Can We Still Have Our Best Premier League Finish?

Everton and West Ham are both in poor form and have some tough fixtures coming in. If we can beat Everton, Cardiff and Bournemouth and perhaps get a point against Arsenal or City then we should come pretty close to finishing 10th. The remaining fixtures:

Palace

Man City (h)
Arsenal (a)
Everton (h)
Cardiff (a)
Bournemouth (h)

West Ham

Chelsea (a)
Manchester United (a)
Leicester (h)
Tottenham (a)
Southampton (h)
Watford (a)

Everton

Arsenal (h)
Fulham (a)
Manchester United (h)
Crystal Palace (a)
Burnley (h)
Tottenham (a)