Question

A poll of 400 randomly selected likely voters in Seanoa City was taken to determine the support for the mayoral candidates in the upcoming election. Of the likely voters selected, 190 stated that they are likely to vote for Candidate \(\mathrm{A}\). If the conclusion is drawn that "approximately 3,120 voters are likely to vote for Candidate A," which of the following is closest to the number of likely voters in Seanoa City? A) 1,482 B) 3,120 C) 4,741 D) 6,568 $$ \begin{gathered} y^2=21-x \\ x=5 \end{gathered} $$

Short answer

The closest number of total likely voters in Seanoa City is approximately 6,568.

Step-by-step solution

Set up the proportion.

We can set up the proportion as follows: \(\dfrac{\text{Number of voters who support A in the sample}}{\text{Total number of voters in the sample}} = \dfrac{\text{Estimated number of voters who support A in the entire city}}{\text{Total number of voters in the entire city}}\)

Plug in the given information.

We are given that there are 190 voters who support Candidate A in the sample of 400 voters, and an estimated 3,120 voters who support Candidate A in the entire city. Let x represent the total number of voters in the entire city. We can now plug in these values into our proportion: \(\dfrac{190}{400}=\dfrac{3,120}{x}\)

Cross-multiply.

To solve for x, we need to cross-multiply: \(190x = 3,120 * 400\)

Solve for x.

Divide both sides of the equation by 190: \(x = \dfrac{3,120 * 400}{190}\) Calculate the result: \(x ≈ 6,568\)

Answer the question.

The closest number of total likely voters in Seanoa City is approximately 6,568. Thus, the correct answer is: D) 6,568