Im pretty sure all u need to do is multiply and you got your answer
By definition, the gravitational force is given by:
![Fg = -Gm1m2 / r ^ 2 ](https://tex.z-dn.net/?f=Fg%20%3D%20-Gm1m2%20%2F%20r%20%5E%202%0A)
Where,
m1 and m2: are the masses of the objects
G: is the gravitational constant
r is the distance between the objects' centers
The vertical asymptote of the function occurs when the denominator is equal to zero.
We have then:
![r ^ 2 = 0 r = 0](https://tex.z-dn.net/?f=r%20%5E%202%20%3D%200%0A%0A%20r%20%3D%200)
In this context, it means that physically, the distance between the center of the objects can not be equal to zero (which is logical).
This would be a triangular prism
Answer:
The sample size required is 228.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.
![\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=%5Cpi%20%5Cpm%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
In which
z is the z-score that has a p-value of
.
The margin of error is of:
![M = z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
90% confidence level
So
, z is the value of Z that has a p-value of
, so
.
In previous years, the proportion has been 0.16.
This means that ![\pi = 0.16](https://tex.z-dn.net/?f=%5Cpi%20%3D%200.16)
Obtain a sample size that will ensure a margin of error of at most 0.04 for a 90% confidence interval.
This is n for which M = 0.04. So
![M = z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=M%20%3D%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
![0.04 = 1.645\sqrt{\frac{0.16*0.84}{n}}](https://tex.z-dn.net/?f=0.04%20%3D%201.645%5Csqrt%7B%5Cfrac%7B0.16%2A0.84%7D%7Bn%7D%7D)
![0.04\sqrt{n} = 1.645\sqrt{0.16*0.84}](https://tex.z-dn.net/?f=0.04%5Csqrt%7Bn%7D%20%3D%201.645%5Csqrt%7B0.16%2A0.84%7D)
![\sqrt{n} = \frac{1.645\sqrt{0.16*0.84}}{0.04}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%20%5Cfrac%7B1.645%5Csqrt%7B0.16%2A0.84%7D%7D%7B0.04%7D)
![(\sqrt{n})^2 = (\frac{1.645\sqrt{0.16*0.84}}{0.04})^2](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%5E2%20%3D%20%28%5Cfrac%7B1.645%5Csqrt%7B0.16%2A0.84%7D%7D%7B0.04%7D%29%5E2)
![n = 227.3](https://tex.z-dn.net/?f=n%20%3D%20227.3)
Rounding up:
The sample size required is 228.
Answer:
#5 is a function, #6 is not a function
Step-by-step explanation: