Mathematics Questions and Answers

Pr. (winning 100m race) = \(\frac{1}{8}\)

Pr. (losing 100m race) = 1 - \(\frac{1}{8}\) = \(\frac{7}{8}\)

Pr. (winning high jump) = \(\frac{1}{4}\)

Pr. (losing high jump ) = 1 - \(\frac{1}{4}\) = \(\frac{3}{4}\)

Pr. (winning only one) = Pr. (Winning 100m race and losing high jump) or Pr.(Losing 100m race and winning high jump)

= (\(\frac{1}{8} \times \frac{3}{4}\)) + (\(\frac{7}{8} \times \frac{1}{4}\))

= \(\frac{3}{32} + \frac{7}{32}\)

= \(\frac{10}{32}\)

= \(\frac{5}{16}\)

mean \(\leq\) 5; \(\frac{2 + 5 + 2x + 7}{4}\) \(\leq\) 5

= \(\frac{14 + 2x}{4} \leq 5\)

= 14 + 2x \(\leq\) 5 x 4

14 + 2x \(\leq\) 20 ; 2x \(\leq\) 20 - 14

2x \(\leq\) 20 - 14

2x \(\leq\) 6

x \(\leq\) \(\frac{6}{2}\)

x \(\leq\) 3

x kmh^-1 = y ms^-1

\(\frac{x km}{1 hr}\) = y ms^-1

\(x \times \frac{1km}{1hr}\) = y ms^-1

\(x \times \frac{1000m}{60 \times 60s}\) = y ms^-1

\(x \times \frac{1000}{3600} \frac{m}{s}\) = y ms^-1

\(x \times \frac{5}{18} ms^{-1}\)

\(x \times \frac{5}{18} ms^{-1}\) = y ms^-1

y = \(\frac{5}{18}\)x

x2 + kx + \(\frac{16}{9}\); Perfect square

But, b2 - 4ac = 0, for a perfect square

where a - 1; b = k; c = \(\frac{16}{9}\)

k2 - 4(1) x \(\frac{16}{9}\) = 0

k2 - \(\frac{64}{9}\) = 0

k2 = \(\frac{64}{9}\)

k = \(\sqrt{\frac{64}{9}}\)

k = \(\frac{8}{3}\)

(x - p)(2x + 1) = 0

2x2 + x - 2px - p = 0

2x2 + x (1 - 2p) - p = 0

2x2 - (2p - 1)x - p = 0

divide through by 2

x2 - \(\frac{(2p - 1)}{2}\)x - \(\frac{p}{2}\) = 0

compare to x2 - (sum of roots)x + product of roots = 0

sum of roots = \(\frac{2p - 1}{2}\)

But sum of roots = 1

Given; \(\frac{2p - 1}{2}\) = 1

2p - 1 = 2 x 1

2p - 1 = 2

2p = 2 + 1 = 3

p = \(\frac{3}{2}\)

p = 1\(\frac{1}{2}\)