If a container is heated with CaCO3, the compound decomposes into CaO and CO2. If the container and CaCO3 originally weigh 30.08g and loss 4.40g during the heat, what is the mass of the empty container?

if the mass of the CO2 liberated was 4.40g, convert that to moles:

moles CO2: 4.4/40=0.11
when you write the balanced equation, that is the same number of moles of CaCO3 you decomposed, and the same number of moles of CaO you ended with.
moles CaO=0.11
moles CaCO3=0.11

mass of original CaCO3=0.11*100=11.0g

so the mass of the container=30.1-11.0