To determine the means of the given proportion [tex]\(\frac{2}{3} = \frac{20}{30}\)[/tex], let's first recall what means are in the context of proportions.
In a proportion of the form [tex]\(\frac{a}{b} = \frac{c}{d}\)[/tex], the numbers [tex]\(b\)[/tex] and [tex]\(c\)[/tex] are called the means, while [tex]\(a\)[/tex] and [tex]\(d\)[/tex] are called the extremes.
Given proportion:
[tex]\[
\frac{2}{3} = \frac{20}{30}
\][/tex]
Here, [tex]\(\frac{2}{3} = \frac{20}{30}\)[/tex] can be written in the form [tex]\(\frac{a}{b} = \frac{c}{d}\)[/tex]:
- [tex]\(a = 2\)[/tex]
- [tex]\(b = 3\)[/tex]
- [tex]\(c = 20\)[/tex]
- [tex]\(d = 30\)[/tex]
According to the definition, the means are the middle terms when the proportion is written as:
[tex]\[
2 : 3 = 20 : 30
\][/tex]
Therefore:
- [tex]\(b = 3\)[/tex] is one of the means.
- [tex]\(c = 20\)[/tex] is the other mean.
So, the numbers that are the means in this proportion are [tex]\(3\)[/tex] and [tex]\(20\)[/tex].
Thus, the correct answer is:
D. 3 and 20
