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The phrase 'an obligation' in the context of the passage refers to a duty or responsibility that The Pathfinder owes to the old woman. It can be replaced with synonyms such as 'a duty', 'a responsibility', 'a commitment', or 'a requirement'. These words all convey the same meaning as 'an obligation' in the context of the passage, which is a moral or legal responsibility.

The word 'overcast' in the context of the passage refers to the sky being covered with clouds; it is cloudy. It can be replaced with synonyms such as 'cloudy', 'clouded over', 'cloud-covered', or 'cloud-filled'. These words all convey the same meaning as 'overcast' in the context of the passage, which is the state of the sky when it is covered with clouds.

The word 'pensively' in the context of the passage refers to the thoughtful or reflective state of Dr Felix Adoka. It can be replaced with synonyms such as 'thoughtfully', 'reflectively', 'contemplatively', or 'meditatively'. These words all convey the same meaning as 'pensively' in the context of the passage, which is the state of being engaged in, involving, or reflecting deep or serious thought.

The following are qualities that the writer advises parents to instil in their children: 1. Parents should inculcate the quality of self-control in their children. 2. Parents should encourage their children in resilience through encouragement. 3. Parents must insil in their children the virtue of humility. 4. Parents must teach their children integrity so that they can be responsible children. 5. Parents must teach their children the value of hard work while trying to make a fortune. 6. Parents should ensure that their children take an active part in chores and duties at home. 7. The principle of humility should be the watchword for every child. 8. Parents should train their children to abide by the fundamental laws of the land. 9. Parents should train their children on the need to have integrity, dignity and manners.

Self-explanatory

The following are qualities that the writer advises parents to instil in their children: 1. Parents should inculcate the quality of self-control in their children. 2. Parents should encourage their children in resilience through encouragement. 3. Parents must insil in their children the virtue of humility. 4. Parents must teach their children integrity so that they can be responsible children. 5. Parents must teach their children the value of hard work while trying to make a fortune. 6. Parents should ensure that their children take an active part in chores and duties at home. 7. The principle of humility should be the watchword for every child. 8. Parents should train their children to abide by the fundamental laws of the land. 9. Parents should train their children on the need to have integrity, dignity and manners.

From ∆PSR |PS| = |SR| (If two tangents are drawn from an external point of the circle, then they are of equal lengths) ∴ ∆PSR is isosceles ∠PSR + ∠SRP + ∠SPR = 180\(^o\) (sum of angles in a triangle) Since |PS| = |SR|; ∠SRP = ∠SPR ⇒ ∠PSR + ∠SRP + ∠SRP = 180\(^o\) ∠PSR + 2∠SRP = 180\(^o\) 36\(^o\) + 2∠SRP = 180\(^o\) 2∠SRP = 180\(^o\) - 36\(^o\) 2∠SRP = 144\(^o\) ∠SRP = \(\frac {144^o}{2} = 72^0\) ∠SRP = ∠PQR (angle formed by a tangent and chord is equal to the angle in the alternate segment) ∴ ∠PQR = 72\(^0\)

1st bag → 4 W, 3 B = 7 marbles 2nd bag → 5 R, 6 B = 11 marbles The only possible way of picking marbles of the same colour is to pick a blue marble from each bag therefore, Pr( same colour) = \(\frac{3}{7}\times \frac{6}{11} = \frac{18}{77}\)

\(8 + 2x - x^2 = 0\) \(8 + 4x - 2x - x^2 = 0\) 4(2 + x) - x(2 + x) = 0 (4 - x)(2 + x) = 0 4 - x = 0 or 2 + x = 0 x = 4 or x =- 2 So, p = 4 and q = -2 ∴ p + q = 2

a. Since K is the centre and KR and KS are radii, ∆SKR is isosceles. ∠SRK + ∠RSK + ∠SKR = 180^\circ (sum of angles in a triangle is 180o) ⇒ ∠SRK + ∠RSK + 80^\circ = 180^\circ ⇒ ∠SRK + ∠RSK = 180^\circ - 80^\circ = 100^\circ Since ∠SRK = ∠RSK (base angles of an isosceles triangle are equal) ∠SRK = ∠RSK = \(\frac{100^0}{2} = 50^0\) ∠RSP = 50^\circ + 41^\circ = 91^\circ ∴ ∠ RQP = 180^\circ - 91^\circ = 89^\circ (opp. angles of a cyclic. quad. are supplementary) b. Since KR is a bisector of angle ∠SRQ: ∠SRK = ∠KRQ = 50^\circ ∠SRQ = 50^\circ + 50^\circ = 100^\circ ∴ ∠SPQ = 180^\circ - 100^\circ = 80^\circ (opp. angles of a cyclic. quad. are supplementary)

Viruses are considered parasitic because they require a host cell to replicate. They do this by injecting their genetic material into the host cell and using the cell's machinery to replicate.

Organisms that feed on dead, decaying tissues of other organisms are known as "saprophytes." Saprophytes, also known as saprotrophs or decomposers, are organisms that obtain their nutrition by feeding on dead, decaying organic matter (detritus) from other organisms.

Holozoic nutrition is a type of nutrition in which organisms consume solid organic materials. This is the type of nutrition seen in most animals, where food is ingested and then broken down through digestion. This is different from symbiotic (where two organisms live together and benefit from each other), saprophytic (where organisms feed on dead and decaying matter), and parasitic (where one organism benefits at the expense of another) nutrition.

A disease vector is an organism that transmits disease-causing pathogens from one host to another. Female Anopheles mosquitoes can carry and transmit the Plasmodium parasite, which causes malaria. When an infected mosquito bites a person, it injects the parasite into the bloodstream, leading to the transmission of the disease.

Irritability, also known as responsiveness or excitability, refers to the ability of cells to detect and respond to various stimuli or changes in their environment.