The correct equation that represents this scenario is:
154⋅2.5=385
Use the image to answer the question.
A coordinate plane of quadrant 1 shows x axis labeled as time in seconds, t, ranging from 0 to 4 in 1 unit increments. The y axis is labeled as distance in feet, d, ranging from 0 to 500 in increments of 100.
The two plotted points are left parenthesis 0 comma 0 right parenthesis and left parenthesis 2.5 comma 385 right parenthesis. The points are labeled. A leader line extends from the origin point label to the point.
The graph represents the distance a major-league outfielder throws a baseball. He can throw a baseball as fast as 105 miles per hour, or 154 feet per second. Which equation represents this scenario?
(1 point)
Responses
105⋅2.5=262.5
105 times 2.5 equals 262.5
154⋅90=13,860
154 times 90 equals 13,860
105⋅90=9,450
105 times 90 equals 9,450
154⋅2.5=385
154 times 2.5 equals 385
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15 answers
If a graph is proportional, what characteristic does it display?(1 point)
Responses
It will pass through the point (0, 0).
It will pass through the point Left Parenthesis 0 comma 0 Right Parenthesis .
It will curve.
It will curve.
It will have y-values larger than their corresponding x-values.
It will have y -values larger than their corresponding x -values.
It will climb rapidly, indicating a steep slope.
It will climb rapidly, indicating a steep slope.
Responses
It will pass through the point (0, 0).
It will pass through the point Left Parenthesis 0 comma 0 Right Parenthesis .
It will curve.
It will curve.
It will have y-values larger than their corresponding x-values.
It will have y -values larger than their corresponding x -values.
It will climb rapidly, indicating a steep slope.
It will climb rapidly, indicating a steep slope.
The correct answer is: It will pass through the point (0, 0). This means that when x is 0, y will also be 0. In other words, the graph will start at the origin (0, 0).
Kevin is told that for a particular math problem, the value of y is always 32 times the value of x . Kevin writes the equation y=32x to show the relationship between x and y . What is the constant of proportionality?(1 point)
The constant of proportionality in the equation y=32x is 32.
A whale swims 200 miles in 5 days. Identify which equation could be used to find how many miles it swims in 16 days.(1 point)
Responses
y=200×16×5
y equals 200 times 16 times 5
y=40×16
y equals 40 times 16
200=16x
200 equals 16 x
y=200×16
Responses
y=200×16×5
y equals 200 times 16 times 5
y=40×16
y equals 40 times 16
200=16x
200 equals 16 x
y=200×16
The equation that could be used to find how many miles the whale swims in 16 days is y=40×16. This equation represents the proportionality between the number of days and the distance traveled by the whale.
Use the tables to answer the question.
Sonia
Number of Problems Minutes of Writing
6 120
18 360
25 500
60 1,200
Maryna
Number of Problems Minutes of Writing
8 200
15 375
20 500
50 1,250
Based on the tables showing the number of minutes two writers spent writing math problems for two different lessons, who spent more time writing per problem? Write the answer in unit rate form.
(1 point)
Responses
Maryna spent less time writing per problem at the unit rate of 1 min.25 problems
.
Maryna spent less time writing per problem at the unit rate of 1 min.25 problems
.
Sonia spent the same amount of time as Maryna time writing per problem at the unit rate of 25 min.1 problem
.
Sonia spent the same amount of time as Maryna time writing per problem at the unit rate of 25 min.1 problem
.
Maryna spent more time writing per problem at the the unite rate of 25min.1 problem
.
Maryna spent more time writing per problem at the the unite rate of 25min.1 problem
.
Sonia spent more time writing per problem at the unit rate of 20 min. 1 problem
.
Sonia spent more time writing per problem at the unit rate of 20 min. 1 problem
.
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Sonia
Number of Problems Minutes of Writing
6 120
18 360
25 500
60 1,200
Maryna
Number of Problems Minutes of Writing
8 200
15 375
20 500
50 1,250
Based on the tables showing the number of minutes two writers spent writing math problems for two different lessons, who spent more time writing per problem? Write the answer in unit rate form.
(1 point)
Responses
Maryna spent less time writing per problem at the unit rate of 1 min.25 problems
.
Maryna spent less time writing per problem at the unit rate of 1 min.25 problems
.
Sonia spent the same amount of time as Maryna time writing per problem at the unit rate of 25 min.1 problem
.
Sonia spent the same amount of time as Maryna time writing per problem at the unit rate of 25 min.1 problem
.
Maryna spent more time writing per problem at the the unite rate of 25min.1 problem
.
Maryna spent more time writing per problem at the the unite rate of 25min.1 problem
.
Sonia spent more time writing per problem at the unit rate of 20 min. 1 problem
.
Sonia spent more time writing per problem at the unit rate of 20 min. 1 problem
.
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To determine who spent more time writing per problem, we need to calculate the unit rate for each writer.
For Sonia:
- For 6 problems, she spent 120 minutes, so the unit rate is 120/6 = 20 minutes per problem.
- For 18 problems, she spent 360 minutes, so the unit rate is 360/18 = 20 minutes per problem.
- For 25 problems, she spent 500 minutes, so the unit rate is 500/25 = 20 minutes per problem.
- For 60 problems, she spent 1200 minutes, so the unit rate is 1200/60 = 20 minutes per problem.
For Maryna:
- For 8 problems, she spent 200 minutes, so the unit rate is 200/8 = 25 minutes per problem.
- For 15 problems, she spent 375 minutes, so the unit rate is 375/15 = 25 minutes per problem.
- For 20 problems, she spent 500 minutes, so the unit rate is 500/20 = 25 minutes per problem.
- For 50 problems, she spent 1250 minutes, so the unit rate is 1250/50 = 25 minutes per problem.
From the calculations, we can see that both Sonia and Maryna spent the same amount of time writing per problem, at a unit rate of 25 minutes per problem. Therefore, the correct answer is: Sonia spent the same amount of time as Maryna writing per problem at the unit rate of 25 min. 1 problem.
For Sonia:
- For 6 problems, she spent 120 minutes, so the unit rate is 120/6 = 20 minutes per problem.
- For 18 problems, she spent 360 minutes, so the unit rate is 360/18 = 20 minutes per problem.
- For 25 problems, she spent 500 minutes, so the unit rate is 500/25 = 20 minutes per problem.
- For 60 problems, she spent 1200 minutes, so the unit rate is 1200/60 = 20 minutes per problem.
For Maryna:
- For 8 problems, she spent 200 minutes, so the unit rate is 200/8 = 25 minutes per problem.
- For 15 problems, she spent 375 minutes, so the unit rate is 375/15 = 25 minutes per problem.
- For 20 problems, she spent 500 minutes, so the unit rate is 500/20 = 25 minutes per problem.
- For 50 problems, she spent 1250 minutes, so the unit rate is 1250/50 = 25 minutes per problem.
From the calculations, we can see that both Sonia and Maryna spent the same amount of time writing per problem, at a unit rate of 25 minutes per problem. Therefore, the correct answer is: Sonia spent the same amount of time as Maryna writing per problem at the unit rate of 25 min. 1 problem.
Unit Rates & Proportions Unit Test
14 of 1614 of 16 Items
Question
Use the image to answer the question.
An illustration shows quadrant one of a coordinate plane where the x-axis and y-axis range from 0 to 6 in increments of 1. The y-axis is titled distance in feet and the x-axis is titled time in seconds. A solid line, labeled A, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 3 comma 6 right parenthesis. A dotted line, labeled B, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 6 right parenthesis. A dashed line, labeled C, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 3 right parenthesis.
Which of these objects would reach 100 feet in the least amount of time?
(1 point)
Responses
object C
object C
object B
object B
object A
object A
They would all reach 100 feet at the same time.
They would all reach 100 feet at the same time.
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14 of 1614 of 16 Items
Question
Use the image to answer the question.
An illustration shows quadrant one of a coordinate plane where the x-axis and y-axis range from 0 to 6 in increments of 1. The y-axis is titled distance in feet and the x-axis is titled time in seconds. A solid line, labeled A, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 3 comma 6 right parenthesis. A dotted line, labeled B, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 6 right parenthesis. A dashed line, labeled C, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 3 right parenthesis.
Which of these objects would reach 100 feet in the least amount of time?
(1 point)
Responses
object C
object C
object B
object B
object A
object A
They would all reach 100 feet at the same time.
They would all reach 100 feet at the same time.
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To determine which object would reach 100 feet in the least amount of time, we can examine the graphs for objects A, B, and C.
From the graphs, we can see that object A reaches a distance of 6 feet when the time is 3 seconds. So, it would require more than 3 seconds for object A to reach a distance of 100 feet.
Object B reaches a distance of 6 feet when the time is 6 seconds. Since it takes 6 seconds for object B to cover a distance of 6 feet, it would also take more than 6 seconds for object B to reach a distance of 100 feet.
Object C reaches a distance of 3 feet when the time is 6 seconds. Therefore, it would take less than 6 seconds for object C to reach a distance of 100 feet.
Based on this information, the correct answer is: object C.
From the graphs, we can see that object A reaches a distance of 6 feet when the time is 3 seconds. So, it would require more than 3 seconds for object A to reach a distance of 100 feet.
Object B reaches a distance of 6 feet when the time is 6 seconds. Since it takes 6 seconds for object B to cover a distance of 6 feet, it would also take more than 6 seconds for object B to reach a distance of 100 feet.
Object C reaches a distance of 3 feet when the time is 6 seconds. Therefore, it would take less than 6 seconds for object C to reach a distance of 100 feet.
Based on this information, the correct answer is: object C.
The temperature is dropping throughout the day as a cold front comes in. In City A, the temperature is changing by −5°F per hour, and in City B the temperature is changing by −3°F per hour. If the temperatures in both cities started at 70°F , which city is warmer, and what is the difference in their temperatures after 5 hours?(1 point)
Responses
City A is warmer by 10°F.
City A is warmer by 10 degrees F .
City B is warmer by 10°F.
City B is warmer by 10 degrees F .
City A is warmer by 2°F.
City A is warmer by 2 degrees F .
City B is warmer by 2°F.
Responses
City A is warmer by 10°F.
City A is warmer by 10 degrees F .
City B is warmer by 10°F.
City B is warmer by 10 degrees F .
City A is warmer by 2°F.
City A is warmer by 2 degrees F .
City B is warmer by 2°F.
To determine which city is warmer and what the difference in their temperatures is after 5 hours, we need to calculate the final temperatures of both cities after 5 hours.
In City A, the temperature is changing by -5°F per hour. Starting from 70°F, after 5 hours the temperature in City A would be:
70°F + (-5°F × 5) = 70°F + (-25°F) = 45°F.
In City B, the temperature is changing by -3°F per hour. Starting from 70°F, after 5 hours the temperature in City B would be:
70°F + (-3°F × 5) = 70°F + (-15°F) = 55°F.
Comparing the temperatures, we can see that City A has a temperature of 45°F after 5 hours, while City B has a temperature of 55°F after 5 hours.
Therefore, City B is warmer by 10°F.
In City A, the temperature is changing by -5°F per hour. Starting from 70°F, after 5 hours the temperature in City A would be:
70°F + (-5°F × 5) = 70°F + (-25°F) = 45°F.
In City B, the temperature is changing by -3°F per hour. Starting from 70°F, after 5 hours the temperature in City B would be:
70°F + (-3°F × 5) = 70°F + (-15°F) = 55°F.
Comparing the temperatures, we can see that City A has a temperature of 45°F after 5 hours, while City B has a temperature of 55°F after 5 hours.
Therefore, City B is warmer by 10°F.
Jimmy reads 15 pages in 5 minutes. Carlo reads 12 pages in 6 minutes. Find each constant of proportionality, showing your work. Then write a sentence to compare the proportional relationships.(2 points)
To find the constant of proportionality for Jimmy and Carlo, we need to calculate the unit rate for each of them.
For Jimmy, he reads 15 pages in 5 minutes. The unit rate can be found by dividing the number of pages by the number of minutes:
Constant of proportionality for Jimmy = 15 pages / 5 minutes = 3 pages/minute.
For Carlo, he reads 12 pages in 6 minutes. The unit rate can be found by dividing the number of pages by the number of minutes:
Constant of proportionality for Carlo = 12 pages / 6 minutes = 2 pages/minute.
To compare the proportional relationships, we can see that Jimmy can read 3 pages in 1 minute, whereas Carlo can only read 2 pages in 1 minute. Therefore, Jimmy's reading speed is faster than Carlo's.
For Jimmy, he reads 15 pages in 5 minutes. The unit rate can be found by dividing the number of pages by the number of minutes:
Constant of proportionality for Jimmy = 15 pages / 5 minutes = 3 pages/minute.
For Carlo, he reads 12 pages in 6 minutes. The unit rate can be found by dividing the number of pages by the number of minutes:
Constant of proportionality for Carlo = 12 pages / 6 minutes = 2 pages/minute.
To compare the proportional relationships, we can see that Jimmy can read 3 pages in 1 minute, whereas Carlo can only read 2 pages in 1 minute. Therefore, Jimmy's reading speed is faster than Carlo's.
1 answer