Correct Answer: C. Morocco

Correct Answer: D. \(\frac{167}{576}\)

Explanation

\(P(Jide) = \frac{1}{12}; P(\text{not Jide}) = \frac{11}{12}\)

\(P(Atu) = \frac{1}{6}; P(\text{not Atu}) = \frac{5}{6}\)

\(P(Obu) = \frac{1}{8}; P(\text{not Obu}) = \frac{7}{8}\)

\(P(\text{only one of them}) = P(\text{Jide not Atu not Obu}) + P(\text{Atu not Jide not Obu}) + P(\text{Obu not Jide not Atu})\)

= \((\frac{1}{12} \times \frac{5}{6} \times \frac{7}{8}) + (\frac{1}{6} \times \frac{11}{12} \times \frac{7}{8}) + (\frac{1}{8} \times \frac{11}{12} \times \frac{5}{6})\)

= \(\frac{35}{576} + \frac{77}{576} + \frac{55}{576}\)

= \(\frac{167}{576}\)

Correct Answer: A. All knowing

Explanation

\(U = {2, 3, 4, 5, 6, 7, 8, 9}\)

\(A = {2, 4, 6, 8}\)

\(B = {2, 3, 7, 9}\)

\(C = {4, 5, 6, 7, 8}\)

(a) \(A \cap (B' \cap C')\) = \({2, 4, 6, 8} \cap ({4, 5, 6, 8} \cap {2, 3, 9})\)

B' = 4,5,6,8

C' = 2,3

B' n C' = Ø

\(A \cap (B' \cap C')\) = \({2, 4, 6, 8} \cap { }\) Ø

= Ø

(b) \((A \cup B) \cap (B \cup C)

= {2, 3, 4, 6, 7, 8, 9} \cap {2, 3, 4, 5, 6, 7, 8, 9}\)

= \({2, 3, 4, 6, 7, 8, 9}\)

Correct Answer: C. 11.00pm

Correct Answer: B. Liver

Correct Answer: C) A much-praised historical novel about colonial East Africa, Paradise (1994) was written by Abdulrazak Gurnah, winner of the 2021 Nobel Prize in Literature.

Explanation

The choice that most effectively uses relevant information from the notes to introduce Paradise to an audience unfamiliar with the novel and its author is: C) A much-praised historical novel about colonial East Africa, Paradise (1994) was written by Abdulrazak Gurnah, winner of the 2021 Nobel Prize in Literature. This choice provides a concise and informative introduction to the novel Paradise, highlighting its historical context and its positive reception by many readers. It also mentions the author, Abdulrazak Gurnah, and his recent achievement of winning the 2021 Nobel Prize in Literature.

Explanation

(a) \(2^{3y + 2} - 7(2^{2y + 2}) - 31(2^{y}) - 8 = 0\)

\(\equiv (2^{2})(2^{y})^{3} - 7(2^{2})(2^{y})^{2} - 31(2^{y}) - 8 = 0\)

Let \(2^{y} = x\),

\(4x^{3} - 28x^{2} - 31x - 8 = 0\)

If x = 8, \(4(8^{3}) - 28(8^{2}) - 31(8) - 8 = 2048 - 1792 - 248 - 8\)

= \(0\)

\(\therefore (x - 8) \text{is a factor}\)

Dividing \(\frac{4x^{3} - 28x^{2} - 31x - 8}{x - 8}\), we get

= \(4x^{2} + 4x + 1 \)

= \((2x + 1)^{2}\)

Therefore, \(x = -\frac{1}{2}, -\frac{1}{2}, 8\)

Recall, \(x = 2^{y}\)

\(2^{y} = -\frac{1}{2}\) has no real solution.

\(2^{y} = 8 = 2^{3} \implies y = 3\)

(b) \(\int (\sqrt{x^{2} + 1}) xdx\)

Let \(u^{2} = x^{2} + 1; 2\frac{\mathrm d u}{\mathrm d x} = 2x\)

\(\mathrm d u = x \mathrm d x\)

\(\therefore \int (\sqrt{x^{2} + 1}) xdx = \int (\sqrt{u^{2}}) \mathrm d u\)

= \(\int u \mathrm d u\)

= \(\frac{u^{2}}{2} + c\)

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

Correct Answer: D. Malnutrition

Correct Answer: A. brings about peaceful co-existence of people