Which ratio is equivalent to 978?(1 point)
Responses
13
Start Fraction 1 over 3 End Fraction
18
Start Fraction 1 over 8 End Fraction
326
Start Fraction 3 over 26 End Fraction
318
28 answers
Start Fraction 3 over 26 End Fraction
Lars purchases a new SUV. The car has a 15-gallon gas tank. If he can drive 330 miles on a full tank of gas, what is the unit rate of miles per gallon he gets?(1 point)
miles per gallon
miles per gallon
To find the unit rate of miles per gallon, we need to divide the total number of miles (330) by the number of gallons of gas (15).
The unit rate is 330 miles per 15 gallons.
Simplifying the fraction, we get:
Start Fraction 330 over 15 End Fraction
Simplifying the fraction further, we get:
22 miles per 1 gallon.
Therefore, the unit rate of miles per gallon Lars gets is 22 miles per gallon.
The unit rate is 330 miles per 15 gallons.
Simplifying the fraction, we get:
Start Fraction 330 over 15 End Fraction
Simplifying the fraction further, we get:
22 miles per 1 gallon.
Therefore, the unit rate of miles per gallon Lars gets is 22 miles per gallon.
What is 78÷34?(1 point)
Responses
2132
Start Fraction 21 over 32 End Fraction
67
Start Fraction 6 over 7 End Fraction
3221
Start Fraction 32 over 21 End Fraction
76
Responses
2132
Start Fraction 21 over 32 End Fraction
67
Start Fraction 6 over 7 End Fraction
3221
Start Fraction 32 over 21 End Fraction
76
Start Fraction 21 over 32 End Fraction
Charla wants to cover a certain rectangular area of her driveway with a picture using chalk. If she completes 23 of the area in 12 hour, how long will it take her to complete the entire picture?(1 point)
of an hour
of an hour
To find out how long it will take Charla to complete the entire picture, we can set up a proportion using the ratio of the completed area to the time taken:
Completed area / Time taken = Entire area / Time to complete entire picture
Given that she completes 23 of the area in 12 hours, we can write:
23 / 12 = 1 / Time to complete entire picture
To solve for the Time to complete the entire picture, we can multiply both sides of the equation by 12:
(23 / 12) * 12 = 1 * Time to complete entire picture
23 = Time to complete entire picture
Therefore, it will take Charla 23 hours to complete the entire picture.
Completed area / Time taken = Entire area / Time to complete entire picture
Given that she completes 23 of the area in 12 hours, we can write:
23 / 12 = 1 / Time to complete entire picture
To solve for the Time to complete the entire picture, we can multiply both sides of the equation by 12:
(23 / 12) * 12 = 1 * Time to complete entire picture
23 = Time to complete entire picture
Therefore, it will take Charla 23 hours to complete the entire picture.
Use the table to answer the question.
Raspberry Lemonade
1 2.5
2 5
4 10
6 15
Rosie is planning to make raspberry lemonade for a party. She needs to add 2 scoops of raspberry to every 5 cups of lemonade. The data table shows the ratios needed. At what ratio does the constant of proportionality appear?
(1 point)
Responses
(2, 5)
left parenthesis 2 comma 5 right parenthesis
(5, 2)
left parenthesis 5 comma 2 right parenthesis
(2.5, 1)
left parenthesis 2.5 comma 1 right parenthesis
(1, 2.5)
Raspberry Lemonade
1 2.5
2 5
4 10
6 15
Rosie is planning to make raspberry lemonade for a party. She needs to add 2 scoops of raspberry to every 5 cups of lemonade. The data table shows the ratios needed. At what ratio does the constant of proportionality appear?
(1 point)
Responses
(2, 5)
left parenthesis 2 comma 5 right parenthesis
(5, 2)
left parenthesis 5 comma 2 right parenthesis
(2.5, 1)
left parenthesis 2.5 comma 1 right parenthesis
(1, 2.5)
(2, 5)
Use the table to answer the question.
# of Trees # of Apples
2 26
3 39
6 78
10 130
12 156
Determine if the quantities in the data table are in a proportional relationship. If they are not in a proportional relationship, indicate why.
(1 point)
Responses
No, the ratio 6:78 is not proportional to the other ratios.
No, the ratio ratio of 6 to 78 is not proportional to the other ratios.
Yes, the data table has a proportional relationship.
Yes, the data table has a proportional relationship.
No, the ratios are not equivalent.
No, the ratios are not equivalent.
No, the table does not count consecutively.
No, the table does not count consecutively.
# of Trees # of Apples
2 26
3 39
6 78
10 130
12 156
Determine if the quantities in the data table are in a proportional relationship. If they are not in a proportional relationship, indicate why.
(1 point)
Responses
No, the ratio 6:78 is not proportional to the other ratios.
No, the ratio ratio of 6 to 78 is not proportional to the other ratios.
Yes, the data table has a proportional relationship.
Yes, the data table has a proportional relationship.
No, the ratios are not equivalent.
No, the ratios are not equivalent.
No, the table does not count consecutively.
No, the table does not count consecutively.
No, the ratios are not equivalent.
Unit Rates & Proportions Unit Test
7 of 157 of 15 Items
Question
Use the image to answer the question.
A coordinate plane shows four quadrants with both the x-axis and the y-axis ranging from negative 10 to positive 10 in increments of 2. Two points are plotted and joined by a line. The plotted points are as follows: left parenthesis 4 comma 9 right parenthesis, left parenthesis 5 comma 0 right parenthesis. A line connects the two plotted points and extends beyond the points in both directions.
Find the slope of the line given its graph.
(1 point)
Responses
−412
negative 4 Start Fraction 1 over 2 End Fraction
9
9
−19
negative Start Fraction 1 over 9 End Fraction
−9
7 of 157 of 15 Items
Question
Use the image to answer the question.
A coordinate plane shows four quadrants with both the x-axis and the y-axis ranging from negative 10 to positive 10 in increments of 2. Two points are plotted and joined by a line. The plotted points are as follows: left parenthesis 4 comma 9 right parenthesis, left parenthesis 5 comma 0 right parenthesis. A line connects the two plotted points and extends beyond the points in both directions.
Find the slope of the line given its graph.
(1 point)
Responses
−412
negative 4 Start Fraction 1 over 2 End Fraction
9
9
−19
negative Start Fraction 1 over 9 End Fraction
−9
To find the slope of the line, we can use the formula:
slope = (change in y) / (change in x)
The coordinates of the two points are (4, 9) and (5, 0).
(change in y) = 0 - 9 = -9
(change in x) = 5 - 4 = 1
slope = (-9) / (1) = -9
Therefore, the slope of the line is -9.
slope = (change in y) / (change in x)
The coordinates of the two points are (4, 9) and (5, 0).
(change in y) = 0 - 9 = -9
(change in x) = 5 - 4 = 1
slope = (-9) / (1) = -9
Therefore, the slope of the line is -9.
Identify the table that demonstrates a proportional relationship.(1 point)
Responses
x y
2 10
5 20
6 30x y 2 10 5 20 6 30
x y
4 2
9 3
16 4x y 4 2 9 3 16 4
x y
8 2
12 3
40 4x y 8 2 12 3 40 4
x y
10 2
15 3
40 8
Responses
x y
2 10
5 20
6 30x y 2 10 5 20 6 30
x y
4 2
9 3
16 4x y 4 2 9 3 16 4
x y
8 2
12 3
40 4x y 8 2 12 3 40 4
x y
10 2
15 3
40 8
x y
2 10
5 20
6 30
This table demonstrates a proportional relationship because as x increases, y also increases in a consistent ratio.
2 10
5 20
6 30
This table demonstrates a proportional relationship because as x increases, y also increases in a consistent ratio.
If a graph is proportional, what characteristic does it display?(1 point)
Responses
It will have y-values larger than their corresponding x-values.
It will have y -values larger than their corresponding x -values.
It will curve.
It will curve.
It will climb rapidly, indicating a steep slope.
It will climb rapidly, indicating a steep slope.
It will pass through the point (0, 0).
Responses
It will have y-values larger than their corresponding x-values.
It will have y -values larger than their corresponding x -values.
It will curve.
It will curve.
It will climb rapidly, indicating a steep slope.
It will climb rapidly, indicating a steep slope.
It will pass through the point (0, 0).
It will pass through the point (0, 0).
If Chase runs 5 miles in 60 minutes, how far will he run in 3 hours if he continues to run at the same rate?(1 point)
Responses
15 miles
15 miles
0.067 miles
0.067 miles
14 miles
Start Fraction 1 over 4 End Fraction miles
36 miles
Responses
15 miles
15 miles
0.067 miles
0.067 miles
14 miles
Start Fraction 1 over 4 End Fraction miles
36 miles
If Chase runs 5 miles in 60 minutes, we can find his rate of running by dividing the distance by the time:
Rate = Distance / Time
Rate = 5 miles / 60 minutes
Simplifying the fraction, we get:
Rate = 1 mile / 12 minutes
Since Chase will be running for 3 hours (which is 180 minutes), we can now find out how far he will run by multiplying his rate by the time:
Distance = Rate * Time
Distance = 1 mile / 12 minutes * 180 minutes
Simplifying, we get:
Distance = 15 miles
Therefore, Chase will run 15 miles in 3 hours if he continues to run at the same rate.
Rate = Distance / Time
Rate = 5 miles / 60 minutes
Simplifying the fraction, we get:
Rate = 1 mile / 12 minutes
Since Chase will be running for 3 hours (which is 180 minutes), we can now find out how far he will run by multiplying his rate by the time:
Distance = Rate * Time
Distance = 1 mile / 12 minutes * 180 minutes
Simplifying, we get:
Distance = 15 miles
Therefore, Chase will run 15 miles in 3 hours if he continues to run at the same rate.
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=200×16
y equals 200 times 16
200=16x
200 equals 16 x
y=40×16
Responses
y=200×16×5
y equals 200 times 16 times 5
y=200×16
y equals 200 times 16
200=16x
200 equals 16 x
y=40×16
To find how many miles the whale swims in 16 days, we can set up a proportion using the given information.
The proportion can be set up as:
Miles / Days = 200 miles / 5 days
To find how many miles the whale swims in 16 days, we can rearrange the proportion and solve for Miles:
Miles = (200 miles / 5 days) * 16 days
Simplifying, we have:
Miles = 40 * 16
So the equation that can be used to find how many miles the whale swims in 16 days is:
y = 40 × 16
The proportion can be set up as:
Miles / Days = 200 miles / 5 days
To find how many miles the whale swims in 16 days, we can rearrange the proportion and solve for Miles:
Miles = (200 miles / 5 days) * 16 days
Simplifying, we have:
Miles = 40 * 16
So the equation that can be used to find how many miles the whale swims in 16 days is:
y = 40 × 16
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
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
.
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
.
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
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
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
.
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
.
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
Maryna spent more time writing per problem at the unit rate of 25 min. 1 problem.
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 A
object A
They would all reach 100 feet at the same time.
They would all reach 100 feet at the same time.
object C
object C
object B
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 A
object A
They would all reach 100 feet at the same time.
They would all reach 100 feet at the same time.
object C
object C
object B
To determine which object would reach 100 feet in the least amount of time, we need to find the slope of each line.
For object A, the slope is (change in y) / (change in x) = (6 - 0) / (3 - 0) = 6/3 = 2.
For object B, the slope is (change in y) / (change in x) = (6 - 0) / (6 - 0) = 6/6 = 1.
For object C, the slope is (change in y) / (change in x) = (3 - 0) / (6 - 0) = 3/6 = 1/2.
The slope represents the rate of change, which in this case is the speed of each object. A higher rate of change (larger slope) means the object reaches a certain distance in less time.
Since object A has a slope of 2, while objects B and C have slopes of 1 and 1/2 respectively, object A would reach 100 feet in the least amount of time.
For object A, the slope is (change in y) / (change in x) = (6 - 0) / (3 - 0) = 6/3 = 2.
For object B, the slope is (change in y) / (change in x) = (6 - 0) / (6 - 0) = 6/6 = 1.
For object C, the slope is (change in y) / (change in x) = (3 - 0) / (6 - 0) = 3/6 = 1/2.
The slope represents the rate of change, which in this case is the speed of each object. A higher rate of change (larger slope) means the object reaches a certain distance in less time.
Since object A has a slope of 2, while objects B and C have slopes of 1 and 1/2 respectively, object A would reach 100 feet in the least amount of time.
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 2°F.
City A is warmer by 2 degrees F .
City B is warmer by 2°F.
City B is warmer by 2 degrees F .
City B is warmer by 10°F.
City B is warmer by 10 degrees F .
City A is warmer by 10°F.
Responses
City A is warmer by 2°F.
City A is warmer by 2 degrees F .
City B is warmer by 2°F.
City B is warmer by 2 degrees F .
City B is warmer by 10°F.
City B is warmer by 10 degrees F .
City A is warmer by 10°F.
City A is warmer by 10°F.
Since the temperature in City A is changing by -5°F per hour, after 5 hours the temperature will have dropped by a total of (5 * -5) = -25°F.
Since the temperature in City B is changing by -3°F per hour, after 5 hours the temperature will have dropped by a total of (5 * -3) = -15°F.
Starting at 70°F, the temperature in City A after 5 hours would be 70°F - 25°F = 45°F.
Starting at 70°F, the temperature in City B after 5 hours would be 70°F - 15°F = 55°F.
The temperature in City A (45°F) is warmer than the temperature in City B (55°F) by a difference of 10°F.
Since the temperature in City A is changing by -5°F per hour, after 5 hours the temperature will have dropped by a total of (5 * -5) = -25°F.
Since the temperature in City B is changing by -3°F per hour, after 5 hours the temperature will have dropped by a total of (5 * -3) = -15°F.
Starting at 70°F, the temperature in City A after 5 hours would be 70°F - 25°F = 45°F.
Starting at 70°F, the temperature in City B after 5 hours would be 70°F - 15°F = 55°F.
The temperature in City A (45°F) is warmer than the temperature in City B (55°F) by a difference of 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)
1 answer