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Anastasy [175]
3 years ago
12

Lucas made a recipe that needed five-

Mathematics
1 answer:
ser-zykov [4K]3 years ago
7 0

Answer:

2/3 cup

Step-by-step explanation:

Well we see that they both have a common demonitator...6

Next we see the difference on the top of 5-1

After this we add 4 back mon top of the bottom(6)

It can be simplified from 4/6--> 2/3

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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
Baldo is paid $80 per day at his job, plus $15 per hour for every hour (h) that he works overtime. One day, his total earnings w
Flauer [41]
15h + 80 = 140

If you wanted to solve how many hours he worked:
15h + 80 = 140
15h = 60
h = 4. 
6 0
3 years ago
Read 2 more answers
How is it going to tell me the answer
Anon25 [30]
I dont know man you gotta ask a question
7 0
3 years ago
Solve for x in the equation x2-8x+41=0
Alinara [238K]

Answer:

d) 4 ± 5i

Step-by-step explanation:

Here we have to use the quadratic formula.

x = \frac{-b +/- \sqrt{b^2 - 4ac} }{2a}

In the given equation x^2 - 8x + 41 = 0, a =1, b = -8 and c = 41

Now plug in the given values in the above formula, we get

x = \frac{-(-8) +/- \sqrt{(-8)^2 - 4*1*41} }{2*1}

Simplifying the above, we get

x = \frac{8 +/- \sqrt{64 - 164} }{2}

x = \frac{8 +/- \sqrt{-100} }{2}

[√-100 = √-1 *√100 = i*10 = 10i] because the value of √-1 = i]

x = (8 ± 10i )/2

Now dividing by 2, we get

x = 4 ± 5i

The answer is d) 4 ± 5i

Hope you will understand the concept.

Thank you.

3 0
2 years ago
Read 2 more answers
Describe one way advertising has played a role in something<br> you've purchased
Bezzdna [24]

Answer:

ye has bad. he nf nv nnfcnxb xx. b DC x b x dnf znfbe xngrh cngbf

7 0
3 years ago
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