Answer:
x ^3 cubed is x and -8 cubed is 2
Step-by-step explanation:
Answer:
6:22
Step-by-step explanation:
4:55 + 1:27 = 6:22
Since perimeter is all of the sides added up..
And we have
side 1 = 4in
side 2 = 4in
side 3 = 5in
side 6 = 6in
Lets just add them all up
4 + 4 + 5 + 6 = 19
So the perimeter of the trapezoid is 19 inches
love, the Pineapple<3
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Answer:
![P(\bar X >70)= P(Z>\frac{70-69}{\frac{4}{\sqrt{36}}})= P(Z>1.5)](https://tex.z-dn.net/?f=%20P%28%5Cbar%20X%20%3E70%29%3D%20P%28Z%3E%5Cfrac%7B70-69%7D%7B%5Cfrac%7B4%7D%7B%5Csqrt%7B36%7D%7D%7D%29%3D%20P%28Z%3E1.5%29)
And for this case we can use the complement rule and the normal standard distribution of excel and we got:
![P(Z>1.5)=1-P(Z,1.5) = 1-0.933=0.0668](https://tex.z-dn.net/?f=%20P%28Z%3E1.5%29%3D1-P%28Z%2C1.5%29%20%3D%201-0.933%3D0.0668)
Step-by-step explanation:
Previous concepts
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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where
and
And we select a sample size of n =70
From the central limit theorem (n>30)we know that the distribution for the sample mean
is given by:
And we want to find this probability:
![P(\bar X >70)](https://tex.z-dn.net/?f=%20P%28%5Cbar%20X%20%3E70%29)
And we can use the z score formula given by:
![z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=%20z%3D%20%5Cfrac%7B%5Cbar%20X%20-%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
And using this formula we got:
![P(\bar X >70)= P(Z>\frac{70-69}{\frac{4}{\sqrt{36}}})= P(Z>1.5)](https://tex.z-dn.net/?f=%20P%28%5Cbar%20X%20%3E70%29%3D%20P%28Z%3E%5Cfrac%7B70-69%7D%7B%5Cfrac%7B4%7D%7B%5Csqrt%7B36%7D%7D%7D%29%3D%20P%28Z%3E1.5%29)
And for this case we can use the complement rule and the normal standard distribution of excel and we got:
![P(Z>1.5)=1-P(Z,1.5) = 1-0.933=0.0668](https://tex.z-dn.net/?f=%20P%28Z%3E1.5%29%3D1-P%28Z%2C1.5%29%20%3D%201-0.933%3D0.0668)
Answer:
(0,-5) and (0,5).
Step-by-step explanation:
We have been given that an equation of hyperbola
.
First of all we will convert our given equation into the standard form of hyperbola.
Let us divide both sides of our equation by 100.
![\frac{4y^2}{100}-\frac{25x^2}{100}=\frac{100}{100}](https://tex.z-dn.net/?f=%5Cfrac%7B4y%5E2%7D%7B100%7D-%5Cfrac%7B25x%5E2%7D%7B100%7D%3D%5Cfrac%7B100%7D%7B100%7D)
![\frac{y^2}{25}-\frac{x^2}{4}=1](https://tex.z-dn.net/?f=%5Cfrac%7By%5E2%7D%7B25%7D-%5Cfrac%7Bx%5E2%7D%7B4%7D%3D1)
Since we know that the positive term in the equation of a hyperbola determines whether the hyperbola opens in the x-direction or in the y-direction. Our hyperbola has a positive
term, so it opens in the y-direction (up and down).
The equation of a vertical hyperbola is :
, where -a and a are vertices of our hyperbola.
![a^2=5^2](https://tex.z-dn.net/?f=a%5E2%3D5%5E2)
![5^2=\pm5](https://tex.z-dn.net/?f=5%5E2%3D%5Cpm5)
Upon comparing our equation with vertical hyperbola equation we can see that vertices of our hyperbola will be (0.-5) and (0,5).