Of all the weld failures in a certain assembly, 85% of them occur in the weld metal itself. Asample of 10 weld failures is exami
1 answer:
Answer:
(a) The probability is 0.95
(b) The probability is 0
(c) The mean is 1.5 base metal failures and the standard deviation is 1.1292 base metal failures
Step-by-step explanation:
This experiment follows a Binomial distribution in which we have n identical and independent events with two possibles results: success and failure. Then, the probability that x of the n events are success is given by:
Where p is the probability of success. Additionally, nCx is calculated as:
So, in this case we have 10 weld failures with a probability 0.85 that it is a weld metal failure and a probability of 0.15 that it is a base metal failure. Then, we are going to call success if the fail is in the base metal so p is equal to 0.15 and n is equal to 10.
(a) The probability that fewer than four of them are base metal failure is the sum of probabilities that 0, 1, 2 and 3 of the 10 weld failures are base metal failures. This is:
P = P(0) + P(1) + P(2) + P(3)
P = 0.1969 + 0.3474 + 0.2759 + 0.1298
P = 0.95
(b) The probability that at least nine of them are base metal failures is the sum of probabilities that 9 and 10 of the 10 weld failures are base metal failures. This is:
P = P(9) + P(10)
P ≈ 0
(c) The mean E(x) and standard deviation S(x) for variables that follows a Binomial distributions are:
Then, the values of the mean and standard deviation of the number of base metal failures are:
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Answer:
Step-by-step explanation:
We have a curve (an ellipse) written as the system of equations
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And we want to calculate the tangent at the point (3,4,9).
The idea in this problem is to consider two variables as functions of the third. Usually we consider and
as functions of
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Recall that the parametric equation of a line has the form
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where is a point on the line (in this particular case is (3,4,9)) and
is the direction vector of the line. In this case, the direction vector of the line is the tangent vector of the ellipse at the point (3,4,9).
Now, if we have the parametric equation of a curve its tangent line will have direction vector
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, we must obtain the tangent vector
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So, let us write the system as
.
Then, taking implicit derivatives:
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Now we substitute the values and
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where the unknowns are and
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The system is
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and its solutions are
and
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Then, the direction vector of the tangent is
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Finally, the tangent line has parametric equation
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Answer:
See explanation
Step-by-step explanation:
1. Draw the dotted line y=-x. This line must be dotted, because the inequality y<-x is with sign < (without notion "or equal to"). Then shade the region that contains all values of y that are less than -x (bottom part that is shaded in red on the attached diagram).
2. Draw the solid line y=x-2. This line must be solid, because the inequality y≤x-2 is with sign ≤ (with notion "or equal to"). Then shade the region that contains all values of y that are less or equal to x-2 (bottom part that is shaded in blue on the attached diagram).
3. Their common part (region that is shaded in both red and blue colors) represents both inequalities.
