Answer:
We need to select at least 1068 sales transactions.
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)
95% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
How many randomly selected sales transactions must be surveyed to determine the percentage that transpired over the Internet?
We need to survey at least n sales transactions.
Within three percentage points, so M = 0.03.
We do not know the population proportion, so we estimate it at
, which is when we are going to need the largest sample size.
![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 = 1.96\sqrt{\frac{0.5*0.5}{n}}](https://tex.z-dn.net/?f=0.03%20%3D%201.96%5Csqrt%7B%5Cfrac%7B0.5%2A0.5%7D%7Bn%7D%7D)
![0.03\sqrt{n} = 1.96*0.5](https://tex.z-dn.net/?f=0.03%5Csqrt%7Bn%7D%20%3D%201.96%2A0.5)
![\sqrt{n} = \frac{1.96*0.5}{0.03}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%20%5Cfrac%7B1.96%2A0.5%7D%7B0.03%7D)
![(\sqrt{n})^{2} = (\frac{1.96*0.5}{0.03})^{2}](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%5E%7B2%7D%20%3D%20%28%5Cfrac%7B1.96%2A0.5%7D%7B0.03%7D%29%5E%7B2%7D)
![n = 1067.1](https://tex.z-dn.net/?f=n%20%3D%201067.1)
Rounding up
1068
We need to select at least 1068 sales transactions.
Answer: <u>31.69$</u>
Step-by-step explanation:
27.56 + 4.124 = <u>31.69!!!</u>
27.56 x .15 = 4.134
Answer:
B. 4.5
Step-by-step explanation:
(6x + 42)° and (18x - 12)° are alternate interior angles. If line l is parallel to line m, therefore,
6x + 42 = 18x - 12
Solve for the value of x. Combine like terms.
6x - 18x = -42 - 12
-12x = -54
Divide both sides by -12
-12x/-12 = -54/-12
x = 4.5
Therefore, x = 4.5 would prove lines l and m are parallel to each other.
Answer:
C
Step-by-step explanation:
since we're being told to convert the ratio to fraction then it is C. note that 4 ratio is also the same as dividing 4 by 6
Part A
A geometric sequence is where the terms increase by the same ratio.
Example:
7, 14, 28, 56, ...
We start at 7 and double each term to get the next term. The common ratio is 2.
============================================================
Part B
The next step is to subtract the two equations straight down. This will cancel the vast majority of the terms, and allow to solve for
to get a fairly tidy formula. Refer to part C for more info.
============================================================
Part C
![S_n = a_1 + a_1r + a_1r^2 + \ldots + a_1r^{n-1}\\\\rS_n = a_1r + a_1r^2 + \ldots + a_1r^{n-1} + a_1r^n\\\\rS_n - S_n = \left(a_1r + a_1r^2 + \ldots + a_1r^{n-1}+a_1r^n\right)-\left(a_1 + a_1r + a_1r^2 + \ldots + a_1r^{n-1}\right)\\\\S_n(r - 1) = a_1r^n - a_1\\\\S_n = \frac{a_1r^n - a_1}{r-1}\\\\S_n = \frac{-a_1(r^n - 1)}{-(-r+1)}\\\\S_n = \frac{a_1(1-r^n)}{1-r}\\\\](https://tex.z-dn.net/?f=S_n%20%3D%20a_1%20%2B%20a_1r%20%2B%20a_1r%5E2%20%2B%20%5Cldots%20%2B%20a_1r%5E%7Bn-1%7D%5C%5C%5C%5CrS_n%20%3D%20a_1r%20%2B%20a_1r%5E2%20%2B%20%5Cldots%20%2B%20a_1r%5E%7Bn-1%7D%20%2B%20a_1r%5En%5C%5C%5C%5CrS_n%20-%20S_n%20%3D%20%5Cleft%28a_1r%20%2B%20a_1r%5E2%20%2B%20%5Cldots%20%2B%20a_1r%5E%7Bn-1%7D%2Ba_1r%5En%5Cright%29-%5Cleft%28a_1%20%2B%20a_1r%20%2B%20a_1r%5E2%20%2B%20%5Cldots%20%2B%20a_1r%5E%7Bn-1%7D%5Cright%29%5C%5C%5C%5CS_n%28r%20-%201%29%20%3D%20a_1r%5En%20-%20a_1%5C%5C%5C%5CS_n%20%3D%20%5Cfrac%7Ba_1r%5En%20-%20a_1%7D%7Br-1%7D%5C%5C%5C%5CS_n%20%3D%20%5Cfrac%7B-a_1%28r%5En%20-%201%29%7D%7B-%28-r%2B1%29%7D%5C%5C%5C%5CS_n%20%3D%20%5Cfrac%7Ba_1%281-r%5En%29%7D%7B1-r%7D%5C%5C%5C%5C)
For more information about the canceling going on from step 3 to step 4, see the attachment below.