Answer:
Step-by-step explanation:
<u>We know that:</u>
<u>Then </u>
- 810° = 810*π/180 = 4.5π radians
Answer:
a) Binomial distribution, with n=20 and p=0.10.
b) P(x>1) = 0.6082
c) P(3≤X≤5) = 0.3118
d) E(X) = 2
e) σ=1.34
Step-by-step explanation:
a) As we have a constant "defective" rate for each unit, and we take a random sample of fixed size, the appropiate distribution to model this variable X is the binomial distribution.
The parameters of the binomial distribution for X are n=20 and p=0.10.
b) The probability of k defective surge protectors is calculated as:
In this case, we want to know the probability that more than one unit is defective: P(x>1). This can be calculated as:
c) We have to calculate the probability that the number of defective surge protectors is between three and five: P(3≤X≤5).
d) The expected number of defective surge protectors can be calculated from the mean of the binomial distribution:
e) The standard deviation of this binomial distribution is:
Eliminate the y’s via elimination (subtract both of the equations):
x^2 - x = 6
x^2 - x - 6 = 0
Factor the quadratic:
(x - 3)(x + 2) = 0
Set each equation equal to 0 and solve.
x - 3 = 0 , x + 2 = 0
x = 3 , x = -2
Plug in the 1st value for x into the second equation:
3 - y = -3
-y = -6
y = 6
Plug in the second value for x into the second equation:
-2 - y = -3
-y = -1
y = 1
Answer:
{(3,6)}
or
{(-2,1)}
Step-by-step explanation:
The point that partitions the segment in a ratio of 3:1 is located at :
Y = -9 + [¾ × (7-(-9)]
= -9 + (¾ × 16)
= -9 + 12
= 3
the coordinates are (2, 3)
The point that partitions the segment in a ratio of 1:3 is located at :
X = 2 + [¼×(2-2)]
= 2 + (¼×0)
= 2+0
= 2
the coordinates are (2, -5)