4 answers
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Which option correctly uses the proportionality symbol to represent all the proportional relationships shown in the table?
(1 point)
Responses
Y∝Z and X∝Y and X∝Z
upper Y proportional to upper Z and upper X proportional to upper Y and upper X proportional to upper Z
Z∝Y and Y∝X and Z∝X
upper Z proportional to upper Y and upper Y proportional to upper X and upper Z proportional to upper X
18∝3 and 3∝1 and 18∝1
18 proportional to 3 and 3 proportional to 1 and 18 proportional to 1
Z∝Y and Y∝X
Bot GPT 3.5
answered
and Z∝X
upper Z proportional to upper Y and upper Y proportional to upper X and upper Z proportional to upper X
SRB
answered
a b c or d
Bot GPT 3.5
answered
d
Explain Bot
answered
To determine which option correctly uses the proportionality symbol to represent all the proportional relationships shown in the table, we need to understand how the proportionality symbol works.
The proportionality symbol ( ∝ ) is used to indicate that two quantities have a proportional relationship, meaning they have a constant ratio. When two variables, say X and Y, are proportional, it means that if one variable increases by a certain factor, the other variable also increases by the same factor, and vice versa.
Looking at the table, we have three columns labeled X, Y, and Z, along with their corresponding values. By examining the values, we can determine the proportional relationships.
In the first row, we can see that when X increases from 3 to 6, the corresponding Y value also doubles from 6 to 12. Similarly, when Y increases from 6 to 12, the corresponding Z value also doubles from 18 to 36. This indicates that X is proportional to Y (X∝Y) and Y is proportional to Z (Y∝Z).
In the second row, we can see that when X increases from 2 to 4, the corresponding Y value doubles from 8 to 16. Similarly, when Y increases from 8 to 16, the corresponding Z value also doubles from 16 to 32. This indicates that X is proportional to Y (X∝Y) and Y is proportional to Z (Y∝Z).
Based on this analysis, the correct option that represents all the proportional relationships shown in the table is:
Z∝Y and Y∝X and Z∝X
(upper Z proportional to upper Y and upper Y proportional to upper X and upper Z proportional to upper X).