We have log12 (2^4) + log12 x = log12 96;
Then, log12 (16x) = log12 96;
16x = 96;
x = 96/16;
x = 6;
The probability of Jamie picking a blue marble is greater. The ratio of this probability would be 7:3
Ok so let us label our equations first
1- 3x+2y+z=7
2- 5x+5y+4z=3
3- 3x+2y+3z=1
subtracting equation 3 from equation 1
3x+2y+3z=1
(-). 3x+2y+z= 7
----------------------
2z=-6----->z=-3
since we already chose equation 1 and 3 we must involve equation 2
substituting the value if z in the second equation
5x+5y-12=3
5x+5y=15
choosing either the first or the third
3x+2y-3=7
3x+2y=10
solving the system
5x+5y=15
3x+2y=10
multipling the first equation by 2 and the second equation by 5
10x+10y=30
15x+10y=50
subtracting the two equations
-5x=-20--->x=4 substituting for the value of x
40+10y=30--->10y=-10y--->y=-1
so our soultion is x=4,y=-1,z==-3 or (4,-1,-3)
Whether the events are dependent or not, the rule for conditional probability applies:
P(a|b) = P(a∩b)/P(b)
P(a|b)×P(b) = P(a∩b)
0.25×0.4 = P(a∩b) = 0.1
The appropriate choice is
C. 0.1
I would go with option C. x, in the first equation.
The X term has a coefficient of 3, the lowest common factor amongst the 3 terms making for easy isolation of the variable.
