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KonstantinChe [14]
3 years ago
8

Simplify (8z - 10) ÷ (-2) + 5(z - 1).       plz show work 

Mathematics
1 answer:
Bess [88]3 years ago
6 0
(8z - 10) ÷ (-2) + 5(z - 1) = 8z - 10 ÷ -2 + 5z - 5 = 8z + 5 + 5z - 5 = 13z
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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
In the after school Dena, Shawn, and Amanda knit scarfs that are the same size with yellow, white, and blue yarn. Denas scarf is
jenyasd209 [6]

Answer:

\frac{8}{20}

Step-by-step explanation:

We have been given that in the after school Dena, Shawn, and Amanda knit scarfs that are the same size with yellow, white, and blue yarn. Denas scarf is 2/5 yellow, Shawn's scarf is 3/5 , and Amanda's scarf is 3/4 yellow.

To make Amanda's argument true, let us compare each fraction by making a common denominator.

We can see that least common denominator of each fraction would be 20.

\text{Dena's scarf}=\frac{2}{5}\Rightarrow\frac{2*4}{5*4}=\frac{8}{20}

\text{Shawn's scarf}=\frac{3}{5}\Rightarrow\frac{3*4}{5*4}=\frac{12}{20}

\text{Amanda's scarf}=\frac{3}{4}\Rightarrow\frac{3*5}{4*5}=\frac{15}{20}

Since \frac{8}{20} , therefore, Amanda's scarf has the most yellow.

8 0
3 years ago
Please help me, im struggling
Molodets [167]

<u>Part 1</u>

<u />f(a)=4-7a+16a^2

<u>Part 2</u>

<u />f(a+h)=4-7(a+h)+16(a+h)^2\\\\=4-7(a+h)+16(a^2 +2ah+h^2)\\\\=4-7a-7h+16a^2 +32ah+16h^2

<u>Part 3</u>

<u />\frac{f(a+h)-f(a)}{h}=\frac{(4-7a-7h+16a^2 +32ah+16h^2-(4-7a+16a^2)}{h}\\\\=\frac{-7h+32ah+16h^2}{h}\\\\=32a+16h-7

7 0
1 year ago
What needs to be corrected in this construction of a line parallel to AB passing through C?
lidiya [134]

Answer:

I think it is c

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Joni has two U.S coins in her pocket. One of the coins is not a dime. If the total value of coins in her pocket is 11 cents, wha
Snezhnost [94]
There is one dime and i penny

because it says one coin is not a dime 
that does dot mean the other coin is not a dime
6 0
3 years ago
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