What is the solution to this inequality? (x | x < 7)
1 answer:
Answer: The answer is at the bottom.
Step-by-step explanation:
Write
x
|
x
|
<
7
as a piecewise.
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{
x
2
<
7
x
≥
0
−
x
2
<
7
x
<
0
Solve
x
2
<
7
when
x
≥
0
.
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0
≤
x
<
√
7
Solve
−
x
2
<
7
when
x
<
0
.
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x
<
0
Find the union of the solutions.
x
<
√
7
The result can be shown in multiple forms.
Inequality Form:
x
<
√
7
Interval Notation:
(
−
∞
,
√
7
)
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Answer:
And replacing we got:
Step-by-step explanation:
For this case we have the following info given:
represent the mean
represent the deviation
We select a sample size of n=100. This sample is >30 so then we can use the central limit theorem. And we want to find the distribution for the sample mean and we know that the distribution is given by:
And replacing we got:
Since , by the remainder theorem this means that <em>x</em> - 6 divides <em>f(x)</em> exactly. This means there are constants <em>a</em>, <em>b</em>, and <em>c</em> such that
Multiplying both sides by <em>x</em> - 6 gives
Then <em>a</em>, <em>b</em>, <em>c</em> satisfy
and solving this system gives <em>a</em> = 2, <em>b</em> = -7, and <em>c</em> = 3.
So, we have
The quadratic term can be factored as
which leaves us with
so that the zeros of <em>f(x)</em> are 6, 1/2, and 3.