Yes it’s a rational number
Answer:
Given two events A and B of a sample set :-
P[A] = 0.20
P[not B]=0.40
![P[B/A]=0.25](https://tex.z-dn.net/?f=P%5BB%2FA%5D%3D0.25)
To find P[A or B]:
![P[A or B] = P[A] + P[B] - P[A \cap B]](https://tex.z-dn.net/?f=P%5BA%20or%20B%5D%20%3D%20P%5BA%5D%20%2B%20P%5BB%5D%20-%20P%5BA%20%5Ccap%20B%5D)
......[1]
Calculate for ![P[B]](https://tex.z-dn.net/?f=P%5BB%5D)
and ![P[A \cap B]](https://tex.z-dn.net/?f=P%5BA%20%5Ccap%20B%5D)
P[B] = 1- P[not B]
Substitute the value P[not B] we get;
P[B] = 1-0.40 = 0.60
![P[A \cap B] = P[B/A] \cdot P[A]](https://tex.z-dn.net/?f=P%5BA%20%5Ccap%20B%5D%20%3D%20P%5BB%2FA%5D%20%5Ccdot%20P%5BA%5D)
Substitute the given values we get;
![P[A \cap B] = 0.25 \cdot 0.20 = 0.05](https://tex.z-dn.net/?f=P%5BA%20%5Ccap%20B%5D%20%3D%200.25%20%5Ccdot%200.20%20%3D%200.05)
Then;
![P[A or B] = 0.20+0.60-0.05 = 0.80-0.05 =0.75](https://tex.z-dn.net/?f=P%5BA%20or%20B%5D%20%3D%200.20%2B0.60-0.05%20%3D%200.80-0.05%20%3D0.75)
Therefore, the value of P[A or B] is, 0.75.
Answer:
Step-by-step explanation:
Given:
The system of equations given are:
If an equation is multiplied by a number throughout, then the equation remains the same by multiplication property of equality. The multiplication property of equality says that if both sides of the equation is multiplied by the same number, then the new equation is equivalent to the previous equation.
For example: If 
is multiplied by 2 on both sides, then the new equation will be 
which is equivalent to .
So, from among all the choices given, the first choice represents the above mentioned property. The equation 
is multiplied by 3 on both sides. So, the equation 
is equivalent to .
The second equation 
has not been changed. So, the equivalent system of equations to the given system is:
Use the substitution method
s+(-7)-1
-3+(-7)-1
-negative sign and + positive sign= - negative sign
-3-7-1
=-10-1
=-11
Answer: -11
Answers:
The series converges
The sum is -8/3
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a = -4 is the first term
r = -1/2 is the common ratio
the reason why is because the expression -4(-1/2)^(n-1) is in the form a(r)^(n-1). Notice how -4 matches with the 'a'; the -1/2 matches with the r
The common ratio will determine if the infinite series converges or not.
r = -1/2 leads to |r| = |-1/2| = 1/2 = 0.5
Since |r| < 1 (in this case 0.5 < 1) is true, this means the series does converge.
Put another way, because r = -1/2 = -0.5 makes -1 < r < 1 true, the series converges.
Use the formula below to find the converging value S
S = a/(1-r)
S = -4/(1-(-1/2))
S = -4/(1+1/2)
S = -4/(2/2+1/2)
S = -4/(3/2)
S = (-4/1)/(3/2)
S = (-4/1)*(2/3)
S = (-4*2)/(1*3)
S = -8/3
The infinite series converges to -8/3
So the sum is -8/3
