Hello !
cos (a+b) = cos a cos b - sin a sin b
sin (a+b) = sin a cos b + sin b cos a
cos (a+b+c) = cos (a+(b+c))
cos (a+b+c) = cos a cos (b+c) - sin a sin (b+c)
cos (a+b+c) = cos a (cos b cos c - sin b sin c) - sin a (sin b cos c + sin c cos b)
cos (a+b+c)=cos a cos b cos c - cos a sin b sin c - sin a sin b cos c - sin a cos b sin c
Answer:
With alpha 0.95 and 8 degrees of freedom χ²= 2.73
And with alpha 0.05 and 8 degrees of freedom χ²=15.51
Step-by-step explanation:
The significance level ∝ = 1- 0.9 = 0.1
But we need the area of the middle so we divide this significance level with 2
so that we get exactly the middle area .
Dividing 0.1/2= 0.05
So we will have two values for chi square
One with 0.9 + 0.05 = 0.95 alpha and one with 0.05 alpha . This is because the chi square is right tailed.
So with alpha 0.95 and 8 degrees of freedom χ²= 2.73
And with alpha 0.05 and 8 degrees of freedom χ²=15.51
This can be shown with a graph.
A + s = 456........a = 456 - s
3.5a + s = 1131
3.5(456 - s) + s = 1131
1596 - 3.5s + s = 1131
-3.5s + s = 1131 - 1596
-2.5s = - 465
s = -465/-2.5
s = 186 <====== student tickets sold
a + s = 456
a + 186 = 456
a = 456 - 186
a = 270 <==== adult tickets sold
Answer if you divide them or x them you'll get the answer!