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solniwko [45]
3 years ago
5

Which of the following are solutions to the equation below?

Mathematics
1 answer:
Natasha2012 [34]3 years ago
5 0
Both A and C would be solutions to the equation.

In order to solve for this you must first get the equation equal to 0. 

2x^2+5x+8=6 ----> subtract 6 from both sides
2x^2 + 5x + 2 = 0

Now knowing this we can use the coefficients of each one in descending order of power as a, b and c. 

a = 2 (because it is the coefficient to x^2)
b = 5 (because it is the coefficient to x)
c = 2 (because it is the end number)

Now we can plug these values into the quadratic equation. 

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

\frac{-5 +/- \sqrt{5^{2} - 4(2)(2) } }{2(2)}

\frac{-5 +/- \sqrt{9} }{4}

\frac{-5 +/- 3 }{4}

\frac{-5 + 3 }{4} or -1/2 for the first answer

\frac{-5 - 3 }{4} or -2 for the second answer

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We conclude that there is no difference in the proportion of cockroaches that died on each surface.

Step-by-step explanation:

We are given that a study investigated the persistence of this pesticide on various types of surfaces.

After 14 days, they randomly assigned 72 cockroaches to two groups of 36, placed one group on each surface, and recorded the number that died within 48 hours. On the glass, 18 cockroaches died, while on plasterboard, 25 died.

<em>Let </em>p_1<em> = proportion of cockroaches that died on glass surface.</em>

<em />p_2<em> = proportion of cockroaches that died on plasterboard surface.</em>

So, Null Hypothesis, H_0 : p_1-p_2 = 0      {means that there is no difference in the proportion of cockroaches that died on each surface}

Alternate Hypothesis, H_A : p_1-p_2\neq 0      {means that there is a significant difference in the proportion of cockroaches that died on each surface}

The test statistics that would be used here <u>Two-sample z proportion</u> <u>statistics</u>;

                       T.S. =  \frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}  } }  ~ N(0,1)

where, \hat p_1 = sample proportion of cockroaches that died on glass surface = \frac{18}{36} = 0.50

\hat p_2 = sample proportion of cockroaches that died on plasterboard surface = \frac{25}{36} = 0.694

n_1 = sample of cockroaches on glass surface = 36

n_2 = sample of cockroaches on plasterboard surface = 36

So, <u><em>test statistics</em></u>  =  \frac{(0.50-0.694)-(0)}{\sqrt{\frac{0.50(1-0.50)}{36}+\frac{0.694(1-0.694)}{36}  } }

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The value of z test statistics is -1.712.

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.

Therefore, we conclude that there is no difference in the proportion of cockroaches that died on each surface.

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Answer:

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