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2 years ago

Find the value of each variable x= y= z=

Mathematics

1 answer:

zvonat [6]2 years ago

7 0

Answer:

Step-by-step explanation:

A 45 degree angle in a right triangle produces 2 equal sides. In this case z and the perpendicular line are equal. So that's were we'll start. Then you move on to the 60 degree angle to get x and y.

Finding z

z^2 + z^2 = (24√2) Combine the left

2z^2 = 24^2 * 2 Divide both sides by 2

2z^2/2 = 24^2/2

z^2 = 24^2 Take the square root of both sides

√z^2 = √24^2

z = 24

Finding x and y

The perpendicular = 24. Because it is a 60 degree angle that's given, we can do this without a calculator.

Tan 60 = opposite over adjacent

sqrt(3) = Perpendicular / z Multiply both sides by z

z*sqrt(3) = perpendicular

The above calculation tells us the perpendicular is 24

z*sqrt(3) = 24 Divide by sqrt 3

z = 24/√3

z = 24/1.73

z = 8√3

Finding x

Use Pythagoras to determine x

Perpendicular^2 + (8√3)^2 = x^2

24^2 + 8^2*3 = x^2

576 + 192 = x^2

768 = x^2

√x^2 = √768

x = 27.71

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Step-by-step explanation:

Given that:

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4.55% are defective or 95.45% is acceptable.

sampling distribution of proportions:

sample size n=1000

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The z - score for this distribution at most 5% of the items is;

$z = \dfrac{0.05 - 0.0455}{\sqrt{\dfrac{0.0455\times 0.9545}{1000}}}$

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$z = \dfrac{0.0045}{\sqrt{4.342975 \times 10^{-5}}}$

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From the z tables

p-value = 0.7526

Thus, the probability that at most 5% of the items in a given batch will be defective = 0.7526

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p-value = P(z ≥ -15.86)

p-value = 1 - P(z < -15.86)

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