Which option describes a synonym?(1 point)
Responses
a word or phrase that has an opposite meaning
a word or phrase that has an opposite meaning
a word or phrase that is unfamiliar
a word or phrase that is unfamiliar
a word or phrase that is a model of something
a word or phrase that is a model of something
a word or phrase that has a similar meaning
a word or phrase that has a similar meaning
Use the sentence to answer the question.
It is widely assumed that the only way to be profitable today is by having a college degree. However, careers attained through trade schools are just as worthwhile.
Which word in the sentences is a synonym for worthwhile?
(1 point)
Responses
assumed
assumed
profitable
profitable
attained
attained
widely
widely
Skip to navigation
profitable
Use the sentence to answer the question.
At times in debate there is dissension. When discussing topics on which people take varying positions, it is especially important to have strong communication skills.
"People take varying positions" is the context clue for the word dissension. Which type of context clue is this?
(1 point)
Responses
antonym
antonym
example
example
synonym
synonym
definition
example
Which ratio is equivalent to 9/78 ?(1 point)
Responses
3/18
Start Fraction 3 over 18 End Fraction
1/3
Start Fraction 1 over 3 End Fraction
3/26
Start Fraction 3 over 26 End Fraction
1/8
3/26
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
To find the unit rate of miles per gallon, we need to divide the number of miles by the number of gallons.
330 miles divided by 15 gallons equals 22 miles per gallon.
Therefore, Lars gets 22 miles per gallon.
What is 7/8÷3/4 ?
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of 3/4 is 4/3.
So, 7/8 ÷ 3/4 is equivalent to 7/8 multiplied by 4/3.
When we multiply fractions, we multiply the numerators together and the denominators together.
(7/8) x (4/3) = (7 x 4) / (8 x 3) = 28/24.
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which in this case is 4.
28/24 simplifies to 7/6.
Therefore, 7/8 ÷ 3/4 is equal to 7/6.
Charla wants to cover a certain rectangular area of her driveway with a picture using chalk. If she completes 2/3 of the area in 1/2 hour, how long will it take her to complete the entire picture?(1 point)
of an hour
To find out how long it will take Charla to complete the entire picture, we need to determine the time it takes to complete 1 unit of the area, which is the reciprocal of 2/3.
The reciprocal of 2/3 is 3/2. This means that it takes Charla 3/2 of an hour to complete 1 unit of the area.
Since she has to complete the entire picture, which is equal to 1 whole unit of the area, it will take her 3/2 of an hour to finish.
Therefore, it will take Charla 3/2 of an hour, or 1 and a half 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
(1, 2.5)
left parenthesis 1 comma 2.5 right parenthesis
(2.5, 1)
left parenthesis 2.5 comma 1 right parenthesis
(5, 2)
The constant of proportionality appears when the ratio between the scoops of raspberry and the cups of lemonade remains constant.
In this case, the constant ratio between the scoops of raspberry and the cups of lemonade is (2, 5).
Therefore, the constant of proportionality appears at the ratio (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
Yes, the data table has a proportional relationship.
Yes, the data table has a proportional relationship.
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.
No, the table does not count consecutively.
No, the table does not count consecutively.
No, the ratios are not equivalent.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratios between the number of trees and the number of apples are equivalent.
Let's calculate the ratios for each row:
- Ratio for 2 trees to 26 apples: 2/26 = 1/13.
- Ratio for 3 trees to 39 apples: 3/39 = 1/13.
- Ratio for 6 trees to 78 apples: 6/78 = 1/13.
- Ratio for 10 trees to 130 apples: 10/130 = 1/13.
- Ratio for 12 trees to 156 apples: 12/156 = 1/13.
Since all the ratios are equivalent (1/13), the quantities in the data table are in a proportional relationship.
Therefore, the correct response is: Yes, the data table has a proportional relationship.
se 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
9
9
−9
negative 9
−412
negative 4 Start Fraction 1 over 2 End Fraction
−19
To find the slope of a line, we need to calculate the change in y divided by the change in x between two points on the line.
In this case, the two points given are (4, 9) and (5, 0).
The change in y is 0 - 9 = -9.
The change in x is 5 - 4 = 1.
Therefore, the slope of the line is -9/1, which can be simplified to -9.
Hence, the correct response is: negative 9.
Identify the table that demonstrates a proportional relationship.(1 point)
Responses
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
2 10
5 20
6 30x y 2 10 5 20 6 30
x y
10 2
15 3
40 8
To determine which table demonstrates a proportional relationship, we need to check if the ratios between x and y remain constant for each row.
Examining the options:
1) In the first option, the ratio of x to y is not constant. For example, 4/2 does not equal 9/3.
2) In the second option, the ratio of x to y is constant. 8/2 equals 12/3 which also equals 40/4.
3) In the third option, the ratio of x to y is not constant. For example, 2/10 does not equal 5/20.
4) In the fourth option, the ratio of x to y is not constant. For example, 10/2 does not equal 15/3.
Therefore, the table that demonstrates a proportional relationship is the second option:
x y
8 2
12 3
40 4
This table shows a constant ratio of x to y, where x/y = 4/1.
Hence, the correct response is: x y
8 2
12 3
40 4
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 climb rapidly, indicating a steep slope.
It will climb rapidly, indicating a steep slope.
It will have y-values larger than their corresponding x-values.
If a graph is proportional, it will pass through the point (0, 0).
Therefore, the correct response is: 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
1/4 miles
Start Fraction 1 over 4 End Fraction miles
36 miles
36 miles
0.067 miles
0.067 miles
15 miles
If Chase runs 5 miles in 60 minutes, we can use unit rate to determine how far he will run in 1 minute.
Chase runs 5 miles in 60 minutes, so he runs 5/60 miles in 1 minute.
To find how far he will run in 3 hours (180 minutes), we can multiply the unit rate by 180.
(5/60) miles per minute x 180 minutes = (5/60) x 180 = 15 miles.
Therefore, Chase will run 15 miles in 3 hours if he continues to run at the same rate.
Hence, the correct response is: 15 miles.
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=40×16
y equals 40 times 16
y=200×16×5
y equals 200 times 16 times 5
200=16x
200 equals 16 x
y=200×16
To find how many miles the whale swims in 16 days, we can use the proportional relationship between miles and days.
If the whale swims 200 miles in 5 days, we can set up the equation as a proportion:
Miles / Days = Miles / Days
Using this equation, we can say:
200 miles / 5 days = x miles / 16 days
To solve for x (the number of miles the whale swims in 16 days), we can cross-multiply:
200 miles * 16 days = x miles * 5 days
Cross-multiplying gives us:
3200 miles = 5x miles
Therefore, the correct equation that could be used to find how many miles the whale swims in 16 days is:
5x = 3200
Or, simplified:
x = 3200/5
x = 640
Hence, the correct response is: 200 = 16x.
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 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 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
.
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
.
To determine who spent more time writing per problem, we can calculate the unit rate for each writer by dividing the number of minutes by the number of problems.
For Sonia:
Number of problems: 6
Minutes of writing: 120
Unit rate for Sonia: 120 minutes / 6 problems = 20 minutes per problem.
For Maryna:
Number of problems: 8
Minutes of writing: 200
Unit rate for Maryna: 200 minutes / 8 problems = 25 minutes per problem.
Comparing the unit rates, we can see that Maryna spent more time writing per problem at the unit rate of 25 min/1 problem.
Hence, the correct response is: 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
object C
object C
object B
object B
They would all reach 100 feet at the same time.
To determine which object would reach 100 feet in the least amount of time, we need to examine the slope of each line. The slope represents the rate of change or the speed at which the distance increases over time.
Object A: The line passes through the points (0, 0) and (3, 6). The slope can be calculated as (change in y) / (change in x) = (6 - 0) / (3 - 0) = 6 / 3 = 2.
Object C: The line passes through the points (0, 0) and (6, 3). The slope can be calculated as (change in y) / (change in x) = (3 - 0) / (6 - 0) = 3 / 6 = 1/2.
Object B: The line passes through the points (0, 0) and (6, 6). The slope can be calculated as (change in y) / (change in x) = (6 - 0) / (6 - 0) = 6 / 6 = 1.
Comparing the slopes of the lines:
Object A has a slope of 2.
Object C has a slope of 1/2.
Object B has a slope of 1.
Since a higher slope indicates a faster rate of increase in distance, Object A would reach 100 feet in the least amount of time.
Therefore, the correct response is: object A.
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 B is warmer by 2°F.
City B is warmer by 2 degrees F .
City A is warmer by 10°F.
City A 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 10°F.
To determine which city is warmer and the difference in their temperatures after 5 hours, we need to calculate the temperature change in each city over this time period.
In City A, the temperature is changing by -5°F per hour. After 5 hours, the temperature would have dropped by 5 x 5 = -25°F.
In City B, the temperature is changing by -3°F per hour. After 5 hours, the temperature would have dropped by 3 x 5 = -15°F.
Given that the initial temperature in both cities is 70°F, let's calculate the final temperatures:
In City A: 70°F - 25°F = 45°F
In City B: 70°F - 15°F = 55°F
Therefore, City B is warmer by 55°F - 45°F = 10°F.
Hence, the correct response is: City B is warmer by 10°F.