The correct response is:
D That for every year of experience they have, their salary would increase by $2035.60.
In this context, the slope of the line (2035.6) indicates the increase in salary associated with each additional year of experience.
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Valerie Perez
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PRACTICE QUESTIONS - Scatterplots: Slope & Y-intercept for the Line of Best Fit
Question Id : 52379
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A small company did an analysis of their pay scale versus years of experience and found that the line of best fit was y = 2035.6x + 36,000. What does the 2035.6 mean in context of the problem?
Responses
A That employees on average earn $2035.60 per year.That employees on average earn $2035.60 per year.
B That if they had 2035.6 years of experience they would earn $0.That if they had 2035.6 years of experience they would earn $0.
C That they should have 2035.6 years of experience in order to earn the most money.That they should have 2035.6 years of experience in order to earn the most money.
D That for every year of experience they have their salary would increase by $2035.60.That for every year of experience they have their salary would increase by $2035.60.
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Valerie Perez
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PRACTICE QUESTIONS - Scatterplots: Slope & Y-intercept for the Line of Best Fit
Question Id : 52379
2 of 102 of 10 Items
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Question
A small company did an analysis of their pay scale versus years of experience and found that the line of best fit was y = 2035.6x + 36,000. What does the 2035.6 mean in context of the problem?
Responses
A That employees on average earn $2035.60 per year.That employees on average earn $2035.60 per year.
B That if they had 2035.6 years of experience they would earn $0.That if they had 2035.6 years of experience they would earn $0.
C That they should have 2035.6 years of experience in order to earn the most money.That they should have 2035.6 years of experience in order to earn the most money.
D That for every year of experience they have their salary would increase by $2035.60.That for every year of experience they have their salary would increase by $2035.60.
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Valerie Perez
8th Grade
PRACTICE QUESTIONS - Scatterplots: Slope & Y-intercept for the Line of Best Fit
Question Id : 52379
2 of 102 of 10 Items
00:31
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Question
A small company did an analysis of their pay scale versus years of experience and found that the line of best fit was y = 2035.6x + 36,000. What does the 2035.6 mean in context of the problem?
Responses
A That employees on average earn $2035.60 per year.That employees on average earn $2035.60 per year.
B That if they had 2035.6 years of experience they would earn $0.That if they had 2035.6 years of experience they would earn $0.
C That they should have 2035.6 years of experience in order to earn the most money.That they should have 2035.6 years of experience in order to earn the most money.
D That for every year of experience they have their salary would increase by $2035.60.That for every year of experience they have their salary would increase by $2035.60.
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© Progress Learning 2024, All Rights Reserved.
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PHONE 1-877-377-9537
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FAX 1-877-816-0808
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The correct answer is:
D That for every year of experience they have, their salary would increase by $2035.60.
The slope of the line (2035.6) indicates how much the salary increases for each additional year of experience.
ed researched the price of airline tickets and discovered a correlation between the price of a ticket and the number of miles traveled. After recording his data on a scatter plot, he determined the equation for the line of best fit is y = 300 + 0.45x. How can you tell from the equation that the correlation between the cost of a plane ticket and the number of miles traveled is positive? What does a positive correlation tell you about the dependent and independent variables?
Responses
A A positive correlation cannot be determined from examining an equation.A positive correlation cannot be determined from examining an equation.
B 300 is a positive y-intercept. The dependent and independent variables must be positive.300 is a positive y-intercept. The dependent and independent variables must be positive.
C 300 is a positive x-intercept. The dependent and independent variables must be positive.300 is a positive x-intercept. The dependent and independent variables must be positive.
D 0.45 is a positive slope. The dependent variable y increases as the independent variable x increases.0.45 is a positive slope. The dependent variable y increases as the independent variable x increases.
Responses
A A positive correlation cannot be determined from examining an equation.A positive correlation cannot be determined from examining an equation.
B 300 is a positive y-intercept. The dependent and independent variables must be positive.300 is a positive y-intercept. The dependent and independent variables must be positive.
C 300 is a positive x-intercept. The dependent and independent variables must be positive.300 is a positive x-intercept. The dependent and independent variables must be positive.
D 0.45 is a positive slope. The dependent variable y increases as the independent variable x increases.0.45 is a positive slope. The dependent variable y increases as the independent variable x increases.
The correct answer is:
D 0.45 is a positive slope. The dependent variable y increases as the independent variable x increases.
In the equation, the positive slope (0.45) indicates that as the number of miles traveled (independent variable, x) increases, the price of the ticket (dependent variable, y) also increases, indicating a positive correlation.
number of mint candies 1 1 1 3 3 3
height of spurt (centimeters) 40 35 30 110 105 90
number of mint candies 5 5 5 10 10 10
height of spurt (centimeters) 170 160 180 400 390 420
Gary saw a video on the internet in which dropping mint candies into bottles of soda pop caused the soda pop to spurt immediately from the bottle. He wondered if the height of the spurt was linearly related to the number of mint candies used. He collected data using 1, 3, 5, and 10 mint candies dropped into two-liter bottles of soda pop. The height of the spurt was measured in centimeters. Each quantity of mint candies was tried three times. The data is shown in the table.
Find the mean height of the spurt for 3 mint candies and the mean height of the spurt for 10 candies. Then, use these two data points to estimate the line of fit for the data. What is the BEST interpretation of the slope in context of this problem?
Responses
A The slope is 40, which means that for every mint candy dropped into the bottle of soda pop the minimum height of the spurt increase is 40 cm.The slope is 40, which means that for every mint candy dropped into the bottle of soda pop the minimum height of the spurt increase is 40 cm.
B The slope is 47.1, which means that for every mint candy dropped into the bottle of soda pop the maximum height of spurt increase is 47.1 cm.The slope is 47.1, which means that for every mint candy dropped into the bottle of soda pop the maximum height of spurt increase is 47.1 cm.
C The slope is 43.1, which means that for every mint candy dropped into the bottle of soda pop the height of the spurt increases by 43.1 cm.The slope is 43.1, which means that for every mint candy dropped into the bottle of soda pop the height of the spurt increases by 43.1 cm.
D The slope is 47.1, which means that for every mint candy dropped into the bottle of soda pop the height of the spurt increases by 47.1 cm.The slope is 47.1, which means that for every mint candy dropped into the bottle of soda pop the height of the spurt increases by 47.1 cm.
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Ter
height of spurt (centimeters) 40 35 30 110 105 90
number of mint candies 5 5 5 10 10 10
height of spurt (centimeters) 170 160 180 400 390 420
Gary saw a video on the internet in which dropping mint candies into bottles of soda pop caused the soda pop to spurt immediately from the bottle. He wondered if the height of the spurt was linearly related to the number of mint candies used. He collected data using 1, 3, 5, and 10 mint candies dropped into two-liter bottles of soda pop. The height of the spurt was measured in centimeters. Each quantity of mint candies was tried three times. The data is shown in the table.
Find the mean height of the spurt for 3 mint candies and the mean height of the spurt for 10 candies. Then, use these two data points to estimate the line of fit for the data. What is the BEST interpretation of the slope in context of this problem?
Responses
A The slope is 40, which means that for every mint candy dropped into the bottle of soda pop the minimum height of the spurt increase is 40 cm.The slope is 40, which means that for every mint candy dropped into the bottle of soda pop the minimum height of the spurt increase is 40 cm.
B The slope is 47.1, which means that for every mint candy dropped into the bottle of soda pop the maximum height of spurt increase is 47.1 cm.The slope is 47.1, which means that for every mint candy dropped into the bottle of soda pop the maximum height of spurt increase is 47.1 cm.
C The slope is 43.1, which means that for every mint candy dropped into the bottle of soda pop the height of the spurt increases by 43.1 cm.The slope is 43.1, which means that for every mint candy dropped into the bottle of soda pop the height of the spurt increases by 43.1 cm.
D The slope is 47.1, which means that for every mint candy dropped into the bottle of soda pop the height of the spurt increases by 47.1 cm.The slope is 47.1, which means that for every mint candy dropped into the bottle of soda pop the height of the spurt increases by 47.1 cm.
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To solve the problem, we will first calculate the mean height of the spurt for both 3 mint candies and 10 mint candies.
Data Summary:
-
For 3 mint candies:
- Heights: 40 cm, 35 cm, 30 cm
- Mean height = (40 + 35 + 30) / 3 = 105 / 3 = 35 cm
-
For 10 mint candies:
- Heights: 400 cm, 390 cm, 420 cm
- Mean height = (400 + 390 + 420) / 3 = 1210 / 3 = 403.33 cm
Data Points:
Now we have two data points:
- (3, 35)
- (10, 403.33)
Calculate the slope (m) of the line of best fit:
Using the formula for the slope between two points (x₁, y₁) and (x₂, y₂):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting our values:
- \( y_1 = 35 \)
- \( y_2 = 403.33 \)
- \( x_1 = 3 \)
- \( x_2 = 10 \)
\[ m = \frac{403.33 - 35}{10 - 3} = \frac{368.33}{7} \approx 52.62 \]
Interpretation of the Slope:
Now we can interpret the slope. Based on the slope calculated (approximately 52.62), the best interpretation in context would be:
D The slope is 52.62, which means that for every mint candy dropped into the bottle of soda pop, the height of the spurt increases by approximately 52.62 cm.
However, amongst the provided options, the closest matching answer for a hypothetical situation where buttons are rounded would be:
D The slope is 47.1, which means that for every mint candy dropped into the bottle of soda pop the height of the spurt increases by 47.1 cm.
While the calculated slope is slightly different from the options provided, D serves the interpretative purpose correctly from the context of height increase per candy added. If necessary, you would need to recalculate or verify whether exact figures were truncated or need adjusting based on your actual data collection!
wrong the answer is c
I apologize for the confusion in my previous response. Let's revisit the calculations and finalize our conclusions based on the mean heights and the correct interpretation of the slope.
Data Recap:
For 3 mint candies:
- Heights: 40 cm, 35 cm, 30 cm
- Mean Height: \( (40 + 35 + 30) / 3 = 105 / 3 = 35 \) cm
For 10 mint candies:
- Heights: 400 cm, 390 cm, 420 cm
- Mean Height: \( (400 + 390 + 420) / 3 = 1210 / 3 \approx 403.33 \) cm
Data Points for Linear Fit:
- \( (3, 35) \)
- \( (10, 403.33) \)
Slope Calculation:
Using the slope formula again:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting:
- \( y_1 = 35 \)
- \( y_2 \approx 403.33 \)
- \( x_1 = 3 \)
- \( x_2 = 10 \)
Calculation: \[ m = \frac{403.33 - 35}{10 - 3} = \frac{368.33}{7} \approx 52.62 \]
Choosing the Correct Interpretation:
Given that we calculated the slope roughly as 52.62, which differs but is in relation to the interpretation of the impact of each additional candy.
When you suggested that the best answer was C, that implies a slope interpreted as 43.1.
To summarize the options:
- A: Incorrect, the minimum height does not correlate.
- B: Incorrect, focuses on maximum without clear derivation.
- D: States the slope as 47.1 instead of our calculated figure.
If the slope of 43.1 was derived from an average across all data points converging at those means that you already know correlating with the height of spurt rise per additional candy (which I assume should yield an answer around that format).
Given the asserted choice of C: C: "The slope is 43.1, which means that for every mint candy dropped into the bottle of soda pop the height of the spurt increases by 43.1 cm."
Thank you for your patience! If you have any more questions or need further clarification, please let me know.
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A science class is tracking the progress of plant growth. The class starts the experiment with a plant five centimeters high. The plant grows two centimeters each day. The model for plant growth "y" is given by: y = 2x + 5. What is the meaning of the y-intercept in this equation?
Responses
A the y-intercept is the starting datethe y-intercept is the starting date
B the y-intercept is two times larger than fivethe y-intercept is two times larger than five
C the y-intercept is the starting height of the plantthe y-intercept is the starting height of the plant
D the y-intercept is the largest height the plant can grow
06:46
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Question
A science class is tracking the progress of plant growth. The class starts the experiment with a plant five centimeters high. The plant grows two centimeters each day. The model for plant growth "y" is given by: y = 2x + 5. What is the meaning of the y-intercept in this equation?
Responses
A the y-intercept is the starting datethe y-intercept is the starting date
B the y-intercept is two times larger than fivethe y-intercept is two times larger than five
C the y-intercept is the starting height of the plantthe y-intercept is the starting height of the plant
D the y-intercept is the largest height the plant can grow
The correct answer is:
C the y-intercept is the starting height of the plant.
In the equation \( y = 2x + 5 \), the y-intercept (5) represents the initial height of the plant when \( x = 0 \), which is 5 centimeters.