The table (B) shows the proportional relationship between a and b.
Further Explanation:
The proportional relationship between any two numbers can be expressed as follows,
![\boxed{\dfrac{a}{b} = c}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cdfrac%7Ba%7D%7Bb%7D%20%3D%20c%7D)
Here, a and b are the two numbers and c is the proportional ratio.
Explanation:
In Table A the values are
and ![\left( {5,20}\right).](https://tex.z-dn.net/?f=%5Cleft%28%20%7B5%2C20%7D%5Cright%29.)
The ratios of a and b can be calculated as follows,
![\dfrac{3}{9} &= \dfrac{1}{3}\dfrac{4}{{12}}&=\dfrac{1}{3}\dfrac{5}{{20}}&= \dfrac{1}{4}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B9%7D%20%26%3D%20%5Cdfrac%7B1%7D%7B3%7D%5Cdfrac%7B4%7D%7B%7B12%7D%7D%26%3D%5Cdfrac%7B1%7D%7B3%7D%5Cdfrac%7B5%7D%7B%7B20%7D%7D%26%3D%20%5Cdfrac%7B1%7D%7B4%7D)
The ratios of all the set of numbers are not equal. Therefore, a and b are not in a proportional relationship in Table (A).
In Table B the values are
and ![\left( {32,40}\right).](https://tex.z-dn.net/?f=%5Cleft%28%20%7B32%2C40%7D%5Cright%29.)
The ratios of a and b can be calculated as follows,
![\dfrac{{20}}{{25}}&=\ddfrac{4}{5}\dfrac{{24}}{{30}}&= \frac{4}{5}\dfrac{{32}}{{40}} &=\dfrac{4}{5}](https://tex.z-dn.net/?f=%5Cdfrac%7B%7B20%7D%7D%7B%7B25%7D%7D%26%3D%5Cddfrac%7B4%7D%7B5%7D%5Cdfrac%7B%7B24%7D%7D%7B%7B30%7D%7D%26%3D%20%5Cfrac%7B4%7D%7B5%7D%5Cdfrac%7B%7B32%7D%7D%7B%7B40%7D%7D%20%26%3D%5Cdfrac%7B4%7D%7B5%7D)
The ratios of all the set of numbers are equal. Therefore, a and b are in a proportional relationship in Table (B).
In Table C the values are
and ![\left( {6,24}\right).](https://tex.z-dn.net/?f=%5Cleft%28%20%7B6%2C24%7D%5Cright%29.)
The ratios of a and b can be calculated as follows,
![\dfrac{4}{12}&=\dfrac{1}{3}\dfrac{5}{{15}}&=\dfrac{1}{3}\dfrac{6}{{24}}&= \dfrac{1}{4}](https://tex.z-dn.net/?f=%5Cdfrac%7B4%7D%7B12%7D%26%3D%5Cdfrac%7B1%7D%7B3%7D%5Cdfrac%7B5%7D%7B%7B15%7D%7D%26%3D%5Cdfrac%7B1%7D%7B3%7D%5Cdfrac%7B6%7D%7B%7B24%7D%7D%26%3D%20%5Cdfrac%7B1%7D%7B4%7D)
The ratios of all the set of numbers are not equal. Therefore, a and b are not in a proportional relationship in Table (C).
In Table D the values are
and ![\left({12,16}\right).](https://tex.z-dn.net/?f=%5Cleft%28%7B12%2C16%7D%5Cright%29.)
The ratios of a and b can be calculated as follows,
![\dfrac{3}{4}&=\dfrac{3}{4}\dfrac{6}{{9}}&=\dfrac{2}{3}\dfrac{12}{{16}}&=\dfrac{3}{4}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B4%7D%26%3D%5Cdfrac%7B3%7D%7B4%7D%5Cdfrac%7B6%7D%7B%7B9%7D%7D%26%3D%5Cdfrac%7B2%7D%7B3%7D%5Cdfrac%7B12%7D%7B%7B16%7D%7D%26%3D%5Cdfrac%7B3%7D%7B4%7D)
The ratios of all the set of numbers are not equal. Therefore, a and b are not in a proportional relationship in Table (D).
Table (A) is not correct.
Table (B) is correct.
Table (C) is not correct.
Table (D) is not correct.
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
1. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Ratio and Proportion
Keywords: proportional relationship, shows, a, b, ratio, table, fraction.