Answer:
.
Step-by-step explanation:
Probability that the car encounters a green light on the first day:
.
To meet the question's conditions, the car needs to encounter another green light on the second day. Given that the colors of the light on each day are "independent," the chance that there's a green light followed by another green light will be
.
- Condition is met on the first two days and green light on the third day:
. - Condition is met on the first three days and green light on the fourth day:
.
To meet the condition on the fifth day, there needs to be a yellow light. The probability that the condition is met on the first four days and on the fifth day will be
.
To meet the condition on the sixth day, all prior days should meet the conditions. Besides, there needs to be a red light on the sixth day. 
- Seventh day:

- Eighth day:
- Ninth day:
- Tenth day:
The question asks that the condition be met on all ten days. As a result, the probability of meeting the condition will be equal to the probability on the tenth day:
.
Thus L.H.S = R.H.S that is 2/√3cosx + sinx = sec(Π/6-x) is proved
We have to prove that
2/√3cosx + sinx = sec(Π/6-x)
To prove this we will solve the right-hand side of the equation which is
R.H.S = sec(Π/6-x)
= 1/cos(Π/6-x)
[As secƟ = 1/cosƟ)
= 1/[cos Π/6cosx + sin Π/6sinx]
[As cos (X-Y) = cosXcosY + sinXsinY , which is a trigonometry identity where X = Π/6 and Y = x]
= 1/[√3/2cosx + 1/2sinx]
= 1/(√3cosx + sinx]/2
= 2/√3cosx + sinx
R.H.S = L.H.S
Hence 2/√3cosx + sinx = sec(Π/6-x) is proved
Learn more about trigonometry here : brainly.com/question/7331447
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Answer:
4.485
Step-by-step explanation:
[divide 17 by 4]
[ ]
Now, Midpoint of 4.25 and 4.472 =
Number between 4.25 and 4.472 =4.485
Or number between and is 4.485.
300miles/20sec=?miles/1min
900miles/60sec=?miles/1min
900miles/1min=?miles/min
?=900 miles
Answer:
49.1
Step-by-step explanation:
Add all the numbers up together and divide by how many there are so....
35 + 61 + 63 + 69 + 49 + 46 + 52 + 32 + 34 + 50 = 491
491 divided by 10 is 49.1
hope this helps!