There is an upcoming election in Deyvi's town. Deyvi asks a random sample of voters whether they plan to vote for the current mayor, against the current mayor, or are undecided. His results are shown on the table. Use his results to predict how many people will be for, against, and undecided in a group of 2,000 voters. Show your Work

To predict the number of people who will be for, against, and undecided in a group of 2,000 voters, we first need to find the proportions of voters for each category based on the sample results.

Given:

For: 25 votes
Against: 12 votes
Undecided: 3 votes

Total number of votes in the sample:

[tex]\sf 25 + 12 + 3 = 40 [/tex]

Now, let's find the proportions for each category:

Proportion of voters for:

[tex]\sf \dfrac{25}{40} = 0.625 [/tex]

Proportion of voters against:

[tex]\sf \dfrac{12}{40} = 0.3 [/tex]

Proportion of undecided voters:

[tex]\sf \dfrac{3}{40} = 0.075 [/tex]

Now, let's use these proportions to predict the number of voters in each category in a group of 2,000 voters:

For: [tex]\sf 0.625 \times 2000 = 1250 [/tex]

Against: [tex]\sf 0.3 \times 2000 = 600 [/tex]

Undecided: [tex]\sf 0.075 \times 2000 = 150 [/tex]

So, in a group of 2,000 voters, we predict that there will be approximately:

1250 voters for the current mayor

600 voters against the current mayor

150 undecided voters.