PLZ HELP AHHHHHHHHHHHHHHHHHHHHHHSimplify 3^4+(7^2−2^4)

Suppose that a researcher is designing a survey to estimate the proportion of adults in your state who oppose a proposed law tha

irinina [24]

Answer:

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

So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.

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".

The population proportion have the following distribution

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

Solution to the problem

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)

If solve n from equation (a) we got:

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

The margin of error desired for this case is $ME= \pm 0.02$ equivalent to 2% points

For this case we need to assume a confidence level, let's assume 95%. And since we don't have prior estimation for the population proportion of interest the best value to do an approximation is $\hat p =0.5$

In order to find the critical value we need to take in count that we are finding the margin of error 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:

$z_{\alpha/2}=\pm 1.96$

Now we have all the values needed and if we replace into equation (b) we got:

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

So without prior estimation for the population proportion, using a confidence level of 95% if we want a margin of error about 2% we need al least a sample size of 2401.

5 0

3 years ago

How many moves are greater than 90 minutes in length?

Olegator [25]

Answer:

x ≤ 90?

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75.percent f

irinina [24]

Answer:

33%

Step-by-step explanation:

Assuming the weight of the mixture to be 100g**, then the weight of ryegrass in the mixture would be 30g.

Also, assume the weight mixture X used in the mixture is Xg, then the weight of mixture Y used in the mixture would be (100-X)g.

So we can now equate the parts of the ryegrass in the mixture as:

0.4X + 0.25(100-X) = 30

<=> 0.4X + 25 - 0.25X = 30

<=> 0.15X = 5

<=> X = 5/0.15 = 500/15 = 100/3

So the weight of mixture X as a percentage of the weight of the mixture

= (weight of X/weight of mixture) * 100%

= (100/3)/100 * 100%

= 33%

3 0

3 years ago

{ x - 3y= -3 & x + y= 5 We are to use the graph to solve the given system of equations, then enter your solution below. I ge

nasty-shy [4]

Answer:

Solution: (3, 2)

Step-by-step explanation:

It's easier to graph when the equation of the lines are in their slope-intercept form, y = mx + b.

x - 3y = -3

-3y = -x - 3

Divide both sides by -3:

$\frac{-3y}{-3} = \frac{-x - 3}{-3}$

y = 1/3x + 1

where slope = 1/3

y-intercept = 1

x + y = 5

Subtract x from both sides to isolate y:

x - x + y = - x + 5

y = -x + 5

where slope = -1

y-intercept, 5

I started by graphing the y-intercepts of each line. Then, I used the slope of each linear equation (rise over run) to plot the next points on the graph. In the attached screenshot of the graph, x - 3y = -3 is the blue line, while x + y = 5 is the green line. Their intersection occurs at point, (3, 2).

Therefore, the solution is (3, 2).

Please mark my answers as the Brainliest if you find my explanations helpful :)

5 0

2 years ago

A football is thrown from the stadium. The height of this football can be represented by the polynomial -16t2 +32t + 20, where t

olasank [31]

Answer:

C

Step-by-step explanation:

related equation

-16t^2 + 32t + 20 = 0

-4t^2 + 8t + 5 = 0

Δ/4 = 16 + 20 = 36

t1 = (-4 + 6)/-4 = -1/2

t2 = (-4 - 6)/-4 = 5/2

-16(t+1/2)(t-5/2)

-16(2t+1/2)(2t-5/2)

-4(2t+1)(2t-5)

5 0

3 years ago