To balance the following chemical equation, the values of the coefficients $x, y$ and $z$ must be respectively : $x \mathrm{Zn(NO_3)_2 \xrightarrow{\Delta} y \mathrm{ZnO + z \mathrm{NO_2 + O_2}}}$

["The question requires the student to balance a chemical equation and find the values of the coefficients x, y, and z.", "The student needs to apply the law of conservation of mass, which states that the number of atoms of each element remains the same before and after a chemical reaction.", "The student needs to analyze the chemical equation and balance the atoms of each element by adding coefficients in front of the formulas of the reactants or products."]