Explanation

Since it is divide into 3 sectors

then \(8x° = 360°\)

\(x° = 45°\)

The 3rd sector = 3 times the size of the other two sectors put together

= \(3(45 + 45) = 3(90) = 270°\)

Perimeter of a sector = \(2r + l\)

where r = radius of the circle ; l = length of arc = \(\frac{\theta}{360°} \times 2\pi r\)

Area of circle = \(\frac{22}{7} \times r^{2} = 154 cm^{2}\)

\(r^{2} = \frac{154 \times 7}{22} = 49\)

\(r = 7 cm\)

\(l = \frac{270}{360} \times 2 \times \frac{22}{7} \times 7 = 33 cm\)

Perimeter of sector = \(2(7) + 33 = 14 + 33 = 47 cm\).

Correct Answer: D. Median

Explanation

The median in a data set is the number that lies directly in the middle. To determine the median, first list the numbers in ascending order: 1,4,5,5,6,9,10,11,12,13,16,17,21,28,32,41,50 Then, count in from both sides to find the number that lies directly in the middle. Therefore the correct answer is median.

Correct Answer: D. 50.00

Correct Answer: B. 3

Explanation

\(\frac{^{n}P_{r}}{^{n}C_{r}} = \frac{\frac{n!}{(n - r)!}}{\frac{n!}{(n - r)! r!}} = \frac{90}{15} = 6\)

\(\frac{n!}{(n - r)!} \times \frac{(n - r)! r!}{n!} = r! = 6\)

\(r = 3\)

Correct Answer: D. 125°

Explanation

Sum of the angle of a pentagon

= (2 x 5 - 4) x 90

= 540^o

126 + 114 + y + 92 + 83 = 540

y = 540 - 415 = 125^o

Correct Answer: B. 0.60m

Explanation

volume of cylinder = \(\pi r^2\)h

0.216\(\pi\) m\(^3\) = \(\pi \times r^2 \times h\)

Since r = h,

0.216 = r\(^3\)

r\(^3\) = 0.216

r = \(\sqrt[3]{0.216}\)

= 0.6

Correct Answer: D. y = 5

Explanation

\(\frac{y + 2}{y^2 - 3y - 10}\)

\(y^2 - 3y - 10 = 0 \implies y^2 - 5y + 2y - 10 = 0\)

\(y(y - 5) + 2(y - 5) = 0\)

\((y - 5)(y + 2) = 0\)

\(\frac{y + 2}{(y - 5)(y + 2)} = \frac{1}{y - 5}\)

\(\therefore\) At y = 5, the expression \(\frac{y + 2}{y^2 - 3y - 10}\) is undefined.

Correct Answer: A. 9

Correct Answer: C. \(\frac{1}{3} (2x + 3)^{\frac{3}{2}} + k\)

Correct Answer: A. Even