<span>The solution:
= 40, p = q = 0.5
P[x] = nCx *p^x *q^(n-x)
when p = q = 0.5, the formula simplifies to
P[x] = nCx/2^n = 40Cx/2^40
at least 18 of each type means 18 to 22 of (say) type I
P(18 <= X <= 22) = 0.5704095 <-------
qb
mean = 40*0.5 = 20
SD = sqrt(npq) = sqrt(40*0.5*0.5) = 3.1623
z1= (18-20)/3.1623 = -0.63 , z2 = (22-20)/3.1623 = 0.63
P(-0.63 < z < 0.63) = 0.4713 <-------</span>
The equivalent expression to the value given using the laws of indices is
Evaluating the options given based on the laws of indices :
Therefore, the only expression which would give a correct way of representing
Learn more : brainly.com/question/12937923?referrer=searchResults
7/12
12/7
1`2/7
7/12
a reciprocal you just flip the fraction
Step-by-step explanation:
![\sin^2 (\frac{\pi}{4} - \alpha) = \frac{1}{2}(1 - \sin 2\alpha)](https://tex.z-dn.net/?f=%20%5Csin%5E2%20%28%5Cfrac%7B%5Cpi%7D%7B4%7D%20-%20%5Calpha%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%281%20-%20%5Csin%202%5Calpha%29%20)
Use the identity
![\sin^2 \theta = \dfrac{1 - \cos 2\theta}{2}](https://tex.z-dn.net/?f=%20%5Csin%5E2%20%5Ctheta%20%3D%20%5Cdfrac%7B1%20-%20%5Ccos%202%5Ctheta%7D%7B2%7D%20)
on the left side.
![\dfrac{1 - \cos [2(\frac{\pi}{4} - \alpha)]}{2} = \frac{1}{2}(1 - \sin 2\alpha)](https://tex.z-dn.net/?f=%20%5Cdfrac%7B1%20-%20%5Ccos%20%5B2%28%5Cfrac%7B%5Cpi%7D%7B4%7D%20-%20%5Calpha%29%5D%7D%7B2%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%281%20-%20%5Csin%202%5Calpha%29%20)
![\dfrac{1 - \cos (\frac{\pi}{2} - 2\alpha)}{2} = \frac{1}{2}(1 - \sin 2\alpha)](https://tex.z-dn.net/?f=%20%5Cdfrac%7B1%20-%20%5Ccos%20%28%5Cfrac%7B%5Cpi%7D%7B2%7D%20-%202%5Calpha%29%7D%7B2%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%281%20-%20%5Csin%202%5Calpha%29%20)
Now use the identity
![\sin \theta = \cos(\frac{\pi}{2} - \theta)](https://tex.z-dn.net/?f=%20%5Csin%20%5Ctheta%20%3D%20%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B2%7D%20-%20%5Ctheta%29%20)
on the left side.
![\dfrac{1 - \sin 2\alpha}{2} = \frac{1}{2}(1 - \sin 2\alpha)](https://tex.z-dn.net/?f=%20%5Cdfrac%7B1%20-%20%5Csin%202%5Calpha%7D%7B2%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%281%20-%20%5Csin%202%5Calpha%29%20)
![\frac{1}{2}(1 - \sin 2\alpha) = \frac{1}{2}(1 - \sin 2\alpha)](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%281%20-%20%5Csin%202%5Calpha%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%281%20-%20%5Csin%202%5Calpha%29%20)