A magazine provided results from a poll of 1500 adults who were asked to identify their favorite pie. among the 1500 respondent
2 answers:
The value of will be the same as the percentage of the 1500 respondents who like chocolate pie. And that percentage as per the data in the question is 12%. Therefore,
=0.12.
The value of simply is
, therefore,
.
The sample size is 1500. Therefore,
The margin of error is given as %. Therefore,
.
The value of is calculated as
=1-Confidence Level
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Answer:
D
Step-by-step explanation:
If the polynomial p(x) is divided by a polynomial of the form x+k (which accounts for all of the possible answer choices in this question), the result can be written as
p(x)/x+k = q(x) + r/x+k
where q(x) is a polynomial and r is the remainder. Since x+k is a degree-1 polynomial (meaning it only includes and no higher exponents), the remainder is a real number.
Therefore, p(x) can be rewritten as p(x) = (x+k)q(x) + r, where r is a real number.
The question states that p(3) = −2, so it must be true that
−2 = p(3) = (3+k)q(3) + r
Now we can plug in all the possible answers. If the answer is A, B, or C, r will be 0, while if the answer is D, r will be −2.
A. −2=p(3)=(3+(−5))q(3)+0
−2=(3−5)q(3)
−2=(−2)q(3)
This could be true, but only if q(3)=1
B. −2=p(3)=(3+(−2))q(3)+0
−2=(3−2)q(3)
−2=(−1)q(3)
This could be true, but only if q(3)=2
C. −2=p(3)=(3+2)q(3)+0
−2=(5)q(3)
This could be true, but only if q(3) = −2/5
D. −2=p(3)=(3+(−3))q(3)+(−2)
−2=(3−3)q(3)+(−2)
−2=(0)q(3)+(−2)
This will always be true no matter what q(3) is.
Of the answer choices, the only one that must be true about p(x) is D, that the remainder when p(x) is divided by x−3 is -2.
The final answer is D.
Answer: D. (x-6)(x-6)
Step-by-step explanation:
We have the following trinomial, which is also known as perfect square trinomial, because the first and the third term are squares:
(1)
First term:
Third term:
If we factorize this expression we have:
As we can see, the trinomial (1) has two factors:
and
Therefore, the correct option is D.