34.04 as a mixed number
1 answer:
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Answer:
Probability that at least one of them suffers from arachnophobia is 0.5160.
Step-by-step explanation:
We are given that a 2005 survey found that 7% of teenagers (ages 13 to 17) suffer from an extreme fear of spiders (arachnophobia).
Also, At a summer camp there are 10 teenagers sleeping in each tent.
Firstly, the binomial probability is given by;
where, n = number of trials(teenagers) taken = 10
r = number of successes = at least one
p = probability of success and success in our question is % of
the teenagers suffering from arachnophobia, i.e. 7%.
Let X = Number of teenagers suffering from arachnophobia
So, X ~
So, probability that at least one of them suffers from arachnophobia
= P(X >= 1) = 1 - probability that none of them suffers from arachnophobia
= 1 - P(X = 0) = 1 -
= 1 - (1 * 1 * ) = 1 - 0.484 = 0.5160 .
Therefore, Probability that at least one of them suffers from arachnophobia is 0.5160 .
Answer: P(t) = 1.25.sin(.t) + 5.65
Step-by-step explanation: A motion repeating itself in a fixed time period is a periodic motion and can be modeled by the functions:
y = A.sin(B.t - C) + D or y = Acos(B.t - C) + D
where:
A is amplitude A=|A|
B is related to the period by: T =
C is the phase shift or horizontal shift:
D is the vertical shift
In this question, the motion of Pluto is modeled by a sine function and doesn't have phase shift, C = 0.
<u>Amplitude</u>:
a =
At t=0, Pluto is the farthest from the sun, a distance 6.9 billions km away. At t=66, it is closest to the star, P(66) = 4.4 billions km. Then:
a =
a = 1.25
<u>b</u>
A time period for Pluto is T=66 years:
66 =
b =
<u>Vertical</u> <u>Shift</u>
It can be calculated as:
d =
d =
d = 5.65
Knowing a, b and d, substitute in the equivalent positions and find P(t).
P(t) = a.sin(b.t) + d
P(t) = 1.25.sin(.t) + 5.65
The Pluto's distance from the sun as a function of time is
P(t) = 1.25.sin(.t) + 5.65