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Nezavi [6.7K]
3 years ago
9

A quality engineer in a light bulb factory is planning a study to estimate the average life of a large shipment of light bulbs.

The engineer wants to estimate the average life within plus or minus 15 hours with 95 percent confidence. Assuming a process standard deviation of 100 hours, determine the sample size for this study
Mathematics
1 answer:
Firlakuza [10]3 years ago
4 0

Answer:

The required sample size is 171.

Step-by-step explanation:

Consider the provided information.

The engineer wants to estimate the average life within plus or minus 15 hours with 95 percent confidence. Assuming a process standard deviation of 100 hours,

First calculate the value of Z_{\frac{\alpha}{2}}

By using the table we get.

Z_{\frac{\alpha}{2}}=1.96

Now use the formula: N=(\frac{Z_{\frac{\alpha}{2}}\times \sigma}{E})^2

Substitute the respective values in the above formula we get.

N=(\frac{1.96\times 100}{15})^2

N=(\frac{1.96\times 100}{15})^2

N=(\frac{196}{15})^2=170.73777

N\approx171

Hence, the required sample size is 171.

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F(x) = 3x + x3
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Answer:

Please check the explanation.

Step-by-step explanation:

Given

f(x) = 3x + x³

Taking differentiate

\frac{d}{dx}\left(3x+x^3\right)

\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'

=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)

solving

\frac{d}{dx}\left(3x\right)

\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'

=3\frac{d}{dx}\left(x\right)

\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dx}\left(x\right)=1

=3\cdot \:1

=3

now solving

\frac{d}{dx}\left(x^3\right)

\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}

=3x^{3-1}

=3x^2

Thus, the expression becomes

\frac{d}{dx}\left(3x+x^3\right)=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)

                    =3+3x^2

Thus,

f'(x) = 3 + 3x²

Given that f'(x) = 15

substituting the value  f'(x) = 15 in f'(x) = 3 + 3x²

f'(x) = 3 + 3x²

15 =  3 + 3x²

switch sides

3 + 3x² = 15

3x² = 15-3

3x² = 12

Divide both sides by 3

x² = 4

\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}

x=\sqrt{4},\:x=-\sqrt{4}

x=2,\:x=-2

Thus, the value of x​ will be:

x=2,\:x=-2

5 0
3 years ago
Somebody help me please ASAP!!!!!!!!!!!!!!
mixer [17]

Answer:

V=-15

Step-by-step explanation:

What you do is you take the negative 3 and multiply it by the 5 at the top which makes -15/v

7 0
3 years ago
Read 2 more answers
Find the value of x to the nearest tenth
Bess [88]

Answer:

X = 7.24 or 7.2

Step-by-step explanation:

Tan46/1 = x/7

Cross multiply to get this outcome:

7tan(46)

Put into calculator

Then your answer will be X = 7.24 or 7.2

Hope that helps :)

7 0
3 years ago
Find the future value of $2000 invested at annual rate of 2.4% compounded quarterly for 8 years. Round your answer to hundredths
MatroZZZ [7]

Answer: $2421.95

Step-by-step explanation:

A = p(1 + r/n) ^nt

A= 2000(1+0.024/4)^4x8

A= 2421.95

3 0
4 years ago
What is the equation of the line written in general form
Vesnalui [34]

Answer:

y = -x + 2.

or

x + y - 2 = 0 (Standard form).

Step-by-step explanation:

Its slope (m) is -1 and y intercept (c) is at y = 2.

y = mx + c

So it's:

y = -1x + 2

Standard form is:

x + y - 2 = 0.

I'm not sure what you mean by General Form.

5 0
2 years ago
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