Answer:
I have a random question. Is The Brain JUST A BOT? He never moderates or anything...
2 answers:
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A) 436 ft
B) t = 5 sec
C) 5.60 s
Step-by-step explanation:
A)
The height of the ball at time t is given by the equation
where
is the acceleration of the ball (acceleration of gravity, downward)
+500 is the initial height of the ball, at time t = 0
Here we want to find the height of the ball after 2 seconds, so at a time of
t = 2 s
Substituting into the equation, we find:
B)
Here we want to find the time it takes for the ball to fall to a height of 100 feet above the ground, so the time t at which
h(t) = 100 ft
As stated in the text of the question, the height of the ball at time t is given by
Since
h(t) = 100, we have
And solving for t we find:
So, the correct solution is the positive one:
t = 5 sec
C)
The ball reaches the ground when the height of the ball has became zero:
The height of the ball at time t is given by
And substituting
h(t) = 0
We get
And solving the equation for t, we find the time t at which the ball reaches the ground:
So, the correct solution is the positive one:
t = 5.60 s
Answer:
(a) Explained below.
(b) 0.0294
(c) 0.0173
(d) 0.09827
(e) 0.0452
Step-by-step explanation:
The complete question is:
According to an airline, flights on a certain route are on time 80% of the time. Suppose 25 flights are randomly selected and the number of on-time flights is recorded.
(a) Explain why this is a binomial experiment.
(b) Find and interpret the probability that exactly 16 flights are on time.
(c) Find and interpret the probability that fewer than 16 flights are on time.
(d) Find and interpret the probability that at least 16 flights are on time.
(e) Find and interpret the probability that between 14 and 16 flights, inclusive, are on time.
Solution:
(a)
Let the random variable <em>X</em> be defined as the number of on-time flights.
A Binomial experiment has the following properties:
- There are a fixed number of trials (n).
- Each trial are independent of the others.
- Each trial has only two outcomes: Success and Failure
- Each trial has the same probability of success (p).
If a random variable <em>X</em> is used in an experiment and the experiment has all the above mentioned properties, then the random variable X is known as a binomial random variable.
All of these properties can be confirmed for the random variable <em>X</em>.
Thus, this is a binomial experiment.
(b)
Compute the probability that exactly 16 flights are on time as follows:
Thus, the probability that exactly 16 flights are on time is 0.0294.
(c)
Compute the probability that fewer than 16 flights are on time as follows:
Thus, the probability that fewer than 16 flights are on time is 0.0173.
(d)
Compute the probability that at least 16 flights are on time as follows:
(e)
Compute the probability that between 14 and 16 flights, inclusive, are on time as follows:
Thus, the probability that between 14 and 16 flights, inclusive, are on time is 0.0452.