Using a discrete probability distribution, it is found that there is a 0.15 = 15% probability that it will take more than 9 minutes for all the customers currently in line to check out.
<h3>What is the discrete probability distribution?</h3>
Researching the problem on the internet, it is found that the distribution for the number of customers in line at the store is given by:
Hence, since each customer takes 3 minutes to check out, the probability that it will take more than 9 minutes for all the customers currently in line to check out is the probability that there are more than 3 customers, hence:
P(X > 3) = P(X = 4) + P(X = 5) = 0.10 + 0.05 = 0.15.
0.15 = 15% probability that it will take more than 9 minutes for all the customers currently in line to check out.
More can be learned about a discrete probability distribution at brainly.com/question/24855677
X < = 1 or x > 8
closed circle on 1, shaded to the left
open circle on 8, shaded to the right
Step-by-step explanation:
(1 + cos θ + sin θ) / (1 + cos θ − sin θ)
Multiply by the reciprocal:
(1 + cos θ + sin θ) / (1 + cos θ − sin θ) × (1 + cos θ + sin θ) / (1 + cos θ + sin θ)
(1 + cos θ + sin θ)² / [ (1 + cos θ − sin θ) (1 + cos θ + sin θ) ]
(1 + cos θ + sin θ)² / [ (1 + cos θ)² − sin² θ) ]
Distribute and simplify:
(1 + cos θ + sin θ)² / (1 + 2 cos θ + cos² θ − sin² θ)
[ 1 + 2 (cos θ + sin θ) + (cos θ + sin θ)² ] / (1 + 2 cos θ + cos² θ − sin² θ)
(1 + 2 cos θ + 2 sin θ + cos² θ + 2 sin θ cos θ + sin² θ) / (1 + 2 cos θ + cos² θ − sin² θ)
Use Pythagorean identity:
(2 + 2 cos θ + 2 sin θ + 2 sin θ cos θ) / (sin² θ + cos² θ + 2 cos θ + cos² θ − sin² θ)
(2 + 2 cos θ + 2 sin θ + 2 sin θ cos θ) / (2 cos² θ + 2 cos θ)
(1 + cos θ + sin θ + sin θ cos θ) / (cos² θ + cos θ)
Factor:
(1 + cos θ + sin θ (1 + cos θ)) / (cos θ (1 + cos θ))
(1 + cos θ)(1 + sin θ) / (cos θ (1 + cos θ))
(1 + sin θ) / cos θ
We know f(x)=5x+1. Plug in f(x) in the g(x) function.
We get
Distribute the 2 to 5x and 1.
Simplify to get
Now, we plug in -1 for x.
Answer:A rectangle that is not a square
Step-by-step explanation:
