Explanation

(a) Foreign policy refers to the strategy and tactics employed by a state in conducting her relationship with other states while pursuing her interest.

(b) The factors that influence Nigeria's foreign policy are:

(i) The population, land mass and the quality of human resources of Nigeria affect her foreign policy.

(ii) The economic resources available to Nigeria, e.g. mineral re-sources and agricultural products affect foreign policy.

(iii)The commitments of previous governments, e.g. treaties and pacts, affect foreign policy.

(iv) The ideological disposition of the rulers affect foreign policy as countries tend to relate more with those countries with similar ideologies.

(v) The military strength of Nigeria (i.e. size of the army and the quality) influences her foreign policy.

(vi) The industrial strength of Nigeria influences her choice of trading partners, e.g. electricity supply to Niger, Gas to Ghana, Republic of Benin and Togo.

(vii) Public opinion on issues can bring changes in government foreign policy, e.g. Anglo — Nigeria pact of 1962.

(viii) The geographical location of a country also exerts some influence on its foreign policy. Africa for example is described as centre piece of Nigeria's foreign policy.

(ix) Historical background of the country also affects her foreign policy, e.g. Nigeria's membership of the Commonwealth.

(x) Types of government, e.g. military or democratic government, can affect foreign policy .

Correct Answer: A. provision of food and employment opportunity

Correct Answer: C. emigrated

Explanation

(a) \(^{n + 1}C_{3} - ^{n - 1}C_{3}\)

= \(\frac{(n + 1)!}{3! (n + 1 - 3)!} - \frac{(n - 1)!}{3! (n - 1 - 3)!}\)

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

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

= \(\frac{(n + 1)(n)(n - 1)}{6} - \frac{(n - 1)(n - 2)(n - 3)}{6}\)

= \(\frac{(n - 1)[(n + 1)(n) - (n - 2)(n - 3)]}{6}\)

= \(\frac{(n - 1)[n^{2} + n - (n^{2} - 5n + 6)}{6}\)

= \(\frac{(n - 1)[6n - 6]}{6}\)

= \(\frac{6(n - 1)^{2}}{6}\)

= \((n - 1)^{2}\)

(b) p(six) = p = \(\frac{1}{6}\), p(not six) = q = \(\frac{5}{6}\).

\((p + q)^{5} = p^{5} + 5p^{4} q + 10p^{3} q^{2} + 10p^{2} q^{3} + 5pq^{4} + q^{5}\)

(i) p( at most 2 sixes) = \(q^{5} + 5pq^{4} + 10p^{2} q^{3}\)

= \((\frac{5}{6})^{5} + 5(\frac{1}{6})(\frac{5}{6})^{4} + 10(\frac{1}{6})^{2} (\frac{5}{6})^{3}\)

= \(\frac{3125}{7776} + \frac{3125}{7776} + \frac{1250}{7776}\)

= \(\frac{7500}{7776} = 0.9645 \approxeq 0.965\) (3 d.p)

(ii) p(exactly 3 sixes) = \(10p^{3} q^{2}\)

= \(10(\frac{1}{6})^{3} (\frac{5}{6})^{2}\)

= \(\frac{250}{7776}\)

= \(0.032\) (3 d.p)

Correct Answer: A) could suggest that there are differences in cognitive ability among the monkeys even though such differences may not actually exist.

Explanation

The choice that most logically completes the text is A) could suggest that there are differences in cognitive ability among the monkeys even though such differences may not actually exist. The text states that the researchers neglected to control for the physical difficulty of the tasks used to evaluate the cognitive abilities of white-faced capuchin monkeys. Monkeys given different types of tasks, varying in physical difficulty, were judged by the same criteria. Therefore, the results of the study may suggest differences in cognitive ability among the monkeys, even though these differences may not actually exist. In other words, the observed variations in performance may be attributed to the physical difficulty of the tasks rather than inherent cognitive differences among the monkeys.

Correct Answer: B. H2SO4

Correct Answer: C. the point of intersection of the perpendicular bisectors of PQ and PR

Explanation

(a) \(\frac{0.09 \times 1.21}{3.3 \times 0.00025} = \frac{9 \times 10^{-2} \times 121 \times 10^{-2}}{33 \times 10^{-1} \times 25 \times 10^{-5}}\)

= \(\frac{33 \times 10^{-4}}{25 \times 10^{-6}}\)

= \(1.32 \times 10^{2}\)

(b) Amount, A = Principal + Interest

= GH¢(5,600 + 1,200)

= GH¢6,800

Compound Interest formula : \(A = P(1 + \frac{r}{100})^{3}\)

\(6,800 = 5,600(1 + \frac{r}{100})^{3}\)

\((1 + \frac{r}{100})^{3} = \frac{6800}{5600} = 1.214\)

\(1 + \frac{r}{100} = \sqrt[3]{1.214} = 1.06686\)

\(\frac{r}{100} = 1.06686 - 1 = 0.06686\)

\(r = 0.06686 \times 100 = 6.686 \approxeq 6.69\) (3 significant figures)

Correct Answer: A. supermarket

Correct Answer: C. Horatio