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3 years ago

20 POINT PLEASE QUICKLY

Mathematics

1 answer:

sdas [7]3 years ago

5 0

Answer: the ordered pair is (-14,-6)

Step by step:

x – 2y = -2 (Eq. 1)

x – 4y = 10 (Eq. 2)

Isolate x in Eq. 2:

x = -2 + 2y

Substitute that solution x in Eq. 2:

x - 4y = 10

-2 + 2y - 4y = 10

Solve for y:

-2 - 2y = 10

-2y = 10 + 2 = 12

y = -6

Then calculate value for x using the above value for y

x = -2 + 2y

x = -2 + 2(-6) = -14

The solution is (x,y)=(-14,-6)

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Five observations taken for two variables follow.

I am Lyosha [343]

Answer:

a) Figure attached

b) If we see the scatter plot we can conclude that the possible relation between x and y is linear and with a positive correlation since when the values of x increases the values for y increases as well.

c) $Cov (X,Y) = \frac{\sum_{i=1}^n (x_i -\bar X)(y_i -\bar Y)}{n-1}$

We can find the numerator like this:

$\sum_{i=1}^5 (6-16)(6-10)+(11-16)(9-10)+(15-16)(6-10)+(21-16)(17-10)+(27-16)(12-10)=106$

And then:

$Cov(X,Y) = \frac{106}{5-1}=26.5$

d) $r=\frac{5(906)-(80)(50)}{\sqrt{[5(1552) -(80)^2][5(586) -(50)^2]}}=0.693$

Step-by-step explanation:

Part a

For this part we use excel in order to create the scatterplot and we got the result on the figure attached.

Part b

If we see the scatter plot we can conclude that the possible relation between x and y is linear and with a positive correlation since when the values of x increases the values for y increases as well.

Part c

The sample covariance is defined as:

$Cov (X,Y) = \frac{\sum_{i=1}^n (x_i -\bar X)(y_i -\bar Y)}{n-1}$

We can find the numerator like this:

$\sum_{i=1}^5 (6-16)(6-10)+(11-16)(9-10)+(15-16)(6-10)+(21-16)(17-10)+(27-16)(12-10)=106$

And then:

$Cov(X,Y) = \frac{106}{5-1}=26.5$

Part d

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:

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

For our case we have this:

n=5 $\sum x = 80, \sum y = 50, \sum xy = 906, \sum x^2 =1552, \sum y^2 =586$

$r=\frac{5(906)-(80)(50)}{\sqrt{[5(1552) -(80)^2][5(586) -(50)^2]}}=0.693$

So then the correlation coefficient would be r =0.693

3 0

3 years ago

A university has ten dormitories for students. All of the dormitories have students of similar ages and offer the same convenien

lina2011 [118]

Answer:

a is correct

Step-by-step explanation:

4 0

3 years ago

Y-1/4x=-1 <br> y-2=4x <br> one solution, no solution or infinite solution?

alexandr1967 [171]

Answer:

One solution

Step-by-step explanation:

To start, let's simplify the equations to slope-intercept form

y - 1/4x = =1

+1/4x +1/4x

y = 1/4x - 1

y - 2 = 4x

+2 +2

y = 4x + 2

As you can see, the equations do not have anything in common worth mentioning. The slopes are different and the y-intercepts are different, so there must be only one solution.

Feel free to ask me any questions in the comments! :D

7 0

3 years ago

Simplify 8^-7 x 8^5 please show work

Pie

When you are multiplying exponents with the same base, you can add the exponents. This is represented as:

$x^a \cdot x^b = x^{(a +b)}$