Factor the following problem: (PLEASE EXPLAIN :)) a^3-b^3

If you were conducting a study about favorite foods among the entire U.S. population, how would you choose

Over [174]

I would use a pie chart because it can show the percentage of people who like different food. It helps display the data in an easier organized way. I wouldn't use a graph because there would be too many numbers and it might be confusing when analyzing the data.

-I hope this helps! Branliest would be appreciated :)

3 0

3 years ago

The number of boys if the total height would of the boys is 16.4 meters and their average height is 1.2 meters

galben [10]

Number of boys= 16.4÷ 1.2=13

3 0

3 years ago

A random sample of 1014 adults in a certain large country was asked "Do you pretty much think televisions are a necessity or a l

arlik [135]

Answer:

a) $\hat p=\frac{538}{1014}=0.531$ estimated proportion of people indicated that televisions are a luxury they could do without

b) Verify that the requirements for constructing a confidence interval about p are satisfied. The sample is a simple random sample, the value of np(1-p)=1014*0.531*(1-0.531)=252.53 is, which is > 10, and the less than or equal to 5% of the population.

c) The 95% confidence interval would be given by (0.500;0.562)

B. We are 95% confident the proportion of adults in the country who believe that televisions are a luxury they could do without is between 0.500 and 0.562

d) We can say that is possible that more than 60% of adult Americans believe that television is a luxury they could do without because we need to remember that the confidence interval is just a point of estimation and iits probable that the true proportion would be not contained on the interval. But we can say that is not that likely that the true proportion is greater than 60%

e) The 95% confidence interval would be given by (0.438;0.500)

Step-by-step explanation:

Notation and definitions

$X=538$ number of people indicated that televisions are a luxury they could do without

$n=1014$ random sample taken

$\hat p=\frac{538}{1014}=0.531$ estimated proportion of people indicated that televisions are a luxury they could do without

$p$ true population proportion of people indicated that televisions are a luxury they could do without

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".

The population proportion have the following distribution

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

a) $\hat p=\frac{538}{1014}=0.531$ estimated proportion of people indicated that televisions are a luxury they could do without.

b) Verify that the requirements for constructing a confidence interval about p are satisfied. The sample is a simple random sample, the value of np(1-p)=1014*0.531*(1-0.531)=252.53 is, which is > 10, and the less than or equal to 5% of the population.

c) In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.531 - 1.96\sqrt{\frac{0.531(1-0.531)}{1014}}=0.500$

$0.531 + 1.96\sqrt{\frac{0.531(1-0.531)}{1014}}=0.562$

The 95% confidence interval would be given by (0.500;0.562)

B. We are 95% confident the proportion of adults in the country who believe that televisions are a luxury they could do without is between 0.500 and 0.562

d) We can say that is possible that more than 60% of adult Americans believe that television is a luxury they could do without because we need to remember that the confidence interval is just a point of estimation and iits probable that the true proportion would be not contained on the interval. But we can say that is not that likely that the true proportion is greater than 60%

e) The new propotion on this case would be

$\hat p =1-0.531=0.469$

$0.469 - 1.96\sqrt{\frac{0.469(1-0.469)}{1014}}=0.438$

$0.469 + 1.96\sqrt{\frac{0.469(1-0.469)}{1014}}=0.500$

The 95% confidence interval would be given by (0.438;0.500)

4 0

4 years ago

PLS HELP f(x)=x^3−2x^2+12x−6 g(x)=4x^2−6x+4 What is (f−g)(x)?

vodomira [7]

Answer:

$(f - g)(x) = {x}^{3} - 6 {x}^{2} + 18x - 10$

Step-by-step explanation:

The given functions are:

$f(x) = {x}^{3} - 2 {x}^{2} + 12x - 6$

and

$g(x) = 4 {x}^{2} - 6x + 4$

We want to find

$(f - g)(x)$

Recall that:

$(f - g)(x) = f(x) - g(x)$

This implies that:

$(f - g)(x) = {x}^{3} - 2 {x}^{2} + 12x - 6 - (4 {x}^{2} - 6x + 4)$

$(f - g)(x) = {x}^{3} - 2 {x}^{2} + 12x - 6 - 4 {x}^{2} + 6x - 4$

We combine similar terms to get:

$(f - g)(x) = {x}^{3} - 6 {x}^{2} + 18x - 10$

7 0

3 years ago

john read the first 114 pages of a novel which is 3 pages less than 1/3 of the novel. write the equation

tatyana61 [14]

The equation is:

$114=\frac{p}{3}-3$

And

Total number of pages are 351

Step-by-step explanation:

The equation has to be formed by using the given information.

Let p be the total number of pages in the novel

Then

1/3rd of the p will pe:

$\frac{p}{3}$

Total pages read by John = 114

Then according to the statement

$114=\frac{p}{3}-3$

We can solve the equation to get the total pages of the novel

$114=\frac{p}{3}-3\\Adding\ 3\ on\ both\ sides\\114+3=\frac{p}{3}-3+3\\117=\frac{p}{3}\\Multiplying\ both\ sides\ by\ 3\\3*117 = \frac{p}{3}*3\\p=351$

The equation is:

$114=\frac{p}{3}-3$

And

Total number of pages are 351

Keywords: Linear equation, variable

Learn more about linear variable at:

#LearnwithBrainly

8 0

4 years ago