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5 + 6 + 4 + 8 + 5 + 2 + x = 35 30 + x = 35 x = 35 - 30 x = 5

at least 2 kinds of food two or more foods i.e(R and p) + (p and Y) + (y and R) + R and y and p = 6 + 2 + 4 + 5 = 17

x : y = 3.5, y : z = 4 : 7 x = 3 x 4 = 12 y = 5 x 4 = 20 y = 4 x 5 = 20 z = 7 x 5 = 35 then x : y : z = 12 : 20 : 35

2y + Reflex angle = 360 Reflex angle = 360 - 2y 360 - 2y = 2(106)(angles at a centre = 2ce < of circum.) 360 - 212 = 2y 148 = 2y y \(\frac{148}{2}\) y = 74o

\(\frac{n}{4} = \frac{m}{4 + 12}\) \(\frac{n}{4} = \frac{m}{16}\) 4m = 16n \(\frac{4m}{4} = \frac{16n}{4}\) m = 4n

Area of shaded portion = Area of semicircle Area of \(\bigtriangleup\) RSO Area of semicircle = \(\frac {\pi r^2}{2} = \frac{22\times 4 \times 4}{7 \times 2}\) = 25.14cm2; Area of \(\bigtriangleup\)RSO =\(\sqrt{s(s - 1)(s - b)(s - c)}\); where s = \(\frac{a + b + c}{2}\) s = \(\frac{4 + 4 + 4}{2}\) = 6cm = \(\sqrt{6(6 - 4)(6 - 4) (6 - 4)}\) = \(\sqrt{6(2) (2) (2)}\) = \(\sqrt{18}\) = 6.93cm2 Area of shaded region = 25.14 - 6.93 = 18.21cm2

Convert \( (42_5) \) to base three: First, convert to decimal: \(42_5 = 4 \times 5 + 2 = 22_{10}\) Now convert \( (22_{10}) \) to base three: 22 \(\div 3 = 7 \quad ; \, r1 \) 7 \(\div 3 = 2 \quad ; \, r1 \) 2 \(\div 3 = 0 \quad ; \, r2\) Read the remainders from bottom to top: \(22_{10} = 211_3\).

(a) \((3.69 \times 10^{5}) \div (1.64 \times 10^{-3})\) = \(\frac{3.69}{1.64} \times 10^{5 - (-3)}\) = \(2.25 \times 10^{8}\) (b) Interest from bank A : \(\frac{y}{100} \times N20,000 = N200y\) Interest on bank B :\(\frac{1.5y}{100} \times N25,000 = N375y\) \(\therefore N(200y + 375y) = N4,600\) \(575y = 4,600 \implies y = 8\)

(a) \(\frac{x^{2} - 8x + 16}{x^{2} - 7x + 12}\) = \(\frac{(x - 4)(x - 4)}{(x - 4)(x - 3)}\) = \(\frac{(x - 4)}{(x - 3)}\) (b) Arithmetic Progression: \(\frac{1}{2}, \frac{1}{x}, \frac{1}{3}\) \(\frac{1}{x} - \frac{1}{2} = \frac{1}{3} - \frac{1}{x}\) \(\frac{2 - x}{2x} = \frac{x - 3}{3x}\) \(\frac{2 - x}{x - 3} = \frac{2x}{3x}\) \(\implies \frac{2 - x}{x - 3} = \frac{2}{3}\)