Correct Answer: B. \( 2\frac{1}{5}\)

Explanation

(a) Let the diagram below represent a section of the polygon

Also, let :

\(i\) represent the size of an interior angle; \(e\) represent the size of an exterior angle.

Then \(\frac{i}{e} = \frac{5}{2}\)

\(\implies i = \frac{5}{2}e\)

But \(i + e = 180°\) (sum of angles on a straight line)

Substitute \(\frac{5}{2}e\) for \(i\) in the equation

\(\frac{5}{2}e + e = 180°\)

\(\frac{7}{2}e = 180°\)

\(e = \frac{180° \times 2}{7} = \frac{360°}{7}\)

Number of sides of the polygon = \(\frac{360°}{\text{size of one exterior angle}}\)

= \(360° \div \frac{360°}{7}\)

\(360° \times \frac{7}{360°} = 7 sides\).

(b)

In the diagram above, < PSR = 68° (interior angle of a cyclic quad = opp exterior angle)

< PSQ = 68° - 40° = 28°

< PRQ = 28° (angles in same segment)

< SRQ = 74° (interior angle of a cyclic quad = opp exterior angle)

hence, < PRS = 74° - 28° = 46°

Correct Answer: C. $656.25

Explanation

\(\frac{20}{100}\) x \(x\) = \(x - 525\)

\(\frac{x}{5} = x\) - 535

x = 5x - 2625

\(\frac{4x}{4} = \frac{2625}{4}\)

x = $656.25

Correct Answer: A. -44

Correct Answer: B. 1\(\frac{1}{2}\)

Explanation

The sum of 2 \(\frac{1}{6}\) and 2\(\frac{7}{12}\)

= \(\frac{13}{6}\) + \(\frac{31}{12}\)

= \(\frac{13 \times 2 + 31}{12}\)

= \(\frac{26 + 31}{12}\)

= \(\frac{57}{12}\)

What should be subtracted from \(\frac{57}{12}\) to give 3\(\frac{1}{4}\)

\(\frac{57}{12}\) - y = 3\(\frac{1}{4}\)

: y = \(\frac{57}{12}\) - 3\(\frac{1}{4}\) = \(\frac{57}{12}\) - \(\frac{13}{4}\)

y = \(\frac{57 - 3 \times 13}{12}\) = \(\frac{57 - 39}{12}\)

y = \(\frac{18}{12}\)

y = \(\frac{3}{2}\) or 1\(\frac{1}{2}\)

Correct Answer: B. 30.6 cm

Explanation

Consider ∠XOB and using Pythagoras theorem

13\(^2\) = 12\(^2\) + h\(^2\)

⇒ 169 = 144 + h\(^2\)

⇒ 169 - 144 =h\(^2\)

⇒ 25 = h\(^2\)

⇒ h = \(\sqrt25\) = 5cm

tan θ = \(\frac {opp}{adj}\)

⇒ tan θ = \(\frac{12}{5}\) = 2.4

⇒ θ = tan\(^{-1}\)(2.4)

⇒ θ = 67.38\(^0\)

∠AOB = 2θ = 2 x 67.38\(^o\) = 134.76\(^o\)

L = \(\frac{θ}{360^o} \times 2\pi r\)

⇒ L = \(\frac {134.76}{360} \times 2 \times \frac {22}{7} \times 13 = \frac {77082.72}{2520}\)

∴ L = 30.6cm (to 3 s.f)

Correct Answer: D. 175

Explanation

From the five(5) men viable for the position of the chairman, one of them must be selected.

This implies; 4 men and 3 women are open for committee membership.

7 C\(_3\) = \(\frac{7!}{3!(7 - 3)!}\) =

\(\frac{7⋅6⋅5⋅4⋅3⋅2⋅1}{3.2.1 \times 4.3.2.1}\)

= 35 \(\times\) 5 = 175

Correct Answer: A. 4.7

Correct Answer: C. 150m

Correct Answer: C. \(\sqrt{\frac{2}{3}}\)