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WARRIOR [948]
3 years ago
11

a horticulturalist is building a fence around a rectangular garden using the side of a building for one side of the enclosure. s

he has 81 feet of fencing. what should the dimensions of the enclosre be so that she can maxmize the gardens area?
Mathematics
1 answer:
Harman [31]3 years ago
5 0
The garden area is maximum when the enclosure is a square.
If a is the length of the side of the square then the length of the building is also a.
The perimeter length is 4a made up of 81+a feet, so 81+a=4a and 3a=81 making a=27 feet.
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Two different samples will be taken from the same population of test scores where the population mean and standard deviation are
Alenkinab [10]

Answer:

The sample consisting of 64 data values would give a greater precision.

Step-by-step explanation:

The width of a (1 - <em>α</em>)% confidence interval for population mean μ is:

\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{n}}

So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (<em>n</em>).

That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.

Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.

The two sample sizes are:

<em>n</em>₁ = 25

<em>n</em>₂ = 64

The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.

Width for n = 25:

\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{25}}=\frac{1}{5}\cdot [2\cdot z_{\alpha/2}\cdot \sigma]        

Width for n = 64:

\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{64}}=\frac{1}{8}\cdot [2\cdot z_{\alpha/2}\cdot \sigma]

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Step-by-step explanation:

you can use the rule of three to answer this question, the data we have is:

inches      feet

     1      →   4 1/2

  2 1/4    →   x

tha last table just indicates what the problem tells us, that one inch is equal to 4 1/2 feet and we want to know how much in feet the 2 1/4 inches are.

For this we multiply the cross quantities:

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