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2 years ago

X² - 40x-129 resolve into factor

Mathematics

1 answer:

Lelu [443]2 years ago

8 0

Answer:

(x - 43)(x + 3)

Step-by-step explanation:

consider the factors of the constant term (- 129) which sum to give the coefficient of the x- term (- 40)

the factors are - 43 and + 3 , since

- 43 × + 3 = - 129 and - 43 + 3 = - 40 , then

x² - 40x - 129 = (x - 43)(x + 3) ← in factored form

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$p_2$ = proportion of cockroaches that died on plasterboard surface.

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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 Two-sample z proportion statistics;

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

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$n_2$ = sample of cockroaches on plasterboard surface = 36

So, test statistics = $\frac{(0.50-0.694)-(0)}{\sqrt{\frac{0.50(1-0.50)}{36}+\frac{0.694(1-0.694)}{36} } }$

= -1.712

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 we fail to reject our null hypothesis.

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3 years ago

X² - 40x-129 resolve into factor​

X² - 40x-129 resolve into factor