Let x and y be the rate per hour for Mechanic 1 and 2 respectively.
Then,
x+y=205 ---------- (1)
Additionally,
10x+15y = 2500 ------ (2)
Solving equations 1 and 2;
Multiply (1) by 10 and subtract two from the result,
10x+10y = 2050
10x +15 y =2500
----------------------
-5 y = --450 => y = 450/5 = $90
Then,
x= 205-90 = $115
Therefore,
Mechanic 1 charged $115 per hour
Mechanic 2 charged $90 per hour
Since the dice are fair and the rolling are independent, each single outcome has probability 1/15. Every time we choose
We have 
and 
, because the dice are fair.
Now we use the assumption of independence to claim that
Now, we simply have to count in how many ways we can obtain every possible outcome for the sum. Consider the attached table: we can see that we can obtain:
- 2 in a unique way (1+1)
- 3 in two possible ways (1+2, 2+1)
- 4 in three possible ways
- 5 in three possible ways
- 6 in three possible ways
- 7 in two possible ways
- 8 in a unique way
This implies that the probabilities of the outcomes of 
are the number of possible ways divided by 15: we can obtain 2 and 8 with probability 1/15, 3 and 7 with probability 2/15, and 4, 5 and 6 with probabilities 3/15=1/5
F(g(-2))=4(-2)^6+4(-2)^3+1
f(g(-2))=4(64)+4(-8)+1
f(g(-2))=256-32+1
f(g(-2))=224+1
f(g(-2))=225
Answer:
Step-by-step explanation:
hello :
Completing The Square x²-4x-2= (x²-4x+4)-4-2 = (x-2)²-6
the vertex is : (2 , -6)
now calculate the solutions : (x-2)²-6 =0
(x-2)²= 6 means : x-2 =√6 or x-2 = -√6
x = 2+√6 or x = 2-√6
