We first determine the z-scores for the given x-values of 64 and 96.
For x = 64: z = (64 - 80) / 8 = -2
For x = 96: z = (96 - 80) / 8 = 2
Therefore we find the probability that -2 < z < 2, which is around 0.95. Therefore, out of 100 students, approximately 100(0.95) = 95 students will weigh between 64 and 96 pounds.
Answer:
g(7)= -4
Step-by-step explanation:
10-2(7)
10-14
=-4
Answer:
the answer to the question is "C"
Answer:
I will study about it and tell u
Answer:
![\alpha=69.28^o](https://tex.z-dn.net/?f=%5Calpha%3D69.28%5Eo)
![\beta=61.26^o](https://tex.z-dn.net/?f=%5Cbeta%3D61.26%5Eo)
![\gamma=49.46^o](https://tex.z-dn.net/?f=%5Cgamma%3D49.46%5Eo)
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Step-by-step explanation:
<u>Triangle Solving</u>
If we had a triangle will its three sides of known length, we can solve for the rest of the parameters of the triangle, i.e. the area, perimeter and internal angles.
The three circles have diameters 900 m, 700 m and 600 m and are tangent to each other externally. The distances from their centers (where houses are located) are the sum of each pair of the radius of the circles. Thus, the sides of the triangle are
![x=450+350=800](https://tex.z-dn.net/?f=x%3D450%2B350%3D800)
![y=450+300=750](https://tex.z-dn.net/?f=y%3D450%2B300%3D750)
![z=350+300=650](https://tex.z-dn.net/?f=z%3D350%2B300%3D650)
The internal angles can be computed by using the cosine's law
![x^2=y^2+z^2-2yzcos\alpha](https://tex.z-dn.net/?f=x%5E2%3Dy%5E2%2Bz%5E2-2yzcos%5Calpha)
![y^2=x^2+z^2-2xzcos\beta](https://tex.z-dn.net/?f=y%5E2%3Dx%5E2%2Bz%5E2-2xzcos%5Cbeta)
![z^2=x^2+y^2-2xycos\gamma](https://tex.z-dn.net/?f=z%5E2%3Dx%5E2%2By%5E2-2xycos%5Cgamma)
Where \alpha, \beta and \gamma are the opposite angles to x, y and z respectively. Solving for each one of them:
![\displaystyle cos\alpha=\frac{y^2+z^2-x^2}{2yz}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20cos%5Calpha%3D%5Cfrac%7By%5E2%2Bz%5E2-x%5E2%7D%7B2yz%7D)
![\displaystyle cos\alpha=\frac{750^2+650^2-800^2}{2\cdot 750\cdot 650}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20cos%5Calpha%3D%5Cfrac%7B750%5E2%2B650%5E2-800%5E2%7D%7B2%5Ccdot%20750%5Ccdot%20650%7D)
![cos\alpha=0.3538](https://tex.z-dn.net/?f=cos%5Calpha%3D0.3538)
![\alpha=69.28^o](https://tex.z-dn.net/?f=%5Calpha%3D69.28%5Eo)
Similarly
![\displaystyle cos\beta=\frac{x^2+z^2-y^2}{2xz}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20cos%5Cbeta%3D%5Cfrac%7Bx%5E2%2Bz%5E2-y%5E2%7D%7B2xz%7D)
![\displaystyle cos\beta=\frac{800^2+650^2-750^2}{2\cdot 800\cdot 650}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20cos%5Cbeta%3D%5Cfrac%7B800%5E2%2B650%5E2-750%5E2%7D%7B2%5Ccdot%20800%5Ccdot%20650%7D)
![cos\beta=0.4808](https://tex.z-dn.net/?f=cos%5Cbeta%3D0.4808)
![\beta=61.26^o](https://tex.z-dn.net/?f=%5Cbeta%3D61.26%5Eo)
The other angle is computed now
![\displaystyle cos\gamma=\frac{x^2+y^2-z^2}{2xy}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20cos%5Cgamma%3D%5Cfrac%7Bx%5E2%2By%5E2-z%5E2%7D%7B2xy%7D)
![\displaystyle cos\gamma=\frac{800^2+750^2-650^2}{2\cdot 800\cdot 750}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20cos%5Cgamma%3D%5Cfrac%7B800%5E2%2B750%5E2-650%5E2%7D%7B2%5Ccdot%20800%5Ccdot%20750%7D)
![cos\gamma=0.65](https://tex.z-dn.net/?f=cos%5Cgamma%3D0.65)
![\gamma=49.46^o](https://tex.z-dn.net/?f=%5Cgamma%3D49.46%5Eo)
The area can be found by
![\displaystyle A=\frac{1}{2}x.y.sin\gamma](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%3D%5Cfrac%7B1%7D%7B2%7Dx.y.sin%5Cgamma)
![\displaystyle A=\frac{1}{2}\cdot 800\cdot 750\cdot sin49.46^o](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%3D%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20800%5Ccdot%20750%5Ccdot%20sin49.46%5Eo)
![A=227980.26\ m^2](https://tex.z-dn.net/?f=A%3D227980.26%5C%20m%5E2)