27 The diagram shows a right-angled triangle and a quarter circle.
D
9 m
А
6 m
B.
The right-angled triangle ABC has angle ABC = 90°
The quarter circle has centre C and radius CB.
Work out the area of the quarter circle.
Give your answer correct to 3 significant figures.
You must show all your working.

A  ≈ 35.3 units²

Step-by-step explanation:

Calculate the radius CB using Pythagoras' identity in the right triangle.

CB² + AB² = AC²

CB² + 6² = 9²

CB² + 36 = 81 ( subtract 36 from both sides )

CB²  = 45 = r²

Then area of quarter circle is

A = × πr² = × π × 45 ≈ 35.3

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.