Data regarding fuel efficiency of an airliner were collected. The graph shows the correlation between the distance traveled (in thousands of miles) and the altitude (in thousands of feet):
image of a scatter plot with Distance Traveled on the x axis and Altitude on the y axis with 2 comma 2, 3 comma 10, 5 comma 15, 10 comma 20, 15 comma 15, 18 comma 10, and 19 comma 2
Estimate the average rate of change from x = 15 to x = 19.
a. −3.25
b. 4
c. −4
d. −0.31
To estimate the average rate of change, we need to find the change in altitude (y) divided by the change in distance traveled (x).
From the graph, we can see that at x = 15, y = 15 and at x = 19, y = 2.
Change in y = 2 - 15 = -13
Change in x = 19- 15 = 4
Average Rate of Change = (Change in y)/(Change in x) = -13/4 = -3.25
Therefore, the estimated average rate of change from x = 15 to x = 19 is -3.25.
The correct answer is a) -3.25.
A new streaming service sent out a survey to 350 households to see who would be interested in its service. The company found that it could charge $55 per month, with a margin of error of ±1.3. If 1,000 people signed up for the service, what is the least amount of monthly revenue the company should expect?
$52,815
$53,700
$54,915
$56,300
To calculate the least amount of monthly revenue the company should expect, we need to consider the margin of error and the number of people who signed up.
The company found that it could charge $55 per month, with a margin of error of ±1.3%. This means that the actual number of people who signed up could be 1.3% higher or lower than the reported number.
Let's calculate the minimum and maximum numbers of people who signed up:
Minimum number of people who signed up = 1,000 - (1.3% * 1,000) = 1,000 - (0.013 * 1,000) = 1,000 - 13 = 987
Maximum number of people who signed up = 1,000 + (1.3% * 1,000) = 1,000 + (0.013 * 1,000) = 1,000 + 13 = 1,013
Now, to calculate the least amount of monthly revenue, we need to multiply the minimum number of people who signed up by the monthly charge:
Least amount of monthly revenue = $55 * 987 = $54,285
Therefore, the least amount of monthly revenue the company should expect is $54,285.
The correct answer is not provided in the options given.
A new streaming service sent out a survey to 350 households to see who would be interested in its service. The company found that it could charge $55 per month, with a margin of error of ±1.3. If 1,000 people signed up for the service, what is the least amount of monthly revenue the company should expect?
The margin of error provided is ±1.3%, not ±1.3.
To calculate the least amount of monthly revenue the company should expect, we need to consider the margin of error and the number of people who signed up.
The company found that it could charge $55 per month, with a margin of error of ±1.3%. This means that the actual number of people who signed up could be 1.3% higher or lower than the reported number.
Let's calculate the minimum and maximum numbers of people who signed up:
Minimum number of people who signed up = 1,000 - (1.3% * 1,000) = 1,000 - (0.013 * 1,000) = 1,000 - 13 = 987
Now, to calculate the least amount of monthly revenue, we need to multiply the minimum number of people who signed up by the monthly charge:
Least amount of monthly revenue = $55 * 987 = $54,285
Therefore, the least amount of monthly revenue the company should expect is $54,285.
The correct answer is not provided in the options given.
Analyze the following statement:
Marcus notices that he runs faster in the mornings rather than the evenings.
Is the statement an example of correlation or causation?
Correlation, because time of day doesn't cause a person to run faster or slower
Causation, because Marcus has noticed this over several trials
No relationship, because time of day has nothing to do with how fast a person runs
There is not enough information to make a conclusion
Based on the statement provided, we can determine that the statement is an example of correlation. This is because Marcus notices a correlation between running faster and the time of day, but it does not necessarily imply that the time of day directly causes him to run faster or slower. Additionally, there is no information provided about any controlled experiments or specific causal factors that would suggest causation. Therefore, the correct answer is:
Correlation, because time of day doesn't cause a person to run faster or slower
Patrick wanted to gather data about the cost of joining a community pool in his area. He plotted the data and determined that the average community pool membership cost consists of a one-time registration fee and a monthly fee modeled by the equation y = 15x + 40.
Identify and interpret the y-intercept in this model.
The y-intercept is 15. This is the cost of registration.
The y-intercept is 15. This is the cost per month.
The y-intercept is 40. This is the cost per month.
The y-intercept is 40. This is the cost of registration.
In the equation y = 15x + 40, the y-intercept is the value of y when x = 0.
In this case, when x = 0, the equation becomes y = 15(0) + 40 = 0 + 40 = 40.
Therefore, the y-intercept in this model is 40.
Interpretation: The y-intercept represents the starting point or the initial cost in this context. In this equation, the y-intercept of 40 represents the cost of registration for joining the community pool.
Question 5(Multiple Choice Worth 1 points)
(04.07 MC)
The average daily profit of an electronics store is $31,435. The company estimates that 15% is lost each day to returns, with a margin of error of ±4%. What is the maximum the company can expect for returned items?
$3457.85
$4621.13
$5972.65
$6638.22
Question 6(Multiple Choice Worth 1 points)
(04.07 MC)
Trey believes there is a correlation between the number of texts sent during class and GPA. He collected data and found that the line of best fit for his data can be modeled by the equation y = 3.8 − 0.4x.
Identify the slope and the type of association.
The slope is −0.4, which indicates a negative correlation.
The slope is 0.4, which indicates a positive correlation.
The slope is −3.8, which indicates a negative correlation.
The slope is 3.8, which indicates a positive correlation.
Question 7(Multiple Choice Worth 1 points)
(04.07 MC)
An observational study determined that there is a strong correlation between getting less than 8 hours of sleep a day and lower test scores. Can it be determined that the low test scores are caused by sleep deprivation? Explain.
Causation cannot be proven because lower test scores can occur for other reasons, such as not studying or poor attendance.
Causation cannot be proven because all students get less than 8 hours of sleep.
Causation can be proven because it is well known that less sleep lowers test scores.
Causation can be proven because an experiment was used to prove this hypothesis.
answer each question sepeately