With all the parts: i, ii and iii.

See below.

Step-by-step explanation:

(i)   Sin 130 = sin ( 180 - 130) = sin 50 = k (answer).

(ii) sin 50 = cos (90 - 50) = cos 40 = k.

The right angle with hypotenuse of 1 and the side opposite the angle  whose sine is k has the adjacent side = √(1 - k^2)  ( by the Pythagoras theorem),

so the sine of (90 - 50) = sin 40 = √(1 - k^2)/ 1.

Therefore tan 40 = sin 40 / cos 40 =  √(1 - k^2) / k (answer)

(iii)  cos ( -220) = cos (360 - 220) = cos 140 = - cos 40

= -k.

Now since sec x  = 1 / cos x :

sec (-220) = -1/k (answer).

answer:   35 % is the probability of a late departure or an early arrival.

step-by-step explanation:

let l represents the late departure and e represents the early departure.

then, according to the question,

p(l) = 12 %,   p(e) = 27 % and = 4 %

and, we have to find out,

but, we know that,

which is the required equation that will use to find the probability of a late departure or an early departure.

therefore,   the probability of a late departure or an early arrival =   35 %