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

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: