If 27\(^{x + 2}\) \(\div\) 9\(^{x + 1}\) = 3\(^{2x}\), find x.
3
4
5
6
Correct answer is B
\(27^{x + 2} \div 9^{x + 1} = 3^{2x}\)
\(3^{3(x + 2)} \div 3^{2(x + 1)} = 3^{2x}\)
\(3^{3x + 6} \div 3^{2x + 2} = 3^{2x}\)
\(\therefore (3x + 6) - (2x + 2) = 2x\)
\(x + 4 = 2x \implies x = 4\)
N525
N1,025
N1,950
N2,975
Correct answer is B
Amount spent on children = \(\frac{15}{100} \times 3500 = N525\)
Amount spent = Amount on children + Additional amount on food
Amount Spent = N525 + N1950 = N2475
Therefore amount left = N3,500 - N2,475 = N1,025
Evaluate \(\frac{21}{9}\) to 3 significant figures
2.30
2.31
2.32
2.33
Correct answer is D
\(\frac{21}{9} = \frac{7}{3}\)
= 2.33 (to 3 sig. figs)
Simply \(\frac{2\frac{2}{3} \times 1\frac{1}{2}}{4\frac{4}{5}}\)
\(1\frac{1}{4}\)
\(1\frac{1}{6}\)
\(\frac{5}{6}\)
\(\frac{4}{5}\)
Correct answer is C
\(\frac{2\frac{2}{3} \times 1\frac{1}{2}}{4\frac{4}{5}}\)
\(\frac{8}{3} \times \frac{3}{2} \div \frac{24}{5}\)
\(\frac{8}{3} \times \frac{3}{2} \times \frac{5}{24}\)
\(\frac{5}{6}\)
Convert 112\(_6\) to a number in base three
2211
2121
1212
1122
Correct answer is D
First, convert to base 10
112\(_6\) = (1 x 6\(^2\)) + (1 x 6\(^1\)) + (2 x 6\(^0\))
= 36 + 6 + 2
= 44\(_{10}\)
\(\begin{array}{c|c} 3 & 44 \\ \hline 3 & 14 & r 2 \\ \hline 3 & 4 & r 2 \\ \hline 3 & 1 & r 1 \\ \hline 3 & 0 & r 1 \end{array}\)
Ans = 1122 = D