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V = ⅓ πr2 h Volume of a cone (Vc) = ⅓ × 3.14 × (5)2 × 6 = 156.93 157cm3

Prob.(A outcome) = \(\frac{1}{6}\), Prob.(B outcome) = ¼ P(A ∪ B) = 1/12, Prob.(A ∩ B) Prob.(A ∩ B) = Prob.(A) + Prob.(B) − Prob.(A ∪ B) 1/6 + 1/4 − 1/12 = (2 + 3 − 1) ÷ 12 = 4/12 = 1/3 Prob.(A ∩ B) = 1/3

Z has 4 elements, power = number of subset = 2p Z = 2n = 24 = 16

\(27^x ÷ 81^{(x + 2y)} = 9 \\ (27)x = 9 × 81^{(x+2y)} \\ (3^3 )^x =32 \times 3^{4(x + 2y)} \\ =3^{(2 + 4x + 8y)}\\ 3^{3x} = 3^{ (2 + 4x + 8y)}\\ 3x = 2 + 4x + 8y\\ 3x − 4x − 8y = 2 … … … (1)\\ x + 4y = 0 … … … (2)\\ − 4y = 2\\ y = (− 2) ÷ 4 = − ½\\ y = − ½\\ \) Substitute the value of y into equation (2) i.e x + 4y = 0 x + 4( − 1/2) = 0 x − 2 = 0 x = 2 ∴ x = 2,y = − ½) Method II \( 27^x ÷ 31^{(x + 2y) }= 9\\ 3^{3x} × 3^{( − 4x − 8y)} = 32\\ 3^{(3x − 8y)} = 32\\ − x − 8y=2 ……… (1)\\ x + 4y = 0 ……… (2)\\ − 4 = 2\\ y= 2/4 = ½\\ y = ½ \) Substitute the value of y into equation 2 x + 4y=0 x + 4 (− 1) ÷ 2) = 0 x − 2 = 0 x = 2 x = 2, y = ½

\(\sqrt{30}\) \times \(\sqrt{40}\) = \(\sqrt{(30 \times 40)}\) \(\sqrt{(3 \times 10 \times 4 \times 10)}\) \(\sqrt{(400 \times 3)}\) \(\sqrt{400}\) \times \(\sqrt{3}\) 20 \times \(\sqrt{3}\) 20\(\sqrt{3}\)

√(2x + 2 ) − √x = 1 √(2x + 2) = 1 + √x Square both sides √(2x + 2)2 = (1 + √x)2 ((2x + 2)2)½ = 1 + √x + √x+ x 2x + 2 = 1 + 2√x +x Collect the like term together 2x − x + 2 − 1 = 2 √x x + 1 = 2√x Square both sides (x + 1)2 = (2√x)2 x2 + 2x + 1 = 4x x2 + 2x − 4x + 1 = 0 (x2− x)(x + 1)= 0 x(x − 1) −1(x − 1) (x − 1)(x −1) Either (x − 1) = 0 or (x − 1) = 0 x = 1 or 1 x = 1 twice

Let x represent the first number; Then, the other is (5 − x) , since their sum is 5 and their product is 14 x(5 − x) = 14 5x − x2 = 14 x2 − 5x − 14 = 0 (x2 − 7x) + (2x − 14) = 0 x(x − 7) + 2(x − 7) = 0 (x − 7)(x + 2) = 0 Either (x − 7) = 0 or (x + 2) = 0 x = 7 or x = − 2 The two numbers are 7 and − 2

\( 5^{(x − 2)} = (125^{−1} )^{(x + 3)}\\ 5^{(x − 2)} = (5− 3)^{x + 3}\\ 5^{(x − 2)} = 5^{− 3x − 9}\\ x + 3x = − 9 + 2\\ 4x = − 7\\ x = \frac{−7}{4} \)

Each exterior angle = 180 − 120=60 Exterior angle =360/n 60 = 360/n n =360/6 = 6

25% of N80 = 25/100 × 80 = N20.00

2.04 x 3.7 = 204 x 37 ----- 7548 = 7.548 = 7.55(2dp)

Let assume the cost price is 100% Marked up price + cost price = 20 + 100 = 120% Discount at 20% = 20/100 × 120 % of cost price Selling price = cost price − gain = (120 − 24)% of cost price = 96% of cost price Loss = (100− 96)% of cost price = 4% of cost price ∴ He will wake 4% loss

5÷ (2 − √3) Using conjugate surds [5 ÷ (2 − √3)]×(2 + √3) ÷ (2 + √3)] [5(2+√3)÷((2− √3))2] [5(2 +√3) ÷ (2)2− (√3)2] [5(2 +√3) ÷(4− 3)] = 5(2 + √3)

The trinomial = \( a^2 − 4a + 4 \\ a^2 − b^2− 4a + 4 = (a^2 − 4a + 4) − b^2 \\ (a^2 − 2a − 2a + 4) − b^2 \\ a(a − 2)− 2(a − 2)] − b^2 \\ (a − 2)2 − b^2 \\ (a − 2 + b)(a − 2 − b )\)

use trial and error method, By substituting any of x = 2, 5, 15, 18 into 7 + x = 4 (mod 9) any value of x that gives 7 + x = 4 (mod 9) is the correct value of x In this case, x = 15.