = Investment / Price - March: $$\frac{1000}{2.60} \approx 384.6154$$ - April: $$\frac{1000}{2.40} = 416.6667$$ - May: $$\frac{1000}{2.14} \approx 467.2897$$ - June: $$\frac{1000}{2.32} \approx 431.0345$$ - July: $$\frac{1000}{2.45} \approx 408.1633$$ 4. **Total units bought:** $$384.6154 + 416.6667 + 467.2897 + 431.0345 + 408.1633 = 2107.7696$$ 5. **Total investment:** $$1000 \times 5 = 5000$$ 6. **Average cost per unit:** $$\frac{5000}{2107.7696} \approx 2.37$$ --- **Next problem:** 1. **Problem:** Which degree sequence can be used to draw a simple graph? 2. **Rule:** The sum of degrees must be even (Handshaking Lemma). 3. **Check each option:** - A: 3+2+2+1+3 = 11 (odd) - Not possible - B: 2+4+4+5+2 = 17 (odd) - Not possible - C: 2+1+1+3+3+2 = 12 (even) - Possible - D: 3+2+1+4+2+1 = 13 (odd) - Not possible 4. **Answer:** Option C can be used to draw a simple graph. --- **Final answers:** - Sector angle wrongly labeled: None - \( n(P \cap Q)' = 8 \) - Average cost per unit: 2.37 - Degree sequence for simple graph: Option C