Explanation

(a) \(f(x) = \frac{4 - 5x}{2} ; g(x) = x + 6, x \in R\)

Let g(x) = y

\(y = x + 6 \implies x = y - 6\)

Let \(x = g^{-1} (x)\) and y = x.

\(g^{-1}(x) = x - 6\)

\(f \cdot g^{-1}(x) = f(g^{-1}(x))\)

= \(\frac{4 - 5(x - 6)}{2}\)

= \(\frac{4 - 5x + 30}{2}\)

= \(\frac{34 - 5x}{2}\)

(b) \(x = \frac{7 \times 4 - 2(5)}{5 + 4}\)

= \(\frac{18}{9}\)

\(x = 2\)

\(y = \frac{4(-5) + 5(7)}{5 + 4}\)

= \(\frac{15}{9}\)

\((x, y) = (2, 1\frac{2}{3})\)

Correct Answer: D. \(\frac{5}{16}\)

Explanation

Pr. (winning 100m race) = \(\frac{1}{8}\)

Pr. (losing 100m race) = 1 - \(\frac{1}{8}\) = \(\frac{7}{8}\)

Pr. (winning high jump) = \(\frac{1}{4}\)

Pr. (losing high jump ) = 1 - \(\frac{1}{4}\) = \(\frac{3}{4}\)

Pr. (winning only one) = Pr. (Winning 100m race and losing high jump) or Pr.(Losing 100m race and winning high jump)

= (\(\frac{1}{8} \times \frac{3}{4}\)) + (\(\frac{7}{8} \times \frac{1}{4}\))

= \(\frac{3}{32} + \frac{7}{32}\)

= \(\frac{10}{32}\)

= \(\frac{5}{16}\)

Correct Answer: (D) me

Correct Answer: D. Faculty registration

Explanation

(a) Saul was made a king over Israel by Samuel and was told to hearken to the words of the Lord. The Lord made it known to him that He was going to punish the Amalekites for their opposition to the Israelites on their way from Egypt to Canaan and Saul was instructed to destroy the Amalekites and not to spare them but to kill both men and women, infants and suckling, oxen and sheep. In obedience to God's command, Saul and his army came to Amalek; laid in wait in the valley. He advised the Kenites who showed kindness to the Israelites to depart from the Amalekites to avoid being destroyed. The Kenites obeyed and departed from the Amalekites.

Saul then defeated the Amalekites in a battle and spared Agag, their king against God's express command. He spared the best of the sheep, oxen, and all that were good, he only destroyed only what was worthless and despised. Saul defended himself rather weakly by stating that he spared the best of the sheep to offer sacrifice to God / He shifted the blame on the people. Samuel decried Saul's action and denounced his non-performance of the commandments given to him by God / to obey is better than sacrifice. For this act of disobedience, he was rejected by God. As Samuel turned to go away from Saul, he held Samuel's skirt and it got torn. Samuel then declared that as Saul had torn his robe, the Lord had torn the kingdom of Israel and had given it to his neighbour.

(b) Lessons from Saul's Experience:

(i) Disobedience leads to suffering and condemnation from God. Saul suffered greatly. God allowed evil spirit to torment him.

(ii) Disobedience can lead to a tragic end. Saul lost his life along with his three sons in a battle,

(iii) One man's disobedience can lead to the suffering of the whole nation as seen in Saul's.

(iv) God's plan for our lives can be distorted through disobedience.

(v) Obedience is better than sacrifice.

(vi) The need to accept responsibility for our actions rather than blaming others.

Correct Answer: D. foil

Correct Answer: A. mass media method

Correct Answer: A. 9 m triangular

Explanation

(a) (i) First discount = 20% of N25,000

= \(\frac{20}{100} \times N25,000 = N5,000\)

Further discount for prompt payment = \(2\frac{1}{2}%\) of N25,000.

= \(\frac{5}{200} \times N25,000 = N625\)

\(\therefore \text{Total amount saved by distributor} = N(5,000 + 625)\)

= \(N5625\)

(ii) Total %age discount for prompt payment = \((20 + 2\frac{1}{2})% = 22\frac{1}{2}%\)

Therefore, the distributor paid \((100% - 22\frac{1}{2}%) \times Nx\)

= \(77\frac{1}{2}% \times Nx\)

\(\implies 77\frac{1}{2}% \times x = 11,700\)

\(x = \frac{11,700 \times 200}{155}\)

= \(N15,096.77\)

(b) \(6y^{2} - 149y - 102 \)

= \(6y^{2} - 153y + 4y - 102\)

= \(3y(2y - 51) + 2(2y - 51)\)

= \((3y + 2)(2y - 51)\)

\(\therefore 6y^{2} - 149y - 102 = 0 \implies (3y + 2)(2y - 51) = 0\)

\(3y + 2 = 0 \implies 3y = -2 \)

\(y = -\frac{2}{3}\)

\(2y - 51 = 0 \implies 2y = 51\)

\(y = 25\frac{1}{2}\)

\(\therefore y = -\frac{2}{3} ; y = 25\frac{1}{2}\)

Correct Answer: B. 5

Explanation

\((m_{1} v_{1} + m_{2} v_{2}) = (m_{1} + m_{2})v\) (Inelastic momentum)

\(8x + (5 \times 2) = (8 + 5) \times 3.85\)

\(8x + 10 = 13 \times 3.85 = 50.05\)

\(8x = 50.05 - 10 = 40.05\)

\(x \approxeq 5 m/s\)