An algebraic expression that represents the product of r cubed and one hundred seven.

Your state is considering raising the legal age for consumption of alcoholic beverages to 21 years old. How large a sample size

julsineya [31]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{2.58})^2}=16641$

And rounded up we have that n=16641

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

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

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 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58$

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 $ME =\pm 0.01$ 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)

For this case we can use as estimator for the proportion $\hat p =0.5$ , since we don't have any other previous info. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{2.58})^2}=16641$

And rounded up we have that n=16641

8 0

3 years ago

F(x)=4^x and g(x)=4^x+2

dsp73

Given:

The two functions are:

$f(x)=4^x$

$g(x)=4^x+2$

To find:

The type of transformation from f(x) to g(x) in the problem above and including its distance moved.

Solution:

The transformation is defined as

$g(x)=f(x+a)+b$ .... (i)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left.
If a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up.
If b<0, then the graph shifts b units down.

We have,

$f(x)=4^x$

$g(x)=4^x+2$

The function g(x) can be written as

$g(x)=f(x)+2$ ...(ii)

On comparing (i) and (ii), we get

$a=0,b=2$

Therefore, the type of transformation is translation and the graph of f(x) shifts 2 units up to get the graph of g(x).

3 0

2 years ago

Carla Compra borrowed $800 at 14% for one year. She paid a $15 processing fee.

Taya2010 [7]

800×0.14=112
112+15=127
(127÷800)*100==15.88%

4 0

3 years ago

Read 2 more answers

Divide to find the quotient. Please help ! Just tell me what write in boxes

vichka [17]

Answer: 8 r 2

Step-by-step explanation:

The closest thing that goes into 26 is 24, which goes into 3 8 times. Subtract 24 from 26, and you are left with 2. The 2 you are left with will be your remainder.

8 0

3 years ago

Read 2 more answers

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Amanda [17]

.125
.5*.5*.5
head*tail*tail

6 0

2 years ago