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2 years ago

Simplify (2^5/3^2)^4 I need help asap within 10 min

Mathematics

1 answer:

Daniel [21]2 years ago

3 0

Answer:

$\frac{2^{20} }{3^{8} }$

Step-by-step explanation:

Exponent Multiplication Rule :

$(\frac{x^{a} }{y^{b} } )^{c} = \frac{x^{ac} }{y^{bc} }$

=============================================================

Solving :

⇒ $(\frac{2^{5} }{3^{2} } )^{4}$

⇒ $\frac{2^{5(4)} }{3^{2(4)} }$

⇒ $\frac{2^{20} }{3^{8} }$

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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 points ( - 6,5) and ( - 7,q) fall on a line with a slope of 10. What is the value of q?

Usimov [2.4K]

If you go on my profile you will see a similar problem that I already answered today.

Lets start by using a formula (don't remember the name)

(y-y1)=M(x-x1)

M is slope and y is first y value and y1 is second y value same applies to X.

Substitute in the values.

(5-q) = 10(-6-(-7))

5-q = 10*(1)

5-q = 10

-q = 5

q = -5

Check:

Substitute in the value of "q" and use the formula to find slope:

(y1-y)/(x1-x)

Substitute

(-5-5)/(-7-(-6))
-10/-1
10

Your Answer:
The value of "q" is -5

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3 years ago

F is the midpoint of GH. Point G is located at 32 and F is at 105. What is the location of point H?

sukhopar [10]

The location of point H is 68.

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3 years ago

Pls help It's so confusing

Genrish500 [490]

9. 9.37, 9.3, 9.219, 9.129

10. 0.101, 0.100, 0.012, 0.001

11. 5.312, 5.231, 5.132, 5.123

12. 62.950, 62.905, 62.833, 62.383

Hope it helps

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3 years ago

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If the perimeter of a square is 24 inches how much is each side ????

mina [271]

Answer: 6 inches each.

Step-by-step explanation: 24/4 because it is a square it has 4 sides all the same length(please vote me brainliest)!

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4 years ago