t 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?
Bot is getting it wrong because you are saying 12 instead of 1/2. The actual answer is (1, 4)
To determine the ratio at which the constant of proportionality appears, let's examine the data table that Julian created:
Distance (miles) | Time (hours)
--------------------------------
2 | 12
The constant of proportionality represents the rate at which distance and time are related. In this case, it represents the number of miles Julian can walk per hour. To find this ratio, we divide the distance by the time:
2 miles ÷ 12 hours = 1/6 mile per hour
Therefore, the ratio at which the constant of proportionality appears is 1/6 mile per hour.
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, 4)
left parenthesis 1 comma 4 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, 14)
To determine the ratio at which the constant of proportionality appears, let's examine the data table that Julian created:
Distance (miles) | Time (hours)
--------------------------------
2 | 12
To find the ratio, we divide the distance by the time:
2 miles ÷ 12 hours = 1/6 mile per hour
Therefore, the ratio at which the constant of proportionality appears is (1, 6).
To determine the ratio at which the constant of proportionality appears in Julian's data table, we'll compare the time it takes him to walk different distances.
Given that it takes Julian 12 hours to walk 2 miles, we can write this as a ratio:
12 hours : 2 miles
Now, let's determine the ratio for another distance. Suppose Julian walks 6 miles. We can set up the following ratio:
x hours : 6 miles
Since we are looking for the constant of proportionality, the two ratios should be equal. Therefore, we can set up the following equation:
12 hours : 2 miles = x hours : 6 miles
To find the value of x, we can cross-multiply:
(12 hours) * (6 miles) = (2 miles) * (x hours)
72 hours = 2x hours
Now, we can solve for x by dividing both sides of the equation by 2:
72 hours / 2 = 2x hours / 2
36 hours = x hours
Therefore, the constant of proportionality is 36, which means for every 1 unit increase in distance (in miles), there is a corresponding increase of 36 units in time (in hours).
To determine the ratio at which the constant of proportionality appears in Julian's data table, we need to examine the relationship between the time and distance he walks.
Given that Julian takes 12 hours to walk 2 miles, we can set up a ratio between the time and distance:
12 hours : 2 miles
Now, let's consider his data table. Each row in the table represents a different distance he wants to walk, and the corresponding time it takes. If there is a constant of proportionality, it means that the ratio between time and distance will remain the same for each entry in the table.
Let's say the data table looks like this:
Distance (miles) | Time (hours)
----------------------------
4 | ?
6 | ?
8 | ?
To find the ratio at which the constant of proportionality appears, we can divide the time (hours) by the distance (miles) for each entry in the table:
For the first entry: ? hours / 4 miles
For the second entry: ? hours / 6 miles
For the third entry: ? hours / 8 miles
If the ratios are equal for all the entries, then there is a constant of proportionality. To determine the ratio, you would need to fill in the missing values in the table with the corresponding times Julian takes to walk those distances. Then, divide the time by the distance for each entry.
For example, let's say for the first entry, Julian takes 24 hours to walk 4 miles. The ratio would be:
24 hours / 4 miles = 6 hours/mile
Repeat the same calculation for other entries in the table. If you find that the ratios are equal for all the entries, then the constant of proportionality appears at a ratio of 6 hours/mile.