Answer:
thus the probability that a part was received from supplier Z , given that is defective is 5/6 (83.33%)
Step-by-step explanation:
denoting A= a piece is defective , Bi = a piece is defective from the i-th supplier and Ci= choosing a piece from the the i-th supplier
then
P(A)= ∑ P(Bi)*P(C) with i from 1 to 3
P(A)= ∑ 5/100 * 24/100 + 10/100 * 36/100 + 6/100 * 40/100 = 9/125
from the theorem of Bayes
P(Cz/A)= P(Cz∩A)/P(A)
where
P(Cz/A) = probability of choosing a piece from Z , given that a defective part was obtained
P(Cz∩A)= probability of choosing a piece from Z that is defective = P(Bz) = 6/100
therefore
P(Cz/A)= P(Cz∩A)/P(A) = P(Bz)/P(A)= 6/100/(9/125) = 5/6 (83.33%)
thus the probability that a part was received from supplier Z , given that is defective is 5/6 (83.33%)
Answer:
The coordinates of C is (-8,1)
Step-by-step explanation:
Looking at the attached image, you'd see that, AB is 1 and BC is 1, that's because we are told that ratio of AB to AC is 1:2 meaning, AC is 2 and AB is 1. Therefore for that ratio to be satisfied BC has to be 1 so that AC would be 2.
Now let's assume the coordinates of C is
.
To get it's coordinates, we use the section formula:

Where (m,n) is the (AB, BC)
Therefore we have

This gives:

and 
From there x = -8 and y = 1
Therefore the coordinates of C is (-8, 1).
Answer:
Step-by-step explanation:
When Riko left his house, Yuto was 5.25 miles along the path.
Average speed of Riko = 0.35 miles per minute
Average speed of Yuto = 0.25 miles per minute
First we will calculate the time in which Riko will catch Yuto on the track.
Relative velocity of Riko as compared to Yuto will be = velocity of Riko - velocity of Yuto
= 0.35 - 0.25
= 0.10 miles per minute
Now we this relative velocity tells that Riko is moving and Yuto is in static position.
By the formula,
Average speed = 
0.10 = 
t = 
t = 52.5 minutes
Now we know that Rico will catch Yuto in 52.5 minutes. Before this time he will be behind Yuto.
So duration of time in which Rico is behind Yuto will be 0 ≤ t ≤ 52.5
Here time can not be less than zero because time can not be with negative notation. It will always start from 0.
Answer:
B
Step-by-step explanation:
Since the triangle is right use the sine/ tangent ratios to solve for x and y
note sin60° =
and tan60° = 
sin60° =
= 
ysin60° = 3
y ×
= 3
multiply both sides by 2 and divide by 
y v= 6
= 6
tan60° =
= 
xtan60° = 3
x ×
= 3
divide both sides by 
x = 3
= 3
The answer to the equation is X = 7