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.

b.

c. earths continental crust is thicker than its lithosphere.

because, the lithosphere is the outermost layer of the earth/ 100 km thick and is defined by its machanical properties.the lithosphere contains oceanic and continental crust that varies in age and thickness across locations and geologic time. the lithosphere is the coolest layer of the earth in terms of temperature. the term lithosphere should not be confused with the use of "geosphere" which is used to indicate all of earth systems, including the atmosphere, hydrosphere   and biosphere. the surface of the earth can be divided into the continental crust and the oceanic crust.   the continental crust is made mostly of granite while the oceanic crust is made of basalt. the average thickness of the continental crust is 25 miles and the average thickness of the oceanic crust is 5 miles.   three types of rock, igneous, sedimentary, and metamorphic, make up the surface of the earth. that's why 3 option is preferable.