Emily spends 3 episodes * 25 minutes = <<3*25=75>>75 minutes watching TV.
Emily spends 4.5 hours * 60 minutes = <<4.5*60=270>>270 minutes sleeping.
Emily spends 2 movies * 1.75 hours * 60 minutes = <<2*1.75*60=210>>210 minutes watching movies.
The total time spent doing activities is 75 + 270 + 210 = <<75+270+210=555>>555 minutes
The total length of the flight is 10 hours * 60 minutes = <<10*60=600>>600 minutes
The number of minutes remaining in the flight is 600 - 555 = <<600-555=45>>45 minutes
#### 45