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3 years ago

11

-3r + 18 = 15r please help!!

2 answers:

Luba_88 [7]3 years ago

8 0

Answer:

r = 1

Step-by-step explanation:

Step 1: Write equation

-3r + 18 = 15r

Step 2: Solve for <em>r</em>

Add 3r to both sides: 18 = 18r
Divide both sides by 18: 1 = r
Rewrite: r = 1

Step 3: Check

<em>Plug in r to verify it's a solution.</em>

-3(1) + 18 = 15(1)

-3 + 18 = 15

15 = 15

VLD [36.1K]3 years ago

7 0

Step-by-step explanation:

- 3r - 15r = -18 .... Moved variables to one side and constants to the other

- 18r = - 18 ..... Simplified

r = 1 ..... Divided to isolate the r

Check:

Plug in 1 for r

-3(1) +18 = 15(1)

- 3+18 = 15

15 = 15 .... Therefore 1 is correct

Answer is 1

Hope this helps!

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Complete Question

A milling process has an upper specification of 1.68 millimeters and a lower specification of 1.52 millimeters. A sample of parts had a mean of 1.6 millimeters with a standard deviation of 0.03 millimeters. what standard deviation will be needed to achieve a process capability index f 2.0?

Answer:

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Step-by-step explanation:

From the question we are told that

The upper specification is $USL = 1.68 \ mm$

The lower specification is $LSL = 1.52 \ mm$

The sample mean is $\mu = 1.6 \ mm$

The standard deviation is $\sigma = 0.03 \ mm$

Generally the capability index in mathematically represented as

$Cpk = min[ \frac{USL - \mu }{ 3 * \sigma } , \frac{\mu - LSL }{ 3 * \sigma } ]$

Now what min means is that the value of CPk is the minimum between the value is the bracket

substituting value given in the question

$Cpk = min[ \frac{1.68 - 1.6 }{ 3 * 0.03 } , \frac{1.60 - 1.52 }{ 3 * 0.03} ]$

=> $Cpk = min[ 0.88 , 0.88 ]$

So

$Cpk = 0.88$

Now from the question we are asked to evaluated the value of standard deviation that will produce a capability index of 2

Now let assuming that

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So

$\frac{ 1.60 - 1.52 }{ 3 * \sigma } = 2$

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=> $\sigma = 0.0133$

So

$\frac{ 1.68 - 1.60 }{ 3 * 0.0133 }$

=> $2$

Hence

$Cpk = min[ 2, 2 ]$

So

$Cpk = 2$

So $\sigma = 0.0133$ is the value of standard deviation required

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Step-by-step explanation:

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