Which ratio is equivalent to 9/78 ?(1 point)

The ratio 9/78 is equivalent to the ratio 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)

To find the unit rate of miles per gallon Lars gets, we divide the total number of miles (330) by the number of gallons (15):

330 miles / 15 gallons = 22 miles per gallon

So, Lars gets a unit rate of 22 miles per gallon.

What is 7/8÷3/4 ?(1 point)

Responses

7/6
Start Fraction 7 over 6 End Fraction

32/21
Start Fraction 32 over 21 End Fraction

6/7
Start Fraction 6 over 7 End Fraction

21/32

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

So, 7/8 ÷ 3/4 can be rewritten as 7/8 * 4/3:

7/8 * 4/3 = (7 * 4) / (8 * 3) = 28/24

Simplifying this fraction, we find that 28/24 is equivalent to 7/6.

Therefore, the answer is 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)

To find out how long it will take Charla to complete the entire picture, we can calculate the ratio of time to the ratio of the area completed.

The ratio of time is 1/2 hour, and the ratio of the area completed is 2/3.

Let's represent the unknown time as x.

The ratio of time to complete the entire picture can be expressed as:

x / 1 = 1/2 / 2/3

To divide by a fraction, we multiply with the reciprocal:

x = 1/2 * 3/2 = 3/4

Thus, it will take Charla 3/4 hour 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)

To determine the ratio where the constant of proportionality appears, we need to find a consistent ratio between the number of scoops of raspberry and the number of cups of lemonade.

Looking at the given table, we can see that for every 2 scoops of raspberry, there are 5 cups of lemonade. This ratio is consistent throughout the table.

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 ratios are not equivalent.
No, the ratios are not equivalent.

No, the table does not count consecutively.

To determine if the quantities in the data table are in a proportional relationship, we need to check if there is a constant ratio between the number of trees and the number of apples.

Looking at the given table, we can see that the ratio between trees and apples is not consistent. For example:

The ratio between 2 trees and 26 apples is 2:26, which simplifies to 1:13.
The ratio between 10 trees and 130 apples is 10:130, which simplifies to 1:13 as well.

However, the ratio between 6 trees and 78 apples is 6:78, which simplifies to 1:13/13 or 1:6.5.

Since the ratios are not equivalent throughout the table, the data table does not represent a proportional relationship.

Therefore, the correct response is: No, the ratios are not equivalent.

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

−9
negative 9

−19
negative Start Fraction 1 over 9 End Fraction

To find the slope of a line, we use the formula:

slope = (change in y) / (change in x)

Looking at the graph, we can see that the line is rising as it moves from left to right. This means that the change in y is positive.

Using the coordinates (4, 9) and (5, 0), we can find the change in y:

change in y = 0 - 9 = -9

Next, we find the change in x:

change in x = 5 - 4 = 1

Now we can calculate the slope:

slope = -9 / 1 = -9

Therefore, the slope of the line is -9.

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 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.

If a graph is proportional, 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

36 miles
36 miles

0.067 miles
0.067 miles

14 miles

If Chase runs 5 miles in 60 minutes, we can calculate his running rate in miles per minute. The rate is:

5 miles / 60 minutes = 1/12 miles per minute

To find out how far Chase will run in 3 hours, which is 180 minutes, we can multiply his running rate by the time:

(1/12 miles per minute) * 180 minutes = 180/12 miles = 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=40×16
y equals 40 times 16

y=200×16
y equals 200 times 16

y=200×16×5
y equals 200 times 16 times 5

200=16x

To find the number of miles the whale swims in 16 days, we can set up a proportion using the given information:

200 miles / 5 days = x miles / 16 days

This equation shows that the distance the whale swims is proportional to the number of days. The proportion can be written as:

(you can cross multiply to solve)

5 * x = 200 * 16

Simplifying this equation gives:

5x = 3200

Dividing both sides of the equation by 5, we have:

x = 640

So, the equation that could be used to find how many miles the whale swims in 16 days is:

y = 200 × 16 = 3200

Therefore, the correct equation is: y = 200 × 16.

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 compare the slopes of the lines.

The slope of a line represents the rate of change, or how quickly the distance increases with respect to time.

Looking at the given lines:

- Object A has a steep slope, as it passes through the coordinates (0, 0) and (3, 6). This means that the distance increases rapidly with time.
- Object B has a slope of 1, as it passes through the coordinates (0, 0) and (6, 6). This means that the distance increases at a constant rate with time.
- Object C has a shallower slope, as it passes through the coordinates (0, 0) and (6, 3). This means that the distance increases at a slower rate with time compared to Object A and B.

Considering that we want to reach 100 feet in the least amount of time, Object A would reach 100 feet in the least amount of time because it has the steepest slope, indicating a faster rate of change.

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 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.
City B is warmer by 2 degrees F .

City A is warmer by 10°F.

City A and City B both start with a temperature of 70°F.

After 5 hours, the temperature in City A would change by -5°F per hour for 5 hours, resulting in a temperature of 70°F - 5°F/hour * 5 hours = 70°F - 25°F = 45°F.

Similarly, the temperature in City B would change by -3°F per hour for 5 hours, resulting in a temperature of 70°F - 3°F/hour * 5 hours = 70°F - 15°F = 55°F.

Therefore, City B is warmer by 55°F - 45°F = 10°F.

The correct response is: 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 each situation, we need to calculate the ratio of pages read to time taken.

For Jimmy, he reads 15 pages in 5 minutes, so the constant of proportionality is 15/5 = 3 pages per minute.

For Carlo, he reads 12 pages in 6 minutes, so the constant of proportionality is 12/6 = 2 pages per minute.

To compare the proportional relationships, we can say:

The constant of proportionality for Jimmy is 3 pages per minute, and the constant of proportionality for Carlo is 2 pages per minute. Therefore, Jimmy reads at a faster rate than Carlo, with a higher constant of proportionality.

So, the sentence to compare the proportional relationships is: Jimmy reads at a faster rate, with a constant of proportionality of 3 pages per minute, compared to Carlo who reads at a rate of 2 pages per minute.

In which form of reproduction will pieces of the parent develop into identical copies of the parent? (1 point)

Responses

vegetative reproduction
vegetative reproduction

binary fission
binary fission

budding
budding

fragmentation

In vegetative reproduction, pieces of the parent plant develop into identical copies of the parent. Therefore, the correct answer is vegetative reproduction.