https://file.aiquickdraw.com/mathbot/file/1726876964291yzv7u40g.jpg

It seems the text extraction from the image was incomplete. I'll work with what I can recognize directly from the image.

### The questions presented are:

**Given the following numbers:**
- \( A = \frac{\frac{7}{5} + 2}{\frac{3}{10} - \frac{1}{2}} \)
- \( B = \left[\frac{14}{7} - \frac{4}{3} \times \left(\frac{7}{6}\right)\right]^{-1} \div \left(-\frac{12}{7} + 2\right) \)
- \( C = 3011 \times 10^{-10} \)

### Tasks:
1. Simplify \( A \).
2. Show that \( B \) is an integer.
3. Write \( C \) in scientific notation.
4. Find among \( A \), \( B \), and \( C \), those that are rational and those that are irrational.

I'll go ahead and solve each part of the problem.The simplified value of \( A \) is \( -17 \).

Next, I will work on showing whether \( B \) is an integer. Let's simplify \( B \).The simplified value of \( B \) is \( \frac{63}{8} \), which is not an integer. Therefore, \( B \) is not an integer.

Next, I'll write \( C \) in standard scientific notation. Given \( C = 3011 \times 10^{-10} \), I'll express this properly.It seems like I can't do more advanced data analysis right now. Please try again later.

However, I can continue explaining some parts of the problem manually if needed.

- \( C = 3011 \times 10^{-10} \) is already close to scientific notation. In proper scientific notation, it would be expressed as \( 3.011 \times 10^{-7} \).

Lastly, let's categorize \( A \), \( B \), and \( C \) as rational or irrational:

- \( A = -17 \) is rational because it can be expressed as a fraction.
- \( B = \frac{63}{8} \) is rational since it's a ratio of two integers.
- \( C = 3.011 \times 10^{-7} \) is also rational, as it is a finite decimal number.

Would you like to go over any part of this, or have any questions?

Here are 5 related questions to explore:
1. How do you determine if a number is rational or irrational?
2. Can all fractions be simplified into integers?
3. What are the properties of numbers in scientific notation?
4. How would \( A \) change if the denominators were different?
5. Is it possible for \( B \) to be an integer in another scenario?

**Tip:** Always simplify fractions and check their inverses carefully when solving equations like \( B \).

Given the following numbers:
A = (7/5 + 2) / (3/10 - 1/2)
B = [(14/7 - 4/3 * (7/6))^-1] ÷ (-12/7 + 2)
C = 3011 * 10^(-10)
1. Simplify A.
2. Show that B is an integer.
3. Write C in scientific notation.
4. Find among A, B, and C, those that are rational and those that are irrational.

In this problem, we simplify fractions, write numbers in scientific notation, and determine which of A, B, and C are rational or irrational. Concepts include fraction operations and scientific notation. Suitable for Grades 9-12.

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