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3 years ago

13. A square based cuboid has a width of 4cm. If the volume of the cuboid is 400 cubic

Mathematics

1 answer:

dsp733 years ago

4 0

Answer:

216 cm²

Step-by-step explanation:

Applying,

V = lwh..................... Equation 1

Where V = volume of the cubiod, l = length of the base, width of the base, h = heigth of the cubiod.

From the question,

Since the base of the cubiod is squared,

Therefore,

w = l = 4 cm, V = 400 cm³

Substitute these values into equation 1

400 = 4×4×h

h = 400/(4×4)

h = 25 cm

A = lw+lh+wh.................. Equation 1

Where A = surface area of the cuboid.

Given: l = 4 cm. w = 4 cm, h = 25 cm

Substitute these values into equation 1

A = (4×4)+(4×25)+(4×25)

A = 16+100+100

A = 216 cm²

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Lady bird [3.3K]

Answer:

$10.08-1.64\frac{0.1}{\sqrt{6}}=10.013$

$10.08+1.64\frac{0.1}{\sqrt{6}}=10.147$

So on this case the 90% confidence interval would be given by (10.013;10.147)

Step-by-step explanation:

Previous concepts

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 means 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.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

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$\sigma =0.1$ represent the population standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=10.08$

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 tabel to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$

Now we have everything in order to replace into formula (1):

$10.08-1.64\frac{0.1}{\sqrt{6}}=10.013$

$10.08+1.64\frac{0.1}{\sqrt{6}}=10.147$

So on this case the 90% confidence interval would be given by (10.013;10.147)

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Step-by-step explanation:

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------------------

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