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

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,