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lana66690 [7]
3 years ago
6

Point V is on line segment UW. Given UW=13 and VW = 11, determine the length of UV

Mathematics
1 answer:
jekas [21]3 years ago
8 0

Answer:

UV = 2

Step-by-step explanation:

Given

UW = 13

VW = 11

Required

Determine UV

From the question, we have

UW = UV + VW

Make UV the subject of formula

UV = UW - VW

Substitute 11 and 13 for VW and UW, respectively

UV = 13 - 11

UV = 2

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Step-by-step explanation:

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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

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(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}

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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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