Answer:
(b) 0.251
Step-by-step explanation:
1. Standard deviation equation:
![SD=\sqrt{\frac{\sum\limits^N_i {(x_{i}-X)^{2} } }{N} }](https://tex.z-dn.net/?f=SD%3D%5Csqrt%7B%5Cfrac%7B%5Csum%5Climits%5EN_i%20%7B%28x_%7Bi%7D-X%29%5E%7B2%7D%20%20%7D%20%7D%7BN%7D%20%7D)
Where X is the mean of the data, and N the amount of data. Then, N=5
2. Estimate the Mean:
![X=\frac{0.750+0.750+0.200+0.600+0.200}{5}=\frac{2.5}{5}=0.5\\](https://tex.z-dn.net/?f=X%3D%5Cfrac%7B0.750%2B0.750%2B0.200%2B0.600%2B0.200%7D%7B5%7D%3D%5Cfrac%7B2.5%7D%7B5%7D%3D0.5%5C%5C)
3. Caclulate Standard deviation:
![SD=\sqrt{\frac{{(0.750-0.500)^{2}+(0.750-0.500)^{2}+(0.200-0.500)^{2}+(0.600-0.500)^{2}+(0.200-0.500)^{2} } }{5} }](https://tex.z-dn.net/?f=SD%3D%5Csqrt%7B%5Cfrac%7B%7B%280.750-0.500%29%5E%7B2%7D%2B%280.750-0.500%29%5E%7B2%7D%2B%280.200-0.500%29%5E%7B2%7D%2B%280.600-0.500%29%5E%7B2%7D%2B%280.200-0.500%29%5E%7B2%7D%20%20%7D%20%7D%7B5%7D%20%7D)
![SD=\sqrt{\frac{0.315}{5} }=\sqrt{0.063}\\SD=0.251](https://tex.z-dn.net/?f=SD%3D%5Csqrt%7B%5Cfrac%7B0.315%7D%7B5%7D%20%7D%3D%5Csqrt%7B0.063%7D%5C%5CSD%3D0.251)
No, the least amount of points you can do on a graph to see the pattern is 3 because than you can get a better line for your graph to see what kind of pattern your graph is.
Answer:
see below
Step-by-step explanation:
![1) -4x + 9x = 5x\\\\2) 6y -8y = -2y\\\\3) -7x+x = -6x\\\\4) 9y-y = 8y\\\\5) -5x-5x = -10x\\\\6) 3y-7y = -4y\\\\7) -x-8x+7 = -9x +7\\\\8) y-2y -3 = -y -3\\\\9) 5+5x-4x = 5 + x\\\\10) 3y-6 +7y-4y = 6y -6\\\\11) -9x-5-8+x = -13 -8x\\\\12) 6-y+5y-6y = 6 -2y\\\\13) 3x-8y+2x-5-5y = 5x -13y -5\\\\14)-9x +3 +2x-9y-8 = -7x -9y -5\\\\15) 5 +6x -3y +x +8y = 7x +5y+5\\\\16) -4x -4 +x -2y +7x = 4x -2y -4\\\\17) -8x +7y-x-6y+4x = -5x +y\\\\18) x+5-2x+3y-y=2y-x+5\\\\19) 9x-3y+7-4x+y-3 = 5x-2y+4\\\\](https://tex.z-dn.net/?f=1%29%20-4x%20%2B%209x%20%3D%205x%5C%5C%5C%5C2%29%206y%20-8y%20%3D%20-2y%5C%5C%5C%5C3%29%20-7x%2Bx%20%3D%20-6x%5C%5C%5C%5C4%29%209y-y%20%3D%208y%5C%5C%5C%5C5%29%20-5x-5x%20%3D%20-10x%5C%5C%5C%5C6%29%203y-7y%20%3D%20-4y%5C%5C%5C%5C7%29%20-x-8x%2B7%20%3D%20-9x%20%2B7%5C%5C%5C%5C8%29%20y-2y%20-3%20%3D%20-y%20-3%5C%5C%5C%5C9%29%205%2B5x-4x%20%3D%205%20%2B%20x%5C%5C%5C%5C10%29%203y-6%20%2B7y-4y%20%3D%206y%20-6%5C%5C%5C%5C11%29%20-9x-5-8%2Bx%20%3D%20-13%20-8x%5C%5C%5C%5C12%29%206-y%2B5y-6y%20%3D%206%20-2y%5C%5C%5C%5C13%29%203x-8y%2B2x-5-5y%20%3D%205x%20-13y%20-5%5C%5C%5C%5C14%29-9x%20%2B3%20%2B2x-9y-8%20%3D%20-7x%20-9y%20-5%5C%5C%5C%5C15%29%205%20%2B6x%20-3y%20%2Bx%20%2B8y%20%3D%207x%20%2B5y%2B5%5C%5C%5C%5C16%29%20-4x%20-4%20%2Bx%20-2y%20%2B7x%20%3D%204x%20-2y%20-4%5C%5C%5C%5C17%29%20-8x%20%2B7y-x-6y%2B4x%20%3D%20-5x%20%2By%5C%5C%5C%5C18%29%20x%2B5-2x%2B3y-y%3D2y-x%2B5%5C%5C%5C%5C19%29%209x-3y%2B7-4x%2By-3%20%3D%205x-2y%2B4%5C%5C%5C%5C)
![20) -x-3+5x+6y+8x-9\\\\21) 4x-4-8y+8-5x+1 = -x-8y+5\\\\22) 3x-x+6y-4x-y = -2x+5y\\\\23) 2x+2y-x-y-7+5y = x+6y-7\\\\24) 6x-8x-4y -x+5y-2y = -3x-y\\\\](https://tex.z-dn.net/?f=20%29%20-x-3%2B5x%2B6y%2B8x-9%5C%5C%5C%5C21%29%204x-4-8y%2B8-5x%2B1%20%3D%20-x-8y%2B5%5C%5C%5C%5C22%29%203x-x%2B6y-4x-y%20%3D%20-2x%2B5y%5C%5C%5C%5C23%29%202x%2B2y-x-y-7%2B5y%20%3D%20x%2B6y-7%5C%5C%5C%5C24%29%206x-8x-4y%20-x%2B5y-2y%20%3D%20-3x-y%5C%5C%5C%5C)
Answer:
This case has NO solutions.
Step-by-step explanation:
Notice that you are in a case of an obtuse triangle (one of its angles is larger than 90 degrees), the side opposite to the obtuse triangle is shorter than the side adjacent to the angle, so no actual triangle can be formed.
This can be found by simply trying to apply the Law of Sines to solve for the value of angle "B" opposite to side "b":
![\frac{sin(A)}{a} =\frac{sin(B)}{b}\\sin(B)=\frac{b\,sin(A)}{a}\\sin(B)=\frac{9\,sin(112^o)}{4}\\\\sin(B)=2.086](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%28A%29%7D%7Ba%7D%20%3D%5Cfrac%7Bsin%28B%29%7D%7Bb%7D%5C%5Csin%28B%29%3D%5Cfrac%7Bb%5C%2Csin%28A%29%7D%7Ba%7D%5C%5Csin%28B%29%3D%5Cfrac%7B9%5C%2Csin%28112%5Eo%29%7D%7B4%7D%5C%5C%5C%5Csin%28B%29%3D2.086)
As shown above, we get an impossible mathematical condition (also call an absurd), since the sine of an angle cannot give a value larger than 1 (one).
Therefore, there is no angle we can find to build a triangle with the given data.
Diameter = 8 cm
radius = diameter/2 = 4 cm
A = pi * r^2
A = pi * (4 cm)^2
A = 16pi cm^2