https://file.aiquickdraw.com/mathbot/file/1725869573847q8xp82rf.jpg

https://file.aiquickdraw.com/mathbot/file/1725869573850h16j0xix.jpg

The two photos present a problem related to set theory and survey analysis in which different coffee preferences are recorded. To summarize the key data and questions:

### Data from the survey (from the first image):
- 221 like espresso.
- 127 like cappuccino and chocolate-flavored coffee.
- 182 like cappuccino.
- 136 like espresso and chocolate-flavored coffee.
- 209 like chocolate-flavored coffee.
- 78 like all three types of coffee.
- 116 like espresso and cappuccino.
- 82 like none of these types of coffee.

### Questions (from the second image):
- **a.** How many of the customers in the survey like only chocolate-flavored coffee?
- **b.** How many like cappuccino and chocolate-flavored coffee but not espresso?
- **c.** How many like espresso and cappuccino but not chocolate-flavored coffee?
- **d.** How many like exactly one of the three types of coffee?

To solve these, we can use Venn diagrams or set theory equations. The key sets are:
- \(E\) = Set of people who like espresso.
- \(C\) = Set of people who like cappuccino.
- \(Ch\) = Set of people who like chocolate-flavored coffee.

Would you like me to proceed with calculating the values based on this data?

How many of the customers in the survey like only chocolate-flavored coffee? How many like cappuccino and chocolate-flavored coffee but not espresso? How many like espresso and cappuccino but not chocolate-flavored coffee? How many like exactly one of the three types of coffee?

Explore how to solve a coffee preference survey problem using set theory and Venn diagrams. Learn how to determine the number of customers who like only chocolate-flavored coffee, those who like cappuccino and chocolate-flavored coffee but not espresso, and more. Ideal for students in Grades 10-12.

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