Let a function y represent the water level in a harbor measured in meters, and let x represent the number of hours since high ti
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Answer:
a. distance of the surveyor to the base of the building = 2051.90 ft
b. height of the building = 1384 ft
c. Angle of elevation from the surveyor to the top of the antenna = 38.31°
d. Height of antenna = 237.08 ft
Step-by-step explanation:
The picture above is a illustration of the described event.
a = the height of the flag
b = the height of the building
c = distance of the surveyor from the base of the building
the angle of elevation from the position of the surveyor on the ground to the top of the building = 34°
distance from her position to the top of the building = 2475 ft
distance from her position to the top of the flag = 2615 ft
(a) How far away from the base of the building is the surveyor located?
using the SOHCAHTOA principle
cos 34° = c/2475
c = 0.8290375726 × 2475
c = 2051.8679921
c = 2051.90 ft
(b) How tall is the building
The height of the building = b
sin 34° = opposite /hypotenuse
0.5591929035 = b/2475
b = 0.5591929035 × 2475
b = 1384.0024361
b = 1384.00 ft
(c) What is the angle of elevation from the surveyor to the top of the antenna?
let the angle = ∅
cos ∅ = adjacent/hypotenuse
cos ∅ = 2051.90/2615
cos ∅ = 0.784665392
∅ = cos-1 0.784665392
∅ = 38.310258303
∅ = 38.31°
(d) How tall is the antenna?
height of the antenna = a
sin 38.31° = opposite/hypotenuse
sin 38.31° = (a + b)/2615
sin 38.31° × 2615 = (a + b)
(a + b) = 0.6199159917 × 2615
(a + b) = 1621.0803182
(a + b) = 1621. 08 ft
Height of antenna = 1621. 08 - 1384.00 = 237.08031822 ft
Height of antenna = 237.08 ft
Answer:
0.2008 = 20.08% probability that among 150 calls received by the switchboard, there are at least two wrong numbers.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval.
The probability that a call received by a certain switchboard will be a wrong number is 0.02.
150 calls. So:
Use the Poisson distribution to approximate the probability that among 150 calls received by the switchboard, there are at least two wrong numbers.
Either there are less than two calls from wrong numbers, or there are at least two calls from wrong numbers. The sum of the probabilities of these events is 1. So
We want to find . So
In which
Then
0.2008 = 20.08% probability that among 150 calls received by the switchboard, there are at least two wrong numbers.