Correct Answer: D. decline

Correct Answer: D. \(x - \frac{5}{x} - \frac{1}{2x^{2}} + c\)

Explanation

\(\frac{x^{3} + 5x + 1}{x^{3}} \equiv 1 + \frac{5}{x^{2}} + \frac{1}{x^{3}}\)

\(\equiv \int (1 + \frac{5}{x^{2}} + \frac{1}{x^{3}}) \mathrm {d} x = \int (1 + 5x^{-2} + x^{-3}) \mathrm {d} x\)

= \((x - 5x^{-1} - \frac{1}{2}x^{-2} + c)\)

= \(x - \frac{5}{x} - \frac{1}{2x^{2}} + c\).

Correct Answer: C. Serve table

Correct Answer: C. more interested in studying than in governance

Correct Answer: C. market value

Explanation

(a) The business resources are:

(i) Money resources

(ii) Materials resources

(iii) Management

(iv) Opportunities

(I)Money resources:Money includes all the working capital available to a business. Money is important because, without it, a business cannot take off. It can be obtained by borrowing, selling shares, etc.

(ii)Material resources. Materials include tools, machinery, equipment, etc used in business. The money resources that are turned into mate rials help the business to operate economically and efficiently.

(iii)Management resources:Management is the resources of business which plans, organizes, directs and controls the operation of the business enterprise. It is also referred to as human resources.

(iv)Opportunities:These include facilities within the environment that are beneficial to the business. These are roads, electricity, telephone services, etc.

(b) Four ways by which government regulates business are:

(i) All business units must be duly registered before they can commence business .

(ii) Business can be regulated through granting of patent right, copyright and trade mark for companies.

(iii) The government ensures the use of standard weights and measures for products.

(iv) The location of a business is approved by the government.

(v) Government approves importation and exportation by the public.

(iv) The Government imposes tax on the profit of business enterprises.

(vii) Business enterprises are compelled to publish their accounts for public consumption.

Correct Answer: D. Establish common price for their products

Explanation

(a) \(Time = \frac{2}{3} hour = \frac{2}{3} \times 60 = 40 mins\)

4 students will take \(\frac{8 \times 40}{4} = 80 minutes\)

\(Time = \frac{1}{3} hour = \frac{1}{3} \times 60 = 20 minutes\)

It will take 20 minutes to fill \(\frac{12 \times 20}{80} = 3 tanks\)

(b)

\(\tan (\frac{\theta}{2}) = \frac{10}{12}\)

\(\frac{\theta}{2} = \tan^{-1} (0.8337) = 39.8°\)

\(\theta = 39.8° \times 2 = 79.6°\)

(ii) Perimeter of minor segment = Length of chord + length of arc

But \(r^{2} = 12^{2} + 10^{2}\)

= \(144 + 100 = 244\)

\(r = \sqrt{244} = 15.62 cm\)

Length of arc = \(\frac{79.6}{360} \times 2 \times 3.142 \times 15.62 = 21.71cm\)

Perimeter of minor segment = 20 + 21.71 = 41.71cm

Correct Answer: C)

2.0 \(\times\) 10-2 moldm\(^{-3}\)

Correct Answer: C. Real interest rates rise

Explanation

If GDP falls, then people demand less money for transactions. As interest rate rise (fall), the demand for money will fall(rise).