A + 2K = 8.75
2A + 5K = 19.75
Change the first expression so that we can subtract the As
2A + 5K = 19.75
2A+4K= 17.50
If the signs are the same, subtract one expression from another
K= 2.25
substitute K into any expression to get A
A+4.50= 8.75
Subtract 4.50
a=4.25
K=$2.50
A= $4.25
Sample space={A,R,I,T,H,M,E,T,I,C}
1ST (Choosing T) ==> P(1st draw) = 2/10 = 1/5 = 0.2
2ND (Choosing again a T) ==> P(2nd draw) = 1/9 = 0.11
Since it's a conditional probability then P (1st T AND 2nd T) = 0.2 x 0.11 =0.022
I think i did it wrong but 1980 is what i got...i am unsure. hope that helped though:)
Answer:
D
Step-by-step explanation:
Consider all options:
A. False, because
![(a^2+b^2)(c^2+d^2)=a^2c^2+a^2d^2+b^2c^2+b^2d^2\\ \\(ab-cd)^2+(ac+bd)^2=a^2b^2-2abcd+c^2d^2+a^2c^2+2abcd+b^2d^2=\\ =a^2b^2+c^2d^2+a^2c^2+b^2d^2\\ \\a^2c^2+a^2d^2+b^2c^2+b^2d^2\neq a^2b^2+c^2d^2+a^2c^2+b^2d^2](https://tex.z-dn.net/?f=%28a%5E2%2Bb%5E2%29%28c%5E2%2Bd%5E2%29%3Da%5E2c%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2%2Bb%5E2d%5E2%5C%5C%20%5C%5C%28ab-cd%29%5E2%2B%28ac%2Bbd%29%5E2%3Da%5E2b%5E2-2abcd%2Bc%5E2d%5E2%2Ba%5E2c%5E2%2B2abcd%2Bb%5E2d%5E2%3D%5C%5C%20%3Da%5E2b%5E2%2Bc%5E2d%5E2%2Ba%5E2c%5E2%2Bb%5E2d%5E2%5C%5C%20%5C%5Ca%5E2c%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2%2Bb%5E2d%5E2%5Cneq%20a%5E2b%5E2%2Bc%5E2d%5E2%2Ba%5E2c%5E2%2Bb%5E2d%5E2)
B. False, because
![(a^2-b^2)(c^2+d^2)=a^2c^2+a^2d^2-b^2c^2-b^2d^2\\ \\(ac-bd)^2-(ad+bc)^2=a^2c^2-2abcd+b^2d^2+a^2d^2+2abcd+b^2c^2=\\=a^2c^2+b^2d^2+a^2d^2+b^2c^2\\ \\a^2c^2+a^2d^2-b^2c^2-b^2d^2\neq a^2c^2+b^2d^2+a^2d^2+b^2c^2](https://tex.z-dn.net/?f=%28a%5E2-b%5E2%29%28c%5E2%2Bd%5E2%29%3Da%5E2c%5E2%2Ba%5E2d%5E2-b%5E2c%5E2-b%5E2d%5E2%5C%5C%20%5C%5C%28ac-bd%29%5E2-%28ad%2Bbc%29%5E2%3Da%5E2c%5E2-2abcd%2Bb%5E2d%5E2%2Ba%5E2d%5E2%2B2abcd%2Bb%5E2c%5E2%3D%5C%5C%3Da%5E2c%5E2%2Bb%5E2d%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2%5C%5C%20%5C%5Ca%5E2c%5E2%2Ba%5E2d%5E2-b%5E2c%5E2-b%5E2d%5E2%5Cneq%20a%5E2c%5E2%2Bb%5E2d%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2)
C. False, because
![(a^2+b^2)(c^2-d^2)=a^2c^2-a^2d^2+b^2c^2-b^2d^2\\ \\(ac+bd)^2-(ad+bc)^2=a^2c^2+2abcd+b^2d^2-a^2d^2-2abcd-b^2c^2=\\=a^2c^2+b^2d^2-a^2d^2-b^2c^2\\ \\a^2c^2-a^2d^2+b^2c^2-b^2d^2\neq a^2c^2+b^2d^2-a^2d^2-b^2c^2](https://tex.z-dn.net/?f=%28a%5E2%2Bb%5E2%29%28c%5E2-d%5E2%29%3Da%5E2c%5E2-a%5E2d%5E2%2Bb%5E2c%5E2-b%5E2d%5E2%5C%5C%20%5C%5C%28ac%2Bbd%29%5E2-%28ad%2Bbc%29%5E2%3Da%5E2c%5E2%2B2abcd%2Bb%5E2d%5E2-a%5E2d%5E2-2abcd-b%5E2c%5E2%3D%5C%5C%3Da%5E2c%5E2%2Bb%5E2d%5E2-a%5E2d%5E2-b%5E2c%5E2%5C%5C%20%5C%5Ca%5E2c%5E2-a%5E2d%5E2%2Bb%5E2c%5E2-b%5E2d%5E2%5Cneq%20a%5E2c%5E2%2Bb%5E2d%5E2-a%5E2d%5E2-b%5E2c%5E2)
D. True, because
![(a^2+b^2)(c^2+d^2)=a^2c^2+a^2d^2+b^2c^2+b^2d^2\\ \\(ac-bd)^2-(ad+bc)^2=a^2c^2-2abcd+b^2d^2+a^2d^2+2abcd+b^2c^2=\\=a^2c^2+b^2d^2+a^2d^2+b^2c^2\\ \\a^2c^2+a^2d^2+b^2c^2+b^2d^2= a^2c^2+b^2d^2+a^2d^2+b^2c^2](https://tex.z-dn.net/?f=%28a%5E2%2Bb%5E2%29%28c%5E2%2Bd%5E2%29%3Da%5E2c%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2%2Bb%5E2d%5E2%5C%5C%20%5C%5C%28ac-bd%29%5E2-%28ad%2Bbc%29%5E2%3Da%5E2c%5E2-2abcd%2Bb%5E2d%5E2%2Ba%5E2d%5E2%2B2abcd%2Bb%5E2c%5E2%3D%5C%5C%3Da%5E2c%5E2%2Bb%5E2d%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2%5C%5C%20%5C%5Ca%5E2c%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2%2Bb%5E2d%5E2%3D%20a%5E2c%5E2%2Bb%5E2d%5E2%2Ba%5E2d%5E2%2Bb%5E2c%5E2)