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2 years ago

Simplify the expression. Write answer using only positive exponents. (1/3a^3)^-4

Mathematics

2 answers:

Fantom [35]2 years ago

8 0

Answer:

81/a^16

Step-by-step explanation:

(1/3a^3)^-4

1/3^-4a^-16

3^4 x 1/a^16

81/a^16

Artemon [7]2 years ago

3 0

Answer:

81/a^12

Step-by-step explanation:

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(1 point) Suppose we want a 95% confidence interval for the average amount spent on books by freshmen in their first year at col

Ne4ueva [31]

Answer:

a) $n=(\frac{1.960(16)}{5})^2 =39.33 \approx 40$

So the answer for this case would be n=40 rounded up to the nearest integer

b) For this case if we see the formula for the margin of error

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (a)

We can see that the margin of error is inversely proportional to the sample size so if we want a samller margin of error we need a LARGER sample

Answer: LARGER

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean

$\sigma=16$ represent the population standard deviation

n represent the sample size

Solution to the problem

Part a

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (a)

And on this case we have that ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got $z_{\alpha/2}=1.960$ , replacing into formula (b) we got:

$n=(\frac{1.960(16)}{5})^2 =39.33 \approx 40$

So the answer for this case would be n=40 rounded up to the nearest integer

Part b

For this case if we see the formula for the margin of error

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (a)

We can see that the margin of error is inversely proportional to the sample size so if we want a samller margin of error we need a LARGER sample

Answer: LARGER

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3 years ago

The table below is representing direct<br> variation.

valentina_108 [34]

Where is the table? I can’t help unless I can see the table

7 0

2 years ago

The measures of two angles in a triangle are 32o and 78o. Which of the following equations could be used to find the measure of

Korvikt [17]

Answer:

32+78+x=180

Step-by-step explanation:

All triangle angles add up to 180, so add 78 and 32 then subtract it from 180 to get x, which in another form is 32+78+x=180.

6 0

3 years ago

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X 5.2.19

Semmy [17]

Answer:

Step-by-step explanation:

y = ax² + bx + c

Plug the points into the equation to get a system of 3 equations with 3 unknowns a, b, and c.

-27 = 4a - 2b + c

-42 = 9a + 3b + c

-12 = a + b + c

(a,b,c) = (-4,1,-9)

y = -4x² + x - 9

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2 years ago

find a rational number that is between 5.2 and 5.5. Explain why it is rational Find an irrational number between 5.2 and 5.5. Ex

DedPeter [7]

A rational number is 5.3 . It's rational because it can be written as a fraction a/b

- that is 5 3/10 or 53/10.

An irrational number between the 2 values would be √29

Enter this into ur calculator and you'll get an answer like 5.385164807 but this number carries on beyond bounds and can't be written as a fraction a/b It is irrational.

6 0

3 years ago

Read 2 more answers