Correct Answer: D) massaging expenses

Correct Answer: a. 7/9

Explanation

Sound waves are longitudinal waves which cannot be plane polarized as polarization is a characteristic of transverse waves only.

Explanation

(a) What is economies of scale? Economics of scale refer to the benefits a firm derives as a result of expanding its productive capacity or the concentration of firms of an industry in an area which lead to an increase in output and a fall in production cost per unit of output.

(b) Outline three internal economies of scale a firm can enjoy:

(i) Financial: Large businesses are better able to raise funds from other sources by selling shares or borrowing from banks and can negotiate for lower interest rales on loans.

(ii) Technical: A firm that is large can apply mechanized/modern technology to increase its output.

(iii) Marketing: Large firms can buy raw materials in bulk at good discounts. afford to advertise often, can package their goods better and reduce transport costs considerably.

(iv) Risk- bearing: Large firms can deal with the risks of trading by diversifying their products and market base lo international markets as Well.

(v) Research: Large firms can carry out research into new areas to improve production by Employing experts and setting up laboratories.

(vi) Administrative/Managerial: Because of its sound financial base. a large firm can employ competent manage to oversee the affairs of the company.

(vii)Welfare: Large firms can motivate their staff with better accommodation. scholarship for children, opportunities for training. etc.

(c) State three factors that can influence where a firm is sited:

(i) Availability and cost of raw materials/availability of natural Resources e.g gold. diamond. etc.

(ii) Access lo the source of power/regular power supply

(iii) Proximity to the market( due to fragility, perishability or bulkiness of the final product).

(iv) Access to specialized transport e.g rail services, etc

(v) Availability of labour (skilled and unskilled)

(vii) Government policy/political influence affect location of firms in specific places.

(vii) Climatic factors/conditions.

Correct Answer: A. shorten his prayer

Explanation

\(\frac{\sqrt{75} - 3}{\sqrt{3} + 1}\)

Rationalizing, \((\frac{\sqrt{75} - 3}{\sqrt{3} + 1})(\frac{\sqrt{3} - 1}{\sqrt{3} - 1}\)

\(\frac{\sqrt{3 \times 75} - \sqrt{75} - 3\sqrt{3} + 3}{3 - \sqrt{3} + \sqrt{3} - 1}\)

= \(\frac{15 - 5\sqrt{3} - 3\sqrt{3} + 3}{2}\)

= \(\frac{18 - 8\sqrt{3}}{2}\)

= \(9 - 4\sqrt{3}\)

(b)(i) The general form of the circle equation is \(x^{2} + y^{2} + 2gx + 2fy + c = 0\) where (x, y) is a point on the circle.

\(\therefore A(7, 3) = 7^{2} + 3^{2} + 7(2g) + 3(2f) + c = 0\)

\(14g + 6f + c = -58 .... (1)\)

\(B(2, 8) = 2^{2} + 8^{2} + 2(2g) + 2(2f) + c = 0\)

\(4g + 4f + c = -68 ..... (2)\)

\(C(-3, 3) = -3^{2} + 3^{2} - 3(2g) + 3(2f) + c = 0\)

\(6f - 6g + c = -18 ....(3)\)

Solving the equations, we get \(g = -2; f = -3; c = -12\)

\(\text{The equation of the circle is} x^{2} + y^{2} - 4x - 6y - 12 = 0\).

(b)(ii) Radius = \(\sqrt{g^{2} + f^{2} - c}\)

= \(\sqrt{-2^{2} + (-3^{2}) - (-12)}\)

\(\sqrt{25} = 5 units\)

Correct Answer: D. diminished

Correct Answer: C. speed

Correct Answer: C. Herod and Pilate became friends

Correct Answer: C. voice, shipping note, bill of lading and freight note