Answer:
See explanations below
Step-by-step explanation:
Given the functions
f(x) = 12x - 12
g(x) = x/12 - 1
To show they are inverses, we, must show that f(g(x)) = g(f(x))
f(g(x)) = f(x/12 - 1)
Replace x with x/12 - 1 into f(x)
f(g(x)) =12((x-12)/12) - 11
f(g(x)) = x-1 - 1
f(g(x)) =x - 2
Similarly for g(f(x))
g(f(x)) = g(12x-12)
g(f(x)) =(12x-12)/12 - 1
12(x-1)/12 - 1
x-1 - 1
x - 2
Since f(g(x)) = g(f(x)) = x -2, hence they are inverses of each other
Answer:
y=3x-9
Step-by-step explanation:
-3x^2 - 10x + 5 = 0
Quadratic formula:
-b +/- sqrt[b^2 - 4(a)(c)]/2(a)
So. . . 10 +/- sqrt[(10^2) - 4(-3)(5)]/2(-3)
10 +/- sqrt[100+60]/ -6
10 +/- sqrt[160]/-6
Answer:
-46.91%
Step-by-step explanation:
Given:
Cost of buying the shares = $53,500
Selling cost of the shares = $3,300
Number of years = 2
Since the selling cost is less than the buying cost, therefore the statement for the loss can be verified
Now,
The loss = Selling cost - cost of buying = $3,300 - $53,500 = - $50,200
thus, the loss per year = 
= -$25100
Hence,
Rate of return = 
or
Rate of return = 
or
Rate of return = -46.91%
Answer:
-$13.5
Step-by-step explanation:
Let x be a random variable of a count of player gain.
- We are told that if the die shows 3, the player wins $45.
- there is a charge of $9 to play the game
If he wins, he gains; 45 - 9 = $36
If he looses, he has a net gain which is a loss = -$9
Thus, the x-values are; (36, -9)
Probability of getting a 3 which is a win is P(X) = 1/6 since there are 6 numbers on the dice and probability of getting any other number is P(X) = 5/6
Thus;
E(X) = Σ(x•P(X)) = (1/6)(36) + (5/6)(-9)
E(X) = (1/6)(36 - (5 × 9))
E(X) = (1/6)(36 - 45)
E(X) = -9/6 = -3/2
E(X) = -3/2
This represents -3/2 of $9 = -(3/2) × 9 = - 27/2 = -$13.5
