Alexandra scored 40 on an exam, receiving 3 points for each right answer and losing 1 point for each wrong answer. Had 4 points been given for each right answer and 2 points deducted for each wrong answer, Alexandra would have scored 50. How many questions were on the exam

there were 20 questions in the exam.

Step-by-step explanation:

Let x represent the number of right answers.

Let y represent the number of wrong answers.

Alexandra scored 40 on an exam, receiving 3 points for each right answer and losing 1 point for each wrong answer. It means that

3x - y = 40- - - - - - - - - - 1

Had 4 points been given for each right answer and 2 points deducted for each wrong answer, Alexandra would have scored 50. It means that

4x - 2y = 50- - - - - - - - - - -2

Multiplying equation 1 by 2 and equation 2 by 1, it becomes

6x - 2y = 80

4x - 2y = 50

Subtracting both equations, it becomes

2x = 30

x = 30/2

x = 15

Substituting x = 15 into equation 1, it becomes

3 × 15 - y = 40

45 - y = 40

y = 45 - 40

y = 5

The number of questions in the exam is

x + y = 15 + 5 = 20

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.