Correct Answer: B. -1/3

Explanation

a, ar, ar\(^2\), ar\(^3\), ar\(^4\), ar\(^5\)

6th term = ar\(^5\) = \(\frac{-2}{27}\)

1st term = a = 18

=> ar\(^5\)

= 18r\(^5\) =\(\frac{-2}{27}\)

r\(^5\) = \(\frac{-2}{27 * 18}\)

→ \(\frac{-1}{27 * 9}\)

r\(^5\) = \(\frac{-1}{243}\)

r = \(^5\)√[\(\frac{-1}{243}\)]

r = \(\frac{-1}{3}\)

Explanation

(a)

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

= \(\frac{2535}{50}\)

= \(50.7\)

(c) Number of students that scored above 60% : 8 + 3 = 11

%age : \(\frac{11}{50} \times 100% = 22%\)

Correct Answer: A. -\(\frac{1}{4}\)

Correct Answer: A. 89

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. But for this set, both of those middle numbers are 89, meaning we don't need to take an average. This gives us the final answer of 89 for the median.

Correct Answer: C. 57\(\frac{1}{2}\)

Correct Answer: B. a ∗ b = a + b - ab

Correct Answer: B. \(\frac{3}{11}\)

Explanation

Total numbers from 40 to 50inclusive = 11 (40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50).

Prime numbers between 40 and 50 (inclusive) are 41, 43, and 47.

There are 3 prime numbers in this range.

therefore, Pr(prime numbers) = \(\frac{3}{11}\)

Explanation

(a)(i) and (iii)Scale: On each axis, 2 cm represents 10 marks.

(ii) \(\bar{x} = \frac{43 + 46 + 48 + 39 + 30 + 60 + 8 + 45 + 40}{9} = \frac{359}{9} = 39.89 \approxeq 39.9\)

\(\bar{y} = \frac{54 + 53 + 63 + 30 + 44 + 75 + 20 + 33 + 48}{9} = \frac{421}{9} = 46.78 \approxeq 46.8\)

\((\bar{x}, \bar{y}) = (39.9, 46.8)\)

(b)

The equation of the line :

\(y - \bar{y} = m(x - \bar{x})\)

\(m = \frac{\sum {xy} - N(\bar{x})(\bar{y})}{\sum {x^{2}} - N(\bar{x})^{2}}\)

= \(\frac{18379 - 9 \times 39.9 \times 46.8}{15979 - (39.9)^{2}} = \frac{18379 - 16805.88}{15979 - 9 \times (39.9)^{2}}\)

= \(\frac{1573.12}{1650.91} \approxeq 0.95\)

Substituting in the equation, \(y - \bar{y} = m(x - \bar{x})\)

\(y - 46.8 = 0.95(x - 39.9)\)

= \(y = 0.95x + 8.895\)

(c) y = 0.95x + 8.895

when x = 28,

\(y = (0.95 \times 28) + 8.895\)

= \(26.6 + 8.895 \approxeq 35.5 marks\).

For a student who scored 28 in Mathematics, his mark in Physics is 35.5.

Correct Answer: C. 12cm

Explanation

\(V= \frac{1}{2}\hspace{1mm}base\hspace{1mm}area\hspace{1mm}\times\hspace{1mm}height\\

120=\frac{1}{3}\times 5 \times 6 \times h; h = \frac{120}{10}=12cm\)

Correct Answer: B. pair of line on opposite sides of LM and parallel to it, each distance 5 cm from LM