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3 years ago

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Identify the property used to simplify the following expression. (7 + x) + 1 = 7 + (x + 1) a) Associative Property of addition b

) Commutative Property of Addition c) Identity Property of Addition d) Distributive Property

2 answers:

gayaneshka [121]3 years ago

7 0

Associative Property of Addition

mariarad [96]3 years ago

5 0

<span> a) Associative Property of addition </span>

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Total value of 11 numbers
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3 years ago

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

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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

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3 years ago

Darla has four buckets shaped like cylinders she is filling the buckets with water by using a scoop shaped like a cone if the co

padilas [110]

Answer:

12 Scoops

Step-by-step explanation:

Darla has 4 Cylinder Shaped Buckets

Volume of the Cylinders $=4*\pi r^2h$

The scoop is cone shaped and:

Volume of the Cone Scoop $=\frac{1}{3} \pi r^2h$

Since the radius and height of the cone scoop and cylindrical buckets are the same,

The number of Cone Scoops it will take to fill the buckets is:

Total Volume of Buckets/Volume of Cone Scoops

$=\dfrac{4*\pi r^2h}{\frac{1}{3} \pi r^2h} \\=4 \div \frac{1}{3}\\=12$

It will take 12 Scoops to fill the 4 buckets.

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