How do I solve a system of equation? Can someone explain it to me?

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

The weekly cost (c) of manufacturing (x) number of remotes is given by the equation below. what is the cost to manufacture 2500

IRISSAK [1]

C= 2000 + 3(2500)
C= 2000 + 7,500
C= $9,500

6 0

3 years ago

Caitlin makes candles and sells them in her online shop. Tall candles cost $8 each and short candles cost $5 each. last month, s

snow_tiger [21]

Answer:

tall candles = 39

Short candles = 52

Step-by-step explanation:

let tall candles be x

and short candles be y

No. Of candles sold = x + y =91

Money made from candles will be equal to = 8x + 5y = $572

These both are simultaneous linear equations.

x + y =91 ( multiply by 5)

5x + 5y = 455

8x + 5y = $572

Subtract them:

-3x = -117

x = -117/3

x = 39

put value of x in

x + y = 91

39 + y = 91

y = 91 - 39

y = 52

x shows tall candles so they are 39

y shows short candles so they are 52

3 0

2 years ago

I would really appreciate some help on this.

8_murik_8 [283]

Answer:

1. terms: 4r, 2, -6, and 3r like terms: 2 and -6, 4r and 3r

2.terms: 5h^2, -3h^2, - 4h, 3h, 7 like terms: 5h^2 and -3h^2, - 4h and 3h

3. 3m + 6

4. 15b + 2

5. 3x + 9

Step-by-step explanation:

1. 4r + 2 - 6 +3r

terms: 4r, 2, -6, and 3r like terms: 2 and -6, 4r and 3r

2. 5h^2 - 3h^2 - 4h + 3h + 7

terms: 5h^2, -3h^2, - 4h, 3h, 7 like terms: 5h^2 and -3h^2, - 4h and 3h

3. 6m + 7 - 3m-1

3m + 6

4. 3(5b +2) - 4

15b + 6 - 4

15b + 2

5. 2x + 4 + 5 + x

3x + 9

5 0

3 years ago

If King sets the price at $2.50 per doll how many disappointed customers will each store have during this week?.explain your pro

Anastasy [175]

Answer: about TWO

Step-by-step explanation:

5 0

2 years ago