Answer:
A sample of 801 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 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)
95% confidence level
So
, z is the value of Z that has a p-value of
, so
.
25% of U.S. homes have a direct satellite television receiver.
This means that ![\pi = 0.25](https://tex.z-dn.net/?f=%5Cpi%20%3D%200.25)
How large a sample is necessary to estimate the true population of homes which do with 95% confidence and within 3 percentage points?
This is n for which M = 0.03. 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 = 1.96\sqrt{\frac{0.25*0.75}{n}}](https://tex.z-dn.net/?f=0.03%20%3D%201.96%5Csqrt%7B%5Cfrac%7B0.25%2A0.75%7D%7Bn%7D%7D)
![0.03\sqrt{n} = 1.96\sqrt{0.25*0.75}](https://tex.z-dn.net/?f=0.03%5Csqrt%7Bn%7D%20%3D%201.96%5Csqrt%7B0.25%2A0.75%7D)
![\sqrt{n} = \frac{1.96\sqrt{0.25*0.75}}{0.03}](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%20%5Cfrac%7B1.96%5Csqrt%7B0.25%2A0.75%7D%7D%7B0.03%7D)
![(\sqrt{n})^2 = (\frac{1.96\sqrt{0.25*0.75}}{0.03})^2](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%5E2%20%3D%20%28%5Cfrac%7B1.96%5Csqrt%7B0.25%2A0.75%7D%7D%7B0.03%7D%29%5E2)
![n = 800.3](https://tex.z-dn.net/?f=n%20%3D%20800.3)
Rounding up:
A sample of 801 is needed.
If you solve for y, the relationship is y = -x + 20. Since the
equation isin the form y = mx + b with m = -1 and b = 20,
the equation is linear. It is not proportional because b ≠ 0.
For this case, the first thing you have to keep in mind is that we are in the presence of a piece function.
We have then:
For [0, 5]:
A car traveling at 46 mi / h slows to a speed of 23 mi / h in 5 seconds.
For [5, 10]:
It maintains that speed for 5 seconds.
For [10, 15]:
then slows to a stop after 5 more seconds.
In this case:
x axis: represents time
y axis: represents the speed.
Answer:
See attached image for the graphic v (t) vs t.
Answer:
![\$68](https://tex.z-dn.net/?f=%5C%2468)
Step-by-step explanation:
1. Approach
To solve this problem, one wants to find the price of a product after its discount has been applied. The discount is 20% off, so the new price of the item is 80% of its original price (percent is out of 100 so if a an item is 20% off, it is 100 - 20 = 80; 80% the original price). To calculate the percent cost, one would divide the percent value by 100, and then multiply it by the price of the item.
2. Solving
The price of the new item is 80% of the price of the original item. To calculate the percent cost, cent, one would divide the percent value by 100, and then multiply it by the price of the item.
Therefore, the equation that will be formed is,
![price * \frac{percent}{100}](https://tex.z-dn.net/?f=price%20%2A%20%5Cfrac%7Bpercent%7D%7B100%7D)
Substitute,
![85 * \frac{80}{100}](https://tex.z-dn.net/?f=85%20%2A%20%5Cfrac%7B80%7D%7B100%7D)
Simplify,
![85 * 0.8\\\\= 68](https://tex.z-dn.net/?f=85%20%2A%200.8%5C%5C%5C%5C%3D%2068)
So first we need to find the total number of boxes that the cookies could fit in:
![\frac{1,692}{36}=47](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%2C692%7D%7B36%7D%3D47%20%20)
Now we know that 47 boxes were made from this amount of cookies.
If Mr. Riley sells each box for 8, then we need to multiply the number of boxes by 8:
![47*8=376](https://tex.z-dn.net/?f=%2047%2A8%3D376%20)
So Mr. Riley will collect a total of 376 from selling all of his cookies.