2) Shawn's cat is currently stuck in a tree. Shawn has a ladder that is 15 feet long and he places the ladder 10 feet from the b
ase of the tree. At what angle of depression is Shawn's cat looking at him?
1 answer:
Answer:
48.19°
Step-by-step explanation:
Check the attachment for the diagram.
The set up is a right angled triangle
Using the SOH, CAH, TOA trigonometry ratio to get the angle of depression theta.
The length of the ladder will be the hypotenuse of the triangle.
If he places the ladder 10 feet from the base of the tree, the adjacent of the triangle will be the base of the triangle.
Given Hypotenuse = 15feet
Adjacently = 10feet
According to CAH;
cos(theta) = Adjacent/Hypotenuse
cos(theta) = 10/15
cos(theta) = 2/3
theta = arccos(2/3)
theta = 48.19°
Shawn cat is looking at him at an angle of depression of 48.19°
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Answer:
(a) The probability of overbooking is 0.2135.
(b) The probability that the flight has empty seats is 0.4625.
Step-by-step explanation:
Let the random variable <em>X</em> represent the number of passengers showing up for the flight.
It is provided that a small regional carrier accepted 19 reservations for a particular flight with 17 seats.
Of the 17 seats, 14 reservations went to regular customers who will arrive for the flight.
Number of reservations = 19
Regular customers = 14
Seats available = 17 - 14 = 3
Remaining reservations, n = 19 - 14 = 5
P (A remaining passenger will arrive), <em>p</em> = 0.52
The random variable <em>X</em> thus follows a Binomial distribution with parameters <em>n</em> = 5 and <em>p</em> = 0.52.
(1)
Compute the probability of overbooking as follows:
P (Overbooking occurs) = P(More than 3 shows up for the flight)
Thus, the probability of overbooking is 0.2135.
(2)
Compute the probability that the flight has empty seats as follows:
P (The flight has empty seats) = P (Less than 3 shows up for the flight)
Thus, the probability that the flight has empty seats is 0.4625.