1. **Solve inequality:** $3 + x > 5$ Subtract 3 from both sides: $$x > 5 - 3$$ $$x > 2$$ So, $x$ must be greater than 2. 2. **Circle problem (diameter 28 cm):** Diameter $d = 28$ cm, radius $r = \frac{28}{2} = 14$ cm. (i) Circumference $C = 2 \pi r = 2 \times 3.14 \times 14 = 87.92$ cm (approx). Given is 176 cm, which is incorrect. Response: "x". (ii) Area $A = \pi r^2 = 3.14 \times 14^2 = 3.14 \times 196 = 615.44$ cm$^2$ (approx). Given is 616 cm$^2$, which is approximately correct. Response: "✓". 3. **Angle equality problem:** Given $\widehat{APC} = \widehat{BPD}$, show $\widehat{APB} = \widehat{CPD}$. Since $\widehat{APC} = \widehat{BPD}$ and points are arranged appropriately, this forms vertical or alternate angles implying $\widehat{APB} = \widehat{CPD}$ by the properties of intersecting lines. 4. **Triangle ABC with PQ parallel to BC through A:** Since $PQ \parallel BC$, corresponding angles are equal. Thus, $\widehat{BAC} = \widehat{PAQ}$. Using the triangle and parallel line properties, angle $\widehat{BAC}$ is equal to the alternate interior angle formed by PQ and BC. 5. **Bearing calculations:** (i) Bearing of B from A is the clockwise angle from north at A towards B. (ii) Bearing of A from B is the clockwise angle from north at B towards A. Exact bearing values depend on diagram specifics not given numerically, so general explanation provided. 6. **Refrigerator pricing:** Selling price (SP) = 72,810; Discount = 10% (i) Marked price (MP) is such that SP = MP - 10% of MP = 0.9 MP. So, $0.9 \times MP = 72,810$; hence, $$MP = \frac{72,810}{0.9} = 81,000$$ (ii) Discount = MP - SP = 81,000 - 72,810 = 8,190 7. **Mean and range of numbers:** Numbers: 17, 15, 18, $x$, 13; Mean = 16 (i) Sum of numbers = $5 \times 16 = 80$ Sum is $17 + 15 + 18 + x + 13 = 63 + x$ Set equal: $$63 + x = 80$$ $$x = 17$$ (ii) Range = Max - Min With $x=17$, numbers are 13, 15, 17, 17, 18 Max = 18, Min = 13 Range = $18 - 13 = 5$ Final answers summarized: - Inequality: $x > 2$ - Circle responses: (i) "x", (ii) "✓" - Angle proof: $\widehat{APB} = \widehat{CPD}$ - Angle $\widehat{BAC}$ equals alternate interior angle with PQ parallel to BC. - Bearings explained qualitatively. - Marked price = 81,000; Discount = 8,190 - Missing number $x=17$; Range = 5