Determine the number that makes the following statement true: 53 - (a certain number) = 65.

$$-x = 65 - 53$$ $$-x = 12$$

$$x = -12$$

The certain number: $\boxed{\mathbf{-12}}$

4.2.1. Calculate the following without the use of a calculator.

$$\frac{50 \times 33 + 25 \times 5}{10 \times 50 - 50 \times 19}$$

Factor out 50.

$$10 \times 50 - 50 \times 19 = 50 \times (10 - 19) = 50 \times (-9) = -450$$

$$\frac{1775}{-450}$$

Divide both numerator and denominator by their greatest common divisor, which is 25.

$$1775 \div 25 = 71$$ $$-450 \div 25 = -18$$ $$\frac{71}{-18} = -\frac{71}{18}$$

The simplified value is $\boxed{\mathbf{-\frac{71}{18}}}$.

4.2.2. Calculate the following without the use of a calculator.

$$-3 - (-2)(5) - (-4)^3$$

$$(-3 + 10) + 64 = 7 + 64 = 71$$

The value is $\boxed{\mathbf{71}}$.

4.2.3. Calculate the following without the use of a calculator.

$$\frac{3^3 - (-\sqrt{4})^2 + \sqrt[3]{-64}}{-4^2 \times 1^3 + 17}$$

$$3^3 = 3 \times 3 \times 3 = 27$$ $$(-\sqrt{4})^2 = (-2)^2 = 4$$ $$\sqrt[3]{-64} = -4 \quad (\text{since } (-4) \times (-4) \times (-4) = -64)$$

$$-4^2 = -(4 \times 4) = -16$$ $$1^3 = 1 \times 1 \times 1 = 1$$

$$\frac{19}{1} = 19$$

The value is $\boxed{\mathbf{19}}$.