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ioda
3 years ago
10

Consider the equation 9 – x = 5. a. Solve the equation by first adding x to both sides. b. Solve the equation by first subtracti

ng 9 from both sides. c. Which approach, (a) or (b), did you prefer? Explain.
Mathematics
1 answer:
WITCHER [35]3 years ago
3 0

Answer:

a.x=4

b.x=4

c.(b)

Step-by-step explanation:

We are given that

9-x=5

a. First we adding x on both sides we get

9-x+x=5+x

9=5+x

Now, subtract 5 on both sides we get

9-5=x

x=4

b.

We are subtracting 9 from both sides we get

9-9-x=5-9

-x=-4

x=4

We can solve equation both approach a and b

But I prefer (b) because in approach (b)

There are only 3 step in which we can get answer but in approach (a) we can get answer in 4 steps .

Hence, I prefer approach (b)

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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
Triangle xyz is similar to triangle xvw. write the congruence statements that must be true.
Lunna [17]

Answer:

∠ Y = ∠ V

∠ Z = ∠ W

\frac{XY}{XV} =\frac{YZ}{VW} =\frac{XZ}{XW}

Step-by-step explanation:

It is given that Δ XYZ is similar to Δ XVW.

Since corresponding angles of similar triangles are equal,

∠ X = ∠ X

∠ Y = ∠ V

∠ Z = ∠ W

Also, since corresponding sides of similar triangles are in proportionate,

\frac{XY}{XV} =\frac{YZ}{VW} =\frac{XZ}{XW}

7 0
3 years ago
Read 2 more answers
A can of soup contains 2 servings. Each serving has 130 calories in it. How many calories are there in the whole can?
Allisa [31]
There are 260 calories in the whole can.
to get this you multiply the calories in one serving by the amount of total servings, in this case 2.
6 0
3 years ago
Read 2 more answers
Finding a parametric description of the solution set of a linear system is the same as solving the system.Choose the correct ans
Grace [21]

Answer:

The answer is "Choice B".

Step-by-step explanation:

Please find the complete question in the attached file.

In this question, in all choices, the choice (B) is Correct because in the declaration of the statement Only when the process has had at least another answer could a candidate solution for more than just a linear model explicitly uses a parametric description that's why the given statement is true.

7 0
3 years ago
I need a bit of help on this problem
Nimfa-mama [501]

Answer: its b

Step-by-step explanation:

bc i used a calculator and it said so

4 0
3 years ago
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