Answer:
1191.4 ; 34.5
Step-by-step explanation:
Given the data:
29; 37; 38; 40; 58; 67; 68; 69; 76; 86; 87; 95; 96; 96; 99; 106; 112; 127; 145; 150
The sample variance and standard deviation can be obtained thus :
Σ(X - m)² / (n - 1)
Where, m = mean of the sample
n = sample size
The standard deviation equals, sqrt(variance )
Using a calculator:
The variance, σ² ;
Mean = Σx / n = 1681 / 20 = 84.05
(x -m)^2
[(29-84.05)^2 + (37-84.05)^2 + (38-84.05)^2 + (40-84.05)^2 + (58-84.05)^2 + (67-84.05)^2 + (68-84.05)^2 + (69-84.05)^2 + (76-84.05)^2 + (86-84.05)^2 + (87-84.05)^2 + (95-84.05)^2 + (96-84.05)^2 + (96-84.05)^2 + (99-84.05)^2 + (106-84.05)^2 + (112-84.05)^2 + (127-84.05)^2 + (145-84.05)^2 + (150-84.05)^2] / 19
22636.95 / 19
= 1191.4184 = 1191.42
Standard deviation = sqrt( Variance)
Standard deviation = sqrt(1191.4184)
Standard deviation = 34.516929 = 34.52
Answer:
Measure of angle A = 55°.
Step-by-step explanation:
From the picture attached,
2 = 2
Corresponding sides of the given triangles ΔACB and ΔNLM are proportional.
Therefore, ΔACB ~ ΔNLM.
m∠A = 180° - (90° + 35°) [By triangle sum theorem]
= 180° - 125°
= 55°
Measure of angle A is 55°.
Both solutions are x<span> = 2 and x = -2 are correct
because
</span>when x = 2 , |2| = 2
and
<span>when x = -2, |-2| = 2
hope it helps</span>
Answer: 896 mm
Step-by-step explanation:
Polar coordinates=<span>(6sqrt 2, 3pi/4)=(r, theta)→r=6 sqrt 2, theta=3pi/4
Rectangular coordinates=(x,y)=?
x=r cos theta=(6 sqrt 2) cos(3pi/4)=(6 sqrt 2)(-sqrt 2 / 2)
x=-3 (sqrt 2)^2=-3(2)→x=-6
y=r sin theta=(6 sqrt 2) sin (3pi/4)=(6 sqrt 2)(sqrt 2 / 2)
y=3 (sqrt 2)^2=3(2)→y=6
Rectangular coordinates of the point = (x,y) =(-6,6)
Answer: Option a. (-6,6) </span>
