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Mathematics

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svp [43]3 years ago

5 0

Answer:

it's quite difficult

Step-by-step explanation:

I think it will...

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An article claims that 12% of trees are infested by a bark beetle. A random sample of 1,000 trees were tested for traces of the

inna [77]

Answer: 0.6812

Step-by-step explanation:

Let p be the population proportion of trees are infested by a bark beetle.

As per given: p= 12%= 0.12

Sample size : n= 1000

Number of trees affected in sample = 1000

Sample proportion of trees are infested by a bark beetle. = $\hat{p}=\dfrac{127}{1000}=0.127$

Now, the z-test statistic : $z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

So, $z=\dfrac{0.127-0.12}{\sqrt{\dfrac{0.12\times 0.88}{1000}}}$

$z=\dfrac{0.007}{\sqrt{\dfrac{0.1056}{1000}}}\\\\\\=\dfrac{0.007}{\sqrt{0.0001056}}\\\\\\=\dfrac{0.007}{0.010276}\approx0.6812$

Hence, the value of the z-test statistic = 0.6812 .

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A cube has a volume of 512 mm^3. If all sides of the cube are divided by 4, what will the resulting volume be?

pshichka [43]

$\bf \textit{volume of a cube}\\\\
V=s^3\qquad \boxed{s=\frac{s}{4}}\implies V=\left( \cfrac{s}{4} \right)^3\implies V=\cfrac{s^3}{4^3}\implies V=s^3\cdot \cfrac{1}{4^3}
\\\\\\
V=s^3\cdot \cfrac{1}{64}\impliedby \frac{1}{64}\textit{ of the original volume, if the original was 512}
\\\\\\
512\cdot \cfrac{1}{64}\implies \cfrac{512}{64}$