Highest common factor of 8 and 10

Nitrates are groundwater contaminants derived from fertilizer, septic tank seepage and other sewage. Nitrate poisoning is partic

o-na [289]

Answer:

a) $n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401$

And rounded up we have that n=2401

b) $n=\frac{0.07(1-0.07)}{(\frac{0.02}{1.96})^2}=625.22$

And rounded up we have that n=626

And we see that if we have previous info about p the sample size varies a lot.

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".

Solution to the problem

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:

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

Part a

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =\pm 0.02$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

Since we don't have prior information about the population proportion we can use ase estimator $\hat p =0.5$ . And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401$

And rounded up we have that n=2401

Part b

For thi case the estimator for p is $\hat p =0.07$

$n=\frac{0.07(1-0.07)}{(\frac{0.02}{1.96})^2}=625.22$

And rounded up we have that n=626

And we see that if we have previous info about p the sample size varies a lot.

4 0

3 years ago

James is six years older than lousie. Eight years from now, James will be 4 times older than loise was 4 years ago. What is the

weeeeeb [17]

Answer: 26 years.

Step-by-step explanation:

Let x = current age of Louise (in years).

Then current age of James = x+6

Eight years from now, James's age = x+6+8= x+14

4 years ago, Louise's age = x-4

According to the question

x+14 = 4(x-4)

⇒ x+14 = 4x-16

⇒ 4x-x = 16+14

⇒ 3x = 30

⇒ x= 10 = current age of Louise (in years).

current age of James = 10+6 = 16 years

Sum of current ages = 16+10=26 years.

hence, the sum of the current ages is 26 years.

8 0

4 years ago

A video game store allows customers to rent games for 4.75 each. Customers can also buy a membership for $54 annually, and video

ankoles [38]

Answer:

24 video games

Step-by-step explanation:

Let x represent number of video games.
We have been given that a video game store allows customers to rent games for $4.75 each. So the cost of renting x video games would be 4.75x.

We are also told that customers can also buys a membership for $54 annually, and video games would only cost $2.50 each. The cost of renting x video games after membership would be 2.50x + 54

To find the number of video-games that will cost same for both options, we will equate both expressions as:

4.75x = 2.50x + 54
4.75x - 2.50x = 2.50x - 2.50x + 54

Therefore, a customer would have rent 24 video games in a year in order for the two options to be equal.

3 0

3 years ago

What is the solution of this system of linear equations?<br> 3y= 3/2x+6<br> 1/2y-1/4x=3

In-s [12.5K]

There is no solution to this system of linear equations

5 0

4 years ago

Which inequality best represents that ice cream at −2°C is cooler than ice cream at 3°C? Group of answer choices −3°C > 2°C −

ollegr [7]

Answer:

3°C > - 2°C

Step-by-step explanation:

Ice cream 1 = - 2°C

Ice cream 2 = 3°C

Lower temperatures are colder (cooler) than higher temperature values.

Hence, ice cream at - 2°C is cooler than ice cream at 3°C.

Hence, a temperature of 3°C is higher (greater) than - 2°C. Hence - 2°C is cooler (colder) than 3°C

Hence,

3°C > - 2°C

5 0

3 years ago