Correct Answer: C. \(\frac{2}{9}\)

Explanation

Total = 8 + 12 + 4

= 24

\(\frac{8}{24} \times (\frac{12}{24} + \frac{4}{24}\))

= \(\frac{1}{3} \times (\frac{1}{2} + \frac{1}{6}\))

= \(\frac{1}{3} \times \frac{3 + 1}{6}\)

\(\frac{1}{3} \times \frac{4}{6} = \frac{2}{9}\)

Correct Answer: B. \(\frac{4}{9}\)

Explanation

28 - x + x + 25 - x = 45

53 - x = 45

x = 53 - 45

x = 8

chemistry only = 28 - 8

= 20

Probability = \(\frac{20}{45}\)

= \(\frac{4}{9}\)

Correct Answer: D. N4,600.00

Explanation

P = \(\frac{100l}{RT} = \frac{100 \times 500}{5 \times 2.5} = \frac{50,000}{12.5}\)

= 4,000

Annual interest is \(\frac{500}{5}\) = 100

for 6 year = 4,000 + 100 + 100 + 100 + 100 + 100 + 100

= N 4,600

Correct Answer: C. \(A = \begin{pmatrix} 3 & -5 \\ -1 & 2 \end{pmatrix}\)

Explanation

\(B.B^{-1} = 1\), let \(B^{-1} = \begin{pmatrix} a & b \\ c & d \end{pmatrix}\)

\(\begin{pmatrix} 2 & 5 \\ 1 & 3 \end{pmatrix}\)\(\begin{pmatrix} a & b \\ c & d \end{pmatrix}\) = \(\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\)

Multiplying \(B \times B^{-1}\), we have the following equations:

\(2a+5c = 1......... (1)\); \(a+3c = 0 ........(2)\)

\(2b+5d = 0 ..........(3)\); \(b+3d = 1..........(4)\)

Solving the equations simultaneously, we have

\(a = 3; b = -5; c = -1; d = 2 \implies B^{-1} = \begin{pmatrix} 3 & -5 \\ -1 & 2 \end{pmatrix}\)

Correct Answer: ?D. ?120\(\sqrt{2}\)

Explanation

\(60^2 + x^2 + x^2\)

\(360^2 = 2x^2\)

\(x^2\) = 1800

x = \(\sqrt{1800}\)

x = 42.4264

x = 42.4264

perimeter = 4x

= 4 x 42.4264

= 169.7056

= 120\(\sqrt{2}\)

= 120\(\sqrt{2}\)

Correct Answer: C. a - b + 1

Explanation

\(\frac{\log 7 \times \log 10}{\log 2}\)

log 7 x log 10 \(\div\) log 2

a + 1 - b

a - b + 1

Correct Answer: D. 4.2

Explanation

x = \(\frac{2 + 3 + 3 + 4 + 5 + 5+ 5+ 7 + 7 + 9}{10}\)

=\(\frac{50}{10}\)

= 5

Variance = \(\frac{\sum{(x - x})^2}{N}\)

\(\frac{9 + 4+ 4+ 1 + 4 + 4 + 16}{10}\)

= \(\frac{42}{10}\)

= 4.2

Correct Answer: D. 4

Explanation

\(\sqrt{128} = \sqrt{64\times2} = 8\sqrt{2}\)

\(\sqrt{32} = \sqrt{16\times2} = 4\sqrt{2}\)

Simplifying, we have \(\frac{8\sqrt{2}}{4\sqrt{2} - 2\sqrt{2}} = \frac{8\sqrt{2}}{2\sqrt{2}}\)

= 4

Correct Answer: C. 14\(ms^{-2}\)

Explanation

\(accl = \frac{\mathrm d V}{\mathrm d t}\)

\(V = 3t^{2} + 2t - 1 \therefore a = \frac{\mathrm d V}{\mathrm d t} = 6t + 2\)

\(a \text{(after 2 seconds)} = (6\times 2) + 2 = 12+2 = 14ms^{-2}\)

Explanation

\(\overrightarrow{MN} = \overrightarrow{RQ}\)

\(\begin{pmatrix} 4 - 10 \\ - 6 - 2 \end{pmatrix} = \begin{pmatrix} x - 8 \\ y - 16 \end{pmatrix}\)

\(\implies 4 - 10 = x - 8\)

\(-6 = x - 8 \implies x = -6 + 8 = 2\)

\(\implies - 6 - 2 = y - 16\)

\(-8 = y - 16 \implies y = -8 + 16 = 8\)

The coordinate of R is (2, 8).