Answer:
0.362
Step-by-step explanation:
When drawing randomly from the 1st and 2nd urn, 4 case scenarios may happen:
- Red ball is drawn from the 1st urn with a probability of 9/10, red ball is drawn from the 2st urn with a probability of 1/6. The probability of this case to happen is (9/10)*(1/6) = 9/60 = 3/20 or 0.15. The probability that a ball drawn randomly from the third urn is blue given this scenario is (1 blue + 5 blue)/(8 red + 1 blue + 5 blue) = 6/14 = 3/7.
- Red ball is drawn from the 1st urn with a probability of 9/10, blue ball is drawn from the 2nd urn with a probability of 5/6. The probability of this event to happen is (9/10)*(5/6) = 45/60 = 3/4 or 0.75. The probability that a ball drawn randomly from the third urn is blue given this scenario is (1 blue + 4 blue)/(8 red + 1 blue + 1 red + 4 blue) = 5/14
- Blue ball is drawn from the 1st urn with a probability of 1/10, blue ball is drawn from the 2nd urn with a probability of 5/6. The probability of this event to happen is (1/10)*(5/6) = 5/60 = 1/12. The probability that a ball drawn randomly from the third urn is blue given this scenario is (4 blue)/(9 red + 1 red + 4 blue) = 4/14 = 2/7
- Blue ball is drawn from the 1st urn with a probability of 1/10, red ball is drawn from the 2st urn with a probability of 1/6. The probability of this event to happen is (1/10)*(1/6) = 1/60. The probability that a ball drawn randomly from the third urn is blue given this scenario is (5 blue)/(9 red + 5 blue) = 5/14.
Overall, the total probability that a ball drawn randomly from the third urn is blue is the sum of product of each scenario to happen with their respective given probability
P = 0.15(3/7) + 0.75(5/14) + (1/12)*(2/7) + (1/60)*(5/14) = 0.362
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
2*(3*x-7)+18-(10)=0
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(2 • (3x - 7) + 18) - 10 = 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
6x - 6 = 6 • (x - 1)
Equation at the end of step 3 :
6 • (x - 1) = 0
Step 4 :
Equations which are never true :
4.1 Solve : 6 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation :
4.2 Solve : x-1 = 0
Add 1 to both sides of the equation :
x = 1
One solution was found :
x = 1
F(4) is 10 all you do is plug in 4 for x
Answer:
(-1, 4)
Step-by-step explanation:
-5+3/2 = -1
6+ 2/2 = 4
(-1, 4)
The 2 small black lines through the sides of the triangle indicate that the 2 sides are the same length.
Because the 2 sides are the same the 2 bottom angles are also the same.
This means that 9x +3 = 84
Now we can solve for x:
9x +3 = 84
Subtract 3 from each side:
9x = 91
Divide both sides by 9:
x = 81 / 9
x = 9
