The following table shows the annual income, in dollars, and amount spent on vacation, in dollars, for a sample of 8 families.

Mathematics

1 answer:

AnnZ [12.3K]3 months ago

4 0

Answer:

a. The scatterplot is included.

b. There is a Positive Correlation!

c. The correlation coefficient computes to be 0.9219

Step-by-step explanation:

To create the scatter plot:

Open a Google Sheets document or an Excel file on your device.
Populate columns B and C with the Income and Vacation data as specified.
Select the data, then click on insert CHART.
Choose the Scatter Chart format.

Click OK.

A scatter plot representing your data should appear as shown.

Open a spreadsheet via Google Sheets.
Double-click on your scatter plot.
In the right panel, select the Customize option, and proceed to Series.
Check the box for the Trend line.

- From the trend line, it is clear that the variables exhibit a positive correlation.

- An increase in income corresponds to an increase in vacation spending.

c. The correlation coefficient can be calculated as follows:

Access an empty cell in your sheet and input the formula
"=CORREL((y-axis range),(x-axis range))"
Hit ENTER.

- According to our Google Sheets calculations, a positive correlation exists between the variables, and the correlation coefficient equals 0.9219.

- This correlation coefficient,r can also be calculated manually:

- Let x stand for income, and y for vacation, and scale all values down by 100 for easier calculations:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2-(\sum x)^2][n\sum y^2-(\sum y)^2}}\\\\\\\sum xy=153914\\\sum x=4485\\\sum y=246\\\sum x^2=2878447\\(\sum x)^2=4485^2=20115225\\(\sum y)^2=246^2=60516\\\sum y^2=8392\\n=8\\\\\#substitute \ and \ solve \ for \ r\\\\=\frac{8\times153914-4485\times 246}{\sqrt{[8\times 2878447-4485^2][8\times 8392-246^2]}}\\\\=0.92186\\\\\approx 0.9219$

24

Step-by-step explanation:

Based on the logarithmic expressions given $log_ax = 3, log_ay = 7, log_az = -2$ , we need to identify the value of $log_a(\frac{x^3y}{z^4} )$

$from\ log_ax = 3, x = a^3\\\\from\ log_ay = 7,y = a^7\\\\from\ log_az = -2, z = a^{-2}$ By substituting x = a³, y = a⁷, and z = a⁻² into the logarithmic function $log_a(\frac{x^3y}{z^4} )$ , we will derive;

$= log_a(\frac{x^3y}{z^4} )\\\\= log_a(\dfrac{(a^3)^3*a^7}{(a^{-2})^4} )\\\\= log_a(\dfrac{a^9*a^7}{a^{-8}} )\\\\= log_a\dfrac{a^{16}}{a^{-8}} \\\\= log_aa^{16+8}\\\\= log_aa^{24}\\\\= 24log_aa\\\\= 24* 1\\\\= 24$

Therefore, the result of the logarithmic expression is 24

6 0

2 months ago

Suppose that the number of drivers who travel between a particular origin and destination during a designated time period has a

zzz [12365]

Answer:

Step-by-step explanation:

It has been established that the count of drivers traveling between a specific origin and destination in a certain time frame follows a Poisson distribution with a mean μ = 20 (as indicated in the article "Dynamic Ride Sharing: Theory and Practice"†).

a) $P(X\leq 15) = 0.1565=0.157$