Customers arrive at a single self-serve coffee machine in a busy mall at the rate of 30 per hour, following Poisson distribution. Each customer takes exactly 72 seconds to get his or her coffee. What is the expected number of customers in line at this coffee machine

Step-by-step explanation:

The waiting line model explains that the utilization of the coffee machine or number of customers at any time is given as

ρ = (λ/μ)

λ = number of customers per hour = 30 customers per hour

μ = rate at which customers use the machine = (1 customer)/(72 seconds)

= [1 ÷ (72/3600)] customer per hour

= 1 ÷

Hope this Helps!!!

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

from the figure we get,

the x axis shows   the months and,

the y-axis shows the number of satisfied customer.

each line or each cell in upward direction (y-axis) shows 500.

the appropriate scale for the y - axis is: -

a = 2000 customers

b = 4000 customers

c = 6000 customers

d = 8000 customers

e = 10000 customers

f = 12000 customers

g = 14000 customers