Me in geometry!
in the step shown of the construction of a line through a point that is perpendicular to the given line, why must the compass point be placed on points a and b? how would the construction be different if the compass point were placed at random points on the original line?

The compass point must be placed on points A and B because you need to make arcs which would allow you to make the perpendicular line through the given line. The construction would be different if the compass point were placed at random points on the original line because then the line would not be lined up correctly in the middle and it will not be correct, hence why you need to put the compass on A and B.

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages