A state Motor Vehicle Department requires learners to pass a written test on the motor vehicle laws of the state. The exam consists of twenty true-or-false questions, of which eighteen must be answered correctly to qualify for a permit. In how many different ways can a learner who answers all the questions on the exam qualify for a permit

211 ways

Step-by-step explanation:

Given :

Number of questions = 20

Number of correct correct questions to be answered in other to qualify should be atleast 18

Hence,

Correct questions could be either 18, 19 or 20 ;

Using combination :

nCr = n! ÷ (n-r)!r!

20C18 = 20! / (20 - 18)!18!

20C18 = (20* 19) / (2 * 1) = 190 ways

20C19 = 20! / (20-19)!19!

20C19 = 20 / 1 = 20 ways

20C20 = 20! / 0! 20! = 1 ways

Hence, total number of possible ways = (190 + 20 + 1) = 211 ways

4 + 5 7/9= 9 7/9

step-by-step explanation:

(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