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jok3333 [9.3K]
4 years ago
6

7) Solve for w: 1/6+ w = 5/6. Simplify your answer. Please help

Mathematics
1 answer:
saw5 [17]4 years ago
3 0

Answer:

w = 2/3

Step-by-step explanation:

1. move constant to the right side and change its sign.

<h3> 1/6 + w = 5/6 </h3><h3> </h3><h3> w = 5/6 - 1/6</h3>

2. subtract the fractions

<h3> w = 5/6 - 1/6</h3>

<h2>Answer: w = 2/3</h2>

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A simple random sample of 110 analog circuits is obtained at random from an ongoing production process in which 20% of all circu
telo118 [61]

Answer:

64.56% probability that between 17 and 25 circuits in the sample are defective.

Step-by-step explanation:

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The expected value of the binomial distribution is:

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The standard deviation of the binomial distribution is:

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Normal probability distribution

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

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When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 110, p = 0.2

So

\mu = E(X) = np = 110*0.2 = 22

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{110*0.2*0.8} = 4.1952

Probability that between 17 and 25 circuits in the sample are defective.

This is the pvalue of Z when X = 25 subtrated by the pvalue of Z when X = 17. So

X = 25

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

Z = \frac{25 - 22}{4.1952}

Z = 0.715

Z = 0.715 has a pvalue of 0.7626.

X = 17

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

Z = \frac{17 - 22}{4.1952}

Z = -1.19

Z = -1.19 has a pvalue of 0.1170.

0.7626 - 0.1170 = 0.6456

64.56% probability that between 17 and 25 circuits in the sample are defective.

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4 years ago
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tankabanditka [31]

Answer:

A.

x = \frac{7\sqrt{6}{3}

y = \frac{7\sqrt{6}}{3}

Step-by-step explanation:

Reference angle = 60°

Opposite = \frac{7\sqrt{2}}{2}

Hypotenuse = x

Adjacent = y

✔️To find x, apply the trigonometric function SOH:

Sin 60° = Opp/Hyp

sin 60° = \frac{\frac{7\sqrt{2}}{2}}{x}

\frac{\sqrt{3}}{2} = \frac{\frac{7\sqrt{2}}{2}}{x} (sin 60 = √3/2)

\frac{\sqrt{3}}{2} = \frac{7\sqrt{2}}{2}*\frac{1}{x}

\frac{\sqrt{3}}{2} = \frac{7\sqrt{2}}{2x}

Cross multiply

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2\sqrt{3}*x = 14\sqrt{2}

Divide both sides by 2

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x = \frac{7\sqrt{2}}{\sqrt{3}}

Rationalize

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x = \frac{7\sqrt{6}{3}

✔️To find y, apply the trigonometric function TOA:

Tan 60° = Opp/Adjacent

Tan 60° = \frac{\frac{7\sqrt{2}}{2}}{y}

\sqrt{3} = \frac{\frac{7\sqrt{2}}{2}}{y} (tan 60 = √3)

\sqrt{3} = \frac{7\sqrt{2}}{2}*\frac{1}{y}

\sqrt{3} = \frac{7\sqrt{2}}{2y}

Cross multiply

\sqrt{3}*2y = 7\sqrt{2}

2\sqrt{3}*y = 7\sqrt{2}

Divide both sides by √3

y = \frac{7\sqrt{2}}{\sqrt{3}}

Rationalize

y = \frac{7\sqrt{2}*\sqrt{3}}{\sqrt{3}*\sqrt{3}}

y = \frac{7\sqrt{6}}{3}

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