Tables:
Pages Lucy Read: 208, 165, 234.
Time (hours): 8, 6, 9
Pages Britney Read: 168, 120, 348
Time (hours): 6, 4, 12
Last month, Lucy and Britney each read three books. The tables show the number of pages in each book and the time it took Lucy and Britney to read each book. Which of the tables, if any, represent a proportional relationship?
A Lucy's table represents a proportional relationship.
B Britney's table represents a proportional relationship.
C Both Lucy's and Britney's tables represent a proportional relationship.
D Neither Lucy's nor Britney's tables represent a proportional relationship.
To determine if the tables represent a proportional relationship, we need to check if the ratios of the pages read to the time taken are the same for each person.
For Lucy, the ratios of pages read to time taken are: 208/8 = 26, 165/6 = 27.5, and 234/9 = 26.
For Britney, the ratios of pages read to time taken are: 168/6 = 28, 120/4 = 30, and 348/12 = 29.
Since the ratios are not the same for both Lucy and Britney, neither of the tables represents a proportional relationship. Therefore, the correct answer is D. Neither Lucy's nor Britney's table represents a proportional relationship.
To determine if a table represents a proportional relationship, we need to compare the ratios of the number of pages read to the time taken to read those pages for both Lucy and Britney.
For Lucy's table:
Ratio 1 = Pages Read 1 / Time Taken 1 = 208 / 8 = 26
Ratio 2 = Pages Read 2 / Time Taken 2 = 165 / 6 = 27.5
Ratio 3 = Pages Read 3 / Time Taken 3 = 234 / 9 = 26
For Britney's table:
Ratio 1 = Pages Read 1 / Time Taken 1 = 168 / 6 = 28
Ratio 2 = Pages Read 2 / Time Taken 2 = 120 / 4 = 30
Ratio 3 = Pages Read 3 / Time Taken 3 = 348 / 12 = 29
In a proportional relationship, the ratios should remain constant. However, in Lucy's table, the ratios are not consistent. The ratios are 26, 27.5, and 26, which are not equal. Therefore, Lucy's table does not represent a proportional relationship.
In Britney's table, the ratios are 28, 30, and 29. These ratios are not equal to each other as well. Therefore, Britney's table also does not represent a proportional relationship.
Thus, the answer is D. Neither Lucy's nor Britney's tables represent a proportional relationship.
To determine if the tables represent a proportional relationship, we need to check if the ratios of pages read to time spent reading are the same for each person.
For Lucy's table:
- The ratio for the first book is 208 pages / 8 hours = 26 pages per hour.
- The ratio for the second book is 165 pages / 6 hours = 27.5 pages per hour.
- The ratio for the third book is 234 pages / 9 hours = 26 pages per hour.
Since the ratios are not consistent, Lucy's table does not represent a proportional relationship.
For Britney's table:
- The ratio for the first book is 168 pages / 6 hours = 28 pages per hour.
- The ratio for the second book is 120 pages / 4 hours = 30 pages per hour.
- The ratio for the third book is 348 pages / 12 hours = 29 pages per hour.
Since the ratios are not consistent, Britney's table does not represent a proportional relationship.
Therefore, the answer is D. Neither Lucy's nor Britney's tables represent a proportional relationship.
Which statement is True?
A The constant of proportionality for Lucy's table is 26.
B The constant of proportionality for Lucy's table is 28.
C The constant of proportionality for Britney's table is 26.
D The constant of proportionality for Britney's table is 28.
The constant of proportionality refers to the value that all ratios in a proportional relationship have in common. In this case, neither Lucy's nor Britney's tables represent a proportional relationship, so there is no constant of proportionality.
Therefore, none of the statements are true, and the answer is None of the above.
My bad. Let me rephrase the question, since one of the numbers is wrong.
Tables:
Pages Lucy Read: 208, 156, 234.
Time (hours): 8, 6, 9
Pages Britney Read: 168, 120, 348
Time (hours): 6, 4, 12
Last month, Lucy and Britney each read three books. The tables show the number of pages in each book and the time it took Lucy and Britney to read each book. Which of the tables, if any, represent a proportional relationship?
A Lucy's table represents a proportional relationship.
B Britney's table represents a proportional relationship.
C Both Lucy's and Britney's tables represent a proportional relationship.
D Neither Lucy's nor Britney's tables represent a proportional relationship.
and Which statement is True?
A The constant of proportionality for Lucy's table is 26.
B The constant of proportionality for Lucy's table is 28.
C The constant of proportionality for Britney's table is 26.
D The constant of proportionality for Britney's table is 28.
To determine if the tables represent a proportional relationship, we need to compare the ratios of the number of pages read to the time taken to read those pages for both Lucy and Britney.
For Lucy's table:
Ratio 1 = Pages Read 1 / Time Taken 1 = 208 / 8 = 26
Ratio 2 = Pages Read 2 / Time Taken 2 = 156 / 6 = 26
Ratio 3 = Pages Read 3 / Time Taken 3 = 234 / 9 = 26
For Britney's table:
Ratio 1 = Pages Read 1 / Time Taken 1 = 168 / 6 = 28
Ratio 2 = Pages Read 2 / Time Taken 2 = 120 / 4 = 30
Ratio 3 = Pages Read 3 / Time Taken 3 = 348 / 12 = 29
In a proportional relationship, the ratios should remain constant. In Lucy's table, the ratios are all equal to 26, so Lucy's table represents a proportional relationship. The answer is A.
For the statement about the constant of proportionality, the constant of proportionality refers to the value that all ratios in a proportional relationship have in common. In Lucy's table, the constant of proportionality is 26 since all the ratios are equal to 26. The answer is A. The constant of proportionality for Lucy's table is 26.
In Britney's table, the ratios are not consistent. Even though the ratios are close in value, they are not equal to each other. Therefore, Britney's table does not represent a proportional relationship. The answer is D. Neither Lucy's nor Britney's tables represent a proportional relationship.
Tables:
A:
x: 1, 2, 3, 4
y: 1, 4, 9, 16
B:
x: 1, 2, 3, 4
y: 1/2, 1, 3/2, 2
C:
x: 1, 2, 3, 4
y: 4, 2, 4/3, 1
D:
x: 1, 2, 3, 4
y: 3, 5, 7, 9
Which table shows y as directionally proportional to x?
To determine if y is directly proportional to x, we need to check if the ratios of y to x are consistent in all the given tables.
For table A:
Ratio 1 = y1 / x1 = 1 / 1 = 1
Ratio 2 = y2 / x2 = 4 / 2 = 2
Ratio 3 = y3 / x3 = 9 / 3 = 3
Ratio 4 = y4 / x4 = 16 / 4 = 4
Since the ratios are consistent (1, 2, 3, 4), table A shows y as directly proportional to x.
For table B:
Ratio 1 = y1 / x1 = (1/2) / 1 = 1/2
Ratio 2 = y2 / x2 = 1 / 2 = 1/2
Ratio 3 = y3 / x3 = (3/2) / 3 = 1/2
Ratio 4 = y4 / x4 = 2 / 4 = 1/2
Since the ratios are consistent (1/2, 1/2, 1/2, 1/2), table B shows y as directly proportional to x.
For table C:
Ratio 1 = y1 / x1 = 4 / 1 = 4
Ratio 2 = y2 / x2 = 2 / 2 = 1
Ratio 3 = y3 / x3 = (4/3) / 3 = 4/9
Ratio 4 = y4 / x4 = 1 / 4 = 1/4
Since the ratios are not consistent (4, 1, 4/9, 1/4), table C does not show y as directly proportional to x.
For table D:
Ratio 1 = y1 / x1 = 3 / 1 = 3
Ratio 2 = y2 / x2 = 5 / 2
Ratio 3 = y3 / x3 = 7 / 3
Ratio 4 = y4 / x4 = 9 / 4
Since the ratios are not consistent (3, 5/2, 7/3, 9/4), table D does not show y as directly proportional to x.
Therefore, the tables that show y as directly proportional to x are A and B.