Correct Answer:

Explanation

Angle of sector:

\(Food = \frac{30}{100} \times 360° = 108°\)

\(Rent = \frac{18}{100} \times 360° = 64.8°\)

\(\text{Car Maintenance} = \frac{25}{100} \times 360° = 90°\)

\(Savings = \frac{12}{100} \times 360° = 43.2°\)

\(Taxes = \frac{5}{100} \times 360° = 18°\)

\(Others = \frac{10}{100} \times 360° = 36°\)

(a)

(b) Annual Salary = N60,000.00

\(\therefore Savings = N(\frac{12}{100} \times 60,000) = N7,200\)

Explanation

(a) \(\log_{10} \sqrt{30} - \log_{10} \sqrt{6} + \log_{10} \sqrt{2}\)

= \(\log_{10} (\sqrt{\frac{30}{6}} \times \sqrt{2})\)

= \(\log_{10} (\sqrt{5} \times \sqrt{2})\)

= \(\log_{10} \sqrt{10}\)

= \(\log_{10} (10^{\frac{1}{2}})\)

= \(\frac{1}{2} \log_{10} 10\)

= \(\frac{1}{2}\).

(b)

(ii) \(A \cap C = { } \)

(iii) \(A \cap B' = {1, 4}\).

Correct Answer: A. 37

Explanation

The median is the middle number of the set, when it is listed in order from smallest to largest or vice versa. In this case we have an odd amount of numbers so we just count from each side until we find the number in the middle. 32,33,33,34,35,37,38,41,42,45,47 This gives us a final answer of 37 for the median.

Explanation

(a) \(\frac{1}{3^{5n}} \times 9^{n - 1} \times 27^{n + 1}\)

\(3^{-5n} \times (3^{2})^{n - 1} \times (3^{3})^{n + 1}\)

\(3^{-5n} \times 3^{2n - 2} \times 3^{3n + 3}\)

\(3^{-5n + 2n - 2 + 3n + 3}\)

= \(3^{1} = 3\)

(b) Let the daughter's age be c and the woman's age be d.

\(c + d = 46 .... (1)\)

In 4 years time, the daughter's age = c + 4

The woman's age = d + 4

\(\frac{d + 4}{c + 4} = \frac{7}{2}\)

\(2(d + 4) = 7(c + 4) \implies 2d + 8 = 7c + 28\)

\(2d - 7c = 28 - 8 \implies 2d - 7c = 20 ... (2)\)

\(c + d = 46 \implies d = 46 - c\)

\(\therefore 2(46 - c) - 7c = 20\)

\(92 - 2c - 7c = 20 \implies 92 - 20 = 9c\)

\(72 = 9c \implies c = 8\)

\(d = 46 - c \implies d = 46 - 8 = 38\)

Therefore, the daughter is 8 years old and the woman is 38 years.

Correct Answer: D. 9

Explanation

(a)

Then \(\sum d_1^2\) = 50

The spearman's coefficient = 1 - \(\frac{6 \times 50}{10(100 - 1)}\) = 1 - 0.30303 = 0.697

(b) We conclude that there exist positive correlation between performance in entrance examination and school performance

Correct Answer: C. 210° and 330°

Correct Answer: B. \(\frac{3x^{2}}{\sqrt[3]{(3x^{3} + 1)^{2}}}\)

Explanation

\(y = \sqrt[3]{3x^{3} + 1} = (3x^{3} + 1)^{\frac{1}{3}}\)

Let u = \(3x^{3} + 1\); y = \(u^{\frac{1}{3}}\)

\(\frac{\mathrm d y}{\mathrm d x} = (\frac{\mathrm d y}{\mathrm d u})(\frac{\mathrm d u}{\mathrm d x})\)

\(\frac{\mathrm d y}{\mathrm d u} = \frac{1}{3}u^{\frac{-2}{3}}\)

\(\frac{\mathrm d u}{\mathrm d x} = 9x^{2}\)

\(\frac{\mathrm d y}{\mathrm d x} = (\frac{1}{3}(3x^{3} + 1)^{\frac{-2}{3}})(9x^{2})\)

= \(\frac{3x^{2}}{\sqrt[3]{(3x^{3} + 1)^{2}}}\)

Correct Answer: A. 1

Correct Answer: B. 12/5