A slope-intercept equation of the line whose graph is perpendicular to 2x + 9y = 8 and has the y-intercept (0, -3)

Step-by-step explanation:

let eqn be y = mx + b.

2x + 9y = 8

9y = -2x + 8

y = -2/9 x + 8/9

since the lines are perpendicular, product of the slope of the two lines = -1.

hence,

m x -2/9 = -1

m = 9/2

sub (0, -3):

-3 = 9/2(0) + b

b = -3

therefore equation is: y = 9/2x - 3

Topic: coordinate geometry

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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.