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3 years ago

Perform the indicated operation and simplify

Mathematics

2 answers:

Alecsey [184]3 years ago

3 0

Answer:

-----

2(a-2)

Step-by-step explanation:

3a+6 a^2 -4

----------- ÷ -----------

8 4a

Copy dot flip

3a+6 4a

----------- * -----------

8 a^2 -4

Factor

3(a+2) 4a

----------- * -----------

8 (a-2) (a+2)

Cancel like terms

3 a

----------- * -----------

2 (a-2)

-----

2(a-2)

rewona [7]3 years ago

3 0

Answer:

Step-by-step explanation:

$\frac{3a+6}{8}$ ÷ $\frac{a^{2} -4}{4a}$ = $\frac{3(a+2)}{8}$ * $\frac{4a}{(a+2)(a-2)}$

take out (a+2) and 4

$\frac{3}{2}$ * $\frac{a}{(a-2)}$ = $\frac{3a}{2(a-2)}$

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3 years ago

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3 years ago

If the drama club collected 25,915 points and gave away 71 shirts, how many shirts would be given away when 33,580 points are co

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3 years ago

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