For this case we have the following expression:
We apply distributive property, which by definition establishes that:
So:
Answer:
What is the solution for x^2 +14x +15
2 answers:
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Answer: An integer added to an integer is an integer, this statement is always true. A polynomial subtracted from a polynomial is a polynomial, this statement is always true. A polynomial divided by a polynomial is a polynomial, this statement is sometimes true. A polynomial multiplied by a polynomial is a polynomial, this statement is always true.
Explanation:
1)
The closure property of integer states that the addition, subtraction and multiplication is integers is always an integer.
If , then a+b\in Z.
Therefore, an integer added to an integer is an integer, this statement is always true.
2)
A polynomial is in the form of,
Where are constant coefficient.
When we subtract the two polynomial then the resultant is also a polynomial form.
Therefore, a polynomial subtracted from a polynomial is a polynomial, this statement is always true.
3)
If a polynomial divided by a polynomial then it may or may not be a polynomial.
If the degree of numerator polynomial is higher than the degree of denominator polynomial then it may be a polynomial.
For example:
Then , which a polynomial.
If the degree of numerator polynomial is less than the degree of denominator polynomial then it is a rational function.
For example:
Then , which a not a polynomial.
Therefore, a polynomial divided by a polynomial is a polynomial, this statement is sometimes true.
4)
As we know a polynomial is in the form of,
Where are constant coefficient.
When we multiply the two polynomial, the degree of the resultand function is addition of degree of both polyminals and the resultant is also a polynomial form.
Therefore, a polynomial subtracted from a polynomial is a polynomial, this statement is always true.
Answer:
(a) 0.09
(b) 0.06
(c) 0.0018
(d) 0.9118
(e) 0.03
Step-by-step explanation:
Let <em>A</em> = boards have solder defects and <em>B</em> = boards have surface defects.
The proportion of boards having solder defects is, P (A) = 0.06.
The proportion of boards having surface-finish defects is, P (B) = 0.03.
It is provided that the events A and B are independent, i.e.
(a)
Compute the probability that either a solder defect or a surface-finish defect or both are found as follows:
= P (A or B) + P (A and B)
Thus, the probability that either a solder defect or a surface-finish defect or both are found is 0.09.
(b)
The probability that a solder defect is found is 0.06.
(c)
The probability that both defect are found is:
Thus, the probability that both defect are found is 0.0018.
(d)
The probability that none of the defect is found is:
Thus, the probability that none of the defect is found is 0.9118.
(e)
The probability that the defect found is a surface finish is 0.03.