given the table for x, lawns mowed and y, money earned:
x - # of lawns | 7 | 6 | 2 | 9 | 3 |
y - $ earned | 294 | 252 | 84 | 378 | 126 |
1. every lawn mowed is _____ dollars earned
A. 84
B. variable
C. 1
D. 42
E. 5
F. 0
G. non linear
H. unit rate
I. decreasing
J. non proportional
K. proportional
2. Dollars/1 lawn mowed is called a _____
A. 84
B. variable
C. 1
D. 42
E. 5
F. 0
G. non linear
H. unit rate
I. decreasing
J. non proportional
K. proportional
2. This relationship is _____ because _____ tickets sold is $0
A. 84
B. variable
C. 1
D. 42
E. 5
F. 0
G. non linear
H. unit rate
I. decreasing
J. non proportional
K. proportional
1. The correct answer is H. unit rate. The number of dollars earned remains constant for each lawn mowed.
2. The correct answer is H. unit rate. Dollars/1 lawn mowed is the unit rate, which shows how much money is earned for each lawn mowed.
3. The correct answer is J. non proportional because the relationship between the number of lawns mowed and the money earned is not consistent. Each additional lawn mowed does not result in the same increase in money earned.
1. To find the dollars earned per lawn mowed, we can divide the total dollars earned by the number of lawns mowed.
For the first data point:
Number of lawns mowed (x) = 7
Money earned (y) = $294
So, dollars earned per lawn mowed (y/x) = 294/7 = 42
Hence, every lawn mowed is 42 dollars earned.
The answer is D. 42.
2. Dollars/1 lawn mowed is called a unit rate.
So, the answer is H. unit rate.
3. To determine if the relationship is non-proportional, we need to check if there is a constant ratio between the variables.
Looking at the given data, if we calculate the ratio of dollars earned to the number of lawns mowed (y/x) for each data point, we get:
For the first data point: y/x = 294/7 = 42
For the second data point: y/x = 252/6 = 42
For the third data point: y/x = 84/2 = 42
For the fourth data point: y/x = 378/9 = 42
For the fifth data point: y/x = 126/3 = 42
Since the ratio is constant for all the data points, the relationship is proportional.
The answer is K. proportional.
To answer these questions, we need to analyze the data provided in the table.
1. To determine the dollars earned per lawn mowed, we need to divide the money earned (y) by the number of lawns mowed (x). Let's calculate it for each entry in the table:
- For the first entry: $294 / 7 = $42
- For the second entry: $252 / 6 = $42
- For the third entry: $84 / 2 = $42
- For the fourth entry: $378 / 9 = $42
- For the fifth entry: $126 / 3 = $42
As we can see, regardless of the number of lawns mowed, the amount of money earned is always $42. Therefore, the answer to question 1 is D. 42.
2. Dollars/1 lawn mowed is called a unit rate. A unit rate is the value of one quantity per unit of another quantity. In this case, it represents the dollars earned per lawn mowed. As we calculated in question 1, the unit rate is $42. Therefore, the answer to question 2 is H. unit rate.
3. For this question, after analyzing the table, we notice that when no lawns are mowed (x = 0), the money earned (y) is $0. This indicates that there is no growth in earnings without mowing any lawns. Therefore, the relationship between the number of lawns mowed and money earned is non-proportional. The answer to question 3 is J. non-proportional.