1. Problem: Calculate the compound interest for an investment of 5000 at 10% per annum for 2 years. Step 1: Use the compound interest formula: $$A = P(1 + r)^t$$ where $P=5000$, $r=0.10$, $t=2$. Step 2: Calculate: $$A = 5000(1 + 0.10)^2 = 5000(1.10)^2 = 5000 \times 1.21 = 6050$$. Step 3: The investment will be 6050 at the end of 2 years. 2. Problem: Simplify the expression $$(3y - 2x + 4) - (y + 2x - 1)$$. Step 1: Distribute the minus sign: $$3y - 2x + 4 - y - 2x + 1$$. Step 2: Combine like terms: $$(3y - y) + (-2x - 2x) + (4 + 1) = 2y - 4x + 5$$. 3. Problem: Determine which point does NOT lie on the line $$y = 2x - 1$$. Step 1: Check each point by substituting $x$ and comparing $y$. - For (0,1): $y = 2(0) - 1 = -1 \neq 1$ (does NOT lie on the line). - For (3,5): $y = 2(3) - 1 = 6 - 1 = 5$ (lies on the line). - For (2,4): $y = 2(2) - 1 = 4 - 1 = 3 \neq 4$ (does NOT lie on the line). - For (3,5) repeated same as above. Step 2: The point (0,1) does NOT lie on the line. 4. Problem: Find the probability of rolling a number greater than 2 and less than 6 on a fair six-sided die. Step 1: Numbers greater than 2 and less than 6 are 3, 4, 5. Step 2: Number of favorable outcomes = 3. Step 3: Total possible outcomes = 6. Step 4: Probability = $$\frac{3}{6} = \frac{1}{2}$$. Final answers: 1. $6050$ 2. $2y - 4x + 5$ 3. Point (0,1) does NOT lie on the line 4. Probability $\frac{1}{2}$