Answer:
And using a calculator, excel ir the normal standard table we have that:
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".
Solution for the problem
Let's say that X represent the random variable "incomes in a certain large population of college", and we know that the distribution for X is:
![X \sim N(\mu = 75000, \sigma= 10000)](https://tex.z-dn.net/?f=%20X%20%5Csim%20N%28%5Cmu%20%3D%2075000%2C%20%5Csigma%3D%2010000%29)
We select 16 teachers and we are interested on the sample mean or average, and we know that the distribution for the sample mean is given by:
![\bar X \sim N(\mu=7500,\sigma_{\bar X}= \frac{\sigma}{\sqrt{n}}=\frac{10000}{\sqrt{16}}=2500)](https://tex.z-dn.net/?f=%5Cbar%20X%20%5Csim%20N%28%5Cmu%3D7500%2C%5Csigma_%7B%5Cbar%20X%7D%3D%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%3D%5Cfrac%7B10000%7D%7B%5Csqrt%7B16%7D%7D%3D2500%29)
And we are interested on this probability:
![P(\bar X>77500)](https://tex.z-dn.net/?f=%20P%28%5Cbar%20X%3E77500%29)
And we can use the z score given by:
![z = \frac{\bar X -\mu}{\sigma_{\bar X}}](https://tex.z-dn.net/?f=%20z%20%3D%20%5Cfrac%7B%5Cbar%20X%20-%5Cmu%7D%7B%5Csigma_%7B%5Cbar%20X%7D%7D)
And using a calculator, excel ir the normal standard table we have that:
The answer is 22 times 19= 418 sq feet
Answer:
![\mathrm{Vertical}:\:x=-1,\:x=2,\:\mathrm{Horizontal}:\:y=\frac{1}{4}](https://tex.z-dn.net/?f=%5Cmathrm%7BVertical%7D%3A%5C%3Ax%3D-1%2C%5C%3Ax%3D2%2C%5C%3A%5Cmathrm%7BHorizontal%7D%3A%5C%3Ay%3D%5Cfrac%7B1%7D%7B4%7D)
Step-by-step explanation:
Your equation is: ![f(x)=\frac{x^2+4}{4x^2-4x-8}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7Bx%5E2%2B4%7D%7B4x%5E2-4x-8%7D)
![\mathrm{If\:the\:degrees\:are\:equal,\:the\:asymptote\:is:\:y=\frac{numerator's\:leading\:coefficient}{denominator's\:leading\:coefficient}}](https://tex.z-dn.net/?f=%5Cmathrm%7BIf%5C%3Athe%5C%3Adegrees%5C%3Aare%5C%3Aequal%2C%5C%3Athe%5C%3Aasymptote%5C%3Ais%3A%5C%3Ay%3D%5Cfrac%7Bnumerator%27s%5C%3Aleading%5C%3Acoefficient%7D%7Bdenominator%27s%5C%3Aleading%5C%3Acoefficient%7D%7D)
That’s not possible but it added to -2 it would be possible
<u>Let's take this problem step-by-step</u>:
<u>The ;unlabeled angle' adjacent to the 'outside angle of measure 78°'</u>
⇒ is on a straight line
⇒ sum of angle measure = 180 degrees
![unlabeled_.angle+78 = 180\\unlabeled_.angle = 102](https://tex.z-dn.net/?f=unlabeled_.angle%2B78%20%3D%20180%5C%5Cunlabeled_.angle%20%3D%20102)
<u>Now we know:</u>
⇒ sum of all angles in a triangle ⇒ 180°
<u>Let's put that in equation form and solve:</u>
![x + 102 + 57=180\\x + 159=180\\x = 21](https://tex.z-dn.net/?f=x%20%2B%20102%20%2B%2057%3D180%5C%5Cx%20%2B%20159%3D180%5C%5Cx%20%3D%2021)
<u>Answer: 21°</u>
<u></u>
Hope that helps!
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