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Naddika [18.5K]

2 years ago

7

rectangle A and B are identical. each has a perimeter of 40cm. they are put together to make a new rectangle. the perimeter of t

he new rectangle is 68cm. work out the length and width of rectangle A.

1 answer:

Doss [256]2 years ago

6 0

Answer:

6 cm by 14 cm

Step-by-step explanation:

The perimeter of the joined figure will be the sum of the perimeters of rectangles A and B, less the lengths of the sides that are joined. The two joined sides have a total length of ...

(40 cm) +(40 cm) -(68 cm) = 12 cm

Then the length of the joined sides is 6 cm. The length of the other side of the rectangle is the difference between half the perimeter and this, or ...

(40 cm)/2 -6 cm = 14 cm

The length and width of rectangles A and B are 14 cm and 6 cm. When put together, they are joined on the 6 cm side.

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Answer:

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Step-by-step explanation:

Normal distribution:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Two variables:

Means $\mu_{a}, \mu_{b}$

Standard deviations $\sigma_{a}, \sigma_{b}$

Sum:

$\mu = \mu_{a} + \mu_{b}$

$\sigma = \sqrt{\sigma_{a}^{2} + \sigma_{b}^{2}}$

In this question:

$\mu_{a} = 40, \mu_{b} = 60, \sigma_{a} = 2, \sigma_{b} = 3$

So

$\mu = \mu_{a} + \mu_{b} = 40 + 60 = 100$

$\sigma = \sqrt{\sigma_{a}^{2} + \sigma_{b}^{2}} = \sqrt{4 + 9} = 3.61$

A) What is the probability that a piece of pottery will befinished within 95 minutes?

This is the pvalue of Z when X = 95.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{95 - 100}{3.61}$

$Z = -1.39$

$Z = -1.39$ has a pvalue of 0.0823

8.23% probability that a piece of pottery will befinished within 95 minutes.

B) What is the probability that it will take longer than 110 minutes?

This is 1 subtracted by the pvalue of Z when X = 110.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{110 - 100}{3.61}$

$Z = 2.77$

$Z = 2.77$ has a pvalue of 0.9972

1 - 0.9972 = 0.0028

0.28% probability that it will take longer than 110 minutes.

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Step-by-step explanation:

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3 years ago