Question

Question

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

1/3
1 third

3/18
3 over 18

3/26
3 over 26

1/8

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find a ratio that is equivalent to 9/78, you can simplify the fraction. The greatest common divisor of 9 and 78 is 3. Dividing both the numerator and denominator by 3 gives 3/26. Therefore, the ratio that is equivalent to 9/78 is 3/26.

Answer 2

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 of gas?(1 point)

Responses

15 miles per gallon
15 miles per gallon

20 miles per gallon
20 miles per gallon

22 miles per gallon
22 miles per gallon

0.046 miles per gallon

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the unit rate of miles per gallon, divide the total number of miles driven by the number of gallons of gas used. In this case, Lars can drive 330 miles on a full tank of 15 gallons.

Dividing 330 by 15 gives the unit rate of miles per gallon, which is 22 miles per gallon. Therefore, the correct answer is "22 miles per gallon".

Answer 4

The amount of money that Sarah earns varies directly with the number of hours worked. If Sarah earns $320 for working 40 hours, determine the constant of proportionality.(1 point)

Answer 5

[AI-generated answer — Bot GPT 3.5]

To determine the constant of proportionality in this scenario, we can use the formula for direct variation, which is y = kx, where y represents the dependent variable (in this case, the amount of money earned), x represents the independent variable (in this case, the number of hours worked), and k represents the constant of proportionality.

Given that Sarah earns $320 for working 40 hours, we can set up an equation as follows:

320 = k * 40

To solve for k, divide both sides of the equation by 40:

k = 320 / 40

Simplifying the right side gives:

k = 8

Therefore, the constant of proportionality in this scenario is 8.

Answer 6

The table represents the time it took Bill to complete sets of math problems. Which equation represents this relationship?

Time in minutes : Numbers of Problems Set
30 : 36
40 : 48
50 : 60
60 : 72
(1 point)
Responses

y=1.2xy is equal to 1 point 2 x

y=12xy is equal to 12 x

y=x+12y is equal to x plus 12

y=x+1.2y is equal to x plus 1 point 2
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Answer 7

[AI-generated answer — Bot GPT 3.5]

To determine the equation that represents the relationship between time and the number of problem sets completed by Bill, we need to examine the data given in the table.

We can see that as the number of problems sets increases, the time taken also increases, but at a constant rate.

Let's compare the time and the number of problem sets.

For the first entry, 30 minutes is the time taken to complete 36 problem sets.

For the second entry, 40 minutes is the time taken to complete 48 problem sets.

For the third entry, 50 minutes is the time taken to complete 60 problem sets.

For the fourth entry, 60 minutes is the time taken to complete 72 problem sets.

From this data, we can see that the time taken is equal to the number of problem sets multiplied by a constant factor.

In this case, the constant factor is 1.2.

Therefore, the equation that represents this relationship is:

Time = 1.2 * Number of problem sets

Or in y = mx form:

y = 1.2x

Answer 8

A whale swims 200 miles in 5 days. Which equation can be used to find how many miles it swims in 16 days?(1 point)

Responses

y=200×16y is equal to 200 times 16

y=200/16y is equal to 200 over 16

200=16x200 is equal to 16 x

y=200/5×16

Answer 9

[AI-generated answer — Bot GPT 3.5]

To find out how many miles the whale will swim in 16 days, we can set up a proportion using the information given.

We know that the whale swims 200 miles in 5 days. Let's set up the proportion:

(200 miles) / (5 days) = (x miles) / (16 days)

To solve for x, we can cross multiply:

5 * x = 200 * 16

Simplifying the equation gives:

5x = 3200

Now, divide both sides of the equation by 5 to solve for x:

x = 3200 / 5

Simplifying further gives:

x = 640

Therefore, the whale will swim 640 miles in 16 days.

The correct equation that represents this relationship is:

y = 200/5 * 16

Answer 10

Which one of these is NOT a characteristic of a proportional graph?(1 point)

Responses

It passes through the origin (0, 0).
It passes through the origin (0, 0).

The y values are always larger than the x values.
The y values are always larger than the x values.

It is a straight line.
It is a straight line.

yx is the same for all points on the line.

Answer 11

[AI-generated answer — Bot GPT 3.5]

The characteristic that is NOT of a proportional graph is "The y values are always larger than the x values."

In a proportional graph, the y values are directly proportional to the x values. This means that as the x values increase, the y values also increase, but not necessarily at a constant rate. Therefore, it is not always the case that the y values are larger than the x values. This characteristic does not hold true for all proportional graphs.

Answer 12

What can you determine from these data tables?

Sonia
Numbers of Problems : Minutes of Writing
6 : 120
18 : 360
25 : 500
60 : 1,200

Maryna
Numbers of Problems : Minutes of Writing
8 : 200
15 : 375
20 : 500
50 : 1,250

(1 point)
Responses

Sonia spent more time writing per problem at the unit rate of 20 min1 problem.
Sonia spent more time writing per problem at the unit rate of 20 min1 problem.

Maryna spent less time writing per problem at the unit rate of 1 problem 25 min.
Maryna spent less time writing per problem at the unit rate of 1 problem 25 min.

Sonia spent the same amount of time as Maryna at the unit rate of 25 min1 problem.
Sonia spent the same amount of time as Maryna at the unit rate of 25 min1 problem.

Maryna spent more time writing per problem at the unit rate of 25 min1 problem.

Answer 13

[AI-generated answer — Bot GPT 3.5]

To determine the relationship between the number of problems and the time spent writing for Sonia and Maryna, we need to compare the data in their respective tables.

Looking at Sonia's table, we see that for 6 problems, she spent 120 minutes, for 18 problems she spent 360 minutes, for 25 problems she spent 500 minutes, and for 60 problems she spent 1,200 minutes.

For Maryna's table, we see that for 8 problems, she spent 200 minutes, for 15 problems she spent 375 minutes, for 20 problems she spent 500 minutes, and for 50 problems she spent 1,250 minutes.

By comparing the data for the same number of problems, we can determine the rate at which they spent time writing per problem.

For example, for Sonia, the unit rate for 6 problems is 120 minutes divided by 6, which equals 20 minutes per problem. We can do the same for the other numbers of problems and time spent to determine the unit rates.

For Maryna, the unit rate for 8 problems is 200 minutes divided by 8, which equals 25 minutes per problem. Again, we can do the same for the remaining entries to determine the unit rates.

Comparing the unit rates, we can see that Sonia spent more time writing per problem with a unit rate of 20 minutes per problem, while Maryna spent less time writing per problem with a unit rate of 25 minutes per problem.

Therefore, the correct response is "Sonia spent more time writing per problem at the unit rate of 20 min per problem."

Answer 14

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 less time writing per problem at the unit rate of 1 problem/25 min.
Maryna spent less time writing per problem at the unit rate of 1 problem/25 min.

Sonia spent the same amount of time as Maryna at the unit rate of 25 min/1 problem.
Sonia spent the same amount of time as Maryna at the unit rate of 25 min/1 problem.

Maryna spent more time writing per problem at the unit rate of 25 min/1 problem.

Answer 15

[AI-generated answer — Bot GPT 3.5]

Apologies for the previous incorrect response. Let's reevaluate the data.

Looking at Sonia's table, we see that for 6 problems, she spent 120 minutes, for 18 problems she spent 360 minutes, for 25 problems she spent 500 minutes, and for 60 problems she spent 1,200 minutes.

For Maryna's table, we see that for 8 problems, she spent 200 minutes, for 15 problems she spent 375 minutes, for 20 problems she spent 500 minutes, and for 50 problems she spent 1,250 minutes.

Comparing the unit rates, we can determine which person spent more or less time per problem.

For Sonia, the unit rate is calculated by dividing the minutes by the number of problems:
- For 6 problems, the unit rate is 120 minutes / 6 problems = 20 minutes/problem.
- For 18 problems, the unit rate is 360 minutes / 18 problems = 20 minutes/problem.
- For 25 problems, the unit rate is 500 minutes / 25 problems = 20 minutes/problem.
- For 60 problems, the unit rate is 1,200 minutes / 60 problems = 20 minutes/problem.

For Maryna, the unit rate is calculated in the same way:
- For 8 problems, the unit rate is 200 minutes / 8 problems = 25 minutes/problem.
- For 15 problems, the unit rate is 375 minutes / 15 problems = 25 minutes/problem.
- For 20 problems, the unit rate is 500 minutes / 20 problems = 25 minutes/problem.
- For 50 problems, the unit rate is 1,250 minutes / 50 problems = 25 minutes/problem.

Comparing both sets of unit rates, we can see that Sonia and Maryna actually spent the same amount of time per problem, with a unit rate of 20 minutes/problem or 25 minutes/problem, respectively.

Therefore, the correct response is: "Sonia spent the same amount of time as Maryna at the unit rate of 25 min/1 problem."