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soldi70 [24.7K]

4 years ago

15

Write each polynomial function in standard form , classify it by degree and determine the end behavior of its graph y=2x^3-6x+3x

^2+12

1 answer:

Leokris [45]4 years ago

3 0

<u>Answer:</u>

$y=2x^3+3x^2-6x+12$

and the degree of this polynomial is 3.

<u>Step-by-step explanation:</u>

We are given the following polynomial and we are supposed to write it in the standard form and also classify it by its degree:

$y=2x^3-6x+3x^2+12$

To write any polynomial in the standard form, you need to look at the degree of each of the terms that are present in the polynomial and then write them in the order of their degree, from highest to lowest (starting from left to write).

So the standard form of the given polynomial will be:

$y=2x^3+3x^2-6x+12$

and the degree of this polynomial is 3.

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Use the identity x^3+y^3+z^3−3xyz=(x+y+z)(x^2+y^2+z^2−xy−yz−zx) to determine the value of the sum of three integers given:

RoseWind [281]

Inserting all the given information into the identity, we have

$684-3(210)=(x+y+z)(110-107)\implies x+y+z=18$

4 0

4 years ago

Which of the two solids below are similar ?

Pachacha [2.7K]

Answer: I and II.

Step-by-step explanation:

By definition, two solids are similar if their corresponding sides are in the same ratio.

Knowing this, let's find which solids are similar:

Corresponding sides ratio of solids I and II:

$\frac{3}{2}=\frac{2}{\frac{4}{3}}=\frac{5}{\frac{10}{3}}$

$\frac{3}{2}=\frac{3}{2}=\frac{3}{2}$

Corresponding sides ratio of solids I and III:

$\frac{3}{\frac{9}{2}}=\frac{2}{3}=\frac{5}{8}$

$\frac{2}{3}=\frac{2}{3}=\frac{5}{8}$

Corresponding sides ratio of solids II and III:

$\frac{2}{\frac{9}{2}}=\frac{\frac{4}{3}}{3}}=\frac{\frac{10}{3}}{8}}$

$\frac{4}{9}=\frac{4}{9}=\frac{5}{12}$

You can observe that the solids I and II are similar.

3 0

3 years ago

Please help me<br> Identify a value of k that transforms f into g, where g(x) = f(x) + k.

NemiM [27]

Answer:uhhhhhhhhhh

Where dem beats been doe i den had to start spitting bars not work on the beats cuz I didn’t have you man bro

Step-by-step explanation:

7 0

3 years ago

PLEASE PLEASE PLEASE PLEASE HELP WITH MATH. ILL GIVE POINTS, BRAINY, AND FRIEND.

Lunna [17]

The slope of a line parallel to another line are equal, and the slope of a line and a perpendicualr line is the reciprocal. So, a line parallel to y = -1/2x + 6 that goes through (4,10) will have an equation of y = -1/2x + 10 (slope is the same and y-intercept changed). The line perpendicular would have an equation that looks like this: y = 2x + 10 (the slope is the reciprocal of the original slope).

7 0

3 years ago

A certain change in a process for manufacturing component parts is being considered. Samples are taken under both the existing a

mr_godi [17]

Answer:

And the 90% confidence interval for the difference would be given by:(-0.022;0.0017).

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p_A$ represent the real population proportion for brand A

$\hat p_A =\frac{80}{2000}=0.04$ represent the estimated proportion for the new process

$n_A=2000$ is the sample size required for Brand A

$p_B$ represent the real population proportion for brand b

$\hat p_B =\frac{75}{1500}=0.05$ represent the estimated proportion for the before process

$n_B=1500$ is the sample size required for before process

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 90% confidence interval the value of $\alpha=1-0.90=0.1$ and $\alpha/2=0.05$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.64$

And replacing into the confidence interval formula we got:

$(0.04 -0.05) - 1.64 \sqrt{\frac{0.04(1-0.04)}{2000} +\frac{0.05(1-0.05)}{1500}}=-0.022$

$(0.04 -0.05) + 1.64 \sqrt{\frac{0.04(1-0.04)}{2000} +\frac{0.05(1-0.05)}{1500}}=0.0017$

And the 90% confidence interval would be given (-0.022;0.0017).

3 0

3 years ago