\[\boxed{\mathbf{1.}}\]
\[M(8;5).\]
\[\boxed{\mathbf{2.}}\]
\[900 - 12 \cdot (x\ :30 + 52) = 180\]
\[12 \cdot (x\ :30 + 52) = 900 - 180\]
\[12 \cdot (x\ :30 + 52) = 720\]
\[x\ :30 + 52 = 720\ :12\]
\[x\ :30 + 52 = 60\]
\[x\ :30 = 60 - 52\]
\[x\ :30 = 8\]
\[x = 8 \cdot 30\]
\[x = 240.\]
\[\boxed{\mathbf{3.}}\]
\[\textbf{а)}\ 15 - 9 = 6\ (ч) -\]
\[велосипедист\ был\ в\ пути.\]
\[\textbf{б)}\ 2\ остановки\ было.\]
\[\textbf{в)}\ 30\ мин -\]
\[продолжительность\ первой\ \]
\[остановки.\]
\[\textbf{г)}\ 16\ \frac{км}{ч} - скорость\ вначале.\]
\[\textbf{д)}\ 20\ \frac{км}{ч} - скорость\ на\ \]
\[обратном\ пути.\]
\[\boxed{\mathbf{4.}}\]
\[\boxed{\mathbf{5.}}\]
\[A = \left\{ \frac{4}{1};\frac{4}{2};\frac{4}{3};\frac{4}{4};\frac{4}{5};\frac{4}{6};\frac{4}{7};\frac{4}{8};\frac{4}{9};\ldots \right\};\]
\[B = \left\{ \frac{1}{7};\frac{2}{7};\frac{3}{7};\frac{4}{7};\frac{5}{7};\frac{6}{7} \right\};\]
\[C = \left\{ \frac{1}{1};\ \frac{2}{1};\frac{2}{2};\frac{3}{1};\frac{3}{2};\frac{3}{2};\ldots \right\}.\]
\[A \cap B = \left\{ \frac{4}{7} \right\};\]
\[B \cap C = \varnothing;\]
\[A \cap C = \left\{ \frac{4}{1};\ \frac{4}{2};\ \frac{4}{3};\ \frac{4}{4} \right\}.\]