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Korolek [52]
3 years ago
7

Write an expression equivalent to 6 - 4(3 - 6m) + 12m that is the product of two factors. Show your work.

Mathematics
1 answer:
atroni [7]3 years ago
4 0

Answer:  6(6m - 1)

Step-by-step explanation:

6 - 4(3 - 6m) + 12m

= 6 -12 + 24m + 12m

= 36m - 6

= 6(6m - 1)

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4 years ago
Suppose that the quarterly sales levels among health care information systems companies are approximately normally distributed w
jok3333 [9.3K]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The sales level that is the cut-off between quarters that are considers as "failure" and those that are not is evaluated as

          y = 6.3 \ million \ dollars

Step-by-step explanation:

   From the question we are told that the

            Mean is \mu = 8 \ million \ dollars

           Standard deviation is \sigma = 1.3 \ million \ dollars

 Let Y be the random variable that denotes the sales made quarterly among health care information system

    The normal distribution for this data is mathematically represented as

                            Y ~ N (\mu = 8 , \sigma^2 = 1.69)

  From the question we are told that a quarter is consider a failure by the company if the sales level that quarter in the bottom 10% of the of all quarterly sales

            So

 The the Probability of obtaining quarterly sales level that is equal to  10% of all quarterly sale (It is not below 10%) is mathematically represented as

                    P[Y < y ] = 0.10

 This can be represented as a normal distribution in this manner

                  P [ \frac{Y- \mu}{\sigma }  < \frac{y -\mu}{\sigma} ] = 0.10

         Where  \frac{Y - \mu }{\sigma }  = Z ~ N(0 , 1)      

{This mean that this equal to the normal distribution between 0, 1  which is the generally range of every probability }

Therefor we have

                   P[Z < \frac{y- 8}{1.3} ]

The cumulative distribution function for a normal distribution of y  is mathematically  represented as

                \phi [\frac{y- 8}{1.3} ] = 0.10

This is because a cumulative distribution function of a random value Y or a distribution of Y evaluated at y is the probability that Y will take will take a value that is less or equal to y

                 \frac{y- 8}{1.3} = \phi ^{-1}(0.10)

Calculating the inverse of the cumulative distribution function value of 0.10 which is negative the  the critical value(Critical values determine what probability a particular variable will have when a sampling distribution is normal or close to normal.) of 0.01

                    \phi ^{-1}(0.10) =- [1 - \frac{0.10}{2}]

                                    =  - 1.28155

                 \frac{y - 8}{1.3}  = - 1.2816

                => y = 8 - (1.2816)(1.3)

                      y = 6.3 \ million \ dollars

                 

     

5 0
3 years ago
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