Correct Answer: C. \(3\log_{3} 2\)

Explanation

\(2\log_{3} 8 - 3\log_{3} 2 = \log_{3} 8^{2} - \log_{3} 2^{3}\)

= \(\log_{3}(\frac{64}{8}) \)

= \(\log_{3} 8 = \log_{3} 2^{3}\)

= \(3 \log_{3} 2\)

Correct Answer: D. \(\begin{pmatrix} 0 & 10 \\ 9 & -4 \end{pmatrix}\)

Explanation

\(P = \begin{pmatrix} 2 & 1 \\ 5 & -3 \end{pmatrix} ; Q = \begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}\)

\(2P = \begin{pmatrix} 4 & 2 \\ 10 & -6 \end{pmatrix}\)

\(2P - Q = \begin{pmatrix} 4 & 2 \\ 10 & -6 \end{pmatrix} - \begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}\)

= \(\begin{pmatrix} 0 & 10 \\ 9 & -4 \end{pmatrix}\)

Correct Answer: B. (2, -7)

Explanation

Given \(M(4, -1)\) and \(N(x, y)\) with midpoint \(P(3, -4)\).

\(\implies \frac{4 + x}{2} = 3; \frac{-1 + y}{2} = -4\)

\(\therefore x = 2; y = -7\)

N = (2, -7)

Correct Answer: B. 6.8 m/s

Explanation

Since the bodies are in an opposite direction, one takes the negative velocity.

\(m_{1}v_{1} + m_{2}v_{2} = (m_{1} + m_{2})v\) (Momentum when the two bodies move in the same direction after collision)

\(3(-2) + 5(V) = (3 + 5)3.5\)

\(-6 + 5V = 28 \implies 5V = 34; V = 6.8 m/s\)

Correct Answer: A. 37

Explanation

g(-3) = 2(-3) + 3 = -6 + 3 = -3

F(-3) = 3 (-3)\(^2\) - 2(-3) + 4

= 27 + 6 + 4 = 37

Explanation

p(defective) = \(\frac{8}{100} = 0.08\)

p(non- defective) = \(1 - 0.08 = 0.92\)

p(at least 3 defective) = \(1 - [p(0) + p(1) + p(2)]\)

\(p(x) = ^{n}C_{x} p^{x} q^{n - x}\)

\(p(0) = ^{10}C_{0} (0.08)^{0} (0.92)^{10} = 0.434\)

\(p(1) = ^{10}C_{1} (0.08)^{1} (0.92)^{9} = 0.378\)

\(p(2) = ^{10}C_{2} (0.08)^{2} (0.92)^{8} = 0.148\)

p(at least 3 defective) = 1 - [0.434 + 0.378 + 0.148]

= 1 - 0.960 = 0.04

Correct Answer: D. -2x + 3y - 6 =0

Explanation

Equation of a straight line : y = mx + b

where m = the slope of the line

b = y- intercept

Given the two points (-3, 0) and (0, 2).

\(m = \frac{2 - 0}{0 - (-3)} = \frac{2}{3}\)

\(y = \frac{2}{3}x + 2 \implies 3y = 2x + 6\)

\(-2x + 3y - 6 = 0\)

Correct Answer: B. II only

Correct Answer: A. x ? -5 or x ? \(\frac{3}{2}\)

Explanation

2x\(^2\) + 7x - 15 ≥ 0

2x\(^2\) -3x + 10x - 15 ≥ 0

x(2x - 3) + 5(2x - 3) ≥ 0

(x+5)(2x-3) ≥ 0

the points on x-axis where the graph ≥ 0

x ≤ -5 or x ≥ \(\frac{3}{2}\)

Explanation

(a) \(p(Kunle) = \frac{1}{3} ; p(\text{not Kunle}) = \frac{2}{3}\)

\(p(Tayo) = \frac{1}{5} ; p(\text{not Tayo}) = \frac{4}{5}\)

\(p(\text{only one solve the question}) = p(\text{Kunle and not Tayo}) + p(\text{Tayo and not Kunle})\)

= \((\frac{1}{3} \times \frac{4}{5}) + (\frac{1}{5} \times \frac{2}{3})\)

= \(\frac{4}{15} + \frac{2}{15}\)

= \(\frac{6}{15} = \frac{2}{5}\)

(b) 10 persons to choose 8

Number of ways = \(^{10}C_{8}\)

= \(\frac{10!}{(10 - 8)! 8!}\)

= \(\frac{10 \times 9}{2}\)

= 45 ways.