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Elina [12.6K]
3 years ago
8

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 110 engines

and the mean pressure was 4.6 lbs/square inch. Assume the standard deviation is known to be 0.8. If the valve was designed to produce a mean pressure of 4.5 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications?
Mathematics
1 answer:
slega [8]3 years ago
7 0

Answer: NO.

Step-by-step explanation:

As per given , we have to test the hypothesis.

H_0:\mu=4.5\\\\ H_a:\mu\neq4.5

∵ H_a is two-tailed , so our test is a two-tailed test.

Also, the standard deviation is known to be 0.8 , so we use z-test.

Test statistic:z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}

, where \overline{x} = Sample mean

\mu = population mean

\sigma = Population standard deviation

n= Sample size

Put  \overline{x}=4.6

\mu=4.5

\sigma=0.8

n=  110 , we get

z=\dfrac{4.6-4.5}{\dfrac{0.8}{\sqrt{110}}}\approx1.31

P-value for two tailed test = 2P(Z>|z|)

= 2P(Z>|1.31|) = 2(1-P(Z<1.31))   [∵ P(Z>z)=1-P(Z<z)]

=2(1- 0.9049)  [By z-table]

=0.1902

Decision : ∵ P-value (0.1902) > Significance level (0.02).

It means we do not reject the null hypothesis.

[When P-values < Significance level then we reject the null hypothesis.]

Conclusion : We do not have sufficient evidence at the 0.02 level that the valve does not perform to the specifications.

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My name is Ann [436]

Answer:

  • 1. 2x + 23 = 30
  • 2. 3x + 19.5 = 30
  • 3. (10x - 20)/ 5 = 3

Explanation:

Work backward:

1. 2x + 23 = 30

Start:

  • x = 3.5

Multiply the equation by 2:

  • 2x = 2 (3.5)
  • 2x = 7

Subtract 30 from both sides

  • 2x - 30 = 7 - 30
  • 2x - 30 = -23

Add 23 and 30 to both sides:

  • 2x + 23 = 30

2. 3x + 19.5 = 30

Start:

  • x = 3.5

Add 6.5 to both sides:

  • x + 6.5 = 10

Multiply by 3:

  • 3(x + 6.5) = 30

Distributive property:

  • 3x + 19.5 = 30

3. (10x - 20)/ 5 = 3

Start:

  • x=3.5

Multiply by 10:

  • 10x = 35

Subtract 20:

  • 10x - 20 = 15

Divide by 5:

  • (10x - 20)/ 5 = 15/5

  • (10x - 20) / 5 = 3
3 0
3 years ago
*50 POINTS -- FRESHMEN ~ ALGEBRA I *
aniked [119]

Step-by-step explanation:

so we know X= Numbers of Large boxes and Y= Numbers of Small boxes

And we know the large boxes weigh <em>7</em><em>5</em><em><u> </u></em><em><u>pounds</u></em> and the small boxes weigh <em>4</em><em>0</em><em> </em><em><u>pounds</u></em>

So I would have to say the the same except you have to flip the inequality sign like this:

75x + 40y

\geqslant  \\

200

And if that doesnt somehow work and the question is wording it wrong then

My guess for why its wrong us because its not in slope intercept form Although you still can solve for either varible ( x or y) using standard form also.

So to get from standard form to Slope intercept form (y=mx+b) these are the steps:

Ax+by=C

75x + 40y ≤ 200

Turn it into a linear equation.

75x+ 40y =200

In order to go from one form to another, all you have to do is change the order of the given numbers. First you want to move the Ax to the opposite side of the equation, by either adding or subtracting it. At this point your equation will be set up By = -Ax + C. Then you want to divide the B from the By and the rest of the equation. Therefore you will have y = - Ax/B + C/B. This is the same thing as the slope-intercept form, just a few of the letters are different.

40y=-75x+200 first subtract 75x

y=−1.875×+5 then dived every varible (everything) by 40. and you have your Linear eqaution.

And your second question would be <em><u>A</u></em><em><u>.</u></em><em><u> </u></em><em><u>>The number of boxes must be a whole number.</u></em><em><u> </u></em>

Because you cannot split boxes in half or in any quarter in a real life scenario.

4 0
3 years ago
Jacob is a plumber. Due to increased material costs, he puts all his prices up by 7%. He now chargers R320 per hour for her serv
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Answer:

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Step-by-step explanation:

Let

x = charge before he put his prices up

New charge = R320

Percentage increase in price = 7%

x + 7% of x = 320

x + 0.07 * x = 320

x + 0.07x = 320

1.07x = 320

x = 320/1.07

x = 299.06542056074

Approximately

x = R290.1

Charge before he put his prices up = R290.1

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RUDIKE [14]

Answer:

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add all terms and set sum equal to 360

the 'hint' of (n-2)180 determines how many degrees there are inside the polygon; if 'n' equals the number of sides and the polygon has 4 sides then sum of interior angles is (4-2)180 or 2x180 which is 360

x + 10 + 3x + x + 2x = 360

combine like terms to get:  7x + 10 = 360

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                                              x = 50

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Answer:

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Step-by-step explanation:

4 0
3 years ago
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