500 people are surveyed and asked to check the boxes that apply to them.
a. i am confident in the economy.
b. i have health insurance.
321 said they were confident about the economy,
403 said they had health insurance, and 63 checked neither box.

1. A Venn diagram is attached. The amount of people that have health insurance and is confident about the economy is 287.

2. The amount of people that have health insurance and is not confident about the economy is 116.

3. The amount of people that have health insurance or  is confident about the economy is 437.

Step-by-step explanation:

1) Using sets theory, we know:

U: 500 people surveyed

A: people who is confident in the economy

B: people that have health insurance

A' and B': people who is not confident in the economy and don't have health insurance.

A=321

B=403

A' and B' =63

In the attached picture we can see a Venn diagram that represents the situation. In order to obtain the intersection of both sets A∩B, we calculate:

(321 - x) + (403 - x) + x + 63 = 500

321 - x + 403 - x + x + 63 +x -500 = 500 +x - 500

321 + 403 + 63 -500 = x

x= 287

2) The amount of people that have health insurance and is not confident about the economy is given by the intersection of the complement of set A and set B:

A' ∩ B can be calculated as:

B - (A ∩ B)= 403 - 287= 116

3) The amount of people that have health insurance or  is confident about the economy is given by:

(A∪B) = (A) + (B) - (A ∩ B)

(A∪B) = 321 + 403 - 287= 437

hello from mrbilldoesmath!

answer:

x - 3

discussion:

x^2 - 9 = (x-3) (x+3)   so

(x^2-9)/ (x + 3) = x-3

you,

mrb