Correct Answer: B. increases

Explanation

(a)(i) < ASO = < AMO = 90° (radius to a tangent)

< SOM = 360° - (3 x 90°) (sum of angles of a rectangle)

= 90°.

\(\therefore\) obtuse < SOT = 360° - (90° + 60° + 60°) = 150°.

(ii) Arc SRT = \(\frac{150°}{360°} \times 2\pi r\)

= \(\frac{150}{360} \times 2 \times \frac{22}{7} \times 10 = \frac{550}{21}\)

= \(26.19cm\)

(iii) \(\tan 60° = \frac{TB}{10}\)

\(TB = 10\tan 60° = 17.32cm\)

(b) Length of the string ASRTB = AS + arc SRT + TB

= 10cm + 26.19cm + 17.32cm

= 53.51cm \(\approxeq\) 54cm.

Correct Answer: C) parasitism

Explanation

This question is asking which of the associations results in much harm to one of the partners. The options are symbiosis, commensalism, parasitism, and mutualism. Symbiosis refers to a close relationship between two different species where both partners benefit. Commensalism refers to a relationship where one partner benefits, and the other partner is neither helped nor harmed. Mutualism refers to a relationship where both partners benefit. On the other hand, parasitism is a relationship where one partner (the parasite) benefits while the other partner (the host) is harmed. The parasite feeds on the host and negatively affects its health. Therefore, the correct option is C: parasitism. Parasites can cause diseases in their hosts, which can lead to severe harm or even death. Examples of parasites include tapeworms, fleas, lice, and ticks. It is essential to take measures to prevent parasitic infections by avoiding contact with infected individuals, maintaining personal hygiene, and using insect repellents. In conclusion, parasitism is an association where one partner benefits at the expense of the other partner, resulting in much harm to the latter.

Correct Answer: C. II, IV

Explanation

Let's look at each statement. I. Always search for the middle number This is false, because what happens if the number set is jumbled. To find median, it's important to oragnize in increasing or decreasing order. II. Always arrange in increasing or decreasing order before searching for the middle number As explained in statement one explanation, this is true. III. Once arranged, if the set has an even number, just take the two middle numbers and subtract them and divide by two This s false, because once there is an even number set, you need to ADD the middle numbers and divide it by two. Essentially, the new value represents the middle of the set. IV. Once arranged, if the set has an even number, just take the two middle numbers and add them and divide by two This is true based on statement three explanation.

Correct Answer: A. \(5\sqrt{3} - 3\)

Explanation

\(F = F \cos \theta i + F \sin \theta j\)

\(10N = 10 \cos 60 i + 10 \sin 60 j\)

\(6N = -6 \cos 330 i - 6 \sin 330 j\)

\(R_{x} = 10 \cos 60 - 6 \cos 330 \)

= \(10 \times \frac{1}{2} - 6 \times \frac{\sqrt{3}}{2}\)

= \(5 - 3\sqrt{3}\)

Correct Answer: A. 20°

Explanation

< DBC = 35° (base angles of an isosceles triangle)

< CDB = 180° - (35° + 35°)

= 110°

< ADB = 70°; < ADB = 90°

\(\therefore\) < BAO = 180° - (70° + 90°)

= 20°

Correct Answer: A. Elfrida Adeho

Correct Answer: A. A person of blood group AB can donate blood only to another person of blood group AB

Correct Answer: C. \(\frac{1}{3}\)

Explanation

Pr(green) = \(\frac{6}{5 + 6 + 7}\)

= \(\frac{6}{18}\)

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

Correct Answer: C. the fat were burnt before any distribution