Check the picture below.
let's notice that the angle -150° has a reference angle of 30°, so any trigonometric function for either angle will be the same value, however, let's recall that the sine or y-coordinate is negative on the III Quadrant, so sin(-150°) is the same as sin(30°) BUT negative, -sin(30°).
Answer:
110°
Step-by-step explanation:
The consecutive interior angles theorem states that when two parallel lines are cut by a transversal, the pair of angles formed which lie inside the parallel lines on the same side of the transversal are known as consecutive interior angles. This consecutive interior angles are supplementary (that is add up to 180°).
Therefore:
∠4 and ∠6 are consecutive interior angles. Hence:
∠4 + ∠6 = 180° (sum of co-interior angles)
∠4 + 70 = 180
∠4 = 180 - 70
∠4 = 110°
Answer:
(a) <em>λ</em> = 2.
(b) P (X = 0) = 0.1353; P (X = 1) = 0.2706;
P (X = 2) = 0.2706; P (X = 3) = 0.1804
(c) P (Delay Problems) = 0.1431.
Step-by-step explanation:
Let <em>X</em> = number of arrivals at the drive-up teller window.
The average number of arrivals at the drive-up teller window per minute is,
<em>p</em> = 0.4 customers/ minute.
(1)
Compute the expected number of customers at the drive-up teller window in <em>n</em> = 5 minutes as follows:
Thus, the mean number of customers that will arrive in a five-minute period is <em>λ</em> = 2.
(2)
The random variable <em>X</em> follows a Poisson distribution with parameter λ = 2.
The probability mass function of <em>X</em> is:
Compute the probability of exactly 0 arrivals in 5 minutes as follows:
Compute the probability of exactly 1 arrivals in 5 minutes as follows:
Compute the probability of exactly 2 arrivals in 5 minutes as follows:
Compute the probability of exactly 3 arrivals in 5 minutes as follows:
Thus, the values are:
P (X = 0) = 0.1353
P (X = 1) = 0.2706
P (X = 2) = 0.2706
P (X = 3) = 0.1804
(3)
Delays occur in the service time if there are more than three customers arrive during any five-minute period.
Compute the probability that there are more than 3 customers as follows:
P (X > 3) = 1 - P (X ≤ 3)
Thus, the probability that delays will occur is 0.1431.