Correct Answer: D. fixed capital

Explanation

Given \(\sin x = 0.6 = \frac{3}{5}\)

\(\therefore Opp = 3; Hyp = 5\)

Using Pythagoras theorem,

\(5^{2} = 3^{2} + Adj^{2}\)

\(Adj = \sqrt{5^{2} - 3^{2}}\)

\(Adj = \sqrt{25 - 9} = \sqrt{16} = 4\)

\(\therefore \cos x = \frac{4}{5} = 0.8\)

\(2\cos x + 3\sin x = 2(\frac{4}{5}) + 3(\frac{3}{5})\)

= \(\frac{8}{5} + \frac{9}{5}\)

= \(\frac{17}{5}\).

(b)

Join O to X and O to Y.

Considering either \(\Delta OXC\) or \(\Delta OYC\),

\(\sin 65 = \frac{r}{30}\)

\(r = 30 \sin 65\)

\(r = 30 \times 0.9063\)

\(r = 27.189 cm \approxeq 27.2 cm\) (to one decimal place)

(b) Area of shaded portion = Area of triangle ABC - Area of semi-circle WXYZ.

= \(\frac{1}{2} bh - \frac{1}{2} \pi r^{2}\)

= \((\frac{1}{2} \times 2c \times 30) - (\frac{1}{2} \times \frac{22}{7} \times (27.189)^{2})\)

From \(\Delta COA, \tan 65 = \frac{c}{30}\)

\(\implies c = 30 \tan 65 \approxeq 64.34 cm\)

\(\therefore\) Area of shaded portion = \(30(64.34) - \frac{8131.659}{7}\)

= \(1930.056 - 1161.666\)

= \(768.39 cm^{2}\)

Correct Answer: C. market segmentation

Correct Answer: D) Feeding the five thousand

Explanation

This question is asking which of the options is not a nature miracle. Nature miracles are events that show Jesus' power over nature. The options are: stilling of the storm, walking on the sea, raising of Lazarus from the dead, and feeding the five thousand.

Option A, stilling of the storm, is a nature miracle where Jesus calmed a stormy sea. Option B, walking on the sea, is also a nature miracle where Jesus walked on water. Option C, raising of Lazarus from the dead, is not a nature miracle since it does not involve control over nature.

Option D, feeding the five thousand, is not a nature miracle and is the correct answer. This event involved Jesus multiplying five loaves of bread and two fish to feed a large crowd. Although it showcases Jesus' power, it does not involve control over nature.

It is important to note the different types of miracles in the Bible, including nature miracles, healing miracles, and exorcisms. Understanding these different categories can help in understanding the significance of each miracle and its message.

Explanation

Reasons for consumers' protection are:

(i) Exploitation: The consumers are protected from exploitation by the manufacturers through indiscriminate price increase. This is done through the Price control Act.

(ii) Sub-standard goods: Manufacturers produce goods without taking into consideration the quality desired. The Standard Organization of Nigeria Act checks such practices.

(iii) Deceptive weights and measures: Sellers may use incorrect weights and measurements in selling goods to customers. The Weight and Measures Act of 1963 helps to prevent such practices.

(iv) Sale of harmful food and drugs: Consumers are also protected from dangerous goods, especially drugs. The Foods and Drugs Act protects the customers against such goods being offered for sale to them.

(v) Credit Purchase Agreement: Consumers are often not well informed about the details of such agreement. They may inadvertently sign false credit facilities. The Hire Purchase Act is aimed at protecting the rights of such customers.

(vi) Misleading advertisement: Many claims made by advertisers about the performance of their products are not correct. Trade Description Act was enacted to check such practices.

Correct Answer: A. Ethyne

Correct Answer: D. all of the above

Explanation

(a)(i) Two industrial uses of hydrogen: —filling of weather balloons. —manufacture of plastics. —manufacture of ammonia by the Haber process. —manufacture of methanol. —oil refinery process/hydrocracking —used in fuel cells. —manufacture of margarine. —in oxy-hydrogen flame (for welding and cutting metals). —as reducing agent in production of metals, e.g. Cu and.Pb from their oxides. —conversion of coal to crude oil. —(liquid) hydrogen is used as rocket fuel/gaseous fuel (Any 2).

(ii) Mg(HCO\(_3\))\(_{2(aq)}\) —> MgCO\(_3\)\(_{(s)}\) + H\(_2\)O\(_{(l)}\) + Cu\(_3\).

In the equation above: (1) the type of hardness of water being removed is temporary hardness of water. (2) two disadvantges of hardness of water are: —scales/furrinab of kettles/pipes causing blockage leading to power wastage. —soap is wasted not suitable for laundry. —not suitable for use in tanning, textiles and paper production (Any 2).

(b)(i) Disadvatnages of using graphite electrodes in the extraction of aluminium by electrolysis: At high temperature oxygen gas produced at the anode reacts with the graphite electrodes to form carbon(IV) oxide.

(ii) Balanced equation of reaction between calcium oxide and water to form slaked lime: CaO + H\(_2\)O \(\to\) Ca(OH)\(_2\)

(iii) One use of slaked lime: —used to treat acidic soil. —used to make mortar/plasters/cement/hold bricks. —in manufacture of glass. —purification of water/removing hardness of water. —manufacture of white wash. —to test for CO\(_2\). —production of bleaching powder: —to recover or produce ammonia from ammonium chloride used in solvay process.

(c)(i) Saponification is the alkaline hydrolysis of fats/oils to produce soap and propane —1,2,3-triol

(ii) Raw materials needed for the manufacture of soap: —oil/fat. —alkali (1) (sodium hydroxide/potassium hydroxide

(iii) Main by-product obtained from the manufacture of soap is propane —1,2,3-triol.

(d) Extraction of iron in the blast furnace using iron-ore, coke and limestone as raw materials with the aid of chemical equations..

(i) Bottom of furnace: The O\(_2\) in the hot air combines with carbon(coke) to produce carbon (IV) oxide which is reduced to carbon (II) oxide.

C + O\(_2\) \(\to\) CO\(_{2(g)}\)

CO\(_{2(g)}\) + C \(\to\) 2CO\(_{(g)}\)

(ii) Middle of the furnace: The calcium carbonate CaCO\(_3\) decomposes under great heat to form CO\(_2\) and CaO and CaCO\(_3\) decomposes to remove the impurities SiO\(_2\)

CaCO\(_3\) —> CaO\(_s\) + CO\(_{2(g)}\)

CaO + SiO\(_2\) --> CaSiO\(_3\).

(iii) Top of furnace: Iron (III) oxide is reduced to metallic iron Fe\(_2\)O\(_2\) + 3CO 2Fe + 3CO\(_2\)

OR Fe\(_3\)O\(_4\) + 4CO —> 3Fe + 4CO\(_2\).

Correct Answer: D. expand the market for the products of member states

Correct Answer: D) Crossed cheque

Explanation

On the other hand, an open cheque does not have any crossing lines on it and can be encashed by anyone who presents it to the bank. This makes it less secure as it can be easily misused or lost.

A bearer cheque is a type of cheque that is payable to the bearer, meaning anyone who possesses the cheque can cash it. This also poses a risk, as anyone who finds or steals the cheque can use it to withdraw the funds.

A post-dated cheque is a cheque that is dated for a future date. It cannot be encashed until that date. While this can provide some protection against loss, it does not offer the same level of security as a crossed cheque.

Therefore, the correct answer is Option D: Crossed cheque. It is the type of cheque that protects the holder against the risk of loss.