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 contant of proportionality appear
To determine at which ratio the constant of proportionality appears in the data table, we need to observe the relationship between the time and distance.
Let's analyze the given information:
- Julian takes 1/2 hour to walk 2 miles.
Knowing that distance is directly proportional to time, we can set up a proportion using the given information:
Time (in hours) : Distance (in miles)
1/2 : 2
To find the constant of proportionality, we need to divide the two corresponding values from the table. In this case, we would divide the distance by the time:
2 / (1/2)
To divide by a fraction, we invert the second fraction and multiply:
2 * 2/1 = 4
So, at a ratio of 4:1, the constant of proportionality appears.
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 the ratio is the constant of proportionality
Using the given information that Ruth can read 15 pages in 30 minutes, we can set up a proportion:
Pages : Time (in minutes)
15 : 30
To find the constant of proportionality, we divide the number of pages by the time:
15 / 30 = 0.5
Therefore, the constant of proportionality in this case is 0.5. This means that Ruth can read 0.5 pages per minute or 1 page every 2 minutes. A ratio of 1:2 represents the constant of proportionality.
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 the ratio is the constant of proportionality
1,30
1 1/2, 30
15, 1/2
2, 60
To determine the ratio at which the constant of proportionality appears, we need to compare the values of pages and time in the data table.
From the given data table:
1 : 30
1 1/2 : 30
15 : 1/2
2 : 60
To find the constant of proportionality, we need to observe the relationship between the two variables. Looking at the table, we can see that as the number of pages increases, the time also increases proportionally.
Let's examine the ratio between the pages and time in each row of the table:
1/30 = 1/1.5 = 15/0.5 = 2/60 = 0.0333...
The ratio between pages and time is constant across all rows and approximately equal to 0.0333, which can be expressed as 1/30.
Therefore, the constant of proportionality appears at a ratio of 1:30 in this data table.
To determine the ratio at which the constant of proportionality appears in Julian's data table, we need to analyze the relationship between time and distance.
Given that Julian takes 1/2 hour to walk 2 miles, we can set up a proportion:
(time taken) / (distance traveled) = (constant of proportionality)
Let's calculate the constant of proportionality using the given data:
1/2 hour / 2 miles = x / y
To do this, we can use cross-multiplication:
(1/2) * y = 2 * x
Simplifying the equation:
y/2 = 2x
Now, we can identify the ratio at which the constant of proportionality appears. The ratio is:
2:1/2
Simplifying this ratio:
2: 1/2
Since 1/2 is equivalent to 0.5, the ratio can be written as:
2: 0.5
Therefore, the constant of proportionality appears at a ratio of 2:0.5 or simplifying further, 4:1.
To determine at which ratio the constant of proportionality appears in Julian's data table, we first need to understand what a proportion is and how it is represented.
A proportion is a statement that two ratios are equal. In the context of Julian's walking distance, we can represent the distance he walks and the time it takes as a ratio. Let's consider the data table Julian created:
| Distance (miles) | Time (hours) |
|------------------|--------------|
| 2 | 1/2 |
| 4 | 1 |
| 6 | 1 1/2 |
| 8 | 2 |
To find the ratio of distance to time, we divide the distance by the time it takes. Let's calculate these ratios for each row:
Ratio for the first row (2 miles in 1/2 hour):
2 / (1/2) = 4
Ratio for the second row (4 miles in 1 hour):
4 / 1 = 4
Ratio for the third row (6 miles in 1 1/2 hours):
6 / (3/2) = 6 x 2/3 = 4
Ratio for the fourth row (8 miles in 2 hours):
8 / 2 = 4
As we can see, the ratio of distance to time (distance/time) is always 4 in each row of the data table. This means that the constant of proportionality is 4. Thus, at a ratio of 4:1, the constant of proportionality appears in Julian's data table.