https://file.aiquickdraw.com/mathbot/file/1725413580434szatide1.jpg

The problem in the image asks:

**True-False Test**: In how many ways can you answer a 12-question true-false test if you answer each question with either a "true" or a "false"?

### Solution:
Each question on the test has 2 possible answers: "True" or "False". Since the test has 12 questions, and each question is independent of the others, the number of different ways you can answer the entire test is calculated by multiplying the number of choices for each question.

Mathematically, this is \( 2^{12} \).

Now, let's calculate that:

\[
2^{12} = 4096
\]

So, there are **4,096** different ways to answer a 12-question true-false test.

Would you like more details, or do you have any other questions?

### Related Questions:
1. How would the number of ways change if the test had 15 questions?
2. What if each question had three possible answers instead of two?
3. Can you generalize the formula for any number of questions?
4. How many different ways are there to answer if you must answer exactly 6 questions as "True"?
5. How does the answer change if each question has a "True," "False," and "Not Answered" option?

### Tip:
When solving counting problems, always start by identifying how many choices are available for each independent decision. Then, use the multiplication rule to find the total number of outcomes.

In how many ways can you answer a 12-question true-false test if you answer each question with either a 'true' or a 'false'?

Discover how to calculate the number of ways to answer a 12-question true-false test. This problem involves key combinatorial concepts and exponential calculations, ideal for students in Grades 6-8.

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