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3 years ago

Den

Mathematics

1 answer:

sergij07 [2.7K]3 years ago

5 0

Answer:

Perimeter of ABCD - Perimeter of PQRS = 4x + 2

Step-by-step explanation:

i. For rectangle ABCD;

length, l = 2x -3

width, w = 4x + 5

Perimeter of a rectangle = 2(l + w)

Perimeter of ABCD = 2((2x -3) + (4x + 5))

= 2(2x -3 + 4x + 5)

= 2(6x + 2)

Perimeter of ABCD = 12x + 4

ii. For rectangle PQRS;

length, l = x - 1

width, w = 3x + 2

Perimeter of a rectangle = 2(l + w)

Perimeter of PQRS = 2((x - 1) + (3x + 2))

= 2(x - 1 + 3x + 2)

= 2(4x + 1)

Perimeter of PQRS = 8x + 2

So that,

Perimeter of ABCD - Perimeter of PQRS = (12x + 4) - (8x + 2)

= 12x + 4 - 8x - 2

= 4x + 2

Perimeter of ABCD - Perimeter of PQRS = 4x + 2

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Answer:

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With:

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Step-by-step explanation:

For this case we know the following propoertis for the random variable X

$\mu = 83, \sigma = 27$

We select a sample size of n = 81

Part a

Since the sample size is large enough we can use the central limit distribution and the distribution for the sampel mean on this case would be:

$\bar X \sim N (\mu, \frac{\sigma}{\sqrt{n}})$

With:

$\mu_{\bar X}= 83$

$\sigma_{\bar X}=\frac{27}{\sqrt{81}}= 3$

Part b

We want this probability:

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We can use the z score formula given by:

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And if we find the z score for 89 we got:

$z= \frac{89-83}{\frac{27}{\sqrt{81}}}= 2$

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Part c

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We can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we find the z score for 75.65 we got:

$z= \frac{75.65-83}{\frac{27}{\sqrt{81}}}= -2.45$

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$z= \frac{89.3-83}{\frac{27}{\sqrt{81}}}= 2.1$

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