Further Mathematics Questions and Answers

\(P(Jide) = \frac{1}{12}; P(\text{not Jide}) = \frac{11}{12}\)

\(P(Atu) = \frac{1}{6}; P(\text{not Atu}) = \frac{5}{6}\)

\(P(Obu) = \frac{1}{8}; P(\text{not Obu}) = \frac{7}{8}\)

\(P(\text{only one of them}) = P(\text{Jide not Atu not Obu}) + P(\text{Atu not Jide not Obu}) + P(\text{Obu not Jide not Atu})\)

= \((\frac{1}{12} \times \frac{5}{6} \times \frac{7}{8}) + (\frac{1}{6} \times \frac{11}{12} \times \frac{7}{8}) + (\frac{1}{8} \times \frac{11}{12} \times \frac{5}{6})\)

= \(\frac{35}{576} + \frac{77}{576} + \frac{55}{576}\)

= \(\frac{167}{576}\)

\(\overrightarrow{BC} = \overrightarrow{BA} + \overrightarrow{AC}\)

\(\overrightarrow{BA} = - \overrightarrow{AB} = -(5i + 3j)\)

= \(-5i - 3j\)

\(\overrightarrow{BC} = (-5i - 3j) + (2i + 5j)\)

= \(-3i + 2j\)

\(P(A) = \frac{7}{12}\)

\(P(A \cap B) = \frac{1}{4} = P(A) \times P(B)\) (Independent events)

\(\frac{1}{4} ÷ \frac{7}{12} = \frac{1}{4} \times \frac{12}{7} \)

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

\(\begin{vmatrix} 4 & x \\ 5 & 3 \end{vmatrix} = 12 - 5x = 32\)

\(5x = 12 - 32 = -20\)

\(x = -4\)

\(\sin 45 = \frac{\sqrt{2}}{2}\)

\(\frac{1}{1 - \sin 45} = \frac{1}{1 - \frac{\sqrt{2}}{2}}\)

\(\frac{2}{2 - \sqrt{2}} = \frac{4 + 2\sqrt{2}}{4 - 2}\)

= \(2 + \sqrt{2}\)