Correct Answer: C. 33

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 odd amount of numbers so we just count from each side until we find the number in the middle. 19,27,29,30,32,33,33,34,38,40,40,40,58 This gives us a final answer of 33 for the median.

Correct Answer: C. (3x - 1) years

Correct Answer: C. \(\frac{1}{8}\)

Explanation

\(\begin{array}{c|c} - & 2 & 3 & 5 & 9 \\ \hline 2 & 0 & 1 & 3 & 7 \\ \hline 4 & 2 & 1 & 1 & 5\\ \hline 6 & 4 & 3 & 1 & 3 \\ \hline 8 & 6 &5 & 3 & 1 \end{array}\)

Note: A {horizontal}

B {vertical}

Pr(Difference of 6 or 7) = \(\frac{2}{16} = \frac{1}{8}\)

Correct Answer: D. 80

Explanation

Sum of ∠s in a pentagon = (n - 2)180 = 540°

x° + 2x° + x° + 60° + x° + 10° + x° - 10° = 540°

6x° + 60° = 540°; x = 80°

Correct Answer: B. 11

Explanation

g(-3) = 5 - 2(-3)

= 5 + 6 = 11

Correct Answer: B. 1

Explanation

y = 1/x; y = \(\frac{k}{x}\)

k =xy → 3 * 4 = 12

x = \(\frac{k}{y}\)

x = \(\frac{12}{12}\) = 1

Correct Answer: A. 1.7N

Explanation

\(F = F \cos \theta + F \sin \theta\)

where \(F \cos \theta = \text{horizontal component}\)

\(F \sin \theta = \text{vertical component}\)

Horizontal component of resultant = sum of horizontal compoents of individual forces

= \(8 \cos 30 + 10 \cos 150 = 6.928 - 8.66 \approxeq - 1.7N\)

Correct Answer: D. 2.33

Explanation

(a) \(f : x \to 2x^{2} - 1 ; g : x \to 3x + 2\)

(i) \(f(x - 1) - 7 = 0\)

\(f(x - 1) = 2(x - 1)^{2} - 1 = 2(x^{2} - 2x + 1) - 1\)

= \(2x^{2} - 4x + 2 - 1\)

\(f(x - 1) - 7 = 2x^{2} - 4x + 1 - 7 = 2x^{2} - 4x - 6 = 0\)

\(2x^{2} - 6x + 2x - 6 = 0 \implies 2x(x - 3) + 2(x - 3) = 0\)

\((2x + 2)(x - 3) = 0 \implies 2x = -2; x = 3\)

\(x = -1 ; 3\)

(ii) \(\frac{f(-\frac{1}{2}) . g(3)}{f(4) - g(5)}\)

\(f(-\frac{1}{2}) = 2(-\frac{1}{2})^{2} - 1 = \frac{1}{2} - 1 = -\frac{1}{2}\)

\(g(3) = 3(3) + 2 = 9 + 2 = 11\)

\(f(4) = 2(4^{2}) - 1 = 32 - 1 = 31\)

\(g(5) = 3(5) + 2 = 15 + 2 = 17\)

\(\frac{f(-\frac{1}{2}) . g(3)}{f(4) - g(5)} = \frac{(-\frac{1}{2}) . (11)}{31 - 17}\)

= \(\frac{-\frac{11}{2}}{14}\)

= \(-\frac{11}{28}\)

(b) \(m \ast n = \frac{-n}{m^{2} + 1}; m, n \in R\)

\(-3 \ast -10 = \frac{-(-10)}{(-3)^{2} + 1}\)

= \(\frac{10}{10} = 1\)

\(-10 \ast -3 = \frac{-(-3)}{(-10)^{2} + 1}\)

= \(\frac{3}{101}\)

Hence, \(\ast\) is not commutative as \(m \ast n \neq n \ast m\).

Correct Answer: A. 3 ≤ x ≤ 4