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Mashcka [7]
4 years ago
5

How do you simply 5/2(6x-7)+4/3(2+9x)

Mathematics
1 answer:
marshall27 [118]4 years ago
6 0

Answer:

27x+−89/6

Step-by-step explanation:

Let's simplify step-by-step.

5/2(6x−7)+4/3(2+9x)

Distribute:

=(5/2)(6x)+(5/2)(−7)+(4/3)(2)+(4/3)(9x)

=15x+−35/2+8/3+12x

Combine Like Terms:

=15x+−35/2+8/3+12x

=(15x+12x)+(−35/2+8/3)

=27x+−89/6

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The temperature fell 12 degrees over 4 hours. What was the average change in temperature per hour?
Artist 52 [7]

The average change is 3 degrees per hour.

To calculate the average of any data we have to divide the change by the time taken for that change.

let us suppose there is a data 4,5,6,7 and 8.

Average of the data will be the sum of data divided by the number of terms.

Average=\frac{4+5+6+7+8}{5}

            =\frac{30}{5}

            = 6

So now we will calculate the average change in temperature per hour,

Given that there is a fall of 12 degrees in 4 hours.

Average change per hour=\frac{12}{4}

                                        = 3 degrees per hour

So, the required change is 3 degrees per hour.

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3 years ago
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Bottles filled by a certain machine are supposed to contain 12 oz of liquid. In fact the fill volume is random with mean 12.01 o
Irina-Kira [14]

Answer:

a

 P(X <  12)  = 0.3660

b

  P(X <  12) = 0.1521

Step-by-step explanation:

Considering question a

From the question we are told that

   The mean is  \mu = 12.01 \ oz

    The standard deviation is  \sigma = 0.35 \  oz

 The standard error of mean is mathematically represented as

      \sigma_{x} =  \frac{\sigma}{\sqrt{n} }

=>   \sigma_{x} =  \frac{0.35}{\sqrt{144} }              

=>   \sigma_{x} =  0.02917

Generally the  probability that the mean volume of a random sample of 144 bottles is less than 12 oz is mathematically represented as

           P(X <  12) = P(\frac{X - \mu }{\sigma_{x}} < \frac{12 - 12.01 }{0.02917 }  )

\frac{X -\mu}{\sigma_{x} }  =  Z (The  \ standardized \  value\  of  \ X )

      P(X <  12) = P(Z < -0.3425  )

From the z table  the area under the normal curve to the left corresponding to   -0.3425  is

      P(X <  12) = P(Z < -0.3425  ) = 0.3660

=>  P(X <  12)  = 0.3660

Considering question a

From the question we are told that

   The mean is  \mu = 12.03 \ oz

Generally the  probability that the mean volume of a random sample of 144 bottles is less than 12 oz is mathematically represented as

           P(X <  12) = P(\frac{X - \mu }{\sigma_{x}} < \frac{12 - 12.03 }{0.02917 }  )

          P(X <  12) = P(Z < -1.0274  )

From the z table  the area under the normal curve to the left corresponding to   -1.0274   is

      P(X <  12) = P(Z < -1.0274  ) =0.1521

=>   P(X <  12) = 0.1521

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