\(\frac{1}{576}\)
\(\frac{55}{576}\)
\(\frac{77}{576}\)
\(\frac{167}{576}\)
Correct answer is D
\(P(Jide) = \frac{1}{12}; P(\text{not Jide}) = \frac{11}{12}\)
\(P(Atu) = \frac{1}{6}; P(\text{not Atu}) = \frac{5}{6}\)
\(P(Obu) = \frac{1}{8}; P(\text{not Obu}) = \frac{7}{8}\)
\(P(\text{only one of them}) = P(\text{Jide not Atu not Obu}) + P(\text{Atu not Jide not Obu}) + P(\text{Obu not Jide not Atu})\)
= \((\frac{1}{12} \times \frac{5}{6} \times \frac{7}{8}) + (\frac{1}{6} \times \frac{11}{12} \times \frac{7}{8}) + (\frac{1}{8} \times \frac{11}{12} \times \frac{5}{6})\)
= \(\frac{35}{576} + \frac{77}{576} + \frac{55}{576}\)
= \(\frac{167}{576}\)
-7i - 8j
-3i + 2j
3i - 2j
3i + 8j
Correct answer is B
\(\overrightarrow{BC} = \overrightarrow{BA} + \overrightarrow{AC}\)
\(\overrightarrow{BA} = - \overrightarrow{AB} = -(5i + 3j)\)
= \(-5i - 3j\)
\(\overrightarrow{BC} = (-5i - 3j) + (2i + 5j)\)
= \(-3i + 2j\)
\(\frac{3}{7}\)
\(\frac{4}{7}\)
\(\frac{5}{7}\)
\(\frac{6}{7}\)
Correct answer is A
\(P(A) = \frac{7}{12}\)
\(P(A \cap B) = \frac{1}{4} = P(A) \times P(B)\) (Independent events)
\(\frac{1}{4} ÷ \frac{7}{12} = \frac{1}{4} \times \frac{12}{7} \)
= \(\frac{3}{7}\)
If \(\begin{vmatrix} 4 & x \\ 5 & 3 \end{vmatrix} = 32\), find the value of x.
4
2
-2
-4
Correct answer is D
\(\begin{vmatrix} 4 & x \\ 5 & 3 \end{vmatrix} = 12 - 5x = 32\)
\(5x = 12 - 32 = -20\)
\(x = -4\)
Express \(\frac{1}{1 - \sin 45°}\) in surd form.
\(2 + \sqrt{2}\)
\(2 + \sqrt{3}\)
\(2 - \sqrt{2}\)
\(1 + 2\sqrt{2}\)
Correct answer is A
\(\sin 45 = \frac{\sqrt{2}}{2}\)
\(\frac{1}{1 - \sin 45} = \frac{1}{1 - \frac{\sqrt{2}}{2}}\)
\(\frac{2}{2 - \sqrt{2}} = \frac{4 + 2\sqrt{2}}{4 - 2}\)
= \(2 + \sqrt{2}\)