Let us use the Pythagorean theorem in identifying what triangle can be formed.
Let us assume that the 2 wooden dowels each measure 8 inches. We cut off one wooden dowel into half, so it becomes 2 pcs of 4 inches each.
The 3 wooden dowels now measure, 4 inches, 4 inches, and 8 inches.
The Pythagorean theorem states:
a² + b² = c²
4² + 4² = 8²
16 + 16 = 64
34 ≠ 64
The measure of the cut wooden dowel must be longer than the uncut wooden dowel to create a triangle.
I also tried this on a piece of paper, I cut each piece according to the assumed measure. No triangle can be formed under this activity.
Answer:
![\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}](https://tex.z-dn.net/?f=%5Cchi%5E2%20%3D%20%5Csum_%7Bi%3D1%7D%5En%20%5Cfrac%7B%28O_i%20-E_i%29%5E2%7D%7BE_i%7D)
The expected values for all the categories is :
![E_i =\frac{150}{3}=50](https://tex.z-dn.net/?f=%20E_i%20%3D%5Cfrac%7B150%7D%7B3%7D%3D50)
And then the statistic would be given by:
![\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4](https://tex.z-dn.net/?f=%5Cchi%5E2%20%3D%20%5Cfrac%7B%2840-50%29%5E2%7D%7B50%7D%2B%5Cfrac%7B%2860-50%29%5E2%7D%7B50%7D%2B%5Cfrac%7B%2850-50%29%5E2%7D%7B50%7D%3D4)
And the best option would be:
b. 4
Step-by-step explanation:
For this problem we have the following observed values:
Yes 40 No 60 No Opinion 50
And we want to test the following hypothesis:
Null hypothesis: All the opinions are uniformly distributed
Alternative hypothesis: Not All the opinions are uniformly distributed
And for this case the statistic would be given by:
![\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}](https://tex.z-dn.net/?f=%5Cchi%5E2%20%3D%20%5Csum_%7Bi%3D1%7D%5En%20%5Cfrac%7B%28O_i%20-E_i%29%5E2%7D%7BE_i%7D)
The expected values for all the categories is :
![E_i =\frac{150}{3}=50](https://tex.z-dn.net/?f=%20E_i%20%3D%5Cfrac%7B150%7D%7B3%7D%3D50)
And then the statistic would be given by:
![\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4](https://tex.z-dn.net/?f=%5Cchi%5E2%20%3D%20%5Cfrac%7B%2840-50%29%5E2%7D%7B50%7D%2B%5Cfrac%7B%2860-50%29%5E2%7D%7B50%7D%2B%5Cfrac%7B%2850-50%29%5E2%7D%7B50%7D%3D4)
And the best option would be:
b. 4
Answer:
33º and 147º
Step-by-step explanation:
x + (x + 114) = 180
2x + 114 = 180
2x = 66
x = 33º
x + 114 = 147º
112 km to 3 h
? km to 9h
112 * 9/3 = 336
answer: 336 km
answers are 110,32,113,72 and 540 degrees