Explanation

(a) p(Kofi passes) = \(\frac{9}{10}\), p(Kofi fails) = \(\frac{1}{10}\)

p(Kwasi passes) = \(\frac{4}{5}\), p(Kwasi fails) = \(\frac{1}{5}\)

p(Ama passes) = x, p(Ama fails) = 1 - x.

p(only one passes) = p(only Kofi passes) + p(only Kwasi passes) + p(only Ama passes)

= \((\frac{9}{10} \times \frac{1}{5} \times (1 - x)) + (\frac{4}{5} \times \frac{1}{10} \times (1 - x)) + (x \times \frac{1}{10} \times \frac{1}{5})\)

= \(\frac{9(1 - x)}{50} + \frac{4(1 - x)}{50} + \frac{x}{50}\)

\(\implies \frac{9}{50} = \frac{9 - 9x + 4 - 4x + x}{50} = \frac{13 - 12x}{50}\)

\(\therefore 13 - 12x = 9 \implies 12x = 4\)

\(x = \frac{4}{12} = \frac{1}{3}\).

(b) p(at least one passes) = 1 - p(none passes).

p(none passes) = \(\frac{1}{10} \times \frac{1}{5} \times \frac{2}{3}\)

= \(\frac{1}{75}\)

p(at least one passes) = \(1 - \frac{1}{75}\)

= \(\frac{74}{75}\)

Correct Answer: D. (2x + 5)(x + 2)

Explanation

Divide \(2x^{3} + 3x^{2} - 17x - 30\) by \((x - 3)\). You get \(2x^{2} + 9x + 10\).

Factorizing, we have \(2x^{2} + 9x + 10 = 2x^{2} + 4x + 5x + 10\)

\(2x(x + 2) + 5(x + 2)\)

= \((2x + 5)(x + 2)\)

Correct Answer: B. 7

Correct Answer: D. 22.5

Explanation

The median is the middle number of the set, when it is listed in order from smallest to largest or vice versa. In this case we have an even amount of numbers in the set meaning there are two middle numbers- 22 and 23. In order to find the median we take the average of 22 and 23: 22+23/2=22.5

Correct Answer: B. 7!

Explanation

From Lami's theorem,

\(\frac{T_{1}}{\sin 150} = \frac{T_{2}}{\sin 140} = \frac{50}{\sin 70}\)

\(T_{1} = \frac{50 \sin 150}{\sin 70}\)

= \(\frac{50 \times 0.5}{0.9397} = 26.6N\)

\(T_{2} = \frac{50 \sin 140}{\sin 70}\)

= \(\frac{50 \times 0.6428}{0.9397} = 34.2N\)

The tensions are 26.6N and 34.2N respectively.

(b)(i) Given F = ?, u = 5 ms\(^{-1}\) ; v = 9 ms\(^{-1}\) ; t = 2s.

acceleration, \(a = \frac{v - u}{t}\)

= \(\frac{9 - 5}{2} = 2 ms^{-2}\)

Force, \(F = ma = 5 \times 2 \)

= \(10N\).

(ii) \(v = u + at\)

\(u = 9 ms^{-1}; a = 2 ms^{-2} ; t = 2s\)

\(v = 9 + 2(3)\)

= \(9 + 6 = 15 ms^{-1}\).

Correct Answer: D. sin x + x cos x

Correct Answer: A. 3.5

Explanation

When finding the median, you are looking for the middle number. Always arrange the numbers in ascending order. Since, the numbers are inceasing, count the numbers in the set. There are six. Then divide six by two. We do this because we will split the number set in half. Because six does divide evenly into two, this means we can't easily determine the median. Since six divided by two is three, we are going to eliminate three numbers from leftmost in number set toward the right direction and three numbers from rightmost in number set toward the left direction. The last number crossed out in both direction are 3 and 4. To find the middle number, just add both numbers and divide by two. 3+4/2=7/2=3.5 That's the final answer.

Correct Answer: C. uvw = 12(u + v)

Correct Answer: C. ∅