They repeat by adding that same number again and again
Start with 3 one-by-one squares. This represents the '3' in 4t+3
Then draw 4 rectangles that are vertical or horizontal. Make sure the rectangle is longer than it is wide, or vice versa. The longer side is t units long (t is just a placeholder for a number). The shorter side is 1 unit long
The longer thin rectangles have an area of 1*t = t square units. Four of them represent t+t+t+t = 4*t = 4t
The small squares have an area of 1*1 = 1. Three of them represent 1+1+1 = 1*3 = 3
This is one possible way to draw it out. See the attached drawing.
Supposing a normal distribution, we find that:
The diameter of the smallest tree that is an outlier is of 16.36 inches.
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We suppose that tree diameters are normally distributed with <u>mean 8.8 inches and standard deviation 2.8 inches.</u>
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In a normal distribution with mean
and standard deviation
, the z-score of a measure X is given by:
- The Z-score measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.<u>
</u>
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In this problem:
- Mean of 8.8 inches, thus
. - Standard deviation of 2.8 inches, thus
.
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The interquartile range(IQR) is the difference between the 75th and the 25th percentile.
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25th percentile:
- X when Z has a p-value of 0.25, so X when Z = -0.675.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![-0.675 = \frac{X - 8.8}{2.8}](https://tex.z-dn.net/?f=-0.675%20%3D%20%5Cfrac%7BX%20-%208.8%7D%7B2.8%7D)
![X - 8.8 = -0.675(2.8)](https://tex.z-dn.net/?f=X%20-%208.8%20%3D%20-0.675%282.8%29)
![X = 6.91](https://tex.z-dn.net/?f=X%20%3D%206.91)
75th percentile:
- X when Z has a p-value of 0.75, so X when Z = 0.675.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![0.675 = \frac{X - 8.8}{2.8}](https://tex.z-dn.net/?f=0.675%20%3D%20%5Cfrac%7BX%20-%208.8%7D%7B2.8%7D)
![X - 8.8 = 0.675(2.8)](https://tex.z-dn.net/?f=X%20-%208.8%20%3D%200.675%282.8%29)
![X = 10.69](https://tex.z-dn.net/?f=X%20%3D%2010.69)
The IQR is:
![IQR = 10.69 - 6.91 = 3.78](https://tex.z-dn.net/?f=IQR%20%3D%2010.69%20-%206.91%20%3D%203.78)
What is the diameter, in inches, of the smallest tree that is an outlier?
- The diameter is <u>1.5IQR above the 75th percentile</u>, thus:
![10.69 + 1.5(3.78) = 16.36](https://tex.z-dn.net/?f=10.69%20%2B%201.5%283.78%29%20%3D%2016.36)
The diameter of the smallest tree that is an outlier is of 16.36 inches.
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A similar problem is given at brainly.com/question/15683591
Answer 1: A and C
Step-by-step explanation:
Use distribution law to see which answer match the equation at the top.
Answer 2: 16q + 4
10q and 6q are like terms
10q + 6q = 16q
+
5 - 1
<span>(x-2/3)+(1/60)=(5/6)
x-2/3= 5/6 - 1/60
x-2/3 = 49/60
x - 2 = 49/20
x = 49/20 + 2
x = 89/20
The answer is: x = 89/20 or x = 4.45.
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