Answer:
a. Scatterplot is attached.
b. Positive Correlation
c. Correlation coefficient=0.9219
Step-by-step explanation:
a.
The following procedure will be used to obtain the scatter plot
- Open an Google Sheets file online or excel sheet on your computer.
- In column B and C, enter the Income and Vacation data as provided above.
- Select the data > click on insert CHART.
- Chose Scatter Chart option
A scatter plot visualizing your data should be displayed as attached.
b.
- On your computer, open a spreadsheet in Google Sheets.
- Double-click on your scatter plot.
- At the right, click on Customize tab and then Series.
- Scroll down and check the Trend line box
-From the trend line, your notice that your variables have a positive correlation.
-As the income increases, so does vacation expenditure.
c. The correlation coefficient can be calculated as follows.
- Click on any empty cell in the sheet and enter the formula
- "=CORREL((y-axis range),(x-axis range))"
- ENTER
-From our Google Sheets calculation our variables have a positive correlation and the correlation coefficient is 0.9219
-The correlation coefficient,r can also be calculated manually:
-let x be income, and y be vacation and divide all the values by 100 to make the smaller and easier to manipulate:
![r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2-(\sum x)^2][n\sum y^2-(\sum y)^2}}\\\\\\\sum xy=153914\\\sum x=4485\\\sum y=246\\\sum x^2=2878447\\(\sum x)^2=4485^2=20115225\\(\sum y)^2=246^2=60516\\\sum y^2=8392\\n=8\\\\\#substitute \ and \ solve \ for \ r\\\\=\frac{8\times153914-4485\times 246}{\sqrt{[8\times 2878447-4485^2][8\times 8392-246^2]}}\\\\=0.92186\\\\\approx 0.9219](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bn%28%5Csum%20xy%29-%28%5Csum%20x%29%28%5Csum%20y%29%7D%7B%5Csqrt%7B%5Bn%5Csum%20x%5E2-%28%5Csum%20x%29%5E2%5D%5Bn%5Csum%20y%5E2-%28%5Csum%20y%29%5E2%7D%7D%5C%5C%5C%5C%5C%5C%5Csum%20xy%3D153914%5C%5C%5Csum%20x%3D4485%5C%5C%5Csum%20y%3D246%5C%5C%5Csum%20x%5E2%3D2878447%5C%5C%28%5Csum%20x%29%5E2%3D4485%5E2%3D20115225%5C%5C%28%5Csum%20y%29%5E2%3D246%5E2%3D60516%5C%5C%5Csum%20y%5E2%3D8392%5C%5Cn%3D8%5C%5C%5C%5C%5C%23substitute%20%5C%20and%20%5C%20solve%20%5C%20for%20%5C%20r%5C%5C%5C%5C%3D%5Cfrac%7B8%5Ctimes153914-4485%5Ctimes%20246%7D%7B%5Csqrt%7B%5B8%5Ctimes%202878447-4485%5E2%5D%5B8%5Ctimes%208392-246%5E2%5D%7D%7D%5C%5C%5C%5C%3D0.92186%5C%5C%5C%5C%5Capprox%200.9219)
Answer:
It should be A.
Step-by-step explanation:
When you're using exponents, anything that has an exponent of 0 will be 1.
You can use a calculator to confirm on your own.
Answer:they are not perpendicular because their slopes are not negative reciprocals.
Step-by-step explanation:
FG’s slope is 3/4 while HJ’s slope is 2/3. i just had this question on my test lol
Answer:
400 m^2.
Step-by-step explanation:
The largest area is obtained where the enclosure is a square.
I think that's the right answer because a square is a special form of a rectangle.
So the square would be 20 * 20 = 400 m^2.
Proof:
Let the sides of the rectangle be x and y m long
The area A = xy.
Also the perimeter 2x + 2y = 80
x + y = 40
y = 40 - x.
So substituting for y in A = xy:-
A = x(40 - x)
A = 40x - x^2
For maximum value of A we find the derivative and equate it to 0:
derivative A' = 40 - 2x = 0
2x = 40
x = 20.
So y = 40 - x
= 40 - 20
=20
x and y are the same value so x = y.
Therefore for maximum area the rectangle is a square.
Answer:
4.25 feet of ribbon cost around $ 8.29
Step-by-step explanation:
We are given the following information in the question:
Length of ribbon to be bought by Brenna = 4.25 feet
Cost of 1 foot of ribbon = $1.95
Total or actual cost of the ribbon =
Cost of ribbon to be purchased by Brenna =
Thus, to find the actual cost Brenna should use the product of total length of ribbon to be bought and the unit cost of the ribbon.
Hence, 4.25 feet of ribbon cost around $ 8.29
