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No expanded working has been attached for this question yet. The verified answer is Option B.

To convert the decimal number 39 to base 2, we can use the method of successive division by 2 and record the remainders. Here’s the process: 1. Divide 39 by 2: \(39 \div 2 = 19 \quad \text{remainder: } 1\) 2. Divide 19 by 2: \(19 \div 2 = 9 \quad \text{remainder: } 1\) 3. Divide 9 by 2: \(9 \div 2 = 4 \quad \text{remainder: } 1\) 4. Divide 4 by 2: \(4 \div 2 = 2 \quad \text{remainder: } 0\) 5. Divide 2 by 2: \(2 \div 2 = 1 \quad \text{remainder: } 0\) 6. Divide 1 by 2: \(1 \div 2 = 0 \quad \text{remainder: } 1\) Now, we read the remainders from bottom to top: Thus, the binary representation of 39 is: 100111\(_2\)

Area of QRST = 4 x 7 = 28 Area of PQRS = \(\frac{1}{2}\)(4 + 11) x 7 = \(\frac{7}{2}\) x \(\frac{15}{1}\) = 28:52.5 = 56:105

From Internal bisection theorem, \(\frac{QP}{PR}\) = \(\frac{QS}{SR}\) = \(\frac{4}{1}\) = 1:4

No expanded working has been attached for this question yet. The verified answer is Option D.

The powers will multiply when the bracket is expanded The multiplied powers: \(\frac{1}{2}\) * 6 → 3 : 4\(^3\) = 4 * 4* 4 → 64

log\(_{10}\)\(\frac{1}{40}\) = log\(_{10}\)1 - (log\(_{10}\)4 + log\(_{10}\)10) = 0 - 1.6021 = -1.6021

PSR = 65º x 2 = 130^\circ PRS = 180º - (130º + 20º) º = 30

\((1.28 \times 10^{4}) \div (6.4 \times 10^{2})\) = \(\frac{1.28 \times 10^{4}}{6.4 \times 10^{2}}\) \(\equiv \frac{12.8 \times 10^{3}}{6.4 \times 10^{2}}\) = \(2 \times 10^{1}\)

(3.2)2 - (1.8)2 = (3.2 + 1.8)(3.2 - 1.8) = 5 x 1.4 = 7

Let x represent his monthly salary before increase 15% of x = 345 % profit = (100 + 15)% = 115% \(\frac{115}{100}\)x = 345 115x = 34500 x = N300.00

(101101)2 \(\begin{array}{c|c} 2^5 & 2^4 & 2^3 & 2^2 & 2^1 & 2^o\\ \hline 1 & 0 & 1 & 1 & 0 & 1\end{array}\) = 1 x 25 + 0 x 24 + 1 x 23 + 1 x 22 + 0 x 21 + 1 x 2o = 32 + 0 + 8 + 4 + 0 + 1 = (45)\(_{10}\)

A : B = 3 : 5 Total ratio = 3 + 5 = 8 Let rept, the total profit, A receives \(\frac{3x}{8}\) \(\frac{5x}{8}\) - \(\frac{3}{x}\) = 3000 \(\frac{5x}{8}\) - \(\frac{3x}{8}\) = 3000 = \(\frac{2x}{8}\) = 3000 2x = 2400 x = 1200 N12,000

x \(\alpha\) y = x \(\alpha\) \(\frac{1}{z}\) x \(\alpha\) \(\frac{1}{z}\) x = k \(\frac{y}{z}\) k = \(\frac{xz}{y}\) = \(\frac{9 \times 8}{24}\) = 3 x = \(\frac{xz}{y}\) = \(\frac{3 \times 5}{6}\) = \(\frac{15}{6}\) = \(\frac{5}{2}\) = 2\(\frac{1}{2}\)

The amount he has to spend per day for the rest of his stay is \(\frac{Y - Xx}{y - x}\) cedis