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A survey of 500 adults was conducted to determine why more undergraduate students do not pursue degrees in science, technology, engineering, and math (STEM). The results of the survey show that 250 respondents believed that students do not pursue STEM degrees because the subjects are too difficult, while 105 respondents believed it is because the subjects do not have applications in their careers. There were ten respondents who believed both, difficulty and lack of applications, were the reasons why no more students pursue STEM degrees.

Part I: Complete the following steps:

Define two sets to represent the two different opinions of the survey's respondents.

show in a Venn diagram to represent the results of this survey.

How many respondents believed students do not pursue STEM degrees only because the subjects are too difficult?

How many respondents believed students do not pursue STEM degrees only because the subjects do not have applications in their careers?

How many respondents believed that neither the difficulty nor the lack of applications of the subjects are reasons why students do not pursue STEM degrees?

Answer :

240 respondents believed that students do not pursue STEM degrees only because the subjects are too difficult, while 95 respondents believed that students do not pursue STEM degrees only because the subjects do not have applications in their careers. 155 respondents believed that neither the difficulty nor the lack of applications of the subjects are reasons why students do not pursue STEM degrees.

How to represent survey results effectively?

The number of respondents who believed students do not pursue STEM degrees only because the subjects are too difficult is 250 - 10 = 240.

The number of respondents who believed students do not pursue STEM degrees only because the subjects do not have applications in their careers is 105 - 10 = 95.

The number of respondents who believed that neither the difficulty nor the lack of applications of the subjects are reasons why students do not pursue STEM degrees is 500 - (240 + 95 + 10) = 155.

Let set A represent the respondents who believe that the subjects are too difficult, and set B represent the respondents who believe that the subjects do not have applications in their careers.

From the diagram, we can see that:

The Venn diagram for the survey results can be drawn as follows:

A: Subjects are too difficult

/ \

/ \

/ 10 \

/ Both \

/_________\

| |

| |

B: Subjects do not have applications in their career

Learn more about: STEM

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