Correct Answer: B. adequate transportation system

Correct Answer: D. manufacture food for animals

Correct Answer: A. pluto

Correct Answer: C. As

Correct Answer: D. cost and comparable data useful in decision-making

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: C. gross national product

Explanation

Gross national product is the total value of goods produced and services provided by a country during one year, equal to the gross domestic product plus the net income from foreign investments. GNP calculation includes income earned by domestic residents abroad minus the income of foreigners earned in the domestic economy. GNP is calculated by taking the sum of personal consumption expenditures, private domestic investment, government expenditure, net exports and any income earned by residents from overseas investments, minus income earned within the domestic economy by foreign residents.

Correct Answer: B. If Stephen is not good at Mathematics, then he is not intelligent

Explanation

If p implies (→) q

then not (~) q → not (~) p

Option B

Explanation

\(R_{1} = \begin{pmatrix} -20 \cos 60° \\ -20 \sin 60° \end{pmatrix} ; R_{2} = \begin{pmatrix} -10 \cos 60° \\ 10 \sin 60° \end{pmatrix} \)

\(R_{3} = \begin{pmatrix} 8\sqrt{2} \cos 45° \\ 8\sqrt{2} \sin 45° \end{pmatrix}\)

\(R = R_{1} + R_{2} + R_{3}\)

\(R = \begin{pmatrix} -20 \cos 60° \\ -20 \sin 60° \end{pmatrix} + \begin{pmatrix} -10 \cos 60° \\ 10 \sin 60° \end{pmatrix} + \begin{pmatrix} 8\sqrt{2} \cos 45° \\ 8\sqrt{2} \sin 45° \end{pmatrix}\)

\(R = \begin{pmatrix} -20 \times \frac{1}{2} \\ -20 \times \frac{\sqrt{3}}{2} \end{pmatrix} + \begin{pmatrix} -10 \times \frac{1}{2} \\ 10 \times \frac{\sqrt{3}}{2} \end{pmatrix} + \begin{pmatrix} 8\sqrt{2} \times \frac{1}{\sqrt{2}} \\ 8\sqrt{2} \times \frac{1}{\sqrt{2}} \end{pmatrix}\)

= \(\begin{pmatrix} - 10 - 5 + 8 \\ -10\sqrt{3} + 5\sqrt{3} + 8 \end{pmatrix}\)

= \(\begin{pmatrix} -7 \\ 8 - 5\sqrt{3} \end{pmatrix} = \begin{pmatrix} -7 \\ -0.66 \end{pmatrix}\)

Let \(\theta\) be the direction from the horizontal.

\(\tan \theta = \frac{-0.66}{-7}\)

\(\tan \theta = 0.0943\)

\(\theta = \tan^{-1} (0.0943) = 5.39°\)

Correct Answer: C. predominance of small farm holdings