Type the correct answer in the box. write your answer as a reduced fraction, using / for the fraction bar. a six-sided fair die is rolled 4 times in a row. the probability of getting a 4 only on the last trial is .

Step-by-step explanation:

The probability of NOT getting a 4 means the probability of getting a 1, 2, 3, 5, or 6 which is 5 out of 6 =

The probability of getting a 4 is 1 out of 6 =

The probability of getting a 4 only on the last roll is:

NOT 4    and     NOT 4    and    NOT 4   and     Yes 4

              x                        x                     x                =      

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

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step-by-step explanation:

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