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3 years ago

According to the Rational Root Theorem, which number is a potential root of f(x) = 9x8 + 9x6 – 12x + 7?

Mathematics

2 answers:

MrRa [10]3 years ago

5 0

7/3 is the answer to your question

telo118 [61]3 years ago

3 0

Answer:

All the potential root of f(x) are $\pm 1,\pm7, \pm \frac{1}{3},\pm \frac{7}{3}, \pm \frac{1}{9},\pm \frac{7}{9}$ .

Step-by-step explanation:

According to the rational root theorem, all the potential root of f(x) are defined as

$x=\pm\frac{p}{q}$

Where, p is factor of constant term and q is factor of leading coefficient.

The given function is

$f(x)=9x^8+9x^6-12x+7$

Here, constant term is 7 and leading coefficient is 9.

Factors of 7 are ±1, ±7 and the factors of 9 are ±1, ±3, ±9.

Using rational root theorem, all the potential root of f(x) are

$x=\pm 1,\pm7, \pm \frac{1}{3},\pm \frac{7}{3}, \pm \frac{1}{9},\pm \frac{7}{9}$

Therefore all the potential root of f(x) are $\pm 1,\pm7, \pm \frac{1}{3},\pm \frac{7}{3}, \pm \frac{1}{9},\pm \frac{7}{9}$ .

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3 years ago

[20 Points] I need help with these questions:

I am Lyosha [343]

Slope-intercept form:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0)

You need to find "m" and "b"

1.) For lines to be perpendicular, their slopes have to be the opposite/negative reciprocal (flipped sign and number)

For example:

slope is 2

perpendicular line's slope is -1/2

slope is -2/3

perpendicular line's slope is 3/2

The given line's slope is -4, so the perpendicular line's slope is 1/4.

y = 1/4x + b

To find "b", you can plug in the point (4, -2) into the equation

y = 1/4x + b

-2 = 1/4(4) + b

-2 = 1 + b

-3 = b

$y=\frac{1}{4} x-3$

2.) To find "m", use the slope formula and plug in the two points:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{8-(-1)}{-2-4}$

$m=\frac{8+1}{-2-4}$

$m=\frac{9}{-6} =-\frac{3}{2}$

y = -3/2x + b

Plug in one of the points to find "b"

y = -3/2x + b

-1 = -3/2(4) + b

-1 = -6 + b

5 = b

$y=-\frac{3}{2}x +5$

3.) y-intercept: 5 (since the given equation's y-intercept is 5)

I'm confused with what they mean by "steep", so I'll try to update this later unless someone else has an answer

So I looked it up, and it says that a steep slope is a line that is more vertical [if that makes sense]. So you could do a slope of +3 (more than 3, like 4, 5, 6...) because the given line's slope is 3, and you need a new line that is more steeper(vertical)

3 0

3 years ago

In a sample of 170 students at an Australian university that introduced the use of plagiarism-detection software in a number of

Kisachek [45]

Answer:

$p_v =P(Z>4.146)=0.0000169$

Based on the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of students who NOT belief that such software unfairly targets students is higher than 0.5 or 50% .

Step-by-step explanation:

1) Data given and notation

n=170 represent the random sample taken

X=58 represent the student's who belief that such software unfairly targets students

$\hat px=\frac{58}{170}=0.341$ estimated proportion of students who belief that such software unfairly targets students

$\hat p=\frac{112}{170}=0.659$ estimated proportion of students who NOT belief that such software unfairly targets students

$p_o=0.50$ is the value that we want to test

$\alpha=0.05$ represent the significance level (no given)

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

p= proportion of student's who belief that such software unfairly targets students

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that that a majority of students at the university do not share this belief. :

Null hypothesis: $p\leq 0.5$

Alternative hypothesis: $p>0.5$

We assume that the proportion follows a normal distribution.

When we conduct a proportion test we need to use the z statistic, and the is given by:

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

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly (different,higher or less) from a hypothesized value $p_o$ .

<em>Check for the assumptions that he sample must satisfy in order to apply the test </em>

a)The random sample needs to be representative: On this case the problem no mention about it but we can assume it.

b) The sample needs to be large enough

$np_o =170*0.5=85>10$

$n(1-p_o)=170*(1-0.5)=85>10$

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.659 -0.5}{\sqrt{\frac{0.5(1-0.5)}{170}}}=4.146$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided is $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a one right side test the p value would be:

$p_v =P(Z>4.146)=0.0000169$

8 0

3 years ago