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arsen [322]
3 years ago
7

Show the work please

Mathematics
1 answer:
Citrus2011 [14]3 years ago
5 0

Answer:

6/5

Step-by-step explanation:

-6(1 - x) + x < - (3 - 2x) + 3

At first, we multiply the first bracket on the left side by - 6.

-6 + 6x + x < - (3 - 2x) + 3

Then, on the right side, we will break the brackets.

-6 + 6x + x < - 3 + 2x + 3

Now we use addand subtract rule,

-6 + 7x < 2x

or, -6 < 2x - 7x

or, - 6 < - 5x

Now we divide both the side by -5. It will reverse the inequality.

or, [-6 ÷ (-5)] > [(-5x ÷ (-5)]

or, (6/5) > x

As we interchange the side, the inequality again reverse.

x < (6/5)

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The tensile strength of stainless steel produced by a plant has been stable for a long time with a mean of 72 kg/mm2 and a stand
Elanso [62]

Answer:

95% confidence interval for the mean of tensile strength after the machine was adjusted is [73.68 kg/mm2 , 74.88 kg/mm2].

Yes, this data suggest that the tensile strength was changed after the adjustment.

Step-by-step explanation:

We are given that the tensile strength of stainless steel produced by a plant has been stable for a long time with a mean of 72 kg/mm 2 and a standard deviation of 2.15.

A machine was recently adjusted and a sample of 50 items were taken to determine if the mean tensile strength has changed. The mean of this sample is 74.28. Assume that the standard deviation did not change because of the adjustment to the machine.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

                         P.Q. = \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean strength of 50 items = 74.28

            \sigma = population standard deviation = 2.15

            n = sample of items = 50

            \mu = population mean tensile strength after machine was adjusted

<em>Here for constructing 95% confidence interval we have used One-sample z test statistics as we know about population standard deviation.</em>

So, 95% confidence interval for the population mean, \mu is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level of

                                                  significance are -1.96 & 1.96}  

P(-1.96 < \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < 1.96) = 0.95

P( -1.96 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X-\mu} < 1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

P( \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

<u><em>95% confidence interval for</em></u> \mu = [ \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } , \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ]

                 = [ 74.28-1.96 \times {\frac{2.15}{\sqrt{50} } } , 74.28+1.96 \times {\frac{2.15}{\sqrt{50} } } ]

                 = [73.68 kg/mm2 , 74.88 kg/mm2]

Therefore, 95% confidence interval for the mean of tensile strength after the machine was adjusted is [73.68 kg/mm2 , 74.88 kg/mm2].

<em>Yes, this data suggest that the tensile strength was changed after the adjustment as earlier the mean tensile strength was 72 kg/mm2 and now the mean strength lies between 73.68 kg/mm2 and 74.88 kg/mm2 after adjustment.</em>

8 0
3 years ago
Help me with this question please!
Amiraneli [1.4K]

Answer:

84 in²

Step-by-step explanation:

12+9=21

21x0.5=10.5

10.5x8=84

7 0
3 years ago
A 12 ounce soda costs $1.25 in the vending machine. At this rate, how much would a 32 ounce soda cost
pochemuha

Answer:

3.75

Step-by-step explanation:

1.25 times 3

5 0
3 years ago
Read 2 more answers
There are 30 students in Mrs. Woodward’s class, and 1/5 of the class has their own cell phone. Of this group of students, 1/2 of
olga_2 [115]

Answer:

3 students

Step-by-step explanation:

There are 30 students in Mrs. Woodward’s class.

\dfrac{1}{5} of the class has their own cell phone, so

\dfrac{1}{5}\cdot 30=\dfrac{1}{5}\cdot \dfrac{30}{1}=6

students have their own cell phones.

\dfrac{1}{2} of those 6 students are allowed to use social media. So,

\dfrac{1}{2}\cdot 6=\dfrac{1}{2}\cdot \dfrac{6}{1}=3

students are allowed to use social media.

3 0
3 years ago
Which is the equation of the parabola?<br><br> will mark brainlyest if correct
luda_lava [24]

Answer:

2

Step-by-step explanation:

I think :)

7 0
2 years ago
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