A math teacher gave her class two tests. The results were 42 percent of the class passed the first test and 50 percent of the class passed thesecond test. Also, 60 percent of the students in the class who passed the first test passed the second test. What percentage of the class passed both tests? Are the events the class passed the first test and the class passed the second test independent? (1 point) A) A total of 30 percent passed both tests. The events are independent.
B) A total of 25.2 percent passed both tests. The events are independent.
C) A total of 25.2 percent passed both tests. The events are not independent.
D) A total of 30 percent passed both tests. The events are not independent.

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step-by-step explanation:

d

step-by-step explanation:

d

(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