Correct Answer: B. 2x³ - x² + x + c

Explanation

(a) Weight of full tomatoes = 130kg

Weight of half tomatoes = \(\frac{130}{2}\) = 65kg

Cost price of half tomatoes = \(\frac{N52,000}{2}\)

= N26,000

Profit = \(\frac{S.P - C.P}{C.P}\) x 100

30 = \(\frac{(S.P - 26,000)}{25,000}\) x 100

S.P = N7800 + N26,000

S.P = N7,800 + N26,000

S.P of half tomatoes = N33,800

Selling price per kg = \(\frac{33,800}{65}\)

= N520 per kg

Reduction in selling price = 12%

= \(\frac{12}{100}\) x 520 = N62.40k per kg

New selling price per kg

= N520 - N62.40k

= N457.60k

(b) 5kg is thrown away remaining 60kg

The selling price of entire 60kg

= 60 x N457.60k = N27,456

The entire selling price

N33,800 + N27,456

= N61,256

% profit = \(\frac{(61.256 - 50,000)}{52,000}\) x 100

= 17.8%

Explanation

(a) Mean \(\bar{x} = \frac{\sum fx}{\sum f}\)

\(\frac{75}{23} = \frac{28m - 9}{8m - 1}\)

\(75(8m - 1) = 23(28m - 9) \implies 600m - 75 = 644m - 207\)

\(-75 + 207 = 644m - 600m\)

\(132 = 44m \implies m = 3\)

(b)(i) Interquartile range = Third quartile - First quartile

Frequency = 8(3) - 1 = 24 - 1 = 23

\(Q_{3} = \frac{3}{4} \times 23 = 17.25th\) position = 4

\(Q_{1} = \frac{1}{4} \times 23 = 5.75th\) position = 2

Interquartile range : 4 - 2 = 2

(ii) P(at least 4 marks) = \(\frac{(m + 5 + 3m - 4)}{23} = \frac{4m + 1}{23}\)

= \(\frac{4(3) + 1}{23} \)

= \(\frac{13}{23}\)

Correct Answer: B. \(\frac{11}{16}\)

Explanation

\(\frac{1}{2} + (\frac{3}{4} \text{ of } \frac{2}{5}) \div 1\frac{3}{5}\)

= \(\frac{1}{2} + (\frac{3}{4} \times \frac{2}{5}) \div \frac{8}{5}\)

= \(\frac{1}{2} + \frac{3}{10} \div \frac{8}{5}\)

= \(\frac{1}{2} + (\frac{3}{10} \times \frac{5}{8})\)

= \(\frac{1}{2} + \frac{3}{16}\)

= \(\frac{11}{16}\)

Explanation

(a)(i) A = {5, 10, 15, 20}

(ii) B = {4, 8, 12, 16, 20}

(iii) C = {3, 6, 9, 12, 15, 18}

(b) (i) \(A \cap B = {20}\)

(ii) \(A \cap C = {15}\)

(iii) \(B \cap C = {12}\)

(c) \((A \cap B) \cup (A \cap C) = A \cap (B \cup C)\)

\((A \cap B) \cup (A \cap C) = {15, 20}\)

\(A \cap (B \cup C) = {5, 10, 15, 20} \cap {3, 4, 6, 8, 9, 12, 15, 16, 18, 20}\)

= \({15, 20}\)

\(\therefore (A \cap B) \cup (A \cap C) = A \cap (B \cup C)\)

Correct Answer: A. 4.19cm²

Explanation

Given q² = 25 - r².....(1)

from pythagora's theorem

P² = q² + r².......(2)

put (1) into (2)

p² = 25 - p² + x²

p² = 25

p = \(\sqrt{25}\)

= 5

Explanation

\(p = \begin{pmatrix} 5 \\ 3 \end{pmatrix}; q = \begin{pmatrix} -1 \\ 2 \end{pmatrix}; r = \begin{pmatrix} 17 \\ 5 \end{pmatrix}\)

\(r = \alpha p + \beta q\)

\(\begin{pmatrix} 17 \\ 5 \end{pmatrix} = \alpha (\begin{pmatrix} 5 \\ 3 \end{pmatrix}) + \beta (\begin{pmatrix} -1 \\ 2 \end{pmatrix}\)

\(17 = 5\alpha - \beta ... (1); 5 = 3\alpha + 2\beta .... (2)\)

\((1) \times 2 : 34 = 10\alpha - 2\beta ... (3)\)

\((3) + (2) : 39 = 13\alpha \implies \alpha = 3\)

\(5 = 3(3) + 2\beta \implies 2 \beta = 5 - 9 = -4\)

\(\beta = -2\)

\(r = 3p - 2q \implies 2q = 3p - r\)

\(q = \frac{1}{2} (3p - r)\)

Correct Answer: C. \(3\frac{3}{5}\)

Explanation

\(5\frac{2}{5}\times \left(\frac{2}{3}\right)^2 ÷ \left(1\frac{1}{2}\right)^{-1}\\

\frac{27}{5}\times \frac{4}{9} \times \frac{3}{2}=3\frac{3}{5}

\)

Correct Answer: A. 1/8

Correct Answer: A. \(\frac{3n}{2p^2}\)

Explanation

M = \(\frac{nk}{p^2}\)

k → \(\frac{mp^2}{n}\) = \(\frac{3x1^2}{2}\)

k = \(\frac{3}{2}\)

: m = \(\frac{3xn}{2p^2}\)