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Lorico [155]
3 years ago
11

name the lengths of the sides of three rectangles that have perimeter of 14 units. use only whole numbers

Mathematics
1 answer:
Dvinal [7]3 years ago
5 0
Ok so I name them Bob, Joe, and Harry


if total perimiter=14 then
Bob has legnth of 1 and width of 1
Joe has legnth of 1 and width of 1
Harry has legnth of 2 and width of 1


if each rectangle has perimiter of 14 then
Bob has legnth of 4 and width of 3
Joe has legnth of 5 and width of 2
Harry has legnth of 6 and width of 1
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(a) \sum x_i=56.68 and \sum x_i^2=197.46

(b) The sample variance is s^2=0.530 and the sample standard deviation is s=0.728

Step-by-step explanation:

(a)

The sum of these 17 sample observations is

\sum x_i=2.79\:+2.57+\:2.73\:+3.75\:+2.27+\:2.75+\:4.00+\:4.22+\:3.88+\:4.35+\:3.41+\:4.57+\:2.38+\:3.73\:+2.75+\:3.47+\:3.06\\\\\sum x_i=56.68

and the sum of their squares is

\sum x_i^2=2.79^2\:+2.57^2+\:2.73^2\:+3.75^2\:+2.27^2+\:2.75^2+\:4.00^2+\:4.22^2+\:3.88^2+\:4.35^2+\:3.41^2+\:4.57^2+\:2.38^2+\:3.73^2\:+2.75^2+\:3.47^2+\:3.06^2\\\\\sum x_i^2=197.46

(b)

The sample variance, denoted by s^2, is given by

s^2=\frac{S_{xx}}{n-1}

where S_{xx} =\sum x_i^2-\frac{(\sum x_i)^2}{n}

Applying the above formula we get that

S_{xx}=197.46-\frac{(56.68)^2}{17}\\\\S_{xx} =8.482

s^2=\frac{8.482}{17-1}=0.530

The sample standard deviation, denoted by <em>s</em>, is the (positive) square root of the variance:

s=\sqrt{s^2}

Applying the above formula we get that

s=\sqrt{0.530}=0.728

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3 years ago
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