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tensa zangetsu [6.8K]
3 years ago
12

Claire Judice

Mathematics
1 answer:
Julli [10]3 years ago
4 0

Answer:

The values of 'x' are -1.2, 0, 0, -4i or 4i.

Step-by-step explanation:

Given:

The equation to solve is given as:

5x^5+6x^4+80x^3+96x^2=0

Factoring x^2 from all the terms, we get:

x^2(5x^3+6x^2+80x+96)=0

Now, rearranging the terms, we get:

x^2(5x^3+80x+6x^2+96)=0

Now, factoring 5x from the first two terms and 6 from the last two terms, we get:

x^2(5x(x^2+16)+6(x^2+16))=0\\x^2(x^2+16)(5x+6)=0

Now, equating each factor to 0 and solving for 'x', we get:

x^2=0\\x=0\ and\ 0\\\\5x+6=0\\x=\frac{-6}{5}=1.2\\\\x^2+16=0\\x^2=-16\\x=\sqrt{-16}=\pm 4i

There are 3 real values and 2 imaginary values. The value of 'x' as 0 is repeated twice.

Therefore, the values of 'x' are -1.2, 0, 0, -4i or 4i.

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Read 2 more answers
(2 points) An article in the Washington Post on March 16, 1993 stated that nearly 45 percent of all Americans have brown eyes. A
lara31 [8.8K]

Answer: a) z=1.43

b) 0.1528

Step-by-step explanation:

The given set of hypothesis :

H_0:p=0.45

H_a:p\neq0.45

Since the alternative hypothesis H_a is two-tailed , so we perform two-tailed test.

Also, it is given that : A random sample of n=76 Americans found 28 with brown eyes.

Sample proportion: \hat{p}=\dfrac{28}{76}=0.3684

a) The z-statistic would be :-

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

\Rightarrow\ z=\dfrac{0.3684-0.45}{\sqrt{\dfrac{0.45(1-0.45)}{76}}}=-1.4299121397\approx-1.43

b) P-value for two-tailed test = 2P(Z>|z|)= 2P(z>|-1.43|)

=2P(z>1.43)

=2(1-P(z≤1.43)

=2-2P(z≤1.43)

= 2-2(0.9236)[Using standard z-table]

= 2-1.8472=0.1528

Hence,  the P-value of the test= 0.1528

6 0
3 years ago
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