4. For which of the following probability assignments are events A and B independent? P(AN B“) – 0.3. P(AN B) = 0.12, and P(Aºn B) = 0.4.
B
P(An BC) = 0.3. P(An B) = 0.3, and P(Aºn B) = 0.3.
C) P(An Bº) = 0.1. P(ANB) = 0.1, and P(Aº n B) = 0.4.
P(An Bº) = 0.3. P (AnB) = 0.0, and P(
AB) = 0.2.
E) P(An Bº) = 0.5, P (ANB) = 0.1 and P (Aºn B) = 0.4

A

Step-by-step explanation:

formatting is so bad lol

but yeah its the first one because for independent events, the probably of a and b is the product of both probabilities, just like how 0.3*0.4=0.12

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2

the answer is b.

step-by-step explanation:

by the trigonometric ratio tangent, tangent equals opposite divided by adjacent.

therefore, tan(50) equals ac/3

multiply each side by 3 to get: ac=3tan(50)

the answer is b.