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The scatter plot shows the data collected from a survey of 19 students, in which they were asked how many hours per week they study (x) and what their GPAs are (y).

Looking at the graph, which statements are TRUE?

(3 points)
Responses

The slope of the line of best fit will be positive and the y-intercept will also be positive.

The relationship is a positive linear relationship.
The relationship is a positive linear relationship.

Your GPA should be 0 when you study 0 hours each week.
Your GPA should be 0 when you study 0 hours each week.

It is a probabilistic interpretation to say that the more you study, the higher your GPA should be.
It is a probabilistic interpretation to say that the more you study, the higher your GPA should be.

We can use a deterministic interpretation to say that the student who studies 20 hours will make at least a 3.0 GPA.
We can use a deterministic interpretation to say that the student who studies 20 hours will make at least a 3.0 GPA.
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11 answers

Based on the description provided of the scatter plot and the context of the relationship between study hours and GPA, here’s an analysis of the statements:

  1. The slope of the line of best fit will be positive and the y-intercept will also be positive.

    • True/False (likely True): If the relationship between hours studied and GPA is positive (more study hours correlate with higher GPAs), the slope will be positive. The y-intercept being positive depends on the specific data, but it is reasonable to assume that if you study 0 hours, a GPA would likely be above 0 in many cases, making it possible for the intercept to be positive.

  2. The relationship is a positive linear relationship.

    • True: This statement suggests that as one variable increases, the other does as well. If the scatter plot shows an upward trend as study hours increase, then this statement is true.

  3. Your GPA should be 0 when you study 0 hours each week.

    • False: It is not deterministic that GPA should be zero for zero study hours. GPAs can vary by factors other than just study hours.

  4. It is a probabilistic interpretation to say that the more you study, the higher your GPA should be.

    • True: This interpretation reflects the typical association seen in data, suggesting that, on average, increased studying is associated with a higher GPA, but it does not guarantee it for every individual.

  5. We can use a deterministic interpretation to say that the student who studies 20 hours will make at least a 3.0 GPA.

    • False: A deterministic interpretation would imply certainty; while more study hours might correlate with a higher GPA, it doesn’t guarantee that a person studying 20 hours will earn at least a 3.0 GPA.

Based on these evaluations, the TRUE statements are:

  • The relationship is a positive linear relationship.
  • It is a probabilistic interpretation to say that the more you study, the higher your GPA should be.

The other statements regarding the slope and y-intercept and the deterministic interpretations are not definitively true.

onsider the data shown on the graph:

(5 points)
a) The y-intercept represents the base price of $ (Response area) for airfare from NYC.

b) The slope represents a cost of (Response area) cents per mile traveled.

c) According to the equation given, someone who traveled 2,000 miles from NYC would pay $ (Response area) for their airfare.

d) According to the equation given, someone who paid $500 for airfare from NYC would have traveled (Response area) miles.

e) If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be (Response area.)

responses
30
1000
y = 50 + 0.30x
y = 30 + 0.50x
200
800

To answer your questions accurately, I'd need to see the graph and the given equation for airfare pricing. However, I can guide you through how to determine each of the responses based on common practices for equations in the form of \( y = mx + b \), where \( y \) is the total airfare price, \( m \) is the cost per mile, \( x \) is the number of miles traveled, and \( b \) is the base price.

Let's work through the prompts based on typical interpretations:

a) The y-intercept represents the base price of $...

  • This value would typically be your base price of airfare when no miles are flown (i.e., when \( x = 0 \)). If you have options, look for the base price within them. If 30 is your y-intercept, you would enter 30.

b) The slope represents a cost of ... cents per mile traveled.

  • The slope represents the cost associated with each mile traveled. If you see 0.30 in the equation, for example, you would enter 30 (since 0.30 dollars = 30 cents).

c) According to the equation given, someone who traveled 2,000 miles from NYC would pay $...

  • You would substitute \( x = 2000 \) into the equation to find \( y \). If using an equation where the slope (m) is, for example, $0.30 per mile, your calculation might look like this: \[ y = b + mx = b + (0.30)(2000) \]
  • Based on your provided choices, you need to calculate and determine which response matches the value you find—let's assume you find 200 based on your calculation.

d) According to the equation given, someone who paid $500 for airfare from NYC would have traveled ... miles.

  • Rearrange the equation to solve for \( x \): \[ x = \frac{y - b}{m} \]
  • Substitute \( y = 500 \) and solve for \( x \). Based on the given choices, you would find the corresponding miles, which might be 800 for instance.

e) If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be ...

  • You would replace the y-intercept with 50 while keeping the slope the same. If the original was \( y = 30 + 0.30x \), the new equation would be: \[ y = 50 + 0.30x \]
  • This means you would enter y = 50 + 0.30x.

Based on the above descriptions, your responses would be some combination of the numbers you've provided, likely being 30, 30, 200, 800, and y = 50 + 0.30x as your final equation.

If you can clarify or provide the equation and graph presented, I can give you the exact values!

A sandwich shop makes home deliveries. The average amount of time from when an order is placed until it is delivered can be modeled by the equation y=2.5x+5
, where x is the number of miles between the shop and the delivery location and y is the time in minutes. Which of these statements are correct according to the model? Select TWO that apply.(2 points)
Responses

The average amount of time the shop needs to prepare the food for delivery is 5 minutes.
The average amount of time the shop needs to prepare the food for delivery is 5 minutes.

The average amount of time the shop needs to prepare the food for delivery is 2.5 minutes.
The average amount of time the shop needs to prepare the food for delivery is 2.5 minutes.

On average, the delivery person travels 2.5 miles every 1 minute.
On average, the delivery person travels 2.5 miles every 1 minute.

On average, it takes the delivery person 5 minutes to travel 1 mile.
On average, it takes the delivery person 5 minutes to travel 1 mile.

On average, the delivery person travels 5 miles every 1 minute.
On average, the delivery person travels 5 miles every 1 minute.

On average, it takes the delivery person 2.5 minutes to travel 1 mile.

Given the equation \( y = 2.5x + 5 \), where \( x \) is the number of miles between the shop and the delivery location and \( y \) is the time in minutes, we can analyze each of the statements to determine which ones are correct.

  1. The average amount of time the shop needs to prepare the food for delivery is 5 minutes.

    • True: The constant term in the equation (5 minutes) represents the time taken for food preparation when the distance \( x = 0 \) (i.e., when the delivery is to a location that is 0 miles away).

  2. The average amount of time the shop needs to prepare the food for delivery is 2.5 minutes.

    • False: The preparation time is represented by the constant term (5 minutes), not 2.5 minutes.

  3. On average, the delivery person travels 2.5 miles every 1 minute.

    • False: The slope of 2.5 means that for every additional mile (\( x \)), the time increases by 2.5 minutes (\( y \)). So, this statement is not accurate.

  4. On average, it takes the delivery person 5 minutes to travel 1 mile.

    • False: Based on the slope of the equation, it takes 2.5 minutes to travel 1 mile, not 5 minutes.

  5. On average, the delivery person travels 5 miles every 1 minute.

    • False: This is incorrect; the equation indicates that the delivery time increases the farther away the location is.

  6. On average, it takes the delivery person 2.5 minutes to travel 1 mile.

    • True: The slope (2.5) implies that for each mile of distance, it takes 2.5 minutes to cover that distance.

Conclusion:

The two correct statements according to the model are:

  1. The average amount of time the shop needs to prepare the food for delivery is 5 minutes.
  2. On average, it takes the delivery person 2.5 minutes to travel 1 mile.
what scatter plot becomes to this graph
x y
1.0 7.6
2.0 7.0
3.0 7.7
4.0 6.1
5.0 6.9
6.0 4.6
7.0 4.5
8.0 3.5
9.0 4.2
10.0 2.4

To analyze the dataset you've provided and understand what the corresponding scatter plot would look like, let's consider the given \( x \) and \( y \) values:

x         y
1.0      7.6
2.0      7.0
3.0       7.7
4.0       6.1
5.0       6.9
6.0       4.6
7.0        4.5
8.0        3.5
9.0        4.2
10.0      2.4

Characteristics of the Data:

  1. Values of \( x \) range from 1 to 10.

  2. Values of \( y \) initially start high and then decrease overall:

    • At \( x = 1 \), \( y = 7.6 \)
    • At \( x = 2 \), \( y = 7.0 \)
    • At \( x = 3 \), \( y = 7.7 \) (slight increase)
    • At \( x = 4 \), \( y = 6.1 \) (decrease)
    • At \( x = 5 \), \( y = 6.9 \) (increase again)
    • At \( x = 6 \), \( y = 4.6 \) (decrease)
    • At \( x = 7 \), \( y = 4.5 \) (slight decrease)
    • At \( x = 8 \), \( y = 3.5 \) (decrease)
    • At \( x = 9 \), \( y = 4.2 \) (increase)
    • At \( x = 10 \), \( y = 2.4 \) (decrease)

Expected Scatter Plot:

  • The scatter plot would display points that indicate a general downward trend over the range of \( x \).
  • Points would be plotted on a Cartesian plane where the x-axis represents the variable \( x \) and the y-axis represents the variable \( y \).
  • The line formed by connecting these points (if you were to draw a line of best fit) would likely show a non-linear relationship, as the points do not follow a straight line but instead have fluctuations (increasing and decreasing).

Visualization:

To summarize:

  • At \( x = 1 \), the high value of \( y = 7.6 \) indicates a point near the top of the graph.
  • As \( x \) increases, the points generally trend downward, dropping to \( y = 2.4 \) when \( x = 10 \).
  • There are slight variations where some points go up and down, particularly between \( x = 3 \) and \( x = 5 \), indicating some variability.

If you were to plot these coordinates on graph paper or using graphing software, you would see the shape of the data more clearly, allowing for easier interpretation of trends such as those described.

Conclusion:

In summary, the scatter plot will likely show a decreasing trend with some fluctuations, starting high at \( x = 1 \) and generally decreasing throughout, with some peaks and valleys along the way.

what scatter plot belongs to this graph
x y
1.0 10.0
2.0 9.0
3.0 8.0
4.0 7.0
5.0 6.0
6.0 5.0
7.0 4.0
8.0 3.0
9.0 2.0
10.0 1.0

To visualize the scatter plot for the dataset you've provided, we can analyze the relationship between the \( x \) and \( y \) values:

x               y
1.0            10.0
2.0            9.0
3.0             8.0
4.0              7.0 
5.0             6.0
6.0             5.0
7.0              4.0 
8.0              3.0
9.0              2.0
10.0            1.0

Characteristics of the Data:

  1. \( x \) Values: Range from 1 to 10.
  2. \( y \) Values: They start at 10 when \( x = 1 \) and decrease linearly down to 1 when \( x = 10 \).

Trend Analysis:

  • The values of \( y \) decrease consistently as \( x \) increases:
    • At \( x = 1 \), \( y = 10 \)
    • At \( x = 2 \), \( y = 9 \)
    • At \( x = 3 \), \( y = 8 \)
    • ...
    • At \( x = 10 \), \( y = 1 \)

This represents a linear relationship between \( x \) and \( y \) with a negative slope.

Expected Scatter Plot:

  • The scatter plot would show points plotted on a Cartesian plane:
    • The x-axis represents the variable \( x \) (values from 1 to 10).
    • The y-axis represents the variable \( y \) (values from 10 down to 1).
  • Each point would reflect the coordinate pairs:
    • (1, 10)
    • (2, 9)
    • (3, 8)
    • (4, 7)
    • (5, 6)
    • (6, 5)
    • (7, 4)
    • (8, 3)
    • (9, 2)
    • (10, 1)

Visualization:

The scatter plot will show these points creating a straight, downward-sloping line. If you draw a line connecting these points, it will create a straight line that goes from the upper left (10 at \( x = 1 \)) to the lower right (1 at \( x = 10 \)).

Conclusion:

In essence, the scatter plot would display a linear descending pattern, illustrating a perfect negative linear correlation where \( y \) decreases by 1 for each increase of 1 in \( x \). This results in a straight line with a slope of \(-1\) if extended.

If you were to plot these coordinates, you would find that they form a straight line, indicating a strong linear relationship. The line can be represented by the equation: \[ y = -x + 11 \] This indicates that \( y \) decreases as \( x \) increases.

what scatter plot belongs to this graph
x y
1.0 8.3
2.0 5.1
3.0 10.3
4.0 5.8
5.0 1.9
6.0 4.9
7.0 8.7
8.0 4.0
9.0 9.5
10.0 6.8

To describe the scatter plot corresponding to the dataset you've provided, let’s analyze the \( x \) and \( y \) values:

x                     y
1.0                  8.3
2.0                 5.1 
3.0                 10.3
4.0                 5.8
5.0                 1.9
6.0                 4.9
7.0                 8.7
8.0                 4.0
9.0                 9.5
10.0               6.8

Characteristics of the Data:

  1. Range of x Values: \( x \) ranges from 1 to 10.
  2. Range of y Values: The values of \( y \) vary significantly without a clear linear trend:
    • At \( x = 1 \), \( y = 8.3 \)
    • At \( x = 2 \), \( y = 5.1 \)
    • At \( x = 3 \), \( y = 10.3 \) (highest)
    • At \( x = 4 \), \( y = 5.8 \)
    • At \( x = 5 \), \( y = 1.9 \) (lowest)
    • At \( x = 6 \), \( y = 4.9 \)
    • At \( x = 7 \), \( y = 8.7 \)
    • At \( x = 8 \), \( y = 4.0 \)
    • At \( x = 9 \), \( y = 9.5 \)
    • At \( x = 10 \), \( y = 6.8 \)

Trend Analysis:

  • The values of \( y \) do not follow a consistent upward or downward trend but rather fluctuate:
    • They start relatively high, drop after the second point, peak at the third point, and continue to vary.
  • This suggests a more nonlinear relationship or possibly a random distribution of points.

Expected Scatter Plot:

  • In a scatter plot, each pair \( (x, y) \) would be represented as a point in a Cartesian coordinate system:
    • (1, 8.3)
    • (2, 5.1)
    • (3, 10.3)
    • (4, 5.8)
    • (5, 1.9)
    • (6, 4.9)
    • (7, 8.7)
    • (8, 4.0)
    • (9, 9.5)
    • (10, 6.8)

Visualization:

When you plot these points:

  • You will likely see a scattered arrangement of points, indicating variability.
  • There isn't a clear line of best fit due to the fluctuations in \( y \).

Conclusion:

The scatter plot will display a distribution of points that don’t conform to a specific linear pattern. Instead, you’ll see a collection of points spread above and below any linear fit line, reflecting a complex relationship between \( x \) and \( y \).

If you're interpreting this data graphically, expect the points to appear somewhat randomly dispersed rather than following a predictable rise or fall. If you were to use graphing software or graph paper to plot these coordinates, you would observe that the points lie at various heights without a consistent trend.