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bezimeni [28]
4 years ago
10

Solve the equation exactly in the complex number system. x^3+4x^2+9x+36=0

Mathematics
1 answer:
daser333 [38]4 years ago
5 0
Factor by grouping.
  0 = (x^3 +4x^2) +(9x +36) = x^2(x+4) +9(x+4) = (x^2+9)(x+4)

The first factor is the difference of squares (in complex numbers), so the form for factoring that can be used:
  a^2 - b^2 = (a -b)(a +b)
Here, a=x, b=3i.

Then the factorization in complex numbers is
  0 = (x -3i)(x +3i)(x +4)
Solutions are the values of x that make these factors be zero.

  x = -4, -3i, 3i
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z=\frac{0.462 -0.35}{\sqrt{\frac{0.35(1-0.35)}{78}}}=2.074  

Now we can calculate the p value with this probability:

p_v =P(z>2.074)=0.019  

If we use a significance level os 0.05 we see that the p value is lower than the significance level so then we can conclude that the true proportion of students with jobs is higher than 0.35 for this case. If we decrease the significance level to 1% the result changes otherwise not.

Step-by-step explanation:

Information given

n=78 represent the random sample taken

X=36 represent the students with jobs

\hat p=\frac{36}{78}=0.462 estimated proportion of students with jobs

p_o=0.35 is the value that we want to test

z would represent the statistic

p_v represent the p value

Hypothesis to test

We want to test if the proportion of students with jobs is higher than 0.35, the system of hypothesis are:  

Null hypothesis:p \leq 0.35  

Alternative hypothesis:p > 0.35  

The statistic is given by:

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

Replacing the info we got:

z=\frac{0.462 -0.35}{\sqrt{\frac{0.35(1-0.35)}{78}}}=2.074  

Now we can calculate the p value with this probability:

p_v =P(z>2.074)=0.019  

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