Your teacher surveyed the class to determine the number of hours that each student spent on social media. Your teacher created a table and scatterplot graph that displayed the number of hours and the average final grade based on the hours. The trend line (equation) for the data is y=−7.2x+98.9. Interpret the slope. How many points does the average final grade decrease for 1 hour on social media?(1 point)
The totals for each row and column in the two-way table are:
Cloudy Sunny Totals
Cold 40 5 45
Warm 10 35 45
Totals 50 40 90
Therefore, the correct way to fill in the totals for the two-way table is shown above.
The slope of the trend line is -7.2. This means that for every additional hour spent on social media, the average final grade decreases by 7.2 points.
Two-Way Tables Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
1 of 51 of 5 Items
Question
Use the table to answer the question.
Cloudy Sunny Totals
Cold 40 5
Warm 10 35
Totals Maria recorded the weather over the last 90 days. How would you fill in the totals in the two-way table?(2 points)
Cloudy Sunny Totals
Cold 40 5
Warm 10 35
Totals
Your teacher surveyed the class to determine the number of hours that each student spent on social media. Your teacher created a table and scatterplot graph that displayed the number of hours and the average final grade based on the hours. The trend line (equation) for the data is y=−7.2x+98.9. Interpret the y-intercept. What is the average grade if a student was on social media for 0 hours?(1 point)
The y-intercept of the trend line is 98.9. This means that if a student did not spend any time on social media (x=0), the average final grade would be 98.9%.
Using Trend Lines Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
4 of 54 of 5 Items
Question
Your company asked you to analyze the investment of their advertising campaign. You create a scatterplot graph of the advertising dollars spent on advertising, x, and compare it to the revenue generated, y, for January to December of the campaign. You find the equation of the trend line to be y=2.53x+43. Predict the revenue generated if your company invests $200.00 in advertising. Write the revenue in dollars and cents.(1 point)
The revenue generated for a $200.00 investment in advertising is $
543.00.
To find the predicted revenue generated for a $200.00 investment in advertising, substitute x=200 into the equation y=2.53x+43:
y = 2.53(200) + 43
y = 506 + 43
y = 549
Therefore, the revenue predicted for a $200.00 investment in advertising is $549.00.
You work for a manufacturing company on a production line that manufactures cell phones. You are paid $30 a day plus $0.75 for each phone that you assemble. Predict your wages if you assemble 100 phone in one day, using the equation of the trend line y=0.75x+30, where x is the number of phones assembled in one day and y is the total wages. Write your wages in dollars and cents.(1 point)
Your wages are $
.
Your wages are $105.00.
To find the predicted wages for assembling 100 phones in one day, substitute x=100 into the equation y=0.75x+30:
y = 0.75(100) + 30
y = 75 + 30
y = 105
Therefore, the predicted wages for assembling 100 phones in one day is $105.00.
You work for a manufacturing company on a production line that manufactures cell phones. You are paid $20 a day plus $1.50 for each phone that you assemble. Interpret the slope and y-intercept of the equation of the trend line y=1.50x+20.(1 point)
Responses
The slope means that, for every phone assembled, you receive $1.50. The y-intercept means that you receive $20 a day regardless of the number of phones produced.
The slope means that, for every phone assembled, you receive $1.50. The , y, -intercept means that you receive $20 a day regardless of the number of phones produced.
The slope means that, for every 20 phones assembled, you receive $1.50. The y-intercept means that you receive $20 a day regardless of the number of phones produced.
The slope means that, for every 20 phones assembled, you receive $1.50. The , y, -intercept means that you receive $20 a day regardless of the number of phones produced.
The slope means that, for every phone assembled, you receive $20. The y-intercept means that you receive $1.50 a day regardless of the number of phones produced.
The slope means that, for every phone assembled, you receive $20. The , y, -intercept means that you receive $1.50 a day regardless of the number of phones produced.
The slope means that, for every 1.50 phones assembled, you receive $1. The y-intercept means that you receive $20 a day regardless of the number of phones produced.
The slope means that, for every 1.50 phones assembled, you receive $1. The , y, -intercept means that you receive $20 a day regardless of the number of phones produced.
The slope means that, for every phone assembled, you receive $1.50. The y-intercept means that you receive $20 a day regardless of the number of phones produced.
The population growth of a city since 1900 is represented by a linear model. Interpret the slope and the y-intercept. Estimate the slope to the nearest hundredth.
(1 point)
Responses
For every year since 1900, the population grew 0.03 thousand.
For every year since 1900, the population grew 0.03 thousand.
For every year since 1900, the population grew 1.59 thousand. in 1900, the population was 20 thousand.
For every year since 1900, the population grew 1.59 thousand. in 1900, the population was 20 thousand.
For every year since 1900, the population grew 0.63 thousand. In 1900, the population was 20 thousand.
For every year since 1900, the population grew 0.63 thousand. In 1900, the population was 20 thousand.
For every 0.63 of a year since 1900, the population grew 1,000. In 1900, the population was 20 thousand.
The correct response is:
The slope represents the average rate of change of the population per year since 1900. The y-intercept represents the population in the year 1900. Since we are not given any specific values, we cannot estimate the slope to the nearest hundredth.
The population growth of a state since 2000 in millions of people is represented by a linear model. Using the trend line, y=0.83x+30, predict the population, y, in the year 2030. Let x=30 because the year 2030 is 30 years after the year 2000.(1 point)
Responses
In 2030, the population of the state will be 54.9 million people.
In 2030, the population of the state will be 54.9 million people.
In 2030, the population of the state will be 30.03 million people.
In 2030, the population of the state will be 30.03 million people.
In 2030, the population of the state will be 0.83 million people.
In 2030, the population of the state will be 0.83 million people.
In 2030, the population of the state will be 60.83 million people.
In 2030, the population of the state will be 54.9 million people.
To find the predicted population for the year 2030, substitute x=30 into the equation y=0.83x+30:
y = 0.83(30) + 30
y = 24.9 + 30
y = 54.9
Therefore, the predicted population for the state in the year 2030 is 54.9 million people.
Your teacher surveyed the class to determine the number of hours that each student spent on social media. Your teacher created a table and scatterplot graph that displayed the number of hours, x, and the average final grade percentage, y, based on the hours. Using the equation of the trend line of the data, y=–7.2x+98.9, predict the average final grade percentage, to the nearest whole number, if a student spent 10 hours on social media.(1 point)
Responses
The average final grade is 99% if a student spent 10 hours on social media.
The average final grade is 99% if a student spent 10 hours on social media.
The average final grade is 27% if a student spent 10 hours on social media.
The average final grade is 27% if a student spent 10 hours on social media.
The average final grade is 7.2 if a student spent 10 hours on social media.
The average final grade is 7.2 if a student spent 10 hours on social media.
The average final grade is 92% if a student spent 10 hours on social media.
The average final grade is 92% if a student spent 10 hours on social media.
To find the predicted average final grade for 10 hours on social media, substitute x=10 into the equation y=−7.2x+98.9:
y = −7.2(10) + 98.9
y = −72 + 98.9
y = 26.9
Rounding to the nearest whole number, the predicted average final grade for a student who spent 10 hours on social media is 92%.
You are snow skiing down a mountain that is represented by the linear model y=–30x+6,000, where y is the number of feet after x seconds. Predict your elevation level in feet if you ski 60 seconds. (1 point)
Responses
After 60 seconds of skiing, you will be 6,030 feet high.
After 60 seconds of skiing, you will be 6,030 feet high.
After 60 seconds of skiing, you will be 7,800 feet high.
After 60 seconds of skiing, you will be 7,800 feet high.
After 60 seconds of skiing, you will be 5,820 feet high.
After 60 seconds of skiing, you will be 5,820 feet high.
After 60 seconds of skiing, you will be 4,200 feet high.
After 60 seconds of skiing, you will be 4,200 feet high.
After 60 seconds of skiing, you will be 4,200 feet high.
To find the predicted elevation level after 60 seconds of skiing, substitute x=60 into the equation y=−30x+6,000:
y = −30(60) + 6,000
y = −1,800 + 6,000
y = 4,200
Therefore, the predicted elevation level after 60 seconds of skiing is 4,200 feet.
Use the table to answer the question.
Baseball Football Totals
Summer 45 15 60
Winter 20 45
Totals 65 40 105
The table indicates preferences in sports and seasons. How would you construct the rest of the two-way table to determine the number of survey participants who prefer winter and football?
(1 point)
Baseball Football Totals
Summer 45 15 60
Winter 20
45
Totals 65 40 105
The correct way to construct the rest of the two-way table is:
Baseball Football Totals
Summer 45 15 60
Winter 20 25 45
Totals 65 40 105
Therefore, the number of survey participants who prefer winter and football is 25.
The table shows data for seventh and eighth graders who can and cannot swim. How would you construct the missing parts of the two-way table?
(2 points)
Can Swim Cannot Swim Totals
7th Graders
15 60
8th Graders
45
Totals 65 40 105
The correct way to construct the missing parts of the two-way table is:
Can Swim Cannot Swim Totals
7th Graders 15 60 75
8th Graders 50 25 75
Totals 65 85 150
Therefore, the completed two-way table is shown above, and it represents both seventh and eighth graders who can and cannot swim.
Use the table to answer the question.
Preferences Mountains Seaside Island
Hiking 45 20 12
Swimming 12 53 40
The table gives information about people’s preferences on vacation destinations and activities. How many prefer hiking, but not in the mountains?
(1 point)
The number of people who prefer hiking, but not in the mountains, is 52.
To find out, we need to add the number of people who prefer hiking and have a preference other than mountains in the corresponding column.
In this case:
- 12 people prefer hiking and swimming
- 20 people prefer hiking and seaside
- 12 people prefer hiking and island
So the total number of people who prefer hiking, but not in the mountains is:
12 + 20 + 12 = 44
Therefore, 44 people prefer hiking but not in the mountains.
Preferences Mountains Seaside Island
Hiking 45 20 12
Swimming 12 53 40
The table gives information about people’s preferences on vacation destinations and activities. How many prefer the seaside or an island?
The number of people who prefer the seaside or an island is 105.
To find out, we need to add the number of people who prefer the seaside to the number of people who prefer the island.
In this case:
- 20 people prefer hiking and seaside
- 53 people prefer swimming and seaside
- 12 people prefer hiking and island
- 40 people prefer swimming and island
So the total number of people who prefer the seaside or an island is:
20 + 53 + 12 + 40 = 125
Therefore, 125 people prefer the seaside or an island.
Use the table to answer the question.
Friday Saturday Totals
7th graders 24
8th graders 35
Totals 52
Construct the two-way table to determine the total number of eighth graders.
(1 point)
Responses
35
35
28
28
63
63
59
The correct way to construct the two-way table to determine the total number of eighth graders is:
Friday Saturday Totals
7th graders 24 x 24 + x
8th graders y 35 y + 35
Totals 24 + y 35 + x 52 + x + y
We know that the total number of 7th graders is 24 + x, and the total number of students is 52. Therefore, the total number of 8th graders is:
y + 35 + (24 + x) = 52
Simplifying and rearranging, we get:
y + x = 13
We cannot determine the values of x and y separately with the given information, but we do know that the sum of x and y is 13.
Therefore, we cannot determine the total number of 8th graders from the given table and information.
Use the table to answer the question.
Pizza Tacos Chicken Totals
7th graders 24 120
8th graders 35 46
Totals 52 71
Constructing the two-way table, what is the total amount of people who like tacos?
(1 point)
Responses
106
106
71
71
35
35
109
The correct way to construct the two-way table is:
Pizza Tacos Chicken Totals
7th graders 24 x y 120
8th graders a 35 46 a + 35 + 46
Totals 24 + a x + 35 y + 46 237
We know that the totals for the column of tacos is:
x + 35 = 71
Solving for x, we get:
x = 71 - 35
x = 36
Therefore, 36 + 35 = 71 people like tacos in the school.
The total amount of people who like tacos is 71.
Use the table to answer the question.
Pizza Tacos
7th Grade 67 72
8th Grade 54 81
A survey was given to seventh and eighth graders to determine their preferences between tacos and pizza. Interpreting the table, how many eighth graders took the survey?
(1 point)
Responses
135
135
54
54
81
81
274
274
The correct answer is:
There are 54 eighth graders in the table who prefer either pizza or tacos. Therefore, the number of eighth graders who took the survey is 54.
Use the table to answer the question.
Baseball Soccer Football
Girls 31 62 51
Boys 57 54 71
A survey was given to girls and boys that asked them to pick their favorite sport from a list of baseball, soccer, and football. The results are shown in the table. How many girls picked a sport other than football as their favorite sport?
(1 point)
Responses
122
122
144
144
51
51
93
93