Answer:
a) We have the mean number of events is interval(5.3 events in 10 minutes), which constitutes the Poisson probability distribution.
b) 5.3
c) 5.3
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 time interval.
a. What probability distributions' properties is this?
We have the mean number of events is interval(5.3 events in 10 minutes), which constitutes the Poisson probability distribution.
b. What is the expected value of the random variable x?
It is known that the mean number of occurrences in ten minutes is 5.3.
So the mean is 
c. What is the variance of the random variable x?
In the Poisson probability distribution, the variance is the same as the mean. So the variance is 5.3.
Answer:
first option, -7 < x < 6
Step-by-step explanation:
add one to all sides
Answer: fourth option
Explanation:1) the pair x = 3 f(x) = 0, leads you to probe this:
f(3) = 0 = A [4 ^ (3 - 1) ] + C = 0
=> A [4^2] = - C
A[16] = - C
if A = 1/4
16 / 4 = 4 => C = - 4
That leads you to the function f(x) = [1/4] 4 ^( x - 1) - 4
2) Now you verify the images for that function for all the x-values of the table:
x = 2 => f(2) + [1/4] 4 ^ (2 - 1) - 4 = [1/4] 4 - 4 = 4 / 4 - 4 = 1 - 4 = - 3 => check
x = 3 => f(3) = [1/4] 4^ (3 - 1) - 4 = [1/4] 4^2 - 4 = 16 / 4 - 4 = 4 - 4 = 0 => check
x = 4 -> f(4) = [1/4] 4^ (4-1) - 4 = [1/4] 4^(3) - 4 = (4^3) / 4 - 4 = 4^2 - 4 = 16 - 4 = 12 => check.
Therefore, you have proved that the answer is the fourth option.
Answer:
B. 8.6 cm
Step-by-step explanation:
⅓*πr²h = Volume formula of a cone (V)
Volume of cone (V) = 225 cm³
diameter of cone (d) = 10 cm
radius of cone (r) = ½(10) = 5 cm
height (h) = ?
Plug in the values into the equation and solve for h
⅓ × π × 5² × h = 225
⅓ × π × 25 × h = 225
(25π × h)/3 = 225
Multiply both sides by 3
(25π × h)/3 × 3 = 225 × 3
25π × h = 675
Divide both sides by 25π
h = 675/25π
h ≈ 8.6 cm (nearest tenth)
16.99 every 30 minutes
3 hours = 180 minutes + 45 minutes
225 minutes.
225/30 = 7.5
16.99(7.5) = 127.43
