Correct Answer: B. 16 : 35

Explanation

m:n = \(2\frac{1}{3} : 1\frac{1}{5}\) = m : n = \(\frac{7}{3} : \frac{6}{5}\)

\(\frac{7}{3} : \frac{6}{5}\) = \(\frac{7}{3} \div \frac{6}{5}\)

\(\frac{m}{n}\) = \(\frac{7}{3} \times \frac{5}{6}\)

\(\frac{m}{n}\) = \(\frac{35}{18}\) = m = \(\frac{35n}{18}\)

n : q = \(1\frac{1}{2} : 1\frac{1}{3}\) = \(\frac{3}{2} : \frac{4}{3}\)

\(\frac{n}{q}\) = \(\frac{3}{2} \times\frac{3}{4}\)

\(\frac{n}{q}\) = \(\frac{9}{8}\) = q = \(\frac{8n}{9}\)

q : m = \(\frac{8n}{9}\) : \(\frac{35n}{18}\)

\(\frac{q}{m}\) = \(\frac{8n}{9} \div \frac{35n}{18}\)

\(\frac{q}{m}\) = \(\frac{8n}{9}\times\frac{18}{35n}\)

=\(\frac{q}{m} = \frac{16}{35}\) = q : m = 16 : 35

Correct Answer: B. make the best use of scarce resources

Explanation

\(2^{(2y+1)} - 5(2^y) + 2\) = 0

Let p = 2\(^y\)

\(2^{2y} (2^1) - 5(2^y)\) + 2 = 0

2p\(^2\) - 5p + 2 = 0

2p\(^2\) - p - 4p + 2 = 0

p (2p - 1) - 2(2p - 1) = 0

(p - 2)(2p - 1) = 0

p = 2 or \(\frac{1}{2}\)

p = 2\(^y\)

when p = 2

2\(^y\) = 2

y = 1

when p = \(\frac{1}{2}\)

2\(^y\) = \(\frac{1}{2}\)

2\(^y\) = 2\(^{-1}\)

y = -1

y = -1 or 1

Correct Answer: C. Morocco

Correct Answer: D. AGT

Correct Answer: D. Simeon

Correct Answer: D. 8

Explanation

The gradient of the equation = \(\frac{y_{1} - y_{0}}{x_{1} - x_{0}} = \frac{\frac{5}{2} - 0}{\frac{5}{4} - 0}\)

= \(\frac{\frac{5}{2}}{\frac{5}{4}} = 2\)

The line passes through the origin, therefore the equation of the line is y = mx

\(y = 2x\)

When x = 4, y = 2 x 4 = 8.

Correct Answer: A. x >7

Correct Answer: D. 2j

Explanation

Recall how to find the mean: Mean/Average=Sum of all valuesNumber of values Average=j+(3j+1)+(j?5)+(3j+4)/ 4=8j/4=2j

Correct Answer: B. s varies inverely as r² and t