An isosceles right triangle is composed of a right angle and two congruent acute angles. In this case, 90 + 2x = 180 where x is the acute angle. x is equal to 45 degrees. Using sine law, 8/sin 90 = y / sin 45 where y is the leg of the triangle. the leg's length is equal to 4 sqrt 2.
<u>Answer-</u>
<em>The probability that in the box there are 1 red and 8 blue markers is</em><em> 0.111 or 11.1%</em>
<u>Solution-</u>
In the box all markers are red or blue. There are total of 9 markers.
So the number of possible combination number of red or blue marker is,
![S=[(0,9),(1, 8),(2,7),(3,6),(4,5),(5,4),(6,3),(7,2),(8,1),(9,0)}]](https://tex.z-dn.net/?f=S%3D%5B%280%2C9%29%2C%281%2C%208%29%2C%282%2C7%29%2C%283%2C6%29%2C%284%2C5%29%2C%285%2C4%29%2C%286%2C3%29%2C%287%2C2%29%2C%288%2C1%29%2C%289%2C0%29%7D%5D)
As at the random drawn, there was a Blue marker, so the condition of (9,0) i.e 9 Red marker and 0 Blue marker is not a case.
So the sample space becomes,
![S=[(0,9),(1, 8),(2,7),(3,6),(4,5),(5,4),(6,3),(7,2),(8,1)}]](https://tex.z-dn.net/?f=S%3D%5B%280%2C9%29%2C%281%2C%208%29%2C%282%2C7%29%2C%283%2C6%29%2C%284%2C5%29%2C%285%2C4%29%2C%286%2C3%29%2C%287%2C2%29%2C%288%2C1%29%7D%5D)
![|S|=9](https://tex.z-dn.net/?f=%7CS%7C%3D9)
Let us assume that E is the event that in the box there are 1 red and 8 blue markers. So
![E=[(1,8)]](https://tex.z-dn.net/?f=E%3D%5B%281%2C8%29%5D)
![|E|=9](https://tex.z-dn.net/?f=%7CE%7C%3D9)
The probability that in the box there are 1 red and 8 blue markers is,
![P(\text{1 Red and 8 Blue})=\dfrac{|E|}{|S|}=\dfrac{1}{9}=0.111=11.1\%](https://tex.z-dn.net/?f=P%28%5Ctext%7B1%20Red%20and%208%20Blue%7D%29%3D%5Cdfrac%7B%7CE%7C%7D%7B%7CS%7C%7D%3D%5Cdfrac%7B1%7D%7B9%7D%3D0.111%3D11.1%5C%25)
Let the number of corn acres be xx and the number of wheat acres be yy.
We are given that:
1- The total number of acres is 180, this means that:
xx + yy = 180 ..............> equation I
2- The number of corn acres is 3 times that of wheat. This means that:
xx = 3yy .........> equation II
Substitute with equation II in equation I to get the value of yy as follows:
xx + yy = 180
3yy + yy = 180
4yy = 180
yy = 45 acres
Now substitute with yy in equation II to get xx as follows:
xx = 3yy
xx = 3*45
xx = 135 acres
Based on the above calculations:
acres of corn = xx = 135 acres
acres of wheat = yy = 45 acres
Answer:
Only b is correctly simplified.
Step-by-step explanation:
Answer:
Step-by-step explanation:
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