On a multiple-choice test, a student has four possible choices for each question. The student receives 1 point for a correct answer and loses ¼ point for an incorrect answer. If the student has no idea of the correct answer for a particular question and merely guesses, what is the student's expected gain or loss on the question? Suppose you were using an

1 / 16

Step-by-step explanation:

Number of options = 4

Number of correct answers = 1

Number points gained for a correct answer = 1

Number of points lost for an incorrect answer = 1/4 = 0.25

Probability of choosing a correct option = 1/4

Probability of choosing an incorrect option = 3/4

x 1 - 1/4

P(x) __ 1/4 3/4

Expected gain or loss :

E(x) = Σx*p(x)

E(x) = (1 * 1/4) + (-1/4 * 3/4)

E(x) = 1/4 - 3/16

E(x) = (4 - 3) / 16

E(x) = 1 /16

A gain of 1/16

(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

-6 is the correct option from the above given options