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Maslowich
3 years ago
5

What is the following quotient? StartFraction RootIndex 3 StartRoot 60 EndRoot Over RootIndex 3 StartRoot 20 EndRoot EndFraction

Mathematics
2 answers:
FrozenT [24]3 years ago
6 0

Answer:

\sqrt[3]{3}

Step-by-step explanation:

We are required to simplify the quotient: \dfrac{\sqrt[3]{60} }{\sqrt[3]{20}}

Since the <u>numerator and denominator both have the same root index</u>, we can therefore say:

\dfrac{\sqrt[3]{60} }{\sqrt[3]{20}} =\sqrt[3]{\dfrac{60} {20}}

=\sqrt[3]{3}

The simplified form of the given quotient is \sqrt[3]{3}.

Novosadov [1.4K]3 years ago
5 0

Answer:

A

Step-by-step explanation:

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Find and interpret a 95% confidence interval to estimate the average number of bolts per box for all boxes in the population. Ro
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Complete Question

The complete question is shown on the first uploaded image

Answer:

The 95% confidence interval is  49.85    < \mu < 54.15

This means that there is 95% chance that the true population mean is within this interval

Step-by-step explanation:

From the question we are told that

    The  sample size is n = 30  

    The sample mean is  \= x  =  52

    The population standard deviation is  \sigma =  6

Given that the confidence level is 95% then the level of confidence is evaluate as

             \alpha  =  100 -  95

            \alpha  =  5\%

            \alpha  =  0.05

Next we obtain the critical value of  \frac{\alpha }{2} from the normal distribution table , the values is

                 Z_{\frac{\alpha }{2} } =  1.96

Generally the margin of error is mathematically represented as

           E =  Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }

substituting values

            E =  1.96  *  \frac{ 6 }{\sqrt{30} }

           E =  2.147

The  95% confidence interval is mathematically represented as

          \= x  - E  < \mu <  \= x  + E

substituting values

         52   - 2.147   < \mu <  52   +   2.147

         49.85    < \mu < 54.15

       

     

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