https://file.aiquickdraw.com/mathbot/file/1725931835748nle9af4t.jpg

https://file.aiquickdraw.com/mathbot/file/17259318357524y9as1y3.jpg

The images contain data and questions regarding a coffee survey, where a gourmet coffee bar has gathered customer preferences for espresso, cappuccino, and chocolate-flavored coffee. 

Here is the extracted data from the first image:

### Coffee Survey Data:
- 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.
- 178 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 customers like only chocolate-flavored coffee?
- **b.** How many customers like cappuccino and chocolate-flavored coffee but not espresso?
- **c.** How many customers like espresso and cappuccino but not chocolate-flavored coffee?
- **d.** How many customers like exactly one of the three types of coffee?

Would you like me to help you solve these questions step by step using set theory (Venn diagrams) and logical operations?

Let me know if you'd like more details or further clarification! Also, here are five related questions for further exploration:

1. How can we set up a Venn diagram to solve this problem?
2. What is the formula for calculating the number of people who like only one specific type of coffee?
3. Can you explain the process of finding the number of people who like all three types of coffee?
4. What strategies can be used to calculate the number of people who like exactly two types of coffee?
5. How do we handle the case of people who like none of the coffee types?

### Tip:
Always use a systematic approach (like a Venn diagram) to organize overlapping sets, as it helps visualize complex relationships and avoid miscounting.

A gourmet coffee bar conducted a survey to determine the preferences of its customers for espresso, cappuccino, and chocolate-flavored coffee. How many customers like only chocolate-flavored coffee, like cappuccino and chocolate-flavored coffee but not espresso, like espresso and cappuccino but not chocolate-flavored coffee, or like exactly one of the three types of coffee?

Solve a set theory problem based on a coffee survey. Determine how many customers like only chocolate-flavored coffee, like cappuccino and chocolate-flavored coffee but not espresso, like espresso and cappuccino but not chocolate-flavored coffee, or like exactly one of the three types. Understand how to apply Venn diagrams, the principle of inclusion-exclusion, and other logical operations to solve this problem. Suitable for Grades 9-12.

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