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Question 1(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 2(Multiple Choice Worth 1 points)

(04.07 MC)

Data regarding the amount of money earned and saved by teenagers were collected. The graph shows the correlation between money earned (in dollars per hour) and money saved (in dollars):

image of a scatter plot with Money Saved on the x axis and Money Earned on the y axis with points 1 comma 20, 3 comma 19, 5 comma 15, 7 comma 11, 9 comma 9, 11 comma 5 and 15 comma 3

Estimate the average rate of change from x = 3 to x = 11.

8
−1.75
−8
−0.57
Question 3(Multiple Choice Worth 1 points)

(04.07 MC)

The price of gas has been increasing over the last month. Renee believes there is a positive correlation between the number of predicted storms and the price of gas.

Number of Storms Predicted Gas Price
1 $2.34
3 $2.44
4 $2.49
6 $2.56
7 $2.61

Use the table to determine the average rate of change from 3 to 6 storms.
0.04
3
0.12
0.27
Question 4(Multiple Choice Worth 1 points)

(04.07 MC)

A new streaming service sent out a survey to 300 households to see who would be interested in its service. The company found that it could charge $50 per month, with a margin of error of ±1.5. If 1,000 people signed up for the service, what is the least amount of monthly revenue the company should expect?

$44,500
$46,500
$48,500
$51,500
Question 5(Multiple Choice Worth 1 points)

(04.07 LC)

Which of the following scenarios best shows causation?

There is a strong correlation between the type of soda a person drinks and grades earned in school.
When I leave the lights on all night, my electric bill is higher than usual.
People who walk to school are more likely to go on long vacations.
When I skip lunch, I perform better on my tests.
Question 6(Multiple Choice Worth 1 points)

(04.07 LC)

Aretha wanted to gather data about the cost of local bowling leagues in her area. She plotted the data and determined that the average bowling league costs consist of a one-time registration fee and a monthly fee modeled by the equation y = 15x + 20.

Identify and interpret the y-intercept in this model.

The y-intercept is 20. This is the cost per month.
The y-intercept is 20. This is the cost of registration.
The y-intercept is 15. This is the cost of registration.
The y-intercept is 15. This is the cost per month.
Question 7(Multiple Choice Worth 1 points)

(04.07 MC)

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 there may be some other factor that causes Marcus to run faster in the mornings
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
Question 8(Multiple Choice Worth 1 points)

(04.07 MC)

Trey believes there is a correlation between the number of texts sent in class and GPA. He collected data and found that the line of best fit for the data can be modeled by the equation y = 4.0 − 0.5x.

Identify the slope and the type of association.

The slope is −4.0, which indicates a negative correlation.
The slope is −0.5, which indicates a negative correlation.
The slope is 4.0, which indicates a positive correlation.
The slope is 0.5, which indicates a positive correlation.
Question 9(Multiple Choice Worth 1 points)

(04.07 MC)

Based on the time recorded for 700 attendees at an amusement park, the average amount of time spent at the park was 7.25 hours with a margin of error of ±1.65 hours. If 3,000 people attended the park on a given day, what is the estimated range of total hours the attendees spent in the park?

8,375 to 16,800 total hours spent in the park
16,800 to 21,785 total hours spent in the park
16,800 to 26,700 total hours spent in the park
16,800 to 35,885 total hours spent in the park
Question 10(Multiple Choice Worth 1 points)

(04.07 MC)

An observational study determined that there is a strong correlation between sitting close to the television and poor eyesight. Can it be determined that sitting too close to the television causes poor eyesight? Explain.

Causation cannot be proven because everyone watches television.
Causation can be proven because it is well known that sitting close to the television causes poor eyesight.
Causation can be proven because there was a strong correlation.
Causation cannot be proven because poor eyesight can occur for other reasons, such as genetics.

1 answer

Here are the answers to your questions:

Question 1:
To find the maximum amount lost to returns:
Average daily profit = $31,435
Expected returns = 15% of $31,435 = 0.15 × $31,435 = $4,715.25
Margin of error ±4%, so:
Maximum expected returns = $4,715.25 + 4% of $31,435 = $4,715.25 + 0.04 × $31,435 = $4,715.25 + $1,257.40 = $5,972.65.
Answer: $5972.65

Question 2:
To find the average rate of change from x = 3 to x = 11:
At x = 3, Money Saved = 19.
At x = 11, Money Saved = 5.
Average Rate of Change = (Money Saved at x = 11 - Money Saved at x = 3) / (11 - 3) = (5 - 19) / (11 - 3) = -14 / 8 = -1.75.
Answer: −1.75

Question 3:
To determine the average rate of change from 3 to 6 storms:
At 3 storms, Gas Price = $2.44.
At 6 storms, Gas Price = $2.56.
Average Rate of Change = (Gas Price at 6 - Gas Price at 3) / (6 - 3) = (2.56 - 2.44) / (6 - 3) = 0.12 / 3 = 0.04.
Answer: 0.04

Question 4:
If the company charges $50 with a margin of error of ±$1.50, the least amount per person is $50 - $1.50 = $48.50.
With 1,000 people signed up:
Least revenue = 1,000 × $48.50 = $48,500.
Answer: $48,500

Question 5:
The best scenario that shows causation is:
Answer: When I leave the lights on all night, my electric bill is higher than usual.

Question 6:
The y-intercept in the equation y = 15x + 20 is 20, which represents the one-time registration fee before any monthly fees.
Answer: The y-intercept is 20. This is the cost of registration.

Question 7:
Marcus' observation could be affected by external factors, indicating it is more of a correlation rather than causation.
Answer: Correlation, because there may be some other factor that causes Marcus to run faster in the mornings.

Question 8:
The slope of the equation y = 4.0 − 0.5x is -0.5, indicating a negative correlation between the number of texts sent in class and GPA.
Answer: The slope is −0.5, which indicates a negative correlation.

Question 9:
To find the estimated range of total hours spent by 3,000 attendees:
Average time spent = 7.25 hours with a margin of error of ±1.65 hours:
Estimated range:
Lower limit = (7.25 - 1.65) × 3,000 = 5.60 × 3,000 = 16,800.
Upper limit = (7.25 + 1.65) × 3,000 = 8.90 × 3,000 = 26,700.
Answer: 16,800 to 26,700 total hours spent in the park.

Question 10:
Causation cannot be proven solely based on correlation, as other factors may contribute to the observed outcome.
Answer: Causation cannot be proven because poor eyesight can occur for other reasons, such as genetics.