Answer
$22.9$ MHz
Work Step by Step
To find the frequency of the wave according to the moving ship, use the equation $$f'=f\sqrt{\frac{1-\beta}{1+\beta}}$$ where $v=\beta c$. Since the ship is moving away from Earth, the received frequency should be lower than the frequency recorded by the spaceship. Using values of $\beta=0.900$ and $f=100MHz$ yields a frequency of $$f'=(100MHz)\sqrt{\frac{1-.900}{1+.900}}=22.9MHz$$
