A Cepheid variable is a star that pulsates radially, changing both in temperature and diameter to produce very regular brightness variations with stable periods and amplitudes. These stars were extensively studied by the American astronomer Henrietta Swan Leavitt (1868–1921). We know that Cepheid variables belong to the Large Magellanic Cloud, which is located 158,200 light-years away, and the speed of light in a vacuum is 300,000 km/s.  Calculate:

a) The speed of light in m/s.

b) The distance from the Large Magellanic Cloud to Earth in kilometres and meters.

c) The astronomical unit (AU) is a unit of length defined as 149,597,870,700 meters, approximately equal to the average distance between the Earth and the Sun. This definition has been in effect since the General Assembly of the International Astronomical Union (IAU) on August 31, 2012. How many astronomical units (AU) away are the Cepheid variables?