According to the Rational Root Theorem, which could be a factor of the polynomial f(x) = 3x3 – 5x2 – 12x + 20?

Answers

Answer 1

Answer:

Answer:

factor of the polynomial $f(x)=3x^(3)-5x^(2)-12x+20$ is

$(x-(5)/(3))(x+2)(x-2)$

Step-by-step explanation:

Rational Root Theorem: It tells us which roots we may find exactly (the rational ones) and which roots we may only approximate (the irrational ones).

$P(x) = a_n x^(n)+a_(n-1)x^(n-1) + ... + a_2 x^(2)+ a_1 x + a_0$

has any rational roots, then they must be of the form:

$\pm(factor of a_0)/(factor of a_1)$

In provided polynomial $f(x)=3x^(3)-5x^(2)-12x+20$

Here, $a_0=20\; \text{and}\; a_n =3$

The number 20 has factors: $\pm1,\pm2,\pm4,\pm5,\pm10,\pm20$ .

These are possible value for p

The number 3 has factors: $\pm1,\pm3$ . these are possible value for q

Find all possible value of $(p)/(q)$

$\mathrm{The\:following\:rational\:numbers\:are\:candidate\:roots:}\quad \pm (1,\:2,\:4,\:5,\:10,\:20)/(1,\:3)$

$\mathrm{Validate\:the\:roots\:by\:plugging\:them\:into}\:3x^3-5x^2-12x+20=0:\quad x=(5)/(3),\:x=-2,\:x=2$

Hence, factor of the polynomial $f(x)=3x^(3)-5x^(2)-12x+20$ is

$(x-(5)/(3))(x+2)(x-2)$

Answer 2

Answer: a)X1=-2

b)X2=2

c)X3=5/3

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What is the term of a 7-term geometric series if the first term is -11 the last term is -45,056 and the common ratio is -4

Answers

I assume you mean to ask how to find the sum of the seven terms?

You have

$a_2=ra_1$
$a_3=ra_2=r^2a_1$
$a_4=ra_3=r^3a_1$
...
$a_7=ra_6=r^6a_1$

So the sum is

$a_1+ra_1+r^2a_1+\cdots+r^6a_1=a_1(1+r+r^2+\cdots+r^6)=a_1*(1-r^7)/(1-r)$

You know that $a_1=-11$ and $r=-4$ , so the sum is equal to

$-4*(1-(-4)^7)/(1-(-4))=-13108$

In which part of a professional email should you try to brief but highly descriptive

Answers

The subject, so that the recipient knows what the email is about but only through a couple words

10x 10y = 1 x = y - 3 what is the value of y?

Answers

Solve the equations by substitution. If the equations are inconsistent and the solution is an empty set, write "no solution".
10x - 10y = 1
x = y - 3
10x - 10y = 1
x = y - 3
The second equation is solved for x, Sosubstitute (y - 3) for x in the first equation10x - 10y = 1
10(y - 3) - 10y = 1
10y - 30 - 10y = 1-30 = 1
The y's all canceled out and left a false numerical equation,-30 in not equal to 1, so there is no solution. The system is called aninconsistent system of equation.

Question 62 pts
(06.03)
A student wants to report on the number of books her friends read each week. The collected data are below:
0 24 1 4 5 2 5 4
Which measure of center is most appropriate for this situation and what is its value? (2 points)
Median; 2
O Median: 4
Mean; 2
O Mean; 4
re to search

Answers

Answer:

median:4

Step-by-step explanation:

IQ is normally distributed with a mean of 100 and a standard deviation of 15. What IQ do you need to be in the 90th percentile?

Answers

Answer:IQ score≈119.7225

Step-by-step explanation:

To find the IQ score that corresponds to the 90th percentile in a normal distribution with a mean of 100 and a standard deviation of 15, you can use the cumulative distribution function (CDF) of the normal distribution. The CDF gives the probability that a random variable (in this case, IQ) is less than or equal to a specific value.

The formula to find the z-score (standard score) corresponding to a given percentile is:

�

invNorm

(

�

)

z=invNorm(p)

Where

�

p is the desired percentile expressed as a decimal (90th percentile would be

�

0.90

p=0.90), and

invNorm

invNorm is the inverse normal distribution function.

Then, you can use the z-score to find the IQ score using the formula:

IQ score

mean

�

standard deviation

IQ score=mean+z×standard deviation

Plugging in the given values:

Mean (

mean

mean) = 100

Standard deviation (

standard deviation

standard deviation) = 15

Percentile (

�

p) = 0.90

First, find the z-score:

�

invNorm

(

0.90

)

z=invNorm(0.90)

You can use a standard normal distribution table, calculator, or software to find the z-score. For a 90th percentile,

�

≈

1.28155

z≈1.28155.

Now, plug the z-score into the IQ score formula:

IQ score

100

1.28155

IQ score=100+1.28155×15

IQ score

≈

119.7225

IQ score≈119.7225

Rounding to the nearest whole number, an IQ score of approximately 120 would place you in the 90th percentile.

Final answer:

To be in the 90th percentile, you would need an IQ score of approximately 119.2.

Explanation:

To find the IQ score corresponding to the 90th percentile, we can use the standard normal distribution table or a calculator. Since the IQ distribution is normally distributed with a mean of 100 and a standard deviation of 15, we can convert the given information into a standard normal distribution by using the formula:

Z = (X - μ) / σ

where Z is the standard score, X is the IQ score, μ is the mean, and σ is the standard deviation.

Since we want to find the IQ score for the 90th percentile, we need to find the Z-score that corresponds to the 90th percentile. From the standard normal distribution table, we find that the Z-score for the 90th percentile is approximately 1.28.

Now, we can solve for X (the IQ score) using the formula:

Z = (X - μ) / σ

Substituting the values, we have:

1.28 = (X - 100) / 15

Solving for X, we get:

X = 1.28 * 15 + 100

Therefore, to be in the 90th percentile, you would need an IQ score of approximately 119.2.

Learn more about calculating iq for a given percentile here:

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A machine that produces a major part for an airplane engine is monitored closely. In the past, 10% of the parts produced would be defective. With a .95 probability, the sample size that needs to be taken if the desired margin of error is .04 or less is

Answers

Answer: 216

Step-by-step explanation:

The formula to find the sample size , if prior population proportion is known :-

$n=p(1-p)((z_(\alpha/2))/(E))^2$

Given : The prior proportion of defective parts : p= 0.10

Significance level : $\alpha=1-0.95=0.05$

Critical value : $z_(\alpha/2)=1.96$

Margin of error : $E=0.04$

Now, the required sample size will be :-

$n=0.1(0.9)(((1.96))/(0.04))^2=216.09\approx216$

Hence, the minimum required sample size = 216

Final answer:

To achieve a margin of error of .04 or less with a 95% confidence level when the defect rate is 10%, at least 217 samples need to be taken.

Explanation:

The question pertains to the field of statistics, specifically sample sizes and margin of error. In order to estimate the minimum sample size needed to achieve a desired margin of error of .04 or less, we can use the formula for sample size in proportions: n = (Z^2*p*(1-p))/E^2.

In this formula:

Z refers to the z-value which, for a 95% confidence level, is 1.96.
p is the estimated proportion of defective parts, which in this case is 0.1 or 10%.
E is the desired margin of error, which is 0.04.

Substitute the values into the formula: n = (1.96^2*0.1*0.9)/(0.04^2), yielding n=216.09.

Since we can't have a fraction of a sample, we round up to get n = 217. Therefore, we need a sample size of 217 to reach a margin of error of .04 or less with a 95% confidence level.

Learn more about Sample Size Calculation here:

brainly.com/question/34288377

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