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kolezko [41]
2 years ago
15

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 2, and the given zeros. -

4,0,2,4
Mathematics
1 answer:
Musya8 [376]2 years ago
4 0

Answer:

A least degree polynomial, having rational coefficients and a leading coefficient of 2, with,-4, 0, 2, and 4 as the zeros of the polynomial is;

f(x) = 2·x⁴ - 4·x³ - 32·x² + 64·x

Step-by-step explanation:

The given parameters of the polynomial are;

The leading coefficient of the polynomial = 2

The zeros of the polynomial = -4, 0, 2, 4

We note that zeros of -4, and 4 gives a factor of the form, (x² - 4²)

For a zero of the polynomial equal to 0, one of the factors of the polynomial is equal to 'x'

To have a leading coefficient of 2, we can add '2' as a factor of the polynomial

Therefore, we can have the factors of the polynomial as follows;

(x² - 4²)·2·x×(x - 2) = 0

From the above equation, using a graphing calculator, we get the following possible polynomial;

(x² - 4²)·2·x×(x - 2) = 2·x⁴ - 4·x³ - 32·x² + 64·x = 0

Therefore, a polynomial, function of least degree that has rational coefficients, a leading coefficient of 2,and the zeros, -4, 0, 2, and 4 is  f(x) = 2·x⁴ - 4·x³ - 32·x² + 64·x.

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"Immediately after a ban on using hand-held cell phones while driving was implemented, compliance with the law was measured. A r
sergiy2304 [10]

Answer:

(a) Null Hypothesis, H_0 : p_1-p_2=0  or  p_1= p_2  

    Alternate Hypothesis, H_A : p_1-p_2\neq 0  or  p_1\neq p_2

(b) We conclude that there is a statistical difference in these two proportions measured initially and then one year later.

Step-by-step explanation:

We are given that a random sample of 1,250 drivers found that 98.9% were in compliance. A year after the implementation, compliance was again measured to see if compliance was the same (or not) as previously measured.

A different random sample of 1,100 drivers found 96.9% compliance."

<em />

<em>Let </em>p_1<em> = proportion of drivers that were in compliance initially</em>

p_2<em> = proportion of drivers that were in compliance one year later</em>

(a) <u>Null Hypothesis</u>, H_0 : p_1-p_2=0  or  p_1= p_2      {means that there is not any statistical difference in these two proportions measured initially and then one year later}

<u>Alternate Hypothesis</u>, H_A : p_1-p_2\neq 0  or  p_1\neq p_2     {means that there is a statistical difference in these two proportions measured initially and then one year later}

The test statistics that will be used here is <u>Two-sample z proportion 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 drivers in compliance initially = 98.9%

\hat p_2 = sample proportion of drivers in compliance one year later = 96.9%

n_1 = sample of drivers initially = 1,250

n_2 = sample of drivers one year later = 1,100

(b) So, <u><em>the test statistics</em></u>  =  \frac{(0.989-0.969)-(0)}{\sqrt{ \frac{0.989(1-0.989)}{1,250} + \frac{0.969(1-0.969)}{1,100}} }  

                                           =  3.33

<u>Now, P-value of the test statistics is given by;</u>

         P-value = P(Z > 3.33) = 1 - P(Z \leq 3.33)

                                            = 1 - 0.99957 = <u>0.00043</u>

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 between -1.96 and 1.96 for two-tailed test.

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

Therefore, we conclude that there is a statistical difference in these two proportions measured initially and then one year later.

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Answer:

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Step-by-step explanation:

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Answer:

9 x (x +5) = 185

Step-by-step explanation:

I'm pretty sure this is how you write it

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I just had this problem at rsm

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Answer:

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Step-by-step explanation:

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