To find the means in the given proportion, we need to understand the concept of a proportion and the identification of its means. A proportion occurs when two ratios are equal to each other and is generally written in the form:
[tex]\[
\frac{a}{b} = \frac{c}{d}
\][/tex]
In this context, the "means" refer to the middle terms of the proportion when written in this form. For example, in the proportion [tex]\(\frac{a}{b} = \frac{c}{d}\)[/tex], the means are the numbers [tex]\(b\)[/tex] and [tex]\(c\)[/tex].
Given the problem:
[tex]\[
\frac{2}{3} = \frac{20}{30}
\][/tex]
First, notice that [tex]\(\frac{20}{30}\)[/tex] simplifies to [tex]\(\frac{2}{3}\)[/tex], but for the purposes of identifying the means, we will treat them as they appear.
Here, the ratios can be identified as [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{20}{30}\)[/tex]:
[tex]\[ a = 2, \quad b = 3, \quad c = 20, \quad d = 30 \][/tex]
The means are the second and third terms of the proportion. Therefore, the means of the proportion are:
[tex]\[ b = 3 \quad \text{and} \quad c = 20 \][/tex]
So, the correct answer is:
D. [tex]\(3\)[/tex] and [tex]\(20\)[/tex]
