1. Problem 12: A car uses 5 liters of gasoline to travel 40 km. How much gasoline is needed to travel 128 km at the same rate? Step 1: Find the rate of gasoline consumption per km. $$\text{Rate} = \frac{5 \text{ liters}}{40 \text{ km}} = \frac{1}{8} \text{ liters per km}$$ Step 2: Calculate gasoline needed for 128 km. $$\text{Gasoline} = 128 \times \frac{1}{8} = 16 \text{ liters}$$ 2. Problem 13: "Drawing > 1, then it expresses ............................." This is incomplete, so no calculation is possible. 3. Problem 14: Given sets $$A = \{9, 10, 8\}, B = \{4, 9, 7\}, C = \{1, 9\}$$ (a) Find $$A \cap B \cap C$$ (intersection of all three sets): Step 1: Find common elements in all three sets. Only element 9 is in all three. $$A \cap B \cap C = \{9\}$$ (b) Find $$A \cup (B \cap C)$$ (union of A and intersection of B and C): Step 1: Find $$B \cap C$$: $$B \cap C = \{9\}$$ Step 2: Find union with A: $$A \cup \{9\} = \{8, 9, 10\}$$ 4. Problem 15: Drawing scale 1:40, Abdul Rahman's height is 160 cm. Step 1: Calculate height in the picture: $$\text{Height in picture} = \frac{160}{40} = 4 \text{ cm}$$ 5. Problem 16: Solve for the missing number in $$2 \times \frac{3}{5} \times \text{?} = 1$$ Step 1: Let the missing number be $$x$$. $$2 \times \frac{3}{5} \times x = 1$$ Step 2: Simplify left side: $$\frac{6}{5} x = 1$$ Step 3: Solve for $$x$$: $$x = \frac{1}{\frac{6}{5}} = \frac{5}{6}$$ 6. Problem 17: Find $$Z^+ \cap Z^-$$ Step 1: $$Z^+$$ is the set of positive integers, $$Z^-$$ is the set of negative integers. Step 2: Their intersection is empty: $$Z^+ \cap Z^- = \emptyset$$ 7. Problem 18: The rational number which has no multiplicative inverse is 0. 8. Problem 19: Find how much $$\frac{3}{4}$$ exceeds $$\frac{3}{8}$$. Step 1: Subtract: $$\frac{3}{4} - \frac{3}{8} = \frac{6}{8} - \frac{3}{8} = \frac{3}{8}$$ 9. Problem 20: Three times a number is 27, find one-third of this number. Step 1: Let the number be $$x$$. $$3x = 27 \Rightarrow x = 9$$ Step 2: One-third of $$x$$: $$\frac{1}{3} \times 9 = 3$$ 10. Problem 21: Given $$A=2, B=-4, C=-3$$, find numerical value of $$\left(\frac{3B}{A}\right) \times C$$ Step 1: Substitute values: $$\left(\frac{3 \times (-4)}{2}\right) \times (-3) = \left(\frac{-12}{2}\right) \times (-3) = (-6) \times (-3) = 18$$ 11. Problem 22: Given sets $$\{3\} ........ \{33\}$$ This is incomplete, no operation specified. 12. Problem 23: If $$X \subset Y$$, then $$X \cap Y = X$$ because the intersection of a subset with its superset is the subset itself. Final answers summary: 12. Gasoline needed = 16 liters 14a. $$\{9\}$$ 14b. $$\{8,9,10\}$$ 15. Height in picture = 4 cm 16. Missing number = $$\frac{5}{6}$$ 17. $$\emptyset$$ 18. 0 19. $$\frac{3}{8}$$ 20. 3 21. 18 23. $$X$$