Explanation

Total ratio = 3 + 5 + 8 = 26

Ali's share is \(\frac{3}{16}\) x N420,000

= N78,000

Yusuf's share is \(\frac{8}{16}\) x N420,000

= N210,000

Sum of Ali's share + Yusuf's share

= N78,750 + N210,000

= N288,750

(b) 2(\(\frac{1}{8}\))\(^2\) = 32\(^{x - 1}\)

2\(^{1}\) x 2\(^{3x}\) = 2\(^{5x - 5}\)

2\(^{1 - 3x}\) = 2\(^{5x - 5}\)

1 - 3x = 5x - 5

-3x - 5x = -5 -1

-8x = -6

x = \(\frac{-6}{-8}\)

= \(\frac{3}{4}\)

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

Explanation

Given, \(a(t) = (3t - 2) ms^{-2}\), the first integration of a(t), with respect to t, gives v(t) (the velocity). The second integration of a(t) or first integration of v(t) gives s(t).

\(v(t) = \int (3t - 2) \mathrm {d} t = \frac{3}{2}t^{2} - 2t\)

\(s(t) = \int (\frac{3}{2}t^{2} - 2t) \mathrm {d} t\)

= \(\frac{t^{3}}{2} - t^{2}\)

When t = 3s,

\(s(3) = \frac{3^{3}}{2} - 3^{2} = \frac{27}{2} - 9 \)

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

Correct Answer: C. 68°

Correct Answer: A. -5

Explanation

x² + 7x + 10 = 0

x² + 5x + 2x + 10 = 0

x(x + 5) + 2(x + 5) = 0

(x + 2)(x + 5) = 0

x + 2 = 0 or x + 5 = 0

x = -2 or x = -5

the smaller value x = -5

Correct Answer: B. 110001_two

Correct Answer: B. 13

Explanation

The median is middle number of a set, when the numbers are arranged in order from least to greatest. In our case we re arrange our numbers in the following fashion: 7, 7, 8, 12, 13, 13, 22, 27, 30 The middle number in our case is the 5th entry. Therefore, the median is 13

Explanation

(a)

(b) \(11.011_{two} = 1 \times 2^{1} + 1 \times 2^{0} + 0 \times 2^{-1} + 1 \times 2^{-2} + 1 \times 2^{-3}\)

= \(2 + 1 + 0 + \frac{1}{4} + \frac{1}{8}\)

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

= \(3.375\)

(c) \(\frac{9.6 \times 10^{18}}{0.24 \times 10^{5}} \equiv \frac{9.6 \times 10^{18}}{2.4 \times 10^{4}}\)

= \(\frac{9.6}{2.4} \times 10^{18 - 4}\)

= \(4 \times 10^{14}\)

Correct Answer: D. 100°

Explanation

TSA = 224\(\pi\) cm\(^2\)

r : 1 = 2: 5

\(\frac{r}{l} = \frac{2}{5}\)

r = \(\frac{2l}{5}\)

\(\frac{3r}{2}\) = l

TSA \(\pi\)rl + \(\pi ^2\)

TSA = \(\pi\)(rl + r\(^2\))

224\(\pi\) = \(\pi\)r(l + r)

224 = r (\(\frac{5r}{2} + \frac{r}{1}\))

224 = r(\(\frac{5r + 2r}{2}\))

224 = \(\frac{7r^2}{2}\)

r\(^2\) = \(\frac{448}{7}\)

r = \(\sqrt{448}{7}\)

r = \(\sqrt{64cm}\)

l = \(\frac{5 \times 8}{2}\)

r = 8cm

l = 20cm

(b) Volume of cone = \(\frac{1}{3}\)\(\pi ^2\)h

h\(^2\) = l\(^2\) - r\(^2\)

h\(^2\) = (20)\(^2\) - (8)\(^2\)

h\(^2\) = 400 - 64

h = \(\sqrt{336}\)

= 18.33cm

Volume = \(\frac{1}{3} \times \frac{22}{7}\) x 8\(^2\) x 18.33

= \(\frac{25,809.06}{21}\)

= 1229 cm\(^3\)

Correct Answer: A. 5

Explanation

The exterior angle of the polygon = 180 – 108 = 72°. The sum of exterior angle of the regular polygon = 360°

The number of sides \(=\frac{360}{72}=5\)