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To determine the proportion of students who plan to vote for each candidate based on the poll results, we need to follow these steps:
### Step-by-Step Solution:
1. Total Number of Votes:
- First, we calculate the total number of votes from all candidates.
[tex]\[ \text{Total votes} = \text{Votes for Velma} + \text{Votes for Ana} + \text{Votes for Marshall} + \text{Votes for Barnaby} \][/tex]
We are given the following numbers:
[tex]\[ \text{Velma} = 22, \quad \text{Ana} = 36, \quad \text{Marshall} = 13, \quad \text{Barnaby} = 4 \][/tex]
Thus,
[tex]\[ \text{Total votes} = 22 + 36 + 13 + 4 = 75 \][/tex]
2. Calculating Proportions:
- To find the proportion of votes each candidate received, we divide the number of votes for each candidate by the total number of votes.
For Velma:
[tex]\[ \text{Proportion of votes for Velma} = \frac{\text{Votes for Velma}}{\text{Total votes}} = \frac{22}{75} \][/tex]
For Ana:
[tex]\[ \text{Proportion of votes for Ana} = \frac{\text{Votes for Ana}}{\text{Total votes}} = \frac{36}{75} \][/tex]
For Marshall:
[tex]\[ \text{Proportion of votes for Marshall} = \frac{\text{Votes for Marshall}}{\text{Total votes}} = \frac{13}{75} \][/tex]
For Barnaby:
[tex]\[ \text{Proportion of votes for Barnaby} = \frac{\text{Votes for Barnaby}}{\text{Total votes}} = \frac{4}{75} \][/tex]
3. Convert Proportions to Percentages:
- To convert these proportions to percentages, we multiply by 100.
Percentage of votes for Velma:
[tex]\[ \frac{22}{75} \times 100 \approx 29.33\% \][/tex]
Percentage of votes for Ana:
[tex]\[ \frac{36}{75} \times 100 \approx 48.00\% \][/tex]
Percentage of votes for Marshall:
[tex]\[ \frac{13}{75} \times 100 \approx 17.33\% \][/tex]
Percentage of votes for Barnaby:
[tex]\[ \frac{4}{75} \times 100 \approx 5.33\% \][/tex]
4. Answer the Question:
- The question asks for the proportion of votes matching one of the given percentages, which include 36%, 49%, 26%, and 65%.
From our calculations, the proportion of votes for Ana matches closely with one of the choices:
- Ana: [tex]\( 48.00\% \)[/tex]
So, the approximate proportion of students who plan to vote for Ana from Gretel's poll is 49%.
### Step-by-Step Solution:
1. Total Number of Votes:
- First, we calculate the total number of votes from all candidates.
[tex]\[ \text{Total votes} = \text{Votes for Velma} + \text{Votes for Ana} + \text{Votes for Marshall} + \text{Votes for Barnaby} \][/tex]
We are given the following numbers:
[tex]\[ \text{Velma} = 22, \quad \text{Ana} = 36, \quad \text{Marshall} = 13, \quad \text{Barnaby} = 4 \][/tex]
Thus,
[tex]\[ \text{Total votes} = 22 + 36 + 13 + 4 = 75 \][/tex]
2. Calculating Proportions:
- To find the proportion of votes each candidate received, we divide the number of votes for each candidate by the total number of votes.
For Velma:
[tex]\[ \text{Proportion of votes for Velma} = \frac{\text{Votes for Velma}}{\text{Total votes}} = \frac{22}{75} \][/tex]
For Ana:
[tex]\[ \text{Proportion of votes for Ana} = \frac{\text{Votes for Ana}}{\text{Total votes}} = \frac{36}{75} \][/tex]
For Marshall:
[tex]\[ \text{Proportion of votes for Marshall} = \frac{\text{Votes for Marshall}}{\text{Total votes}} = \frac{13}{75} \][/tex]
For Barnaby:
[tex]\[ \text{Proportion of votes for Barnaby} = \frac{\text{Votes for Barnaby}}{\text{Total votes}} = \frac{4}{75} \][/tex]
3. Convert Proportions to Percentages:
- To convert these proportions to percentages, we multiply by 100.
Percentage of votes for Velma:
[tex]\[ \frac{22}{75} \times 100 \approx 29.33\% \][/tex]
Percentage of votes for Ana:
[tex]\[ \frac{36}{75} \times 100 \approx 48.00\% \][/tex]
Percentage of votes for Marshall:
[tex]\[ \frac{13}{75} \times 100 \approx 17.33\% \][/tex]
Percentage of votes for Barnaby:
[tex]\[ \frac{4}{75} \times 100 \approx 5.33\% \][/tex]
4. Answer the Question:
- The question asks for the proportion of votes matching one of the given percentages, which include 36%, 49%, 26%, and 65%.
From our calculations, the proportion of votes for Ana matches closely with one of the choices:
- Ana: [tex]\( 48.00\% \)[/tex]
So, the approximate proportion of students who plan to vote for Ana from Gretel's poll is 49%.
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