WAEC Past Questions and Answers - Page 2254

Orderliness is the art by which things are arranged in a proper, neat and systematic manner.
Politeness is the practical application of good manners or etiquette so as not to offend others.

Consider |NS|
θ = 180° - (90° + 35°) (sum of angles on a straight line is 180°)
= 180° - 90° - 35°
= 90° - 35°
= 55°
∴ His new bearing is N55°E.

Total numbers from 40 to 50 inclusive = 11 (40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50).

Prime numbers between 40 and 50 (inclusive) are 41, 43, and 47.

There are 3 prime numbers in this range.

therefore, Pr(prime numbers) = \(\frac{3}{11}\)

Converting each number to base 10
\(110_{two} = 1 × 2^2 + 1 × 2^1 + 0 × 2^0\)
= 1 × 4 + 1 × 2 + 0 × 1
= 4 + 2 + 0
= \(6_{ten}\)
\(31_{eight} = 3 × 8^1 + 1 × 8^0\)
= 3 × 8 + 1 × 1
= 24 + 1
= \(25_{ten}\)
\(42_{five} = 4 × 5^1 + 2 × 5^0\)
= 4 × 5 + 2 × 1
= 20 + 2
= \(22_{ten}\)
Hence, \(31_{eight} > 42_{five} > 110_{two}\)
In ascending order, \(110_{two}, 42_{five}, 31_{eight}\)

given that diameter = 140cm ⇒radius = 70cm, volume of cylinder = 200litres = \(200,000cm^3\)

volume of cylinder = base area times height = \(\pi r^2h\)

\( 200,000cm^3 = \frac{22}{7} \times 70 \times 70 \times h\)

\(200,000 = \frac{107,800h}{7}\)

cross multiply

1,400,000 = 107,800h 

\( h = \frac{1,400,000}{107,800}\)

   = 13cm (to the nearest cm).