Let's go through the problems one by one and solve them:

19. Find the mean of the integers: 11, -7, -14, 10, -5

To find the mean, sum all the numbers and divide by how many numbers there are. $\text{Mean} = \frac{11 + (-7) + (-14) + 10 + (-5)}{5} = \frac{-5}{5} = -1$ So, the mean is -1.

20. Fill in the blank with >, <, or =:

$4 \ \_ \ | -8 |$ Since the absolute value of -8 is 8, we are comparing 4 and 8. Therefore, $4 < 8$ So the answer is <.

21. Evaluate the expression when $x = 5, y = -3, z = -2$:

The expression is: $\frac{y + z}{x} = \frac{-3 + (-2)}{5} = \frac{-5}{5} = -1$ So the value of the expression is -1.

22. A NASCAR driver receives -25 points for each violation. What integer represents the change in points after 4 violations?

Each violation results in a loss of 25 points. Therefore, after 4 violations: $-25 \times 4 = -100$ The change in points is -100.

23. Write the rational number $\frac{1}{9}$ as a decimal.

Dividing 1 by 9 gives: $\frac{1}{9} = 0.1111\ldots$ So, $\frac{1}{9}$ as a decimal is 0.111... (repeating).

24. Subtract:

$2.86 - 12.1$ This equals: $2.86 - 12.1 = -9.24$ So, the result is -9.24.

25. Solve $\frac{17}{12} - \left( -\frac{1}{8} \right)$:

This simplifies to: $\frac{17}{12} + \frac{1}{8}$ To add the fractions, find a common denominator: $\frac{17}{12} = \frac{68}{48}, \quad \frac{1}{8} = \frac{6}{48}$ Adding them together: $\frac{68}{48} + \frac{6}{48} = \frac{74}{48} = \frac{37}{24}$ So, the result is $\frac{37}{24}$ or approximately 1.54.

26. Solve $-4.4 \cdot (-6.2)$:

Multiplying two negative numbers gives a positive result: $-4.4 \times -6.2 = 27.28$ So, the result is 27.28.

Would you like any more details or clarifications on these problems?

Here are 5 follow-up questions to practice similar concepts:

1. What is the median of the integers: 15, -9, 8, -3, 12?
2. Solve $-7.3 \times 5.4$.
3. Evaluate the expression $\frac{y - z}{x}$ when $x = 6, y = -2, z = -7$.
4. Convert $\frac{5}{8}$ to a decimal.
5. Find the result of subtracting $\frac{9}{5} - \left( \frac{-4}{15} \right)$.

Tip: When dealing with absolute values, always remember they represent the distance from zero, so they are always non-negative.