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3 years ago

Exponential form of xyyzzz

Mathematics

1 answer:

Trava [24]3 years ago

8 0

Answer:

xy²z³

Step-by-step explanation:

An exponent is a way to indicate the number of times the factor is repeated. When it is 1, it is rarely shown.

x is repeated once, so will appear without an exponent

y is repeated twice, so will have an exponent of 2

z is repeated 3 times, so will have an exponent of 3

xyyzzz = xy²z³

_____

In plain text, an exponent is indicated with a caret (^).

xy^2z^3

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A population has a standard deviation of 5.5. What is the standard error of the sampling distribution if the sample size is 81?

VladimirAG [237]

Answer:

$\sigma = 5.5$

And we have a sample size of n =81. We want to estimate the standard error of the sampling distribution $\bar X$ and for this case we know that the distribution is given by:

$\bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})$

And the standard error would be:

$\sigma_{\bar x}= \frac{\sigma}{\sqrt{n}}$

And replacing we got:

$\sigma_{\bar x}=\frac{5.5}{\sqrt{81}}= 0.611$

Step-by-step explanation:

For this case we know the population deviation given by:

$\sigma = 5.5$

And we have a sample size of n =81. We want to estimate the standard error of the sampling distribution $\bar X$ and for this case we know that the distribution is given by:

$\bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})$

And the standard error would be:

$\sigma_{\bar x}= \frac{\sigma}{\sqrt{n}}$

And replacing we got:

$\sigma_{\bar x}=\frac{5.5}{\sqrt{81}}= 0.611$

4 0

3 years ago

1 + tanx / 1 + cotx =2

Lera25 [3.4K]

Answer:

x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or x = tan^(-1)(-(i sqrt(3))/2 + 1/2) + π n_2 for n_2 element Z

Step-by-step explanation:

Solve for x:

1 + cot(x) + tan(x) = 2

Multiply both sides of 1 + cot(x) + tan(x) = 2 by tan(x):

1 + tan(x) + tan^2(x) = 2 tan(x)

Subtract 2 tan(x) from both sides:

1 - tan(x) + tan^2(x) = 0

Subtract 1 from both sides:

tan^2(x) - tan(x) = -1

Add 1/4 to both sides:

1/4 - tan(x) + tan^2(x) = -3/4

Write the left hand side as a square:

(tan(x) - 1/2)^2 = -3/4

Take the square root of both sides:

tan(x) - 1/2 = (i sqrt(3))/2 or tan(x) - 1/2 = -(i sqrt(3))/2

Add 1/2 to both sides:

tan(x) = 1/2 + (i sqrt(3))/2 or tan(x) - 1/2 = -(i sqrt(3))/2

Take the inverse tangent of both sides:

x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or tan(x) - 1/2 = -(i sqrt(3))/2

Add 1/2 to both sides:

x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or tan(x) = 1/2 - (i sqrt(3))/2

Take the inverse tangent of both sides:

Answer: x = tan^(-1)((i sqrt(3))/2 + 1/2) + π n_1 for n_1 element Z

or x = tan^(-1)(-(i sqrt(3))/2 + 1/2) + π n_2 for n_2 element Z

4 0

3 years ago

PLS HELP WILL GIVE BRAINLIEST

Vanyuwa [196]

Answer:

The correct answer is the last choice. It travels for 2 hours, then stops for 1 hour, and finally travels again for 2 hours.

Step-by-step explanation:

In the first segment of the trip, the car goes from 0 to 2 hours and the line is moving up. Therefore, it traveled for 2 hours.

In the second segment, the line went straight horizontal for 1 hour. That means the distance didn't change, in other words, it didn't move.

In the last segment, it moved up again for 2 hours.

7 0

3 years ago

Read 2 more answers

Suppose f(7) = 5, f'(7) = 8, g(7) = 3, and g'(7) = 4. Find h(7) and h'(7), where h(x ) = 4f (x) + 3g(x).

dusya [7]

Answer:

h(7) = 29

h'(7) = 44

Step-by-step explanation:

If $h(x) =4f(x)+3g(x)$ , to find h(7) we can substitute the values of f(7) and g(7) and we get:

$h(7)=4f(7)+3g(7)\\h(7)=4(5)+3(3)\\h(7)=20+9\\h(7)=29$

To find the derivative, we know that the derivative of a sum of functions equals the sum of the derivatives of those functions.

This would mean that $h'(x)=4f'(x)+3g'(x)$ , we can substitute the values for f'(7) and g'(7)

$h'(7)=4f'(7)+3g'(7)\\h'(7)=4(8)+3(4)\\h'(7)=32+12\\h'(7)=44$

7 0

3 years ago

1) A right triangle has a side that measures 4 m and a hypotenuse that measures8.5 m. What is the measure of the other side of t

hammer [34]

1) Use the pathagreom theorem; a^2+b^2=c^2
(The hypotenuse is always c. The other two legs can be either a or b.)
*use x for the unknown side*
1. Plug in the measurements
4^2+x^2=8.5^2
2. Solve
16+x^2=72.25
RADICAL(56.25)=> 7.5
The measure of the other side of the triangle (x) is= 7.5 m

2) Draw a square with the measure of 20 cm on each side.
Draw a diagonal line across the square.
(Use the pathagroeam theorem)
We know that the legs are 20, and 20. The hypotenuse is what we are trying to find (x).
1. Plug in the measurements
20^2+20^2=x^2
2. Solve
800= x^2
20 RADICAL(2)=> 28.28
The measure of the other side of the triangle (x) is= 28.3 cm

3 0

3 years ago