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djyliett [7]
3 years ago
8

30 points if you answer this question and please show work !

Mathematics
1 answer:
ASHA 777 [7]3 years ago
8 0
h(x)=\dfrac{f(x)}{g(x)}=\dfrac{x^2+x-20}{x+5}=\dfrac{x^2+x+4x-4x-20}{x+5}=\\\\\\=
\dfrac{x^2+5x-4x-20}{x+5}=\dfrac{x(x+5)-4(x+5)}{x+5}=\dfrac{(x+5)(x-4)}{x+5}=\\\\\\=\boxed{x-4}

We see, that g(x) is in denominator, so:

g(x)\neq0\\\\x+5\neq0\\\\\boxed{x\neq-5}

and the domain of h(x) i<span>s the set of all real numbers without x=-5.
</span>
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Answer: (20.86, 22.52)

Step-by-step explanation:

Formula to find the confidence interval for population mean :-

\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}

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By considering the given question , we have

\overline{x}= 21.69

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Using z-table, the critical z-value for 95% confidence = z* = 1.96

Then, 95% confidence interval for the amount of time spent on administrative issues will be :

21.69\pm (1.96)\dfrac{3.23}{\sqrt{58}}

=21.69\pm (1.96)\dfrac{1.7}{7.61577}

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\approx21.69\pm0.83

=(21.69-0.83,\ 21.69+0.83)=(20.86,\ 22.52)

Hence, the 95% confidence interval for the amount of time spent on administrative issues = (20.86, 22.52)

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