Geometry

noam walks home from school by walking 8 blocks north and then 6 blocks east. how much shorter would his walk be if there were a direct path from the school to his house? assume that the blocks are squares.

He would walk 4 blocks less if there were a straight path

Step-by-step explanation:

You need to use pitagoras in this one.

Noam goes north and east, forming a right angle. A direct path would close the other paths forming a right triangle. Knowing this, you can do:

8^2 + 6^2 = X^2

64 + 36 = X^2

100 = X^2

X = 10 blocks

You know that he walks 14 blocks (8+6) to school normally, so a direct path would be 4 blocks shorter

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).

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