Mathematics Questions and Answers

\(\frac{2\sqrt{14} \times 3\sqrt{21}}{7 \sqrt{24} \times 2\sqrt{98}}\) = \(\frac{6\sqrt{14} \times 3 \times \sqrt{7} \times \sqrt{3}}{7 \times 2 \sqrt{6} \times \sqrt{7} \times \sqrt{14}}\)

= \(\frac{3\sqrt{3}}{14\sqrt{6}}\)

= \(\frac{3\sqrt{3}}{14\sqrt{2} \times \sqrt{3}}\)



= \(\frac{3\sqrt{2}}{28}\)

log\(_2\)6 - log\(_2\)3 = log\(_2\) (\(\frac{6}{3}\))

= log\(_2\)2... A

log\(_2\)8 - 2log\(_2\)\(\frac{1}{2}\)

log\(_2\)8 - log\(_2\)\(\frac{1}{2}\)\(^2\)

log\(_2\)8 - log\(_2\)\(\frac{1}{4}\)

= log\(_2\) 32... B

\(\frac{A}{B}\) = \(\frac{log_22}{log_232}\)

N.B. log\(_2\)2 = 1

= \(\frac{1}{5}\)
 

(0.008) -\(\frac{1}{3}\) x (0.16) - \(\frac{3}{2}\) = (8 x 10^-3)10^-3 x (16 x 10^-2)-\(\frac{3}{2}\)

= \(\frac{(2^3)}{10^3}\) - 3 x \(\frac{(2^4)}{10}\) - \(\frac{-3}{2}\)

= \(\frac{625}{8}\)

Let x represents number of boys that can work at \(\frac{5}{4}\) the rate at which the 10 girls work

For 1hr. x boys will work for \(\frac{\frac{1}{5}}{4}\) x 10

x = \(\frac{4}{5}\) x 10 = 8 boys

8 boys will do the work of ten girls at the same rate 4 + 8 = 12 boys cut the field in 5 hrs

For 3 hrs, \(\frac{12 \times 5}{3}\) boys will be needed = 20 boys

profit 8% of N1.35 = \(\frac{8}{100}\) x N1.35 = N0.08

Cost price = N1.35 - N0.10 = N1.25

If he sells the 20 oranges for N1.10 now

%loss = \(\frac{\text{actual loss}}{\text{Cost price}}\) x 100

\(\frac{125 - 1.10}{1.25}\) x 100

= \(\frac{0.15 \times 100}{1.25}\)

= \(\frac{15}{1.25}\)

= 12%