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mojhsa [17]
3 years ago
7

15 points

Mathematics
2 answers:
serg [7]3 years ago
6 0
In this exercise is given that a triangle has a vertex R at the coordinate (-4,1) and it is says that this point was rotated 90 degrees counterclockwise from the origin. It is asked to find the rotation which is equivalent to 90 degree counterclockwise rotation. 

First of all a 90 degree counterclockwise rotation is define by the rule
(x,y)--(-y,x), which means that every time a 90 degree counterclockwise rotation occurs the given point has to be changed according to the previous mention rule.

In the other hand, a 90 degree clockwise rotation is define by the rule (x,y)--(y,-x). A 360 degree counterclockwise rotation is define by (x,y)--(x,y), and a 270 degree clockwise rotation is represented by the rule (x,y)--(-y,x).

By the previous said, the rotation which is equivalent to a 90 degree counterclockwise rotation is a 270 degree clockwise rotation.
melisa1 [442]3 years ago
5 0
Clockwise 270 degrees is the answer
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Consider a data set containing the following values: 70 65 71 78 89 68 50 75 The mean of the preceding values is 70.75. The devi
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Answer:

If this is the sample data, the sample variance is 125.07 and the sample standard deviation is 11.18

If this is a population data, the population variance is 109.44 and the population standard deviation is 10.46

Step-by-step explanation:

We are given the following data-set:

70, 65, 71, 78, 89, 68, 50, 75

Deviations from the mean

–0.75, –5.75 , 0.25, 7.25, 18.25, –2.75, –20.75, 4.2

Sample size, n = 8

Sample:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.

Sum of squares of differences =

0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5

s = \sqrt{\dfrac{875.5}{7}} = 11.18

\text{ Sample variance} = s^2 = 125.07

Population:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.

Sum of squares of differences =

0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5

\sigma = \sqrt{\dfrac{875.5}{8}} = 10.46

\text{ Population variance} = \sigma^2 = 109.44

7 0
3 years ago
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