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### Problem 12:
The cost \( C \) of a set of iron wheels is given by the formula:
\[
C = 6500 + 4000 \cdot n,
\]
where \( n \) is the number of wheels. We need to find the cost when \( n = 13 \).

Substituting \( n = 13 \):
\[
C = 6500 + 4000 \times 13 = 6500 + 52000 = 58500.
\]

**Answer:** 58500 rubles.

---

### Problem 13:
The inequality shown on the number line includes values between -7 and 7. This corresponds to:
\[
x^2 - 49 < 0.
\]

Since \( x^2 - 49 \) factors as \( (x - 7)(x + 7) < 0 \), the solution is between -7 and 7.

**Answer:** Option 1.

---

### Problem 14:
The mass of a radioactive isotope decreases by half every 7 minutes. The initial mass is 640 mg, and we need to find the mass after 42 minutes.

The number of 7-minute intervals in 42 minutes is:
\[
\frac{42}{7} = 6.
\]

The mass after 6 intervals is:
\[
640 \times \left(\frac{1}{2}\right)^6 = 640 \times \frac{1}{64} = 10.
\]

**Answer:** 10 mg.

---

### Problem 15:
In triangle \( ABC \), \( \angle C = 90^\circ \), \(\tan B = \frac{5}{9}\), and \( BC = 27 \). We need to find \( AC \).

Using the definition of tangent:
\[
\tan B = \frac{BC}{AC} = \frac{5}{9}.
\]

Substituting \( BC = 27 \):
\[
\frac{27}{AC} = \frac{5}{9} \implies AC = \frac{27 \times 9}{5} = 48.6.
\]

**Answer:** 48.6.

---

### Problem 16:
Triangle \( ABC \) is inscribed in a circle with center \( O \). Points \( O \) and \( C \) lie on the same half-plane relative to line \( AB \). Angle \( AOB = 153^\circ \). Find \( \angle ACB \).

Using the property of inscribed angles:
\[
\angle ACB = \frac{1}{2} \times \angle AOB = \frac{153^\circ}{2} = 76.5^\circ.
\]

**Answer:** 76.5 degrees.

Would you like to go over any of these solutions in more detail, or solve another problem?

### Follow-up Questions:
1. How would the formula in Problem 12 change if each wheel cost 5000 rubles instead of 4000?
2. Can you solve inequality \( x^2 - 49 > 0 \)?
3. How would the mass change in Problem 14 after 49 minutes?
4. How to find the hypotenuse of triangle \( ABC \) if both legs are given?
5. How would you solve Problem 16 if the angle \( AOB \) was instead 120 degrees?

**Tip:** Remember, for half-life problems, calculating the number of intervals is crucial before applying the reduction formula.

In the firm 'Clean Water,' the cost (in rubles) of a set of iron wheels is calculated using the formula C = 6500 + 4000 * n, where n is the number of wheels installed in the well. Using this formula, calculate the cost of the well with 13 wheels.

Calculate the total cost of iron wheels for a well using the linear formula C = 6500 + 4000 * n, where n is the number of wheels. This problem demonstrates arithmetic operations and linear equation concepts.

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