Correct Answer: B. prudence concept

Explanation

Prudence also known as conservatism. This principles state that the accountant should not anticipate income and will normally take the figure that will understate rather than overstate the profit.

Correct Answer: C. is raining

Correct Answer: B. chewing

Explanation

Grasshoppers are herbivorous insects that primarily feed on plant material. Their mouthparts are well adapted for chewing, allowing them to consume various parts of plants, such as leaves, stems, and flowers.The mouthparts of a grasshopper consist of several structures that work together during feeding: Mandibles, Maxillae and Labium and Labrum

Explanation

(a) Relationship between agriculture and industries are:

(i) Agriculture provides market for industrial products, e.g. farm machinery, chemicals, fertilizer, etc.

(ii) Provides food to industrial workers.

(iii) both agriculture and industry compete for labour.

(iv) agricultural development allows for a shift of factors of production to the industry.

(v) rise in agricultural income due to efficient and economic factor combination brings about development of the industrial sector of the economy.

(vi) industries provide a large range of d desirable things that farmers want to buy.

(vii) agriculture provides the raw materials for industries.

(viii) industries produce agrochemicals for agricultural uses, e.g. pesticides, fertilizers, vaccines, herbicides etc.

(ix) industries provide storage facilities for agricultural produce, d e.g. pesticides, fertilizers, vaccines, herbicides etc.

(x) industries provide processing facilities for agricultural produce.

(xi) industries produce machinery and equipment for agricultural uses e.g. tractors, ploughs, cutlasses, hoes, etc.

(b) Factors affecting the success of commercial agriculture in Nigeria include:

(i) sufficient money/capital expand or inadequate finance.

(ii) problems of land tenure which do not allow for use of large expanse of land suitable for commercial agriculture

(iii) availability of storage facilities.

(iv) availability of processing facilities.

(v) availability of basic amenities & infrastructures.

(vi) inadequate tools and machinery.

(vii) poor pricing and marketing incentives.

(viii) bad government policies / inconsistent government policies.

(ix) infestation of pests.

(x) outbreak of diseases.

(xi) climatic effect.

(c) Agricultural research institutes in Nigeria are:

(i) Cocoa Research Institute of Nigeria (CRIN), Ibadan.

(ii) Rubber Research Institute of Nigeria (RRIN), Benin.

(iii) National Cereal Research Institute (NCRI), Badegi

(iv) National Root Crops Research Institute (NRCRI), Umudike.

(v) National Institute for Horticultural Research (NIHORT), Ibadan.

(vi) Nigerian Institute for Oil Palm Research (NIFOR), Benin

(vii) Forestry Research Institute of Nigeria (FRIN), Ibadan

(viii) National Institute for Oceanography and Marine Research (NIOMAR), Lagos

(ix) National Institute for Fisheries and Fresh Water Research, Kainji.

(x) Nigerian Stored Products Research Institute, florin.

(xi) National Veterinary Research Institute (NVRI), Vom, Jos.

(xii) National Institute for Trypanosomiasis Research (NITR), Kaduna.

(xiii) International Institute of Tropical Agriculture (iITA), Ibadan.

(xiv) Leather Research Institute of Nigeria, Zaria.

(xv) Lake Chad Research Institute, Maiduguri.

(xvi) Institute of Agricultural Research ( IAR), Zaria

(xvii) Institute of Agricultural Research and Training (IART), Ibadan

Explanation

(a) \(\frac{1\frac{1}{4} + \frac{7}{9}}{1\frac{4}{9} - 2\frac{2}{3} \times \frac{9}{64}}\)

\(1\frac{1}{4} + \frac{7}{9} = \frac{5}{4} + \frac{7}{9}\)

= \(\frac{45 + 28}{36}\)

= \(\frac{73}{36}\)

\(1\frac{4}{9} - 2\frac{2}{3} \times \frac{9}{64} = \frac{13}{9} - (\frac{8}{3} \times \frac{9}{64})\)

= \(\frac{13}{9} - \frac{3}{8}\)

= \(\frac{104 - 27}{72}\)

= \(\frac{77}{72}\)

\(\therefore \frac{1\frac{1}{4} + \frac{7}{9}}{1\frac{4}{9} - 2\frac{2}{3} \times \frac{9}{64}} = \frac{73}{36} \div \frac{77}{72}\)

= \(\frac{73}{36} \times \frac{72}{77}\)

= \(\frac{146}{77}\)

= \(1\frac{69}{77}\)

(b) \(\sin x = \frac{2}{3}\)

In \(\Delta ABC, 3^{2} = 2^{2} + |BC|^{2}\)

\(\therefore |BC|^{2} = 9 - 4 = 5\)

\(|BC| = \sqrt{5}\)

\(\tan x = \frac{2}{\sqrt{5}} ; \cos x = \frac{\sqrt{5}}{3}\)

\(\therefore \tan x - \cos x = \frac{2}{\sqrt{5}} - \frac{\sqrt{5}}{3}\)

= \(\frac{6 - 5}{3\sqrt{5}}\)

= \(\frac{1}{3\sqrt{5}}\)

Rationalizing, we have

\(\frac{1}{3\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{\sqrt{5}}{15}\)

Correct Answer: A. to the advantage of their members

Explanation

A pressure group, also known as an interest group or lobby, is an organization formed by like-minded people who seek to influence PUBLIC POLICY to promote an interest. Motives for action may be based on a shared political, religious, moral, health or commercial position.

Correct Answer: B. energy flow within the system

Correct Answer: C. community

Correct Answer: D. possesses high e.m.f

Explanation

(a) \(y = 6 - x - x^{2}\)

When x = 0, y = 6.

When y = 0, \(x^{2} + x - 6 = 0\)

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

\(x = -3 ; x = 2\)

Graph passes through (0, 6), (-3, 0) (2, 0).

Turning point : \(\frac{\mathrm d y}{\mathrm d x} = - 1 - 2x\)

\(-1 - 2x = 0 \implies x = \frac{-1}{2}\)

When \(x = \frac{-1}{2}\), \(y = 6 - (-\frac{1}{2}) - (\frac{-1}{2})^{2} = 6\frac{1}{4}\).

Turning point : \((-\frac{1}{2}, 6\frac{1}{4})\).

\(y = 3x^{2} - 2x + 3\)

When x = 0, y = 3.

\(b^{2} - 4ac = (-2)^{2} - 4(3)(3) = 4 - 36 < 0\)

Graph does not cut x - axis.

\(\frac{\mathrm d y}{\mathrm d x} = 6x - 2\)

At turning point, \(6x - 2 = 0 \implies x = \frac{2}{6} = \frac{1}{3}\)

When \(x = \frac{1}{3}, y = 3(\frac{1}{3})^{2} - 2(\frac{1}{3}) + 3 = 2\frac{2}{3}\)

Turning point : \((\frac{1}{3}, 2\frac{2}{3})\).

(b) For the x- coordinates, we use the equation.

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

\(4x^{2} - x - 3 = 0 \implies 4x^{2} - 4x + 3x - 3 = 0\)

\(4x(x - 1) + 3(x - 1) = 0 \implies (4x + 3)(x - 1) = 0\)

\(x = -\frac{3}{4} ; 1\)

(c) Area of shaded portion :

\(\int_{-\frac{3}{4}} ^{1} [(6 - x - x^{2}) - (3x^{2} - 2x + 3)] \mathrm {d} x\)

= \(\int_{-\frac{3}{4}} ^{1} (3 + x - 4x^{2}) \mathrm {d} x\)

= \([3x + \frac{x^{2}}{2} - \frac{4}{3}x^{3}]|_{-\frac{3}{4}} ^{1}\)

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

= \(\frac{13}{6} - (-\frac{45}{32})\)

= \(\frac{343}{96} sq. units\)