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

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

Step 1: Let the certain number be $x$. $53 - x = 65$

Step 2: Subtract 53 from both sides of the equation. $-x = 65 - 53$ $-x = 12$

Step 3: Multiply both sides by -1 to solve for $x$. $x = -12$ The certain number: $\boxed{-12}$

4.2.1. Calculate the following without the use of a calculator. $\frac{50 \times 33 + 25 \times 5}{10 \times 50 - 50 \times 19}$

Step 1: Calculate the numerator. $50 \times 33 + 25 \times 5 = 1650 + 125 = 1775$

Step 2: Calculate the denominator. Factor out 50. $10 \times 50 - 50 \times 19 = 50 \times (10 - 19) = 50 \times (-9) = -450$

Step 3: Form the fraction and simplify. $\frac{1775}{-450}$ 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{-\frac{71{18}}}.

4.2.2. Calculate the following without the use of a calculator. $-3 - (-2)(5) - (-4)^3$

Step 1: Evaluate the multiplication term. $(-2)(5) = -10$

Step 2: Evaluate the exponential term. $(-4)^3 = (-4) \times (-4) \times (-4) = 16 \times (-4) = -64$

Step 3: Substitute these values back into the expression. $-3 - (-10) - (-64)$

Step 4: Simplify the double negative signs. $-3 + 10 + 64$

Step 5: Perform the additions from left to right. $(-3 + 10) + 64 = 7 + 64 = 71$ The value is $\boxed{71}$.

4.2.3. Calculate the following without the use of a calculator. $\frac{3^3 - (-\sqrt{4})^2 + \sqrt[3]{-64}}{-4^2 \times 1^3 + 17}$

Step 1: Evaluate the terms in the numerator. $3^3 = 3 \times 3 \times 3 = 27$ $(-\sqrt{4})^2 = (-2)^2 = 4$ $\sqrt[3]{-64} = -4 \quad (since (-4) \times (-4) \times (-4) = -64)$

Step 2: Substitute these values into the numerator and simplify. $27 - 4 + (-4) = 27 - 4 - 4 = 23 - 4 = 19$

Step 3: Evaluate the terms in the denominator. $-4^2 = -(4 \times 4) = -16$ $1^3 = 1 \times 1 \times 1 = 1$

Step 4: Substitute these values into the denominator and simplify. $-16 \times 1 + 17 = -16 + 17 = 1$

Step 5: Form the fraction with the simplified numerator and denominator. $\frac{19}{1} = 19$ The value is $\boxed{19}$.