Answer:
Probability that this whole shipment will be accepted is 0.7324.
Step-by-step explanation:
We are given that a company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 30 components and accept the whole batch if there are fewer than 3 defectives.
The above situation can be represented through Binomial distribution;
where, n = number of trials (samples) taken = 30 components
r = number of success = fewer than 3
p = probability of success which in our question is % rate
of defects, i.e; 6%
<em>LET X = Number of defective components</em>
So, it means X ~ 
Now, Probability that this whole shipment will be accepted only when there are fewer than 3 defectives = P(X < 3)
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
= 
= 
= 0.7324
Therefore, probability that this whole shipment will be accepted is 0.7324.
Answer: The distance is decreasing
Step-by-step explanation:
Answer:
x = 1 or x = -5
Step-by-step explanation:
We are given;
- The quadratic equation, x² + 4x - 13 = -8
We are required to solve the equation using the completing square method.
To do this, we use the following steps;
Step 1: We make sure the coefficient of x² is one
x² + 4x - 13 = -8
Step 2: Combine the like terms (take the constant term to the other side)
x² + 4x - 13 = -8
x² + 4x = -8 + 13
we get
x² + 4x = 5
Step 3: We add the square of half the coefficient of x on both sides of the equation
Coefficient of x = 4
Half of coefficient of x = 2
Square of half the coefficient of x = 2² (4)
We get;
x² + 4x + (2²) = 5 + (2²)
Step 4: Put x and 2 under one square and the solve the other side of the equation.
We get
(x + 2)² = 5 + 4
(x + 2)² = 9
Step 5: Get the square root on both sides of the equation;
(x + 2)² = 9
√(x + 2)² = ±√9
(x + 2)= ±3
Therefore;
x+2 = + 3 or x + 2 = -3
Thus, x = 1 or -5
The solution of the equation is x = 1 or x = -5
No, 50 is not a perfect square. A perfect square is any number that can be divided by any number to get the quotient as the same number AND the quotient must be rational. When you divide 50 so that the quotient equals the divisor, you will get an irrational number. Therefore, 50 is not a perfect square.
