Correct Answer: B. \(\frac{\sqrt{2}}{4}(\sqrt{3} - 1)\)

Explanation

\(\cos(a + b) = \cos a\cos b - \sin a\sin b\)

\(\cos75° = \cos(30 + 45) = (\cos30)(\cos45) - (\sin30)(\sin45)\)

= \((\frac{\sqrt{3}}{2} \times \frac{\sqrt{2}}{2}) - (\frac{1}{2} \times \frac{\sqrt{2}}{2})\)

= \(\frac{\sqrt{6} - \sqrt{2}}{4}\)

= \(\frac{\sqrt{2}(\sqrt{3} - 1)}{4}\)

Correct Answer: B. is convicted of a serious crime

Explanation

(a) \(\frac{2}{5}(x - 2) - \frac{1}{6}(x + 5) \leq 0\)

Multiplying through by the LCM of 5 and 6 (i.e 30)

\(12(x - 2) - 5(x + 5) \leq 0\)

\(12x - 24 - 5x - 25 \leq 0\)

\(7x - 49 \leq 0 \implies 7x \leq 49\)

\(x \leq 7\).

(b) (i) \(\frac{x^{2} - y^{2}}{x^{2} + xy}\)

P = \(\frac{(x - y)(x + y)}{x (x + y)}\)

P = \(\frac{x - y}{x}\)

(ii) When x = -4, y = -6

\(P = \frac{-4 - (-6)}{-4}\)

\(P = \frac{2}{-4}\)

\(P = - \frac{1}{2}\)

Correct Answer: C. a desert

Correct Answer: D. battle of Adwa

Explanation

The Battle of Adwa is the correct answer. The battle was led by Emperor Menelik II of Ethiopia and the Ethiopian forces defeated the Italo-Egyptian invaders on March 1, 1896.

Correct Answer: A. the corners of the pages of my book are crumpled

Explanation

Fold down the corner of (a page of a book or magazine)

Correct Answer: A. grazing paddocks

Explanation

(a) State Characteristics of Local Craft Industries:- Individual/family ownership -Skills passed on from generation to generation -Traditional in nature -Simple tools are used - Low technology is used -Local raw materials are used -Less capital intensive -Production is low -Product for local market -Employs few people -Less power supply required -Limited space required -some with long period of apprenticeship-All year round employment Energy/time consuming -Irregular working hours -Small Scale in plant size -Irregular income -Product of high artistic value -Less government support -Needs less electric power -Prices of product are negotiable -?se of family labour-Mostly located in rural areas Shortage -Some practiced on part-time basis.

(b) Identify Limitations of Local Craft Industries:-Shortage of labour -Inadequate capital/little access to loan -Poor/inadequate transport-High freight charges -Taste for foreign products - Shortage of raw materials -Competition from imported substitutes -Low patronage/demand -Limited production -Little or no government support -Irregular working hours -Irregular income -Low interest shown by the youth towards the industry-Limited research application Inadequate publicity.

(C) Explain Factors that have contributed to the High Volume of Trade Between the Developed and Tropical African Countries:--Non similarity of products -Differences in taste and culture - Differences in prices of goods -Preference of imported goods -Political consideration -need to improve standard of living -Political stability -Absence of trade unions or barriers -Differences in import duties -Differences in quality of products -Colonial ties-Differences in climate -Desire for new products -Need for foreign exchange-Generation of revenue --Need for expansion of market -For increased Gross Domestic Products (GDP) -Employment opportunity-Acquisition of skills/expertise-Differences in natural resource endowment-Stimulation of other sectors of the economy -To enhance balance oI payment~Benefit of comparative cost advantage.

Correct Answer: B. Adam and Jesus Christ

Correct Answer: C. Legislature

Explanation

The legislature is made up of those who write the laws. it is a is therefore a group of people who vote for new laws or make changes to the old laws.