Explanation

a.

Median position = \(\frac{∑F + 1}{2}\) (since ∑F is odd so we added 1)

\(\frac{27 + 1}{2} = \frac{28}{2}\) = 14th position.

counting down the frequency column, the median position occurs at 4. Therefore, the median height is 5m.

b

i. mean(x?) = \(\frac{Σfx}{Σf}\)

= \(\frac{144}{27}\)

∴ x? = 5.3m ( to 1 d.p)

ii.

Standard deviation = \(\sqrt{vaiance} = \sqrt{\frac{Σfx^2}{Σf} - (\frac{Σfx}{Σf})^2}\)

S D = \(\sqrt{\frac{834}{27} - (\frac{144}{27})^2}\)

S.D = \(\sqrt{30.888 - (5.333)^2}\)

= \(\sqrt{30.888 - 28.441}\) = \(\sqrt{2.447}\) = 1.5738 ≈ 1.6 ( to 1 d.p)

Correct Answer: D. 50°

Explanation

Latitudinal difference = 65

Correct Answer: A. 20

Explanation

cos(x + 25^o) = sin 45^o

using cos \(\theta\) = sin(90 - \(\theta\))

cos(x + 25^o) = cos(90 - 45)

cos(x + 25^o) = cos 45

x + 25 = 45

x = 45 - 25

x = 20^o

Correct Answer: D. x = 2, y = -3

Explanation

4x - y = 11....(1) x 2 8x - 2y = 22....(3)

5x + 12y = 4....(2) x 1 5x + 2y = 4....(4)

add eqn (3) and (4)

13x = 26

x = 2

4(2) - y = 11 \(\implies\) y = 8 - 11

y = -3.

Correct Answer: D. 210

Correct Answer: B. II only

Explanation

Using the formula, \((n - 2) \times 180°\) to get the sum of the interior angles. Then we can have

\((n - 2) \times 180° = 108n\) ... (1)

\((n - 2) \times 180° = 116n\) ... (2)

\((n - 2) \times 180° = 120n\) ... (3)

Solving the above given equations, where n is not a positive integer then that angle is not the interior for a regular polygon.

(1): \(180n - 360 = 108n \implies 72n = 360\)

\(n = 5\) (regular pentagon)

(2): \(180n - 360 = 116n \implies 64n = 360\)

\(n = 5.625\)

(3): \(180n - 360 = 120n \implies 60n = 360\)

\(n = 6\) (regular hexagon)

Hence, 116° is not an angle of a regular polygon.

Correct Answer: D. 13/15

Correct Answer: D. \(\begin{pmatrix} -4 & 3 \\ -2 & 9 \end{pmatrix}\)

Explanation

\(\begin{pmatrix} 1 & -2 \\ 3 & 4 \end{pmatrix} \(\begin{pmatrix} -2 & 3 \\ 1 & 0 \end{pmatrix}\)

=\(\begin{pmatrix} (1 \times -2) + (-2 \times 1) & (1 \times 3) + (-2 \times 0) \\ (3 \times -2) + (4 \times 1) & (3 \times 3) + (4 \times 0) \end{pmatrix}\)

= \(\begin{pmatrix} -4 & 3 \\ -2 & 9 \end{pmatrix}\)

Correct Answer: D. 1/4

Correct Answer: A. 50