Answer:
the distance of the Bird (B) from the plane (P) is = 10779 ft
Step-by-step explanation:
From the given information:
a diagrammatic representation is attached below for better understanding and solution to the question.
From the diagram;
Let the Bird (B) be represent as A
The plane (P) be represented by B
The observer be represented by O
and the tower T be represented by C
we will see that:
![\overline {AB} \ \| \ \overline {OC}](https://tex.z-dn.net/?f=%5Coverline%20%7BAB%7D%20%20%5C%20%5C%7C%20%5C%20%5Coverline%20%7BOC%7D)
Also;
![\angle ABO = \angle BOC = 33^0](https://tex.z-dn.net/?f=%5Cangle%20ABO%20%3D%20%5Cangle%20BOC%20%3D%2033%5E0)
AO = BC = 7000
Let consider the trigonometry of triangle BAO
tan θ = opposite/adjacent
tan 33° = 7000/x
0.6494 = 7000/x
x = 7000/0.6494
x = 10779.18
x = 10779 ft ( to the nearest whole number)
Thus; the distance of the Bird (B) from the plane (P) is = 10779 ft
200=35.27t
Divide 35.72 on both sides
t=<span>5.670542</span>
Answer:
0.1971 ( approx )
Step-by-step explanation:
Let X represents the event of weighing more than 20 pounds,
Since, the binomial distribution formula is,
![P(x)=^nC_r p^r q^{n-r}](https://tex.z-dn.net/?f=P%28x%29%3D%5EnC_r%20p%5Er%20q%5E%7Bn-r%7D)
Where, ![^nC_r=\frac{n!}{r!(n-r)!}](https://tex.z-dn.net/?f=%5EnC_r%3D%5Cfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D)
Given,
The probability of weighing more than 20 pounds, p = 25% = 0.25,
⇒ The probability of not weighing more than 20 pounds, q = 1-p = 0.75
Total number of samples, n = 16,
Hence, the probability that fewer than 3 weigh more than 20 pounds,
![P(X](https://tex.z-dn.net/?f=P%28X%3C3%29%20%3D%20P%28X%3D0%29%2BP%28X%3D1%29%2BP%28X%3D2%29)
![=^{16}C_0 (0.25)^0 (0.75)^{16-0}+^{16}C_1 (0.25)^1 (0.75)^{16-1}+^{16}C_2 (0.25)^2 (0.75)^{16-2}](https://tex.z-dn.net/?f=%3D%5E%7B16%7DC_0%20%280.25%29%5E0%20%280.75%29%5E%7B16-0%7D%2B%5E%7B16%7DC_1%20%280.25%29%5E1%20%280.75%29%5E%7B16-1%7D%2B%5E%7B16%7DC_2%20%280.25%29%5E2%20%280.75%29%5E%7B16-2%7D)
![=(0.75)^{16}+16(0.25)(0.75)^{15}+120(0.25)^2(0.75)^{14}](https://tex.z-dn.net/?f=%3D%280.75%29%5E%7B16%7D%2B16%280.25%29%280.75%29%5E%7B15%7D%2B120%280.25%29%5E2%280.75%29%5E%7B14%7D)
![=0.1971110499](https://tex.z-dn.net/?f=%3D0.1971110499)
![\approx 0.1971](https://tex.z-dn.net/?f=%5Capprox%200.1971)