To determine which statement expresses a true proportion, we need to evaluate the given ratios in each pair and see if they are equivalent. Here’s the step-by-step process for each option:
### Option A: [tex]\( 42: 7 = 6: 2 \)[/tex]
First, simplify the ratios:
[tex]\[ \frac{42}{7} = 6 \][/tex]
[tex]\[ \frac{6}{2} = 3 \][/tex]
Clearly, [tex]\( 6 \neq 3 \)[/tex], so this is not a true proportion.
### Option B: [tex]\( 3: 5 = 12: 20 \)[/tex]
First, simplify the ratios:
[tex]\[ \frac{3}{5} = 0.6 \][/tex]
[tex]\[ \frac{12}{20} = \frac{12 \div 4}{20 \div 4} = \frac{3}{5} = 0.6 \][/tex]
Since both ratios equal [tex]\( 0.6 \)[/tex], this is a true proportion.
### Option C: [tex]\( 14: 6 = 28: 18 \)[/tex]
First, simplify the ratios:
[tex]\[ \frac{14}{6} = \frac{14 \div 2}{6 \div 2} = \frac{7}{3} \approx 2.333 \][/tex]
[tex]\[ \frac{28}{18} = \frac{28 \div 2}{18 \div 2} = \frac{14}{9} \approx 1.556 \][/tex]
Since [tex]\( \frac{7}{3} \neq \frac{14}{9} \)[/tex], this is not a true proportion.
### Option D: [tex]\( 2: 3 = 3: 2 \)[/tex]
First, simplify the ratios:
[tex]\[ \frac{2}{3} \approx 0.667 \][/tex]
[tex]\[ \frac{3}{2} = 1.5 \][/tex]
Since [tex]\( 0.667 \neq 1.5 \)[/tex], this is not a true proportion.
Based on these evaluations, the only true proportion is given in:
[tex]\[ \boxed{\text{B}} \, 3:5 = 12:20 \][/tex]
