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2^5/(-3)=2^5/(-3)=2^5/(-3)
Answer:
$618
Step-by-step explanation:
$1854 divided by 18 months = $103 per month
$103 x 12 months = $1236 paid in one year.
$1854originally owed - $1236 paid in a year = $618 still owed after one year of payments.
Answer:
X=1.132589
Step-by-step explanation:
If im correct the answer would be x=1.132589
3
x2−1
−2(x+3)=
5
x+1
3
(x+1)(x−1)
+−2x−6=
5
x+1
Multiply all terms by (x+1)(x-1) and cancel:
3+(−2x−6)(x+1)(x−1)=5(x−1)
−2x3−6x2+2x+9=5x−5(Simplify both sides of the equation)
−2x3−6x2+2x+9−(5x−5)=5x−5−(5x−5)(Subtract 5x-5 from both sides)
−2x3−6x2−3x+14=0
(Use cubic formula)
x=1.132589
And dont forget to check your answer
We're told that
![P(A\cap B)=0.15](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%29%3D0.15)
![P(A\cup B)^C=0.06\implies P(A\cup B)=0.94](https://tex.z-dn.net/?f=P%28A%5Ccup%20B%29%5EC%3D0.06%5Cimplies%20P%28A%5Ccup%20B%29%3D0.94)
![P(B\mid A)=P(B^C\mid A)=0.5](https://tex.z-dn.net/?f=P%28B%5Cmid%20A%29%3DP%28B%5EC%5Cmid%20A%29%3D0.5)
where the last fact is due to the law of total probability:
![P(A)=P(A\cap B)+P(A\cap B^C)](https://tex.z-dn.net/?f=P%28A%29%3DP%28A%5Ccap%20B%29%2BP%28A%5Ccap%20B%5EC%29)
![\implies P(A)=P(B\mid A)P(A)+P(B^C\mid A)P(A)](https://tex.z-dn.net/?f=%5Cimplies%20P%28A%29%3DP%28B%5Cmid%20A%29P%28A%29%2BP%28B%5EC%5Cmid%20A%29P%28A%29)
![\implies 1=P(B\mid A)+P(B^C\mid A)](https://tex.z-dn.net/?f=%5Cimplies%201%3DP%28B%5Cmid%20A%29%2BP%28B%5EC%5Cmid%20A%29)
so that
and
are complementary.
By definition of conditional probability, we have
![P(B\mid A)=P(B^C\mid A)](https://tex.z-dn.net/?f=P%28B%5Cmid%20A%29%3DP%28B%5EC%5Cmid%20A%29)
![\implies\dfrac{P(A\cap B)}{P(A)}=\dfrac{P(A\cap B^C)}{P(A)}](https://tex.z-dn.net/?f=%5Cimplies%5Cdfrac%7BP%28A%5Ccap%20B%29%7D%7BP%28A%29%7D%3D%5Cdfrac%7BP%28A%5Ccap%20B%5EC%29%7D%7BP%28A%29%7D)
![\implies P(A\cap B)=P(A\cap B^C)](https://tex.z-dn.net/?f=%5Cimplies%20P%28A%5Ccap%20B%29%3DP%28A%5Ccap%20B%5EC%29)
We make use of the addition rule and complementary probabilities to rewrite this as
![P(A\cap B)=P(A\cap B^C)](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%29%3DP%28A%5Ccap%20B%5EC%29)
![\implies P(A)+P(B)-P(A\cup B)=P(A)+P(B^C)-P(A\cup B^C)](https://tex.z-dn.net/?f=%5Cimplies%20P%28A%29%2BP%28B%29-P%28A%5Ccup%20B%29%3DP%28A%29%2BP%28B%5EC%29-P%28A%5Ccup%20B%5EC%29)
![\implies P(B)-[1-P(A\cup B)^C]=[1-P(B)]-P(A\cup B^C)](https://tex.z-dn.net/?f=%5Cimplies%20P%28B%29-%5B1-P%28A%5Ccup%20B%29%5EC%5D%3D%5B1-P%28B%29%5D-P%28A%5Ccup%20B%5EC%29)
![\implies2P(B)=2-[P(A\cup B)^C+P(A\cup B^C)]](https://tex.z-dn.net/?f=%5Cimplies2P%28B%29%3D2-%5BP%28A%5Ccup%20B%29%5EC%2BP%28A%5Ccup%20B%5EC%29%5D)
![\implies2P(B)=[1-P(A\cup B)^C]+[1-P(A\cup B^C)]](https://tex.z-dn.net/?f=%5Cimplies2P%28B%29%3D%5B1-P%28A%5Ccup%20B%29%5EC%5D%2B%5B1-P%28A%5Ccup%20B%5EC%29%5D)
![\implies2P(B)=P(A\cup B)+P(A\cup B^C)^C](https://tex.z-dn.net/?f=%5Cimplies2P%28B%29%3DP%28A%5Ccup%20B%29%2BP%28A%5Ccup%20B%5EC%29%5EC)
![\implies2P(B)=P(A\cup B)+P(A^C\cap B)\quad(*)](https://tex.z-dn.net/?f=%5Cimplies2P%28B%29%3DP%28A%5Ccup%20B%29%2BP%28A%5EC%5Ccap%20B%29%5Cquad%28%2A%29)
By the law of total probability,
![P(B)=P(A\cap B)+P(A^C\cap B)](https://tex.z-dn.net/?f=P%28B%29%3DP%28A%5Ccap%20B%29%2BP%28A%5EC%5Ccap%20B%29)
![\implies P(A^C\cap B)=P(B)-P(A\cap B)](https://tex.z-dn.net/?f=%5Cimplies%20P%28A%5EC%5Ccap%20B%29%3DP%28B%29-P%28A%5Ccap%20B%29)
and substituting this into
gives
![2P(B)=P(A\cup B)+[P(B)-P(A\cap B)]](https://tex.z-dn.net/?f=2P%28B%29%3DP%28A%5Ccup%20B%29%2B%5BP%28B%29-P%28A%5Ccap%20B%29%5D)
![\implies P(B)=P(A\cup B)-P(A\cap B)](https://tex.z-dn.net/?f=%5Cimplies%20P%28B%29%3DP%28A%5Ccup%20B%29-P%28A%5Ccap%20B%29)
![\implies P(B)=0.94-0.15=\boxed{0.79}](https://tex.z-dn.net/?f=%5Cimplies%20P%28B%29%3D0.94-0.15%3D%5Cboxed%7B0.79%7D)