To determine how many citizens are in favor of establishing a democratic government, we start by identifying the key pieces of information given in the problem:
1. The total number of citizens in Genovia is 50,000.
2. According to the poll, [tex]\( \frac{3}{4} \)[/tex] of the respondents are in favor of the democratic government.
First, we need to understand what [tex]\( \frac{3}{4} \)[/tex] signifies. The fraction [tex]\( \frac{3}{4} \)[/tex] means that out of every 4 citizens, 3 are in favor of the democratic government.
Next, we need to find [tex]\( \frac{3}{4} \)[/tex] of the total number of citizens. To do this, we multiply the total number of citizens by [tex]\( \frac{3}{4} \)[/tex]:
[tex]\[ \text{Number of citizens in favor} = 50,000 \times \frac{3}{4} \][/tex]
Carrying out the multiplication:
[tex]\[ 50,000 \times \frac{3}{4} = 50,000 \times 0.75 \][/tex]
This gives us:
[tex]\[ 50,000 \times 0.75 = 37,500 \][/tex]
Therefore, approximately 37,500 citizens are in favor of establishing a democratic government.
Thus, the correct answer is:
(C) 37,500
