Answer:
If A and B are two rational numbers such that A<B
Then X = A + (B-A)/π would be an example of an irrational number
such that A < X < B
Hope this helps
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For number 4 the equation is 12 divided by 3/4 and when you solve that you get 16 which is the answer. For question 5 the equation would be 40 5/8 divided by 4. The first to do this is make 40 5/8 an improper fraction which is 325/8. Then you would flip the 4/1(this is the same thing as 4) to get 1/4. Then you would multiply 325/8 * 4 to get 325/32 and as a mixed number 10 5/32 which is the answer.
Answer:
![\chi^2 = \frac{(83-90)^2}{90} +\frac{(68-72)^2}{72}+\frac{(85-78)^2}{78}+\frac{(64-60)^2}{60} = 1.66](https://tex.z-dn.net/?f=%5Cchi%5E2%20%3D%20%5Cfrac%7B%2883-90%29%5E2%7D%7B90%7D%20%2B%5Cfrac%7B%2868-72%29%5E2%7D%7B72%7D%2B%5Cfrac%7B%2885-78%29%5E2%7D%7B78%7D%2B%5Cfrac%7B%2864-60%29%5E2%7D%7B60%7D%20%3D%201.66)
And the answer would be:
c. 1.66
Step-by-step explanation:
We need to conduct a chi square test
The statistic to check the hypothesis is given by:
the observed values for this case are:
![Freshemen=83](https://tex.z-dn.net/?f=%20Freshemen%3D83)
![Sophomores=68](https://tex.z-dn.net/?f=%20Sophomores%3D68)
![Juniors = 85](https://tex.z-dn.net/?f=%20Juniors%20%3D%2085)
![Seniors= 64](https://tex.z-dn.net/?f=Seniors%3D%2064)
The expected values for this case are:
![Fres_E =0.3*300= 90](https://tex.z-dn.net/?f=%20Fres_E%20%3D0.3%2A300%3D%2090)
![Sop_E =0.24*300= 72](https://tex.z-dn.net/?f=%20Sop_E%20%3D0.24%2A300%3D%2072)
![Jun_E = 0.26*300 =78](https://tex.z-dn.net/?f=Jun_E%20%3D%200.26%2A300%20%3D78)
![Sen_E = 0.20*300= 60](https://tex.z-dn.net/?f=%20Sen_E%20%3D%200.20%2A300%3D%2060)
Then the statistic would be given by:
![\chi^2 = \frac{(83-90)^2}{90} +\frac{(68-72)^2}{72}+\frac{(85-78)^2}{78}+\frac{(64-60)^2}{60} = 1.66](https://tex.z-dn.net/?f=%5Cchi%5E2%20%3D%20%5Cfrac%7B%2883-90%29%5E2%7D%7B90%7D%20%2B%5Cfrac%7B%2868-72%29%5E2%7D%7B72%7D%2B%5Cfrac%7B%2885-78%29%5E2%7D%7B78%7D%2B%5Cfrac%7B%2864-60%29%5E2%7D%7B60%7D%20%3D%201.66)
And the answer would be:
c. 1.66
The function g is:
![g(x) = |4x| + 4](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%7C4x%7C%20%2B%204)
----------------------
Horizontally shrinking a function f(x) by a factor of
is equivalent to finding f(ax).
----------------------
In this question, the function is:
![f(x) = |2x| + 4](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%7C2x%7C%20%2B%204)
Horizontally shrinking by a factor of
means that
, so:
![g(x) = f(ax) = f(2x) = |2(2x)| + 4 = |4x| + 4](https://tex.z-dn.net/?f=g%28x%29%20%3D%20f%28ax%29%20%3D%20f%282x%29%20%3D%20%7C2%282x%29%7C%20%2B%204%20%3D%20%7C4x%7C%20%2B%204)
Thus, the function g is:
![g(x) = |4x| + 4](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%7C4x%7C%20%2B%204)
A similar question is given at brainly.com/question/20379647