Question
Question 3
A)
The table below shows the amount that must be repaid, y, when x dollars are borrowed.
Amount Borrowed Amount Repaid
$100 $135
$200 $260
$500 $635
$800 $1,010
(1 point)
Responses
y=54x+10
y is equal to 5 fourths x plus 10
y=54x
y is equal to 5 fourths x
y=45x+55
y is equal to 4 fifths x plus 55
y=45x
y is equal to 4 fifths x
Question 4
A)
Fill in the missing numbers in the table of values to correspond with the graph.
(4 points)
x y
0 $$
1 $$
2 $$
4 $$
Question 5
A)Some states pay $0.05 for each can that is recycled. Which graph represents the amount of money earned, y, by recycling x cans in these states?(1 point)
Responses
Question 6
A)Movies Plus charges its customers a $10 monthly service fee plus $2 for each movie the customer rents. Movies For Less charges $3 for each movie but does not have a monthly service fee. The costs of renting movies during the same month is represented in the table below.(4 points)
Number of
Movies
Movies Plus
(Cost in $)
Movies for Less
(Cost in $)
0 10 0
2 14 6
4 18 12
10 30
15
When purchasing 15 movies, Movies for Less cost
Movies Plus.
Question 7
A)
A group of friends are going to see a movie. The admission cost is $8 per person. The table below represents the number of friends and the total cost.
Number of Friends (x) 2 3 4 5
Total Cost in Dollars (y)
Which set of ordered pairs can be written from the table?
(1 point)
Responses
(10, 2), (11, 3), (12, 4), (13, 5)
(10, 2), (11, 3), (12, 4), (13, 5)
(16, 2), (24, 3), (32, 4), (40, 5)
(16, 2), (24, 3), (32, 4), (40, 5)
(2, 10), (3, 11), (4, 12), (5, 13)
(2, 10), (3, 11), (4, 12), (5, 13)
(2, 16), (3, 24), (4, 32), (5, 40)
(2, 16), (3, 24), (4, 32), (5, 40)
Question 8
A)An Internet store charges a base fee of $5 plus $1.50 per pound to ship items. The table shows samples of their shipping rates. Fill in the missing values in the table.(3 points)
Weight of Package
(in pounds)
Shipping Cost
(in dollars)
2 8.00
5 12.50
7
9 18.50
10
17 30.50
Derek wants to ship items that weigh a total of 7 pounds, and Keisha wants to ship items that weigh a total of 10 pounds. Keisha spent
more than Derek.
Question 9
A)
Healthy Gym charges members a fee for each visit, while Fitness Gym charges members a one-time yearly charge plus a fee for each visit. The equations below represent the amounts members pay at each gym, where t represents the total yearly cost and n represents the number of visits.
Healthy Gym: 6n=t
Fitness Gym: 50+5n=t
Which statement about the total yearly cost of the memberships is true?
(1 point)
Responses
The total yearly cost will always be higher at Fitness Gym than at Healthy Gym.
The total yearly cost will always be higher at Fitness Gym than at Healthy Gym.
The total yearly cost at Healthy Gym is about $50 lower than the total yearly cost at Fitness Gym.
The total yearly cost at Healthy Gym is about $50 lower than the total yearly cost at Fitness Gym.
The total yearly cost is the same at both gyms when members make 10 visits to each one.
The total yearly cost is the same at both gyms when members make 10 visits to each one.
The total yearly cost is $300 at each gym for 50 visits.
The total yearly cost is $300 at each gym for 50 visits.
Question 10
A)
The admission to a local carnival is $8.25 per person and $1.50 for each ride. How much more will it cost a group of 3 friends to ride 8 rides each than to ride 3 rides each?
NOTE: Type the numerical answer into the blank to receive credit for this question. For example, if the answer is fifteen dollars and twenty-five cents, you would type 15.25 into the blank. DO NOT type the $ symbol into the blank.
(1 point)
$ $$
Question 11
A)
What is the value of x in the equation 4x+8y=40
when y=0.8
?
NOTE: Type the numerical value as a decimal into the blank to receive credit for this question.
(1 point)
x = $$
Question 12
A)
Last month Maria hiked a total of 90 miles on two trails: a 5-mile mountain trail and a 10-mile canal trail. Let x represent the number of times Maria hiked the mountain trail, and let y represent the number of times Maria hiked the canal trail.
Fill in the blanks to write the equation for the total number of miles Maria hiked.
(3 points)
x + 10
=
Question 13
A)
Barbara sells iced tea for $1.49 per bottle, y, and water for $1.25 per bottle, x. She wrote an equation to find the number of bottles she needs to sell to earn $100.
1.25x+1.49=100
What error did Barbara make in writing the equation?
(1 point)
Responses
Barbara’s equation did not consider the number of bottles of water.
Barbara’s equation did not consider the number of bottles of water.
Barbara’s equation did not consider the number of bottles of iced tea.
Barbara’s equation did not consider the number of bottles of iced tea.
Barbara’s equation did not use the correct price for the bottles of iced tea.
Barbara’s equation did not use the correct price for the bottles of iced tea.
Barbara's equation did not use the correct total for sales.
Barbara's equation did not use the correct total for sales.
Question 14
A)
What is the value of x in the equation when y=4
?
8x−2y=48
(1 point)
Responses
x=14
x is equal to 14
x=7
x is equal to 7
x=6
x is equal to 6
x=28
x is equal to 28
A)
The table below shows the amount that must be repaid, y, when x dollars are borrowed.
Amount Borrowed Amount Repaid
$100 $135
$200 $260
$500 $635
$800 $1,010
(1 point)
Responses
y=54x+10
y is equal to 5 fourths x plus 10
y=54x
y is equal to 5 fourths x
y=45x+55
y is equal to 4 fifths x plus 55
y=45x
y is equal to 4 fifths x
Question 4
A)
Fill in the missing numbers in the table of values to correspond with the graph.
(4 points)
x y
0 $$
1 $$
2 $$
4 $$
Question 5
A)Some states pay $0.05 for each can that is recycled. Which graph represents the amount of money earned, y, by recycling x cans in these states?(1 point)
Responses
Question 6
A)Movies Plus charges its customers a $10 monthly service fee plus $2 for each movie the customer rents. Movies For Less charges $3 for each movie but does not have a monthly service fee. The costs of renting movies during the same month is represented in the table below.(4 points)
Number of
Movies
Movies Plus
(Cost in $)
Movies for Less
(Cost in $)
0 10 0
2 14 6
4 18 12
10 30
15
When purchasing 15 movies, Movies for Less cost
Movies Plus.
Question 7
A)
A group of friends are going to see a movie. The admission cost is $8 per person. The table below represents the number of friends and the total cost.
Number of Friends (x) 2 3 4 5
Total Cost in Dollars (y)
Which set of ordered pairs can be written from the table?
(1 point)
Responses
(10, 2), (11, 3), (12, 4), (13, 5)
(10, 2), (11, 3), (12, 4), (13, 5)
(16, 2), (24, 3), (32, 4), (40, 5)
(16, 2), (24, 3), (32, 4), (40, 5)
(2, 10), (3, 11), (4, 12), (5, 13)
(2, 10), (3, 11), (4, 12), (5, 13)
(2, 16), (3, 24), (4, 32), (5, 40)
(2, 16), (3, 24), (4, 32), (5, 40)
Question 8
A)An Internet store charges a base fee of $5 plus $1.50 per pound to ship items. The table shows samples of their shipping rates. Fill in the missing values in the table.(3 points)
Weight of Package
(in pounds)
Shipping Cost
(in dollars)
2 8.00
5 12.50
7
9 18.50
10
17 30.50
Derek wants to ship items that weigh a total of 7 pounds, and Keisha wants to ship items that weigh a total of 10 pounds. Keisha spent
more than Derek.
Question 9
A)
Healthy Gym charges members a fee for each visit, while Fitness Gym charges members a one-time yearly charge plus a fee for each visit. The equations below represent the amounts members pay at each gym, where t represents the total yearly cost and n represents the number of visits.
Healthy Gym: 6n=t
Fitness Gym: 50+5n=t
Which statement about the total yearly cost of the memberships is true?
(1 point)
Responses
The total yearly cost will always be higher at Fitness Gym than at Healthy Gym.
The total yearly cost will always be higher at Fitness Gym than at Healthy Gym.
The total yearly cost at Healthy Gym is about $50 lower than the total yearly cost at Fitness Gym.
The total yearly cost at Healthy Gym is about $50 lower than the total yearly cost at Fitness Gym.
The total yearly cost is the same at both gyms when members make 10 visits to each one.
The total yearly cost is the same at both gyms when members make 10 visits to each one.
The total yearly cost is $300 at each gym for 50 visits.
The total yearly cost is $300 at each gym for 50 visits.
Question 10
A)
The admission to a local carnival is $8.25 per person and $1.50 for each ride. How much more will it cost a group of 3 friends to ride 8 rides each than to ride 3 rides each?
NOTE: Type the numerical answer into the blank to receive credit for this question. For example, if the answer is fifteen dollars and twenty-five cents, you would type 15.25 into the blank. DO NOT type the $ symbol into the blank.
(1 point)
$ $$
Question 11
A)
What is the value of x in the equation 4x+8y=40
when y=0.8
?
NOTE: Type the numerical value as a decimal into the blank to receive credit for this question.
(1 point)
x = $$
Question 12
A)
Last month Maria hiked a total of 90 miles on two trails: a 5-mile mountain trail and a 10-mile canal trail. Let x represent the number of times Maria hiked the mountain trail, and let y represent the number of times Maria hiked the canal trail.
Fill in the blanks to write the equation for the total number of miles Maria hiked.
(3 points)
x + 10
=
Question 13
A)
Barbara sells iced tea for $1.49 per bottle, y, and water for $1.25 per bottle, x. She wrote an equation to find the number of bottles she needs to sell to earn $100.
1.25x+1.49=100
What error did Barbara make in writing the equation?
(1 point)
Responses
Barbara’s equation did not consider the number of bottles of water.
Barbara’s equation did not consider the number of bottles of water.
Barbara’s equation did not consider the number of bottles of iced tea.
Barbara’s equation did not consider the number of bottles of iced tea.
Barbara’s equation did not use the correct price for the bottles of iced tea.
Barbara’s equation did not use the correct price for the bottles of iced tea.
Barbara's equation did not use the correct total for sales.
Barbara's equation did not use the correct total for sales.
Question 14
A)
What is the value of x in the equation when y=4
?
8x−2y=48
(1 point)
Responses
x=14
x is equal to 14
x=7
x is equal to 7
x=6
x is equal to 6
x=28
x is equal to 28
Answers
GPT-4o mini
Sure! Here are the answers and explanations for the questions provided:
### Question 3
Based on the given data:
To find the equation of the relationship between borrowed amount (x) and repaid amount (y), we can set up the ratios or find a pattern.
1. Calculate the ratio of amount repaid to the amount borrowed for the first row.
Example: For $100 borrowed, the amount repaid is $135.
Ratio = \( \frac{135}{100} = 1.35\) (which can also be viewed as a slope)
2. Then for all rows, this should be consistent. The linear equation can be represented as \( y = mx + b \)
After analyzing the data:
- The factor for y can be deduced from the differences; when simplified, one might derive:
\[ y = \frac{5}{4}x + 10 \]
Therefore, the correct response is:
**y is equal to 5 fourths x plus 10.**
### Question 4
Without the graph, I cannot fill in specific values, but typically you could evaluate the relationship between x and y based on the known values, then interpolate or extrapolate to find y values.
### Question 5
The graph representing the relationship \( y = 0.05x \) would be a straight line through the origin, indicating that for every additional can, the earned money increases by $0.05.
### Question 6
For Movies Plus:
- Monthly service: $10
- Cost per movie: $2
For 15 movies:
Total Cost = \( 10 + (15 * 2) = 10 + 30 = 40 \)
For Movies for Less:
- Cost per movie: $3
For 15 movies:
Total Cost = \( 15 * 3 = 45 \)
Thus, when purchasing 15 movies, Movies for Less costs $5 more than Movies Plus.
### Question 7
If the admission cost is $8 per person, the total cost `y` can be expressed for `x` (number of friends):
- For 2 friends: \( y = 2 * 8 = 16 \)
- For 3 friends: \( y = 3 * 8 = 24 \)
- For 4 friends: \( y = 4 * 8 = 32 \)
- For 5 friends: \( y = 5 * 8 = 40 \)
Ordered pairs:
**(2, 16), (3, 24), (4, 32), (5, 40)**
### Question 8
Calculate the shipping cost for 7 pounds:
Cost = Base Fee + (Cost per pound * Weight) = \( 5 + (1.5*7) = 5 + 10.50 = 15.50 \)
For 10 pounds:
Cost = \( 5 + (1.5*10) = 5 + 15 = 20 \)
So:
Derek pays $15.50, and Keisha pays $20; hence Keisha spent $4.50 more than Derek.
### Question 9
Set the two equations for total costs to find their equivalences based on `n` visits.
To check when both costs will equal:
\[ 6n = 50 + 5n \]
\[
n = 50 \text{ when both cost } = 300 \text{ dollars for 50 visits.}
\]
So:
**The total yearly cost is $300 at each gym for 50 visits.**
### Question 10
For a group of 3 friends and riding 8 rides each:
Costs:
Admission: \( 3 * 8.25 = 24.75 \)
Rides: \( 3 * 8 * 1.50 = 36.00 \)
For riding 3 rides each:
Rides: \( 3 * 3 * 1.50 = 13.50 \)
Difference in total costs between 8 and 3 rides = \( (24.75 + 36.00) - (24.75 + 13.50) = 22.50 \)
### Question 11
Substituting \( y = 0.8 \) into the equation:
\[ 4x + 8(0.8) = 40 \]
\[ 4x + 6.4 = 40 \]
\[ 4x = 33.6 \]
\[ x = 8.4\]
### Question 12
Total number of miles equation:
\[ 5x + 10y = 90 \] (based on trail distances)
### Question 13
Correct equation:
\[ 1.49y + 1.25x = 100 \]
Error in not including both x and y in her total sales equation.
Correct response:
**Barbara’s equation did not consider the number of bottles of iced tea.**
### Question 14
Substituting \( y = 4 \):
\[ 8x - 2(4) = 48 \]
\[ 8x - 8 = 48 \]
\[ 8x = 56 \]
\[ x = 7. \]
Thus answers 1 by 1 for the questions summarized.
If you need any additional help with the questions or more calculations, feel free to ask!
### Question 3
Based on the given data:
To find the equation of the relationship between borrowed amount (x) and repaid amount (y), we can set up the ratios or find a pattern.
1. Calculate the ratio of amount repaid to the amount borrowed for the first row.
Example: For $100 borrowed, the amount repaid is $135.
Ratio = \( \frac{135}{100} = 1.35\) (which can also be viewed as a slope)
2. Then for all rows, this should be consistent. The linear equation can be represented as \( y = mx + b \)
After analyzing the data:
- The factor for y can be deduced from the differences; when simplified, one might derive:
\[ y = \frac{5}{4}x + 10 \]
Therefore, the correct response is:
**y is equal to 5 fourths x plus 10.**
### Question 4
Without the graph, I cannot fill in specific values, but typically you could evaluate the relationship between x and y based on the known values, then interpolate or extrapolate to find y values.
### Question 5
The graph representing the relationship \( y = 0.05x \) would be a straight line through the origin, indicating that for every additional can, the earned money increases by $0.05.
### Question 6
For Movies Plus:
- Monthly service: $10
- Cost per movie: $2
For 15 movies:
Total Cost = \( 10 + (15 * 2) = 10 + 30 = 40 \)
For Movies for Less:
- Cost per movie: $3
For 15 movies:
Total Cost = \( 15 * 3 = 45 \)
Thus, when purchasing 15 movies, Movies for Less costs $5 more than Movies Plus.
### Question 7
If the admission cost is $8 per person, the total cost `y` can be expressed for `x` (number of friends):
- For 2 friends: \( y = 2 * 8 = 16 \)
- For 3 friends: \( y = 3 * 8 = 24 \)
- For 4 friends: \( y = 4 * 8 = 32 \)
- For 5 friends: \( y = 5 * 8 = 40 \)
Ordered pairs:
**(2, 16), (3, 24), (4, 32), (5, 40)**
### Question 8
Calculate the shipping cost for 7 pounds:
Cost = Base Fee + (Cost per pound * Weight) = \( 5 + (1.5*7) = 5 + 10.50 = 15.50 \)
For 10 pounds:
Cost = \( 5 + (1.5*10) = 5 + 15 = 20 \)
So:
Derek pays $15.50, and Keisha pays $20; hence Keisha spent $4.50 more than Derek.
### Question 9
Set the two equations for total costs to find their equivalences based on `n` visits.
To check when both costs will equal:
\[ 6n = 50 + 5n \]
\[
n = 50 \text{ when both cost } = 300 \text{ dollars for 50 visits.}
\]
So:
**The total yearly cost is $300 at each gym for 50 visits.**
### Question 10
For a group of 3 friends and riding 8 rides each:
Costs:
Admission: \( 3 * 8.25 = 24.75 \)
Rides: \( 3 * 8 * 1.50 = 36.00 \)
For riding 3 rides each:
Rides: \( 3 * 3 * 1.50 = 13.50 \)
Difference in total costs between 8 and 3 rides = \( (24.75 + 36.00) - (24.75 + 13.50) = 22.50 \)
### Question 11
Substituting \( y = 0.8 \) into the equation:
\[ 4x + 8(0.8) = 40 \]
\[ 4x + 6.4 = 40 \]
\[ 4x = 33.6 \]
\[ x = 8.4\]
### Question 12
Total number of miles equation:
\[ 5x + 10y = 90 \] (based on trail distances)
### Question 13
Correct equation:
\[ 1.49y + 1.25x = 100 \]
Error in not including both x and y in her total sales equation.
Correct response:
**Barbara’s equation did not consider the number of bottles of iced tea.**
### Question 14
Substituting \( y = 4 \):
\[ 8x - 2(4) = 48 \]
\[ 8x - 8 = 48 \]
\[ 8x = 56 \]
\[ x = 7. \]
Thus answers 1 by 1 for the questions summarized.
If you need any additional help with the questions or more calculations, feel free to ask!