Answer:
The minimum sample size required is 71.
Step-by-step explanation:
The (1 - <em>α</em>)% confidence interval for population mean is:
The margin of error for this interval is:
It is provided that the population standard deviation <em>σ</em> can be estimated by the sample standard deviation <em>s</em>.
The given information is:
<em>s</em> = 18000,
Margin of error = $4200.
Confidence level = 95%
The <em>z</em>-value for 95% confidence level is,
*Use a <em>z</em>-table for the critical value.
Compute the sample size required as follows:
![n=[\frac{z_{\alpha/2}\times \sigma }{MOE}]^{2}](https://tex.z-dn.net/?f=n%3D%5B%5Cfrac%7Bz_%7B%5Calpha%2F2%7D%5Ctimes%20%5Csigma%20%7D%7BMOE%7D%5D%5E%7B2%7D)
![=[\frac{18000\times 1.96}{4200}]^{2}](https://tex.z-dn.net/?f=%3D%5B%5Cfrac%7B18000%5Ctimes%201.96%7D%7B4200%7D%5D%5E%7B2%7D)
Thus, the minimum sample size required is 71.
Answer:
They are not congruent; they are similar.
Step-by-step explanation:
If you analyze the coordinates, you can see that Triangle PQR has been dilated by 1/4 to become Triangle P'Q'R'. Because the triangle has been dilated but not transformed in any other way, you can say that the triangles are similar, but not congruent.
To be congruent, the triangles would have to have the same sizes and the same lengths (you may refer to the diagram below for a visual reference). To be similar, the triangles would have to have the same angles, but with different side lengths. With the dilation, the side lengths have changed, but the angles have not changed.
Hope this helps!
Answer:
Eighty three billion.
Step-by-step explanation:
Eighty three billion.
Eighty three billion.
Answer:
8
Step-by-step explanation:
25% of 12 is 4
or
1/4 of 12 is 4
12-4=8
Answer:
30 mi/ 24 mi (6 mi slower)
Step-by-step explanation:
distance = rate x time
distance = 20 mph * X hr = 20 X miles
return trip:
distance = 16 mph * X hr + 6 miles = 16X + 6
They are the same:
20X = 16X + 6
4X = 6
X = 6/4 = 3/2
20 mph * 3/2 hr = 30 miles.
On the return trip: 16 mph * 3/2 hr = 24 miles, which is 6 miles short of 30 mi.
The distance is 30 miles.
The bird flies all 30 miles in 3/2 hr = 1 and 1/2 hour = 1 hour 30 minutes.
On the return trip, the bird flies 24 miles in 1.5 hours, which is 6 miles short.
