Some bed bugs had mutations in their genetic code which allowed them to survive the chemical pesticide and they produced chemically resistant offspring. how can this be explained?

Random mutations led to evolution of pesticide resistance genes in bed bugs.

Explanation:

Random mutations in genome of bed bug imparted them the pesticide resistance. Since the bed bugs having the mutation of pesticide resistance were able to survive under presence of pesticides, this variation was favored by natural selection. The bugs with pesticide resistance transmitted this trait to their progeny. In time, the bed bug population consisted of most of the bugs having the pesticide resistance.

answer; i believe that the correct answer is ; males are hemizygous for the x chromosome;

substitution is the answer in this case