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Mathematics

1 answer:

Molodets [167]3 years ago

8 0

Answer:

ticket in Japan: 17.23 $

ticket in Switzerland: 13.26 $

Step-by-step explanation:

let the price of one movie ticket in Switzerland be Y

let the price of one movie ticket in Japan be X

then accordingly,

it is given that

3x + 2y = 78.21

and

2x +3y = 74.24

multiplying the first equation by 2 and second by 3 we get

6x + 4y = 156.42

6x + 9y = 222.72

subtracting 1st equation from second we get

5y = 66.3

y = 13.26

by putting in the value of y in equation 2 we get:

2x + 39.78 = 74.24

2x= 34.46

x= 17.23

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What is the value of the correlation coefficient r of the data set?

enyata [817]

The correct option will be: C) 0.84

Explanation

Formula for Correlation coefficient :

$r= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^2-(\Sigma x)^2][n\Sigma y^2-(\Sigma y)^2]}}$

First, for each point(x, y), we need to calculate x², y² and xy .

Then, we will find sum all x, y, x², y² and xy, which gives us Σx, Σy, Σx², ∑y² and Σxy

(Please refer to the attached image for the table )

Here we got, ∑x = 44 , ∑y = 183 , ∑x² = 362 , ∑y² = 6575 and ∑xy = 1480

'n' is the total number of data set, which is 7 here.

So, plugging those values into the above formula..........

$r= \frac{n(\Sigma xy)-(\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^2-(\Sigma x)^2][n\Sigma y^2-(\Sigma y)^2]}}\\ \\ r=\frac{7(1480)-(44)(183)}{\sqrt{[7(362)-(44)^2][7(6575)-(183)^2]}}\\ \\ r=\frac{10360-8052}{\sqrt{(598)(12536)}}\\ \\ r=\frac{2308}{\sqrt{7496528}}\\ \\ r=0.84$