Correct Answer: D. 5

Correct Answer: B. 40°

Explanation

Exterior angle \(=\frac{360}{n}\) where n = no of sides

\(=\frac{360}{9}=40^{\circ}\)

Correct Answer: A. 3

Explanation

log_a270 - log_a10 + log_a\(\frac{1}{3}\) = 2

log_a270 + log_a\(\frac{1}{3}\) - log_a10 = 2

log_a(270\(\frac{\frac{1}{3}}{10}\)) = 2

log_a9 = 2

a^a = 9

a = \(\sqrt{9}\) = 3

Correct Answer: D. 8

Explanation

\(x \propto \frac{1}{y}\)

\(x = \frac{k}{y}\)

\(\frac{2}{3} = \frac{k}{9}\)

\(3k = 18 \implies k = 6\)

\(x = \frac{6}{y}\)

When y = \(\frac{3}{4}\),

x = \(\frac{6}{\frac{3}{4}}\)

= \(\frac{6 \times 4}{3}\)

= 8

Correct Answer: D. \(\frac{x^3}{3} - 2x - \frac{1}{x} + c\)

Explanation

\((x - \frac{1}{x})^{2} = x^2 - 2 + \frac{1}{x^2}\)

\(\int (x^2 + \frac{1}{x^2} - 2) \mathrm {d} x\)

= \(\int (x^2 + x^{-2} - 2) \mathrm {d} x\)

= \(\frac{x^3}{3} - 2x - \frac{1}{x}\)

Correct Answer: A. 2

Explanation

Note: sin 20° = cos 70° hence

\(\frac{\sin 20}{\cos 70} = 1\)

Also, cos 65° = sin 25°

\(\frac{\cos 65}{\sin 25} = 1\)

\(\therefore \frac{\sin 20}{\cos 70} + \frac{\cos 65}{\sin 25}\)

= 1 + 1

= 2

Explanation

(b) (i) Lower quartile = 40 hours

(ii) Median = 49 hours

(iii) 40th percentile = 45.5 hours

(iv) Employees that spent at least 50 hours 30 mins = 80 - 45 = 35

Explanation

(a) Vehicles produced in February = 40 + 25 + 30 = 95

(b) Fraction of the vehicles in February that were cars = \(\frac{40}{95} = \frac{8}{19}\)

(c) Total number of buses from January to March = 20 + 30 + 50 = 100

(d) Ratio of lorries in February to that in March = \(25 : 35 \equiv 5 : 7\).

Correct Answer: D. 8

Explanation

List the numbers in ascending order: 2,3,4,4,6,8,9,11,13,15,16 The median is the middle number, or 8.

Explanation

(a)

(b)(i) Median = N30.50

(ii) 80th percentile = N45

(c) The modal weekly profit = Lower class boundary of modal class + \(\frac{(f - f_{1}) \times c}{(f - f_{1}) + (f - f_{2})}\)

where \(f_{1}\) = frequency above the modal class ; \(f_{2}\) = frequency below modal class; c = class width; f = frequency of modal class.

\(\therefore \text{Modal profit} = 20.5 + \frac{(12 - 6) \times 10}{(12 - 6) + (12 - 11)}\)

= \(20.5 + \frac{60}{7}\)

= \(N29.07\)