Question

A group of 31 randomly selected adults were asked in a survey if they have either a nut allergy, a wheat

allergy, or both. Of those adults 14 had only a nut allergy, 5 had only a wheat allergy, 6 had both. Fill in the
following Venn Diagram to display this information. Each number in the Venn diagram represents the count
within the smallest enclosed region that contains the number. Input 0 for portions of the diagram that
don't have any items.

Answer 1

step by step:

Let's represent the number of adults with a nut allergy as N, the number of adults with a wheat allergy as W, and the number of adults with both allergies as B.

Based on the given information:

The total number of adults surveyed is 31.

14 adults had only a nut allergy (N).

5 adults had only a wheat allergy (W).

6 adults had both a nut allergy and a wheat allergy (B).

To fill in the Venn Diagram, you can start by placing the numbers provided in their respective regions:

N

/ \

B/ \W

/ \

/_______\

Now, let's calculate the remaining values:

To find the number of adults with both a nut allergy and a wheat allergy (B), we already know that 6 adults fall into this category.

To find the number of adults with only a nut allergy (N), we subtract the number of adults with both allergies (B) and the number of adults with only a wheat allergy (W) from the total surveyed (31): N = 31 - B - W.

To find the number of adults with only a wheat allergy (W), we subtract the number of adults with both allergies (B) and the number of adults with only a nut allergy (N) from the total surveyed (31): W = 31 - B - N.

Using the given information, we can calculate the remaining values:

N = 31 - B - W = 31 - 6 - 5 = 20

W = 31 - B - N = 31 - 6 - 20 = 5

Now we can fill in the numbers in the Venn Diagram:

20

/ \

6/ \5

/ \

/_______\

Please note that these numbers are based on the given data, and you may need to adjust the Venn Diagram based on the actual dimensions and labels of the regions.