Correct Answer: B) ?8,500

Correct Answer: D) Retained profit

Explanation

Option A: Trade credit is not an internal source of capital. It refers to the practice of buying goods or services on credit from suppliers. This means that the business can delay payment for a certain period of time, but it is still a liability to the business.

Option B: Debenture is not an internal source of capital. It is a long-term loan that a company takes from individuals or institutions. This is considered an external source of capital.

Option C: Overdraft is not an internal source of capital. It is a facility provided by a bank that allows a company to withdraw more money than it currently has in its account. It is a form of short-term borrowing and is considered an external source of capital.

Option D: Retained profit is the correct answer. Retained profit refers to the portion of a company's profit that is not distributed to shareholders as dividends, but is instead kept within the company for reinvestment or future use. It is an internal source of capital because it comes from the company's own earnings.

In summary, the correct answer is Option D: Retained profit, as it is an internal source of capital that comes from a business's own earnings

Explanation

(a)(i) Position vector of A, \(\overrightarrow{OA} = i + 5j\)

Position vector of B, \(\overrightarrow{OB} = 3i + 9j\)

Position vector of C, \(\overrightarrow{OC} = -i + j\)

The points A, B and C are collinear if \(|\overrightarrow{AB}| = k|\overrightarrow{BC}|\), where k is a constant.

If k > 0, then \(\overrightarrow{AB}\) and \(\overrightarrow{BC}\) are in the same direction.

If k < 0, then they are in opposite directions, in this case they are A, C, B.

\(\overrightarrow{AB} = \overrightarrow{AO} + \overrightarrow{OB} = - \overrightarrow{OA} + \overrightarrow{OB}\)

= \(- i - 5j + (3i + 9j) = 2i + 4j = 2(i + 2j)\)

\(\overrightarrow{BC} = \overrightarrow{BO} + \overrightarrow{OC} = - \overrightarrow{OB} + \overrightarrow{OC}\)

= \(- 3i - 9j + (-i + j) = - 4i - 8j = -4(i + 2j)\)

\(\overrightarrow{AB} = -\frac{1}{2} \overrightarrow{BC}\)

\(\therefore\) A, B and C are collinear with \(\overrightarrow{AB}\) and \(\overrightarrow{BC}\) in opposite directions.

(ii) \(|\overrightarrow{AB}| : |\overrightarrow{BC}| = 1 : 2\)

(b)

We take moments about X.

Clockwise moment = \(500 \times 8 + 100 \times 12 = 5200N\)

Anticlockwise moment = \(T_{2} \times 20\)

From the principles of moment,

\(20T_{2} = 5200N \implies T_{2} = 260N\)

For vertical equilibrium,

\(T_{1} + T_{2} = 600N\)

\(\therefore T_{1} = 600 - T_{2} = 600 - 260 =340N\)

The tensions in the strings are 340N and 260N respectively.

Correct Answer: A. lampoon

Correct Answer: C. 80.0%

Explanation

Efficiency = output x 100

= \(\frac{\frac{200 {\times} 10 {\times} {6}}{10}}{1500}\) x \(\frac{100}{1}\)

= 80%

Correct Answer: B. Marketing research

Correct Answer: D. recommend

Correct Answer: D. Sporulation

Explanation

Sporulation is a method of reproduction observed in some groups of organisms, such as fungi and certain types of protists. It involves the formation and release of spores, which are specialized reproductive structures that can develop into new individuals under suitable conditions. Sporulation is not a method of reproduction in animals.

Correct Answer: D. negative

Correct Answer: A. Ibrahim Babangida