Solve the proportion 20/16=X/80 A=6.25 B=1600 C=100 D=160
1 answer:
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Answer:
The probability of one or more catastrophes in:
(1) Two mission is 0.0166.
(2) Five mission is 0.0410.
(3) Ten mission is 0.0803.
(4) Fifty mission is 0.3419.
Step-by-step explanation:
Let <em>X</em> = number of catastrophes in the missions.
The probability of a catastrophe in a mission is, P (X) = .
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> and <em>p</em>.
The probability mass function of <em>X </em>is:
In this case we need to compute the probability of 1 or more than 1 catastrophes in <em>n</em> missions.
Then the value of P (X ≥ 1) is:
P (X ≥ 1) = 1 - P (X < 1)
= 1 - P (X = 0)
(1)
Compute the compute the probability of 1 or more than 1 catastrophes in 2 missions as follows:
(2)
Compute the compute the probability of 1 or more than 1 catastrophes in 5 missions as follows:
(3)
Compute the compute the probability of 1 or more than 1 catastrophes in 10 missions as follows:
(4)
Compute the compute the probability of 1 or more than 1 catastrophes in 50 missions as follows:
Answer:
about 81 years
Step-by-step explanation:
A graphing calculator can give you the answer easily.
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You can solve the problem algebraically by putting in the given number and solving for t.
30000 = 32000/(1 +12.8e^(-.065t))
12.8e^(-.065t) = (32000/30000) -1 = 1/15
e^(-.065t) = 1/(15·12.8) = 1/192 . . . . . divide by 12.8
-0.065t = ln(1/192) ≈ -5.257 . . . . . . take the natural log
t = -5.257/-0.065 ≈ 80.88 . . . . . . . .divide by the coefficient of t
It will take about 81 years for the number of trees to reach 30,000.
