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4 years ago

Factor the polynomial

Mathematics

2 answers:

harina [27]4 years ago

7 0

Answer:

5y(2y-3)^2

Step-by-step explanation:

marshall27 [118]4 years ago

3 0

Answer:

5y(2y-3)^2

Steps:

Factor 5y out of 20y^3 - 60y^2 + 45y

5y ( 4y^2) - 60y^2 + 45y

5y ( 4y^2) +5y ( - 12y ) + 45y

5y ( 4y^2) +5y ( - 12y ) + 5y ( 9 )

5y ( 4y^2 - 12y ) + 5y ( 9 )

5y ( 4y^2 - 12y + 9 )

Factor using the perfect square rule

5y ( (2y)^2 - 12y + 9 )

5y ( (2y)^2 - 12y + 3^2 )

2ab = 2 • ( 2y ) • - 3

Simplify.

2ab = - 12y

Answer :

5y ( 2y - 3 ) ^2.

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A researcher is interested in finding a 95% confidence interval for the mean number minutes students are concentrating on their

Sever21 [200]

Answer:

A. Normal

B. Between 40.08 minutes and 43.92 minutes.

C. About 95 percent of these confidence intervals will contain the true population mean number of minutes of concentration and about 5 percent will not contain the true population mean number of minutes of concentration.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

Question A:

By the Central Limit Theorem, a normal distribution.

Question B:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96\frac{12}{\sqrt{150}} = 1.92$

The lower end of the interval is the sample mean subtracted by M. So it is 42 - 1.92 = 40.08 minutes

The upper end of the interval is the sample mean added to M. So it is 42 + 1.92 = 43.92 minutes

Between 40.08 minutes and 43.92 minutes.

Question C:

x% confidence interval -> x% will contain the true population mean, (100-x)% wont.

So, 95% confidence interval:

About 95 percent of these confidence intervals will contain the true population mean number of minutes of concentration and about 5 percent will not contain the true population mean number of minutes of concentration.

3 0

3 years ago

I need help on this subject.

mel-nik [20]

Answer:

0.43

Step-by-step explanation:

To calculate the relative frequency of any of the values in the frequency table, divide the value by the total (120)

For example, the relative frequency of boys who prefer math is:

43 ÷ 120 = 0.36

Reading from the frequency table, the total number of boys is 52. Therefore, the relative frequency for the total number of boys is:

52 ÷ 120 = 0.43

5 0

2 years ago

Solve the following integral.<br><br> <img src="https://tex.z-dn.net/?f=%5Cint4x%5Ccos%282-3x%29dx" id="TexFormula1" title="\int

bagirrra123 [75]

Hi there!

$\boxed{-\frac{4x}{3}sin(2-3x) + \frac{4}{9}cos(2-3x) + C}$

To find the indefinite integral, we must integrate by parts.

Let "u" be the expression most easily differentiated, and "dv" the remaining expression. Take the derivative of "u" and the integral of "dv":

u = 4x

du = 4

dv = cos(2 - 3x)

v = 1/3sin(2 - 3x)

Write into the format:

∫udv = uv - ∫vdu

Thus, utilize the solved for expressions above:

4x · (-1/3sin(2 - 3x)) -∫ 4(1/3sin(2 - 3x))dx

Simplify:

-4x/3 sin(2 - 3x) - ∫ 4/3sin(2 - 3x)dx

Integrate the integral:

∫4/3(sin(2 - 3x)dx

u = 2 - 3x

du = -3dx ⇒ -1/3du = dx

-1/3∫ 4/3(sin(2 - 3x)dx ⇒ -4/9cos(2 - 3x) + C

Combine:

$-\frac{4x}{3}sin(2-3x) + \frac{4}{9}cos(2-3x) + C$

7 0

3 years ago

Read 2 more answers

Write three ratios equivalent to this:18 right handed students for every 4 left handed?

kotegsom [21]

18:4,18/4,18 to 4
18/4 equals 4 1/2

3 0

3 years ago

Read 2 more answers

Which of the following statements is false? (5 points)

photoshop1234 [79]

Answer:

A: The sum of two rational numbers is always rational. I just took the test.

Step-by-step explanation:

Rational numbers are numbers that can be written as a fraction or ratio where irrational number cannot be written as a fraction or ratio.So the product or sum of two rational number is rational. Since your needed to find the false statement then the first one was the correct one.

5 0

3 years ago