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R = P (base ∠s of isc \Delta, ps = RS) ∴R = 40^\circ ∠PSQ = R (∠s in alternate segment) ∴∠PSQ = 40^\circ

Midpoint of PQ \(\frac{x_2 + x_1}{2};\frac{y_2 + y_1}{2}\) =\(\frac{-1+(-3)}{2};\frac{6-4}{2}\) =\(\frac{-4}{2};\frac{2}{2}\) = -2, 1 Midpoint of QR = \(\frac{x_2 + x_1}{2};\frac{y_2 + y_1}{2}\) \(\frac{-3+1}{2};\frac{-4-4}{2}\) \(\frac{-2}{2};\frac{-8}{2}\) -1, -4 Midpoint of PQ and QR = (-2,1) and (-1,-4)

Standard deviation = \(\frac{\sum(x - \overline{x})^2}{\text{n}}\) \(\overline{x}\) = \(\frac{ 3 + 6 + 4 + x + 7}{5}\) = 5 = 20 + x = 25 x = 25 - 20 = 5. x x - \(\overline{x}\) (x - \(\overline{x}\))\(^2\) 3 3 - 5 -2 = 4 4 4 - 5 -1 = 1 5 5 - 5 0 = 0 6 6 - 5 1 = 1 7 7 - 5 2 = 4 \(\sum\) (x - \(\overline{x}\))\(^2\) = 10 Standard deviation = \(\frac{\sum(x - \overline{x})^2}{\text{n}}\) = \(\frac{\sqrt{10}}{5}\) = \(\sqrt{2}\)

The graph should start at its lowest point(-1) at -\(\frac{\pi}{2}\), rise to cross the origin (0, 0), and continue upward to reach its peak (1) at \(\frac{\pi}{2}\). It then turns downward, crossing the x- axis(0) at \(\pi\) and ends back at its lowest point (-1) at \(\frac{3\pi}{2}\)

The two dice produce 36 equally likely outcomes in total. The sums divisible by 3 are exactly 3, 6, 9, and 12. The complete list of favorable pairs \((d_1, d_2)\) is: Sum = 3 (2 ways): (1,2), (2,1) Sum = 6 (5 ways): (1,5), (2,4), (3,3), (4,2), (5,1) Sum = 9 (4 ways): (3,6), (4,5), (5,4), (6,3) Sum = 12 (1 way): (6,6) Total favourable outcomes: 2 + 5 + 4 + 1 = 12. Therefore, the probability is \(\frac{12}{36} = \frac{1}{3}.\)

\(\begin{array}{c|c} \text{Age in years} & 10 & 20 & 30 & 40 & 50 \\\hline \text{frequency} & 3 & 4 & 5 & 6 & 2\end{array}\) \(\sum f \) = number of people involved in the pollution \(\sum f\) = 3 + 4 + 5 + 6 + 2 = 20

No expanded working has been attached for this question yet. The verified answer is Option B.

Course Material means any documentation, slides, hand-outs or other materials for a Course. Option D ''Material'' is correct because the adverb ''writers'' is in plural form, hence the noun ''material'' can't be in plural form too. The statement would read; Course material writers are to reflect local colour

No expanded working has been attached for this question yet. The verified answer is Option A.

“If you saw the photograph of the man, would you be able to identify him?” In the sentence, a hypothetical situation is expressed. This is expressed with the use of "if" in the first clause. "would" and not "will" is used since the situation because it is a hypothetical situation and not something that actually happens. "would" and not "could" is used because the use of "could" would be redundant or unnecessary because the ability to identify "him" is already expressed with the use of "be able to".

''Man'' is the correct option. whenever ''some'' is used before a singular noun like man, It means that the person being talked about is unknown to d speaker. Hence we have. As Obande does not know anyone in this city, he hopes that some kind man will put him up for the night?

No expanded working has been attached for this question yet. The verified answer is Option C.

The word "elite" is a collective noun that refers to a group of highly distinguished or influential people. When referring to an individual who belongs to this group, we say: "She is one of the elite of the society."

Were; is a second person singular past, plural past. The speaker is reporting an event that had already happened, affecting multiple people and their residents. Three-quarters of the people in the village were killed, but only half of their huts were affected

No expanded working has been attached for this question yet. The verified answer is Option D.