Simplify- 10x-8y +3x-2y

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

If Bill

777dan777 [17]

Answer:

$3,623.84 Exact answer without rounding | $3,623.85 ~ (Approximent Answer with rounding.)

Step-by-step explanation:

Compound Interest Has a Specific Formula:

This case is Exponential Growth.

Formula: y= ab^x

You need to set up the equation.

First we need to define the rate of growth meaning what do you have to do for the 6.5%.

You need to do 100% + 6.5% = 106.5%

You need to convert the percent to a decimal which will be 1.065

Now we need to start plugging things into our formula to solve.

Your initial Starting amount was $3000

So you need to have y=3000(b)^x

We now know that the rate of growth is 1.065 so the b would be 1.065

y=3000(1.065)^x

Our power to x is our 3.5 years.

Our Equation now:

y=3000(1.065)^3

Now you need to use a calculator to do this due to the amount of decimals and digits.

Remember pemdas when doing this!!!

The answer should result to $3,623.84 but if rounded then: $3,623.85

4 0

2 years ago

Jessica opened a bank account that earns 2 percent interest compounded annually. Her initial deposit was $100, and she uses the

klasskru [66]

Answer:

x = 1.02.

Step-by-step explanation:

The x is a factor worked out from the annual interest written as a decimal fraction.

So we have 2% = 2/100 = 0.02.

The amount at the end of the first year is $100 + 0.02*100

= $100* 1.02, and in the second year it will be $100* 1.02^t where t = 2 and so on.

So we see that x in the given expression is 1.02.

5 0

3 years ago

Find the perimeter and the area of the polygon with the given vertices. W (11,2), X (11,8), Y (14,8), Z (14,2)

liberstina [14]

Answer:

The perimeter of the polygon = 18 units

The area of the polygon will be $A=18$ square units

Step-by-step explanation:

Computing the Perimeter of the Polygon: 

Considering the polygon with vertices

W (11,2)

X (11,8)

Y (14,8)

Z (14,2)

As the polygon is drawn in coordinate plane as shown in figure a.

From the attached figure a, we can observe that

The length of the side $WZ = 3$ units

The length of the side $ZY = 6$ units

The length of the side $WX = 6$ units

The length of the side $XY = 3$ units

So, the perimeter of the polygon can be calculated by taking the sum of the lengths of all sides i.e.

The perimeter of the polygon = $WZ + ZY + WX + XY$

= 3 + 6 + 6 + 3

= 18 units

Computing the Area of the Polygon: 

Area can be calculated by multiplying the length and width of the polygon.

$A=lw$

So, the area will be:

$A=lw$

$A=(3)(6)$

$A=18$

Therefore, the area of the polygon will be $A=18$ square units

Keywords: area, perimeter, polygon

Learn more about area and perimeter from brainly.com/question/2328840

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5 0

3 years ago

What is equivalent to -3(x-9)

ivolga24 [154]

$-3(x-9)=-3\cdot x-3\cdot(-9)=-3x+27$

6 0

3 years ago

Read 2 more answers