The volume of a cube shaped shipping container is 2744 in.³ find the edge length of the shipping container

Mathematics

1 answer:

Dima020 [189]3 years ago

7 0

Answer:

The edge length of the shipping container is 14 in.

Step-by-step explanation:

The volume enclosed by a cube is the number of cubic units that will exactly fill a cube.

To find the volume of a cube we need to recall that a cube has all edges the same length. The volume of a cube is found by multiplying the length of any edge by itself twice. Or as a formula:

$V=s^3$

where, <em>s</em> is the length of any edge of the cube.

To find the edge length of the shipping container we use the fact that the volume of a cube shaped shipping container is 2744 in³ and the above formula.

$2744=s^3\\\\s^3=2744\\\\s=\sqrt[3]{2744}\\\\s = 14\:in$

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A random sample of 9 wheels of cheese yielded the following weights in pounds has a sample mean of 20.90 and a sample variance o

Ronch [10]

Answer:

$2.002 \leq \sigma^2 \leq 11.365$

Step-by-step explanation:

1) Data given and notation

s represent the sample standard deviation

$s^2$ represent the sample variance

n=9 the sample size

Confidence=90% or 0.90

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

On this case we need to find the sample standard deviation with the following formula:

$s=sqrt{\frac{\sum_{i=1}^9 (x_i -\bar x)^2}{n-1}}
The sample variance given was [tex]s^2=3.45$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=9-1=8$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical values.