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Time (min) 1 2 3 7 10

Water Used (gal) 5 10 15 35 50
Determine if the quantities in the data table re in a proportional relationship. If they do not have 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 table does not count consecutively.
No, the table does not count consecutively.

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

No, the ratio 7:35 is not proportional to the other ratios.

9 answers

To determine if the quantities in the data table are in a proportional relationship, we need to look at the ratios of water used (in gallons) to time (in minutes) for each given data point.

Let's calculate the ratios:

  1. For 1 min: \( \frac{5 \text{ gal}}{1 \text{ min}} = 5 \)
  2. For 2 min: \( \frac{10 \text{ gal}}{2 \text{ min}} = 5 \)
  3. For 3 min: \( \frac{15 \text{ gal}}{3 \text{ min}} = 5 \)
  4. For 7 min: \( \frac{35 \text{ gal}}{7 \text{ min}} = 5 \)
  5. For 10 min: \( \frac{50 \text{ gal}}{10 \text{ min}} = 5 \)

All these ratios are equal to 5. Therefore, the relationship between the time and water used is proportional.

So the correct response is:

Yes, the data table has a proportional relationship.

Hours Miles walked
14 1
12 2
34 3
1 4
It takes Julian 12 hour to walk 2 miles. He decides to start walking in his spare time, but because he wants to make sure he has enough time to go a desired distance he created the data table. At which ratio does the constant of proportionality appear?

(1 point)
Responses

(1, 14)
left parenthesis 1 comma Start Fraction 1 over 4 End Fraction right parenthesis

(14, 1)
left parenthesis Start Fraction 1 over 4 End Fraction comma 1 right parenthesis

(4, 1)
left parenthesis 4 comma 1 right parenthesis

(1, 4)

To determine the constant of proportionality from the data table, we need to analyze the pairs of hours walked and the corresponding miles walked. The constant of proportionality can be found by calculating the ratio of miles to hours for each pair.

Let's look at the mile per hour ratio from the provided data:

  1. For (14, 1): \( \frac{1 \text{ mile}}{14 \text{ hours}} = \frac{1}{14} \)
  2. For (12, 2): \( \frac{2 \text{ miles}}{12 \text{ hours}} = \frac{1}{6} \)
  3. For (34, 3): \( \frac{3 \text{ miles}}{34 \text{ hours}} = \frac{3}{34} \)
  4. For (1, 4): \( \frac{4 \text{ miles}}{1 \text{ hour}} = 4 \)

To identify the constant of proportionality, we want the ratio of miles to hours to be consistent. The data does not provide a consistent ratio across all points. However, based on the option choices provided, let's clarify the pairs:

  • (1, 4) corresponds to 4 miles walked in 1 hour, which shows a more straightforward and significant ratio since it represents a clear proportional relationship (4 miles for every 1 hour).

Thus, the correct answer among the choices provided, where the most significant constant of proportionality appears, is:

(1, 4).

Time (hours) Pages read
1/2 15
1 30
1 1/2 45
2 60
Ruth can read 15 pages in 30 minutes. She decides to create a table to keep track of her progress. From the data provided, at what ratio is the constant of proportionality?

(1 point)
Responses

(1, 30)
left parenthesis 1 comma 30 right parenthesis

(15, 1/2)
left parenthesis 15 comma Start Fraction 1 over 2 End Fraction right parenthesis

(1 1/2, 30)
left parenthesis 1 Start Fraction 1 over 2 End Fraction comma 30 right parenthesis

(2, 60)

To find the constant of proportionality from the given data table, we need to analyze the ratio of pages read to time in hours for each provided pair.

We can calculate the ratios as follows:

  1. For \( \left( \frac{1}{2}, 15 \right) \): \[ \text{Ratio} = \frac{15 \text{ pages}}{\frac{1}{2} \text{ hours}} = 15 \times 2 = 30 \]

  2. For \( (1, 30) \): \[ \text{Ratio} = \frac{30 \text{ pages}}{1 \text{ hour}} = 30 \]

  3. For \( (1 \frac{1}{2}, 45) \) (which is \( \frac{3}{2} \)): \[ \text{Ratio} = \frac{45 \text{ pages}}{\frac{3}{2} \text{ hours}} = 45 \times \frac{2}{3} = 30 \]

  4. For \( (2, 60) \): \[ \text{Ratio} = \frac{60 \text{ pages}}{2 \text{ hours}} = 30 \]

In all cases, the constant of proportionality is consistently 30 pages per hour.

Based on the options provided, the constant of proportionality appears in the following ratio:

(1, 30).

Hours Biked Miles Traveled
1 12
2 26
3 30
4 48
Determine if the quantities in the data table are in a proportional relationship. If they do not have a proportional relationship, indicate why.

(1 point)
Responses

Yes, this data table has a proportional relationship.
Yes, this data table has a proportional relationship.

No, you can’t bike 12 miles in an hour.
No, you can’t bike 12 miles in an hour.

No, not all of the ratios are proportional or have equivalence.
No, not all of the ratios are proportional or have equivalence.

No, none of the ratios have equivalence.

To determine if the quantities in the data table represent a proportional relationship, we need to calculate the ratios of miles traveled to hours biked for each data point and see if they are consistent (i.e., yield the same value).

Let's calculate the ratios:

  1. For 1 hour: \( \frac{12 \text{ miles}}{1 \text{ hour}} = 12 \)
  2. For 2 hours: \( \frac{26 \text{ miles}}{2 \text{ hours}} = 13 \)
  3. For 3 hours: \( \frac{30 \text{ miles}}{3 \text{ hours}} = 10 \)
  4. For 4 hours: \( \frac{48 \text{ miles}}{4 \text{ hours}} = 12 \)

Now, let's summarize the ratios:

  • 1 hour = 12 miles → ratio = 12
  • 2 hours = 26 miles → ratio = 13
  • 3 hours = 30 miles → ratio = 10
  • 4 hours = 48 miles → ratio = 12

Since the ratios are not equivalent (12, 13, 10, 12), we can conclude that the quantities do not represent a proportional relationship.

Thus, the correct response is:

No, not all of the ratios are proportional or have equivalence.

Hours Money ($)
1 9
2 18
3 27
4 36
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 ratios are not equivalent.
No, the ratios are not equivalent.

No, the ratio of 3 hours to $27 is not proportional.
No, the ratio of 3 hours to $27 is not proportional.

Yes, the ratios are in a proportional relationship.
Yes, the ratios are in a proportional relationship.

To determine if the quantities in the data table represent a proportional relationship, we need to calculate the ratios of money to hours for each data point and check if these ratios are equivalent.

Let's calculate the ratios:

  1. For 1 hour: \( \frac{9 \text{ dollars}}{1 \text{ hour}} = 9 \)
  2. For 2 hours: \( \frac{18 \text{ dollars}}{2 \text{ hours}} = 9 \)
  3. For 3 hours: \( \frac{27 \text{ dollars}}{3 \text{ hours}} = 9 \)
  4. For 4 hours: \( \frac{36 \text{ dollars}}{4 \text{ hours}} = 9 \)

The ratios are all equal to 9.

Since these ratios are consistent, we can conclude that the quantities are in a proportional relationship.

Thus, the correct response is:

Yes, the ratios are in a proportional relationship.