engage vs throw out

engage

verb
  • To draw into conversation. 

  • To enter into conflict with (an enemy). 

  • To come into gear with. 

  • To enter into (an activity), to participate (construed with in). 

  • To mesh or interlock (of machinery, especially a clutch). 

  • To attract, to please; (archaic) to fascinate or win over (someone). 

  • To guarantee or promise (to do something). 

  • To engross or hold the attention of; to keep busy or occupied. 

  • To arrange to employ or use (a worker, a space, etc.). 

  • To bind through legal or moral obligation (to do something, especially to marry) (usually in passive). 

  • To enter into battle. 

throw out

verb
  • To put into a state of confusion. 

  • To offer an idea for consideration. 

  • To dismiss or expel someone from any longer performing duty or attending somewhere. 

  • To produce in a haphazard fashion. 

  • To emit. 

  • To cause or experience debilitating muscle or joint pain in (a body part). 

  • To cause to project. 

  • To utter carelessly. 

  • To outdistance; to leave behind. 

  • To discard; to dispense with something; to throw away. 

How often have the words engage and throw out occurred in a corpus of books? (source: Google Ngram Viewer )