Solve the equation on the interval [0,2pi) 2cos² θ/2 -3cosθ=0

To solve this problem, you first have to know the half angle identify of cosine.
cos(θ/2)=+/-√(1+cosθ)/2, so  cos² (θ/2)=(1+cosθ)/2, and 2cos² (θ/2)=1+cosθ

2cos² (θ/2) -3cosθ=0
1+cosθ-3cosθ=0
2cosθ=1
cosθ=1/2
θ=π/3, or (5/3)π

0.23

Step-by-step explanation:

Given that while investigating customer complaints, the customer relations department of Sonic Air found that 15 percent of the flights arrive early and 25 percent arrive on time.

i.e. remaining 60% arrive late.

Overbooked = 65%

Hence not overbooked = %

Late or not overbooked = 72%

Late of not overbooked = Late+not overbooked - both

Probability for late and not overbooked = 23% = 0.23