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m_a_m_a [10]
3 years ago
5

What are the possible rational zeros for f(x)=3x^4+x^3-13x^2-2x+9?

Mathematics
1 answer:
zaharov [31]3 years ago
4 0

Answer:

Option 4 (±1, ±1/3, ±3, ±9) is the correct option.

Step-by-step explanation:

The given expression is f(x)=3x^{4}+x^{3}-13x^{2}-2x+9

We have to find the possible rational zeros for the function.

So by the rational zero theorem factors will be

=±(Factors of constant term 9)/±factors of coefficient of x^{4}

=±(Factors of 9)/±(Factors of 3)

=±(1, 3, 9)/±(1, 3)

=±(1, 3, 9, 1/3)

So option 4 is the correct answer.

You might be interested in
A study randomly assigned adult subjects to one of three exercise treatments: (1) a single long exercise period five days per we
Katen [24]

Answer:

Step-by-step explanation:

Hello!

For this study adult subjects were randomly assigned to three different exercise treatments establishing three different groups:

Group 1: Single long exercise period five days per week

Group 2: Several 10' exercise periods five days per week

Group 3: Several 10' exercise periods five days per week using a home treadmill

All subjects were weighed before and after 6 months of training and their weight loss was determined.

The objective of this study is to determine if there is any difference between the treatments, meaning, if the weight loss is the same regarding the type of exercise or if the type of exercise has some influence over it.

To test this you have to conduct an ANOVA, with the hypothesis:

H₀: μ₁= μ₂= μ₃

H₁: At least one μi differs from the others. ∀ i=1, 2, 3

α: 0.05

The statistic is:

F= \frac{MS_{Tr}}{MS_{Er}} ~~F_{k-1; n-k}

Normally it is better to have the raw data to conduct the analysis using statistical software, but it is not impossible to calculate the statistic using the descriptive statistics for each group.

As you know the statistic is calculated as the ratio between the mean square of the treatments (between groups) and the mean squares of errors.

Each means square is calculated as the sum of squares by the degrees of freedom of the category: SS/Df

So first you need to determine the SS and Df of treatments and errors, then the MS and finally the value of F.

Treatments:

> The degrees of freedom between treatments are k-1 (k represents the number of treatments):

DfTr: 3-1= 2

>The sum of squares is:

SSTr: ∑ni(Ÿi - Ÿ..)²

Ÿi= sample mean of sample i ∀ i= 1,2,3

Ÿ..= grand mean is the mean that results of all the groups together.

So the Sum of squares of treatments (SSTr) is the sum of the square of the difference between the sample mean of each group and the grand mean.

To calculate the grand mean you can sum the means of each group and dive it by the number of groups:

Ÿ..= (Ÿ₁ + Ÿ₂ + Ÿ₃)/ k = (10.2+9.3+10.2)/3= 29.7/3= 9.9

SSTr= (Ÿ₁ - Ÿ..)² + (Ÿ₂ - Ÿ..)² + (Ÿ₃ - Ÿ..)²= (10.2 - 9.9)² + (9.3 - 9.9)² + (10.2 - 9.9)²= 0.54

> The Means Squares is:

MSTr= SSTr/DFTr= 0.54/2= 0.27

Errors

>Degrees of freedom of error DfEr= N-k Where N is the total of observations of the experiment (N= n₁+n₂+n₃) and k is the number of treatments.

DfEr= N-k= 30-3= 27

>The mean square error (MSEr) is the estimation of the variance error (σ_{e}^2 → S_{e}^2), you have to use the following formula:

S_{e}^2= \frac{(n_1-1)S^2_1+(n_2-1)S_2^2+(n_3-1)S^2_3}{N-k}= \frac{(9*17.64)+(9*20.25)+(9*27.04)}{27}= \frac{584.37}{27}= 21.643

Finally you calculate the statistic:

F_{H_0}= \frac{MS_{Tr}}{MS_{Er}}= \frac{0.27}{21.643}= 0.012

This test is One-tailed right, meaning that you'll reject to high values of the statistic and there is one critical value:

F_{k-1;N-k;1-\alpha }= F_{2;27;0.95}= 3.35

Using the critical value approach, the decision rule is:

If F_{H_0} ≥ 3.35, reject the null hypothesis.

If F_{H_0} < 3.35, do not reject the null hypothesis.

The calculated value is less than the critical value, the decision is to not reject the null hypothesis.

So at a 5% significance level, there is not enough evidence to conclude that the treatments influence significantly in weight loss. The population mean weight loss is the same for the treatments "Single long exercise period five days per week", "Several 10' exercise periods five days per week" and "Several 10' exercise periods five days per week using a home treadmill"

I hope this helps!

5 0
3 years ago
PLEASE HELP!!!<br>what is the length of segment SR? units​
AlekseyPX

Answer:

x=2

Step-by-step explanation:

2x+8=8x-4

2x+12=8x

12=6x

2=x

x=2

4 0
3 years ago
Ginger's cat gave birth to a kitten that weighed 3 3/8 ounces when it was born. On the day Ginger sold the kitten to its new own
KiRa [710]
The kitten grew 2.12 lbs
8 0
3 years ago
Read 2 more answers
Write an inequality for the graph. Then, in words, describe all the values of that make the inequality true.
kow [346]
-3 > x

The values that make this inequality true are those that are less than -3. The inequality does not include -3.
7 0
2 years ago
A company makes 140 bags. 39 of the bags have buttons but no zips. 21 of the bags have zips but no buttons. 23 of the bags have
sleet_krkn [62]

Subtraction is a mathematical operation that reflects the removal of things from a collection. The number of bags that zips on them is 78.

<h3>What is subtraction?</h3>

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

Given the number of bags that the company makes is 140. 39 of the bags have buttons but no zips. 21 of the bags have zips but no buttons. 23 of the bags have neither zips nor buttons.

Bags that have both zip and button

= Total number of bags - Number of bags with zips but no buttons - Number of bags with buttons but no zips - Number of bags with nor zips nor the buttons

= 140 - 21 - 39 - 23

= 57

Now, the number of bags that has zips will be the bags that only have zips and the number of bags that has zips and buttons. Therefore, the number of bags with zips is,

n = Bags that have both zip and button + Number of bags with zips but no buttons

   = 37 + 21

   = 78

Hence, the number of bags that zips on them is 78.

Learn more about Subtraction:

brainly.com/question/1927340

#SPJ1

4 0
1 year ago
Read 2 more answers
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