<h3>
Answer: Choice A. P = 1000M</h3>
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Explanation:
Use the log rule
log(A/B) = log(A) - log(B)
this works for any valid log base
So we can say
- log(P/N) = log(P) - log(N)
- log(M/N) = log(M) - log(N)
meaning that
- log(P/N) = 8 turns into log(P) - log(N) = 8
- log(M/N) = 5 turns into log(M) - log(N) = 5
We have this system of equations
![\begin{cases}\log(P)-\log(N) = 8\\ \log(M)-\log(N) = 5\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%5Clog%28P%29-%5Clog%28N%29%20%3D%208%5C%5C%20%5Clog%28M%29-%5Clog%28N%29%20%3D%205%5Cend%7Bcases%7D)
Subtract the equations straight down. You'll find the log(N) terms cancel out and we have the new equation log(P) - log(M) = 3 which transforms into log(P/M) = 3
Lastly, convert the log equation into its exponential equivalent form using the idea that log(b,x) = y turns into y = b^x, where b is the base
Throughout this problem, the base wasn't given. Instead its implied we're talking about base 10.
So,
log(P/M) = 3
P/M = 10^3
P/M = 1000
P = 1000M
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Alternatively,
log(P/N) = 8 turns into P/N = 10^8
log(M/N) = 5 turns into M/N = 10^5
meaning that we can divide the two equations to get P/M = (10^8)/(10^5). That simplifies to P/M = 1000 and rearranges to P = 1000M
Answer:
A sample of 796 is needed.
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 zscore that has a pvalue of
.
The margin of error is:
![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)
In this question, we have that:
![\pi = 0.53](https://tex.z-dn.net/?f=%5Cpi%20%3D%200.53)
91% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
How large should a sample be if the margin of error is .03 for a 91% confidence interval
We need a sample of n, which is found when
. 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)
![0.03 = 1.695\sqrt{\frac{0.53*0.47}{n}}](https://tex.z-dn.net/?f=0.03%20%3D%201.695%5Csqrt%7B%5Cfrac%7B0.53%2A0.47%7D%7Bn%7D%7D)
![0.03\sqrt{n} = 1.695\sqrt{0.53*0.47}](https://tex.z-dn.net/?f=0.03%5Csqrt%7Bn%7D%20%3D%201.695%5Csqrt%7B0.53%2A0.47%7D)
![\sqrt{n} = \frac{1.695\sqrt{0.53*0.47}}{0.03}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%20%5Cfrac%7B1.695%5Csqrt%7B0.53%2A0.47%7D%7D%7B0.03%7D)
![(\sqrt{n})^2 = (\frac{1.695\sqrt{0.53*0.47}}{0.03})^{2}](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%5E2%20%3D%20%28%5Cfrac%7B1.695%5Csqrt%7B0.53%2A0.47%7D%7D%7B0.03%7D%29%5E%7B2%7D)
![n = 795.2](https://tex.z-dn.net/?f=n%20%3D%20795.2)
Rounding up
A sample of 796 is needed.
Answer:
y = 4x - 3
Explanation:
4x – y + 6 = 9 Subtract 6 from each side
4x – y = 3 Subtract 4x rom each side
-y = -4x + 3 Multiply each side by -1
y = 4x - 3
Answer:
The domain of the function is ![(-\infty, -3)\cup(-3,\infty)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C%20-3%29%5Ccup%28-3%2C%5Cinfty%29)
Step-by-step explanation:
Consider the provided rational function.
![f(x)=\frac{x-1}{x+3}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7Bx-1%7D%7Bx%2B3%7D)
We need to determine the domain of the rational function.
Domain of a rational function is all real numbers except those for which the denominator is 0.
The denominator of the rational function is ![x+3](https://tex.z-dn.net/?f=x%2B3)
From the above definition we know that:
![x+3\neq 0](https://tex.z-dn.net/?f=x%2B3%5Cneq%200)
![x\neq -3](https://tex.z-dn.net/?f=x%5Cneq%20-3)
That means for x=-3 the denominator is 0. Therefore, the domain of the function is all real number except -3.
Thus, the domain of the function is ![(-\infty, -3)\cup(-3,\infty)](https://tex.z-dn.net/?f=%28-%5Cinfty%2C%20-3%29%5Ccup%28-3%2C%5Cinfty%29)
Answer:
gfdswqertyuio
Step-by-step explanation: