Correct Answer: C. Le 3,600,000.00

Explanation

sectoral angle representing food

= 360^o - (80 + 70 + 90)^o

= 120^o

Amount spent on food

= \(\frac{\tect{sectoral angle}}{360^o}\) x Le 10,800,000

= Le 3,600,000

Correct Answer: B. 24

Correct Answer: B. \(\frac{1}{6}\)

Explanation

\(\begin{array}{c|c}

& 1 & 2 & 3 & 4 & 5 & 6 \\

\hline

1 & 1,1 & 1,2 & 1,3 & 1,4 & 1,5 & 1,6 \\ \hline 2 & 2,1 & 2,2 & 2,3 & 2,4 & 2,5 & 2,6 \\ \hline 3 & 3,1 & 3,2 & 3,3 & 3,4 & 3,5 & 3,6 \\ \hline 4 & 4,1 & 4,2 & 4,3 & 4,4 & 4,5 & 4,6 \\ 5 & 5,1 & 5,2 & 5,3 & 5,4 & 5,5 & 5,6 \\ \hline 6 & 6,1 & 6,2 & 6,3 & 6,4 & 6,5 & 6,6\end{array}\)

From the table above, event space, n(E) = 6

sample space, n(S) = 36

Hence, probability sum of scores is at least 10, is;

\(\frac{n(E)}{n(S)}\)

= \(\frac{6}{36}\)

= \(\frac{1}{6}\)

Correct Answer: A. \(-540x^{3}y^{3}\)

Explanation

Listing out in order, the terms of this expansion have coefficients: \(^{6}C_{6}, ^{6}C_{5}, ^{6}C_{4}, ^{6}C_{3}, ^{6}C_{2}, ^{6}C_{1}, ^{6}C_{0}\)

The 4th term = \(^{6}C_{3}(3x)^{3}(-y)^{3} = 20 \times 27x^{3} \times -y^{3}\)

= \(-540x^{3}y^{3}\).

Correct Answer: C. 81cm²

Explanation

Area of \(\Delta\) QNP = \(\frac{1}{2} \times 9 \times 6 \) = 27cm²

Area of \(\Delta\) QMN = Area of \(\Delta\) QNP

= Area of \(\Delta\) PNO (triangles between the same parallels)

Hence, area of the trapezium

3 x area of \(\Delta\) QNP

= 3 x 27

= 81cm²

Correct Answer: B. 4cm²

Explanation

On a map, 1cm represents 5km. Then it follows that 1cm² represents 25km². Acm² represents 100km². By apparent cross-multiplication, 1cm² x 100km² = Acm²x 25km²

therefore A = \(\frac{100}{25}\) = 4cm²

Correct Answer: C. 13

Explanation

First, arrange the marks in order of magnitude; 3, 4, 5, 7, 10, 13, 14, 16

Hence range = 16 - 3 = 13

Correct Answer: D. \(\frac{56}{33}\)

Explanation

\(\tan (x + y) = \frac{\tan x + \tan y}{1 - \tan x\tan y}\)

\(\tan x = \frac{5}{12} ; \tan y = \frac{3}{4}\)

\(\tan (x + y) = \frac{\frac{5}{12} + \frac{3}{4}}{1 - (\frac{5}{12} \times \frac{3}{4}})\)

= \(\frac{\frac{14}{12}}{\frac{33}{48}}\)

= \(\frac{56}{33}\)

Correct Answer: B. \(\frac{1}{\sqrt{29}}(-2i + 5j)\)

Explanation

The unit vector, \(\hat{n}\) is given by \(\hat{n} = \frac{\overrightarrow{r}}{|\overrightarrow{r}|}\)

= \(\frac{(-2i + 5j)}{\sqrt{(-2)^{2} + 5^{2}}} = \frac{(-2i + 5j)}{\sqrt{29}}\)

= \(\frac{1}{\sqrt{29}}(-2i + 5j)\)

Explanation

(a) \(\frac{1 + 4 + k + (k + 4) + 11}{5} = k + 1\)

\(\frac{2k + 20}{5} = k + 1\)

\(2k + 20 = 5(k + 1) \implies 2k + 20 = 5k + 5\)

\(20 - 5 = 5k - 2k \implies 15 = 3k\)

\(k = 5\)

(b) Mean \(\bar{x} = 6\)

\(\sigma = \sqrt{\frac{\sum fx^{2}}{\sum f} - (\frac{\sum fx}{\sum f})^{2}}\)

= \(\sqrt{\frac{244}{5} - (\frac{30}{5})^{2}}\)

= \(\sqrt{48.8 - 36}\)

= \(\sqrt{12.8} = 3.58\)