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Question 1

A)
Use the table to answer the question.
HoursMiles walked
1
4
1
1
2
2
3
4
3
1 4
It takes Julian 1
2 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)
(1, 4)
(4, 1)
1
4 , 1
( )
1, 1
4
( )

9 answers

To determine the constant of proportionality from the table, you need to identify the ratio of miles walked to hours spent walking.

From your provided data table, it looks like we have the following pairs of (hours, miles walked):

  • (1, 4)
  • (1, 1)
  • (2, 2)
  • (3, 4)
  • (3, 1)

Now, let's consider the correct values to find the constant of proportionality (the ratio of miles over hours):

  • For (1, 4): 4 miles / 1 hour = 4
  • For (1, 1): 1 mile / 1 hour = 1
  • For (2, 2): 2 miles / 2 hours = 1
  • For (3, 4): 4 miles / 3 hours = approximately 1.33
  • For (3, 1): 1 mile / 3 hours = approximately 0.33

The only time where a constant ratio seems to apply is at the pair (1, 4), which gives us a ratio of 4 miles for 1 hour.

Since multiple entries (like (2,2) and (1,1)) suggest different ratios, it seems (1, 4) is the pair that maximizes the speed of walking.

Therefore, the correct answer for the constant of proportionality based on the given options is:

(1, 4).

Question 2
A)
Use the table to answer the question.
Time
(
hours
)
Pages read
1
2
15
1
1
2
1
2
30
45
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)
(1, 30)
15, 1
( )
2
11
( )
2
, 30
(2, 60)

To find the constant of proportionality based on the data provided in the table, we need to find the ratio of pages read to time in hours.

First, let's clarify the given data:

  • Time (hours): 1, 1, 1, 1, 2
  • Pages read: 2, 15, 30, 45, 60

Now, we convert 30 minutes into hours since the time is given in hours. Since 30 minutes is half an hour, we express 15 pages in relation to 0.5 hours (or 1/2 hour).

Now we will calculate the ratios for different pairs of (Time, Pages) to find the constant of proportionality:

  1. For the first pair (1, 2):
    • Ratio = 2 pages / 1 hour = 2
  2. For the second pair (1, 15):
    • Ratio = 15 pages / 1 hour = 15
  3. For the third pair (1, 30):
    • Ratio = 30 pages / 1 hour = 30
  4. For the fourth pair (1, 45):
    • Ratio = 45 pages / 1 hour = 45
  5. For the fifth pair (2, 60):
    • Ratio = 60 pages / 2 hours = 30

From these calculations, we see there are different ratios for different time intervals.

The constant of proportionality appears to be 30 for the last pair (2, 60) and the pair (1, 30).

Considering the options given, the correct answer for the constant of proportionality based on the provided data would be:

(2, 60).

Question 3
A)
Use the table to answer the question.
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)
No, the ratios are not equivalent.
No, the ratio 7:35 is not proportional to the other ratios.
No, the table does not count consecutively.
Yes, the data table has a proportional relationship.

To determine if the quantities in the data table are in a proportional relationship, we need to examine the ratios of water used (in gallons) to time (in minutes).

Let's calculate the ratios for each pair of (Time in minutes, Water Used in gallons):

  1. For (1, 5):
    • Ratio = 5 gal / 1 min = 5
  2. For (2, 10):
    • Ratio = 10 gal / 2 min = 5
  3. For (3, 15):
    • Ratio = 15 gal / 3 min = 5
  4. For (7, 35):
    • Ratio = 35 gal / 7 min = 5
  5. For (10, 50):
    • Ratio = 50 gal / 10 min = 5

Now, let's summarize the findings:

  • All the ratios calculated (5, 5, 5, 5, and 5) are equivalent.

Because the ratios of water used to time are constant and equal across all observations (each computes to 5), we conclude that the data table does represent a proportional relationship.

Thus, the correct answer is:

Yes, the data table has a proportional relationship.

Question 4
A)
Use the table to answer the question.
Hours Biked Miles Traveled
1
2
3
4
12
26
30
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)
No, you can’t bike 12 miles in an hour.
No, none of the ratios have equivalence.
Yes, this data table has a proportional relationship.
No, not all of the ratios are proportional or have equivalence

To determine if the quantities in the data table are in a proportional relationship, we need to calculate the ratios of miles traveled to hours biked for each pair of data.

Here are the values in the table:

  • Hours Biked: 1, 2, 3, 4
  • Miles Traveled: 12, 26, 30, 48

Now let's calculate the ratios for each pair:

  1. For (1 hour, 12 miles):
    • Ratio = 12 miles / 1 hour = 12
  2. For (2 hours, 26 miles):
    • Ratio = 26 miles / 2 hours = 13
  3. For (3 hours, 30 miles):
    • Ratio = 30 miles / 3 hours = 10
  4. For (4 hours, 48 miles):
    • Ratio = 48 miles / 4 hours = 12

Now we summarize the results:

  • Ratios calculated:
    • 12 for 1 hour
    • 13 for 2 hours
    • 10 for 3 hours
    • 12 for 4 hours

The ratios are not equivalent: 12, 13, 10, 12.

Since not all ratios are the same, the data does not represent a proportional relationship.

The correct answer is:

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

Question 5
A)
Use the table to answer the question.
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)
No, the ratio of 3 hours to $27 is not proportional.
No, the ratio of 1 hour to $9 is not proportional.
Yes, the ratios are in a proportional relationship.
No, the ratios are not equivalent

To determine if the quantities in the data table are in a proportional relationship, we need to calculate the ratios of money earned to hours worked for each pair of data.

Here are the values in the table:

  • Hours: 1, 2, 3, 4
  • Money ($): 9, 18, 27, 36

Now, let's calculate the ratios for each pair:

  1. For (1 hour, $9):
    • Ratio = $9 / 1 hour = 9
  2. For (2 hours, $18):
    • Ratio = $18 / 2 hours = 9
  3. For (3 hours, $27):
    • Ratio = $27 / 3 hours = 9
  4. For (4 hours, $36):
    • Ratio = $36 / 4 hours = 9

Now we can summarize the results:

  • All calculated ratios are equal to 9.

Since all the ratios are the same (9), this indicates that the relationship is proportional.

The correct answer is:

Yes, the ratios are in a proportional relationship.