Sally is completely unprepared for a three-question multiple-choice pop quiz, so she randomly guesses the answer to each question. if each question has four choices, then what is the probability that she gets at least two questions correct?
a) 0.0469
b) 0.0625
c) 0.1406
d) 0.1563

Option: D is the correct answer.

D) 0.1563

There are a total of 3 questions in a quiz.

We are asked to find the probability that at least two questions were correct.

Hence, we have to use binomial in order to find the probability.

We know that the probability of k success in n experiments is calculated by the formula:

where p is the probability of success.

and q is the probability of failure.

Here p is the probability that the question is correct.

i.e. p=1/4

( Since out of the 4 choices 1 choice is correct)

Similarly,

q=3/4

( Since out of the 4 choices 3 are incorrect)

Hence, we are asked to find:

i.e. we have to find:

Here we have, n=3

            Hence, the probability is:

                      0.1563

(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

false

step-by-step explanation:

rulers and compasses arent required in order to bisect an angle because when bisecting angles, you're making a "half circle" and considering in order to bisect an angle it wouldn't be straight, you wouldn't need either of the two