Correct Answer: C. department store

Explanation

A department store is a very large store that is usually located in a mall that sells everything from clothes to shoes to sheets to towels to appliances to lots of things. It has different stores under that roof. An example in Nigeria is shoprite mall

Correct Answer: A. prime cost and factory overhead

Explanation

(a) \(f(x) = \frac{x - 3}{2x - 1}, x \neq \frac{1}{2}\)

\(g(x) = \frac{x - 1}{x + 1}, x \neq -1\)

\(g \circ f = g(f(x)) = \frac{\frac{x - 3}{2x - 1} - 1}{\frac{x - 3}{2x - 1} + 1}\)

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

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

= \(\frac{- x - 2}{3x - 4}\) or \(\frac{-(x + 2)}{3x - 4}\).

(b)(i) \(y = 9x - x^{3}\)

If x = 0, y = 0.

If y = 0, \(9x - x^{3} = 0\)

\(x(9 - x^{2}) = x (3 - x)(3 + x) = 0\)

\(\implies x = 0, -3, 3\)

Turning points : \(\frac{\mathrm d y}{\mathrm d x} = 9 - 3x^{2}\)

\(9 - 3x^{2} = 0 \implies 9 = 3x^{2}\)

\(x^{2} = 3 \implies x = \pm \sqrt{3} = \pm 1.73\)

When x = 1.73, \(y = 9(1.73) - (1.73)^{3} = 15.57 - 5.18 = 10.39\)

Point is (1.73, 10.39).

When x = -1.73, \(y = 9(-1.73) - (-1.73)^{3} = -15.57 + 5.18 = -10.39\)

Point is (-1.73, -10.39).

Maximum or minimum ?

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

At x = 1.73, \(\frac{\mathrm d^{2} y}{\mathrm d x^{2}} < 0 \therefore (1.73, 10.39) \text{ is a maximum point}\)

At x = -1.73, \(\frac{\mathrm d^{2} y}{\mathrm d x^{2}} > 0 \therefore (-1.73, -10.39) \text{ is a maximum point}\).

Areas between x = -3 to x = 0 and x = 0 and x = 3 are equal.

\(\therefore Area = 2 \int_{0} ^{3} (9x - x^{3}) \mathrm {d} x = 2[\frac{9x^{2}}{2} - \frac{x^{4}}{4}]_{0} ^{3}\)

= \(81 - 40\frac{1}{2} = 40\frac{1}{2} sq. units\)

Explanation

Effects of inflation on the economy of a country are:

(i) Inflation discourages savings. Since the real value of the sum saved falls in time of inflation, people will prefer to spend it now rather than later.

(ii) Inflation could have adverse effects on the balance of payments of a country. Imports will become cheaper than exports.

(iii) Inflation badly affects people living on fixed incomes. During inflation borrowers gain and lenders lose.

(iv) During the period of inflation, cost of production increases thereby increasing the prices of goods and services.

(v) The margin of profit to businessmen increases and more goods can be produced. Increase in production increases the level of employment.

(vi) During inflationary period, money completely loses its value and people prefer holding real assets.

Correct Answer: C. tourism

Correct Answer: D. 8

Explanation

\(x \propto \frac{1}{y}\)

\(x = \frac{k}{y}\)

\(\frac{2}{3} = \frac{k}{9}\)

\(3k = 18 \implies k = 6\)

\(x = \frac{6}{y}\)

When y = \(\frac{3}{4}\),

x = \(\frac{6}{\frac{3}{4}}\)

= \(\frac{6 \times 4}{3}\)

= 8

Correct Answer: B. 50%

Correct Answer: D. fragmentation

Correct Answer: D. Mickey

Correct Answer: D. 54

Explanation

Find the median of the following data set: 1,43,117,42,2952,54,18,97,112,23,117 To find the median, we should first put our numbers in increasing order: 1,18,23,42,43,54,97,112,117,117,2952 Next, the median will simply be the number in the middle. We have 11 terms, so our median will be the 6th term in the sequence: 1,18,23,42,43,54,97,112,117,117,2952 So 54 is our median