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3 years ago

The length of a rectangle is twice the width. The perimeter is 25. The system to help find the length and width is:

Mathematics

2 answers:

svet-max [94.6K]3 years ago

8 0

9514 1404 393

Answer:

(L, W) ≈ (8.33, 4.17)

Step-by-step explanation:

Substituting for L, we have ...

2(2W) +2W = 25

6W = 25

W = 25/6 ≈ 4.17

L = 25/3 ≈ 8.33

The rounded "exact" solution is ...

(L, W) = (8.33, 4.17)

user100 [1]3 years ago

5 0

Let the width be x
Since the question mentions the length is twice the width,
let the length be 2x
The total perimeter given is 25cm and as we know, perimeter for a rectangle :
=> P = 2(Length + width)
So,

25cm = 2(2x + x)
25 = 4x + 2x
25 = 6x
25/6 = x
4.166666667 = x

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Answer:

(a) The sample size required is 43.

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Step-by-step explanation:

The (1 - α) % confidence interval for population mean is:

$CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}$

The margin of error for this interval is:

$MOE=z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}$

(a)

The information provided is:

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MOE = 72 seconds = 1.2 minutes

Confidence level = 95%

α = 5%

Compute the critical value of z for α = 5% as follows:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a z-table.

Compute the sample size required as follows:

$MOE=z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}$

$n=[\frac{z_{\alpha/2}\times \sigma}{MOE} ]^{2}$

$=[\frac{1.96\times 4}{1.2}]^{2}\\\\=42.684\\\\\approx 43$

Thus, the sample size required is 43.

(b)

The information provided is:

<em>σ</em> = 4 minutes

MOE = 1 minute

Confidence level = 95%

α = 5%

Compute the critical value of z for α = 5% as follows:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a z-table.

Compute the sample size required as follows:

$MOE=z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}$

$n=[\frac{z_{\alpha/2}\times \sigma}{MOE} ]^{2}$

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Thus, the sample size required is 62.

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