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Nikitich [7]
3 years ago
12

Please help 6.Simplify and put in standard form: (2x5+x3−3x4−x+8)−(7 x 5+2x4−12+6x−5 x 3+x2)

Mathematics
1 answer:
Oxana [17]3 years ago
6 0
We are given this:
(2 x^{5} + x^{3}-3 x^{4} -x+8)-(7 x^{5} +2 x^{4} - 12+6x-5 x^{3} + x^{2} ) 


First step is to get rid of brackets. There is no sign in front of first brackets, so we do not change the sign. In front of second brackets there is negative sign so we need to change sign for each term inside of those brackets.
2 x^{5} + x^{3}-3 x^{4} -x+8-7 x^{5} -2 x^{4} + 12-6x+5 x^{3} - x^{2}

Next step is to group terms with same exponent in descending order.
2 x^{5} -7 x^{5} -3 x^{4}-2 x^{4}+ x^{3} +5 x^{3}- x^{2}-x-6x+8 + 12

Now we add or substract terms with same exponent.

-5 x^{5} -5 x^{4}+ 6x^{3}- x^{2}-7x+20

Standard form means ordering terms in a descending order of an exponent.
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A lathe is set to cut bars of steel into lengths of 6 cm. The lathe is considered to be in perfect adjustment if the average len
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Answer:

t=\frac{5.97-6}{\frac{0.4}{\sqrt{93}}}=-0.723    

E. -0.723

df=n-1=93-1=92  

p_v =2*P(t_{(92)}  

Since the p value is very high we don't have enough evidence to conclude that the true mean for the lengths is different from 6 cm.

Step-by-step explanation:

Information provided

\bar X=5.97 represent the sample mean for the length

s=0.4 represent the sample standard deviation

n=93 sample size  

\mu_o =6 represent the value that we want to test

\alpha=0.05 represent the significance level

t would represent the statistic  

p_v represent the p value for the test

System of hypothesis

We need to conduct a hypothesis in order to check if the lathe is in perfect adjustment (6cm), then the system of hypothesis would be:  

Null hypothesis:\mu = 6  

Alternative hypothesis:\mu \neq 6  

since we don't know the population deviation the statistic is:

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (1)  

Replacing in formula (1) we got:

t=\frac{5.97-6}{\frac{0.4}{\sqrt{93}}}=-0.723    

E. -0.723

P value

The degrees of freedom are given by:

df=n-1=93-1=92  

Since is a two tailed test the p value would be:  

p_v =2*P(t_{(92)}  

Since the p value is very high we don't have enough evidence to conclude that the true mean for the lengths is different from 6 cm.

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Answer:

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Step-by-step explanation:

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