The probability of Julia picking 49 is 1/100 ( one number out of 100)
The probability of Shelly picking 49 is also 1/100 ( one number out of 100)
The probability of both picking the same number is
1/100 x 1/100 = 2/100 = 1/50 = 0.02 = 2%
Answer: 1. D. IV
2. A. I
3. A. I
Step-by-step explanation: 1. You have to move the quadrilateral (the shape) 7 units to the right and down 5 units. You can see that it is in the fourth quadrant.
2. You have to flip the shape over the y-axis. It moves to the first quadrant.
3. If you rotate the shape to the right around the origin, it ends up in the first quadrant.
Answer:
81 cubic feet.
Step-by-step explanation:
multiply the volume value by 27
Answer: (1/3,2)
Step-by-step explanation:
Let O(x,y) be the circumference of the triangle PQR,
Thus, by the property of circumcenter all the vertices of the triangle are at same distance from this circumcenter.
Thus, PO = QO
By the distance formula,
![(x+2)^2+(y-5)^2 = (x-4)^2+(y-1)^2](https://tex.z-dn.net/?f=%28x%2B2%29%5E2%2B%28y-5%29%5E2%20%3D%20%28x-4%29%5E2%2B%28y-1%29%5E2)
![\impliesx^2+ 4x + 4 + y^2+ 25 - 10 y = x^2+16 - 8 x + y^2+1 - 2y](https://tex.z-dn.net/?f=%5Cimpliesx%5E2%2B%204x%20%2B%204%20%2B%20y%5E2%2B%2025%20-%2010%20y%20%3D%20x%5E2%2B16%20-%208%20x%20%2B%20y%5E2%2B1%20-%202y)
![\implies 4x + 4 + 25 - 10 y = 16 - 8 x + 1 - 2y](https://tex.z-dn.net/?f=%5Cimplies%204x%20%2B%204%20%2B%2025%20-%2010%20y%20%3D%2016%20-%208%20x%20%2B%201%20-%202y)
![\implies 4x +8x-10y+2y = 16 + 1 -25-4](https://tex.z-dn.net/?f=%5Cimplies%204x%20%2B8x-10y%2B2y%20%3D%2016%20%2B%201%20-25-4)
![\implies 12x - 8y = 17 - 29](https://tex.z-dn.net/?f=%5Cimplies%2012x%20-%208y%20%3D%2017%20-%2029)
---------(1)
Similarly, QO = RO
![\implies (x-4)^2 + (y-1)^2 = (x+2)^2+(y+3)^2](https://tex.z-dn.net/?f=%5Cimplies%20%28x-4%29%5E2%20%2B%20%28y-1%29%5E2%20%3D%20%28x%2B2%29%5E2%2B%28y%2B3%29%5E2)
![\implies x^2 + 16 - 8x + y^2+ 1 - 2y = x^2+ 4 + 4 x +y^2+ 9 + 6 y](https://tex.z-dn.net/?f=%5Cimplies%20x%5E2%20%2B%2016%20-%208x%20%2B%20y%5E2%2B%201%20-%202y%20%3D%20x%5E2%2B%204%20%2B%204%20x%20%2By%5E2%2B%209%20%2B%206%20y)
![\implies 16 - 8x + 1 - 2y = 4 + 4 x + 9 + 6 y](https://tex.z-dn.net/?f=%5Cimplies%2016%20-%208x%20%2B%201%20-%202y%20%3D%204%20%2B%204%20x%20%2B%209%20%2B%206%20y)
![\implies - 8x -4x-2y-6y=4+9-16-1](https://tex.z-dn.net/?f=%5Cimplies%20-%208x%20-4x-2y-6y%3D4%2B9-16-1)
![\implies -12 x - 8 y = 13 - 17](https://tex.z-dn.net/?f=%5Cimplies%20-12%20x%20-%208%20y%20%3D%2013%20-%2017)
------------(2)
By adding equation (1) and (2),
24 x = - 8
x = 1/3
By putting this value in equation (1),
We get,
Thus, 4 - 8 y = -12
8 y = 16
y = 2