\(\frac{3}{7}\)
\(\frac{4}{7}\)
\(\frac{5}{7}\)
\(\frac{6}{7}\)
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
\(\begin{vmatrix} 4 & x \\ 5 & 3 \end{vmatrix} = 12 - 5x = 32\)
\(5x = 12 - 32 = -20\)
\(x = -4\)
Profit expressed as a fraction of the selling price is known as
Mark-up
Margin
Gross profit
Net profit
Correct answer is B
No explanation has been provided for this answer.
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
\(\sin 45 = \frac{\sqrt{2}}{2}\)
\(\frac{1}{1 - \sin 45} = \frac{1}{1 - \frac{\sqrt{2}}{2}}\)
\(\frac{2}{2 - \sqrt{2}} = \frac{4 + 2\sqrt{2}}{4 - 2}\)
= \(2 + \sqrt{2}\)
Given that \(f '(x) = 3x^{2} - 6x + 1\) and f(3) = 5, find f(x).
\(f(x) = x^{3} - 3x^{2} + x + 20\)
\(f(x) = x^{3} - 3x^{2} + x + 31\)
\(f(x) = x^{3} - 3x^{2} + x + 2\)
\(f(x) = x^{3} - 3x^{2} + x - 13\)
Correct answer is C
\(f ' (x) = 3x^{2} - 6x + 1\)
\(f(x) = \int (3x^{2} - 6x + 1) \mathrm {d} x\)
= \(x^{3} - 3x^{2} + x + c\)
\(f(3) = 5 = 3^{3} - 3(3^{2}) + 3 + c\)
\(27 - 27 + 3 + c = 5 \implies 3 + c = 5\)
\(c = 2\)
\(f(x) = x^{3} - 3x^{2} + x + 2\)