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1 year ago

What is the completely factored form of f(x) = 6x3 – 13x2 – 4x + 15?

Mathematics

2 answers:

nasty-shy [4]1 year ago

8 0

Answer:

Option D is the correct answer.

Step-by-step explanation:

masya89 [10]1 year ago

5 0

We have to determine the complete factored form of the given polynomial

$f(x)=6x^3-13x^2-4x+15$ .

Let x= -1 in the given polynomial.

So, $f(-1)= 6(-1)^3-13(-1)^2-4(-1)+15 = -6-13+4+15 = 0$

So, by factor theorem

(x+1) is a factor of the given polynomial.

So, dividing the given polynomial by (x+1), we get quotient as $6x^2-19x+15$ .

So, $6x^3-13x^2-4x+15$ = (x+1) $6x^2-19x+15$ .

= $(x+1)(6x^2-10x-9x+15)$

= $(x+1)[ 2x(3x-5)-3(3x-5)]$

= $(x+1)(2x-3)(3x-5)$ is the completely factored form of the given polynomial.

Option D is the correct answer.

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Step-by-step explanation:

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Santiago hopes to buy a 4 horse trailer for about $12000. Describe all the numbers that when rounded to the nearest hundred are

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2 years ago

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A school teacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the s

marin [14]

Answer:

H0 ; μ ≤ 4 pCi/L

Ha ; μ > 4 pCi/L

The null hypothesis is that the concentration of dangerous, cancer-causing radon gas in her classroom is less than or equal to the safe level of 4pCi/L

H0 ; μ ≤ 4 pCi/L

The alternative hypothesis is that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L.

Ha ; μ > 4 pCi/L

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

The null hypothesis is that the concentration of dangerous, cancer-causing radon gas in her classroom is less than or equal to the safe level of 4pCi/L

H0 ; μ ≤ 4 pCi/L

The alternative hypothesis is that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L.

Ha ; μ > 4 pCi/L

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2 years ago

Find the length of DF or state what additional information you would need to find it.

hichkok12 [17]

Answer:

DF=3.75

Step-by-step explanation:

24/6=15/x

cross multiply to get 24x=90

x=3.75

5 0

1 year ago

The fraction of defective integrated circuits produced in a photolithography process is being studied. A random sample of 300 ci

Olenka [21]

Answer:

The correct answer is

(0.0128, 0.0532)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence interval $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

Z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$

For this problem, we have that:

In a random sample of 300 circuits, 10 are defective. This means that $n = 300$ and $\pi = \frac{10}{300} = 0.033$

Calculate a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool.

So $\alpha$ = 0.05, z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{300}} = 0.033 - 1.96\sqrt{\frac{0.033*0.967}{300}} = 0.0128$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{300}} = 0.033 + 1.96\sqrt{\frac{0.033*0.967}{300}} = 0.0532$

The correct answer is

(0.0128, 0.0532)

4 0

1 year ago