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Otrada [13]
3 years ago
12

Which is the value of this expression when j = negative 2 and k = negative 1?

Mathematics
2 answers:
Minchanka [31]3 years ago
7 0

Answer:

The answer is A.

Step-by-step explanation:

I did the test, and I also solved it. Its the only logical answer.

Natalija [7]3 years ago
3 0

Answer:

Option A.

Step-by-step explanation:

It is given that

j=-2, k=-1

The given expression is

\left(\dfrac{jk^{-2}}{j^{-1}k^{-3}}\right)^3

Substitute the given values in the above expression.

\left(\dfrac{(-2)(-1)^{-2}}{(-2)^{-1}(-1)^{-3}}\right)^3

\Rightarrow \left(\dfrac{(-2)(1)}{\dfrac{1}{-2}(-1)}\right)^3

\Rightarrow \left(\dfrac{-2}{\dfrac{1}{2}}\right)^3

\Rightarrow \left(-4\right)^3

\Rightarrow -64

Therefore, the correct option is A.

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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:

The value required is  \sigma =  0.0133

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

         \frac{\mu - LSL  }{ 3 *  \sigma } =  2

So

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

=>    0.08 = 6 \sigma

=>     \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

3 0
3 years ago
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