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No expanded working has been attached for this question yet. The verified answer is Option D.

(64.764 - 35.236)(64.764 + 35.236) = 29.528 x 100 = 2950 to 3 sig. fig.

\(\frac{2}{x} - {\frac{3}{y}}\) = 2.....(1) \(\frac{4}{x} + {\frac{3}{y}}\) = 10 ... (2) (1) + (2): \(\frac{6}{x}\) = 12 \(\to\) x = \(\frac{6}{12}\) x = \(\frac{1}{2}\) put x = \(\frac{1}{2}\) in equation (i) = 4 - \(\frac{3}{y}\) = 2 = 4 - 2 = \(\frac{3}{y}\) therefore y = \(\frac{3}{2}\)

\( \theta _3 \) shows the angle of deviation

Examples of transverse waves include: ripples on the surface of water. vibrations in a guitar string. a Mexican wave in a sports stadium. electromagnetic waves – eg light waves, microwaves, radio waves. Some basic properties of light : Reflection of light. Refraction of light. Diffraction of light. All kinds of waves have the same fundamental properties of reflection, refraction, diffraction and interference, and all waves have a wavelength, frequency, speed and amplitude.

Now in permanent hardness of water, when washing soda is treated with water, the carbonate ions from sodium carbonate react with calcium and magnesium ions in water and produce an insoluble product. Therefore, calcium carbonate is precipitated out.

(0.006)3 + (0.004)3 = 2.16 x 10-7 (2.16 + 0.64) x 10-7 = 2.8 x 10-7

loga 13.5 = loga \(\frac{27}{2}\) = 3loga 3 - log2a = 3 x 1.097 - 0.693 = 2.598

8\({\frac{x}{2}}\) = \(2^{\frac{3}{8}})(4^{\frac{3}{4}}\)) applying the laws of indices. (\(2^{3\times (\frac{x}{2})}) = (2^{\frac{3}{8}})(2^{2\times (\frac{3}{4})}\)) \(2^{\frac{3x}{2}} = (2^{\frac{3}{8}})(2^{(\frac{3}{2})}\)) \(\frac{3x}{2} = \frac{3}{8} + \frac{3}{2}\) \(\frac{3x}{2} = \frac{3 + 12}{8}\) \(\frac{3x}{2} = \frac{15}{8}\) 24x = 30 x = \(\frac{30}{24} = \frac{5}{4}\)

\(\frac{(2\sqrt{3} + 3\sqrt{5})(3\sqrt{5} + 2\sqrt{3})}{(3\sqrt{5} - 2\sqrt{3})(3\sqrt{5} - 2\sqrt{3})}\) = \(\frac{57 + 12\sqrt{15}}{33}\) =\(\frac{19 + 4\sqrt{15}}{11}\)

1 = \(\frac{PRT}{100}\) 1 = 1240 - 1000 = 240 R = \(\frac{240 \times 100}{100 \times 3}\)% = 8%

\(Y \cup Z\) = \({s, e, n, o, u, p, r}\) \(X \cap (Y \cup Z)\) = \({p, e, n}\)

Let the number of students that speak Hausa and Igbo be represented by H and I respectively. n(H only) = 80 - 9 = 71. n(I only) = 20 - 9 = 11. n(neither H nor I) = 100 - (71 + 9 + 11) = 100 - 91 = 9 students.

x + 1 = 0, x = -1; f(x) = x3 + 2x2 + qx - 6 0 = -1 + 2 - q - 6 q = -5

y = X2 - 3x + 2, \(\frac{dy}{dx}\) = 2x - 3 at turning pt, \(\frac{dy}{dx}\) = 0 ∴ 2x - 3 = 0 ∴ x = \(\frac{3}{2}\) \(\frac{d^2y}{dx^2}\) = \(\frac{d}{dx}\)(\(\frac{d}{dx}\)) = 270 ∴ ymin = 2\(\frac{3}{2}\) - 3\(\frac{3}{2}\) + 2 = \(\frac{9}{4}\) - \(\frac{9}{2}\) + 2 = -\(\frac{1}{4}\)