A 24 inch board is to be cut into three pieces so that the second piece is twice as long as the first piece and the third piece is 5 times as long as the first piece. If x represents the length of the first piece, find the length of all three pieces

F=length of first piece=x; S=length of second piece=2x

T=length of third piece=3x

.

F+S+T=24 inches

x+2x+3x=24 inches

6x=24in

F=x=4in

ANSWER 1: The length of the first piece is 4 inches.

.

S=2x=2(4in)=8in

ANSWER 2: The length of the second piece is 8 inches.

.

T=3x=3(4in)=12 inches.

ANSWER 3: The length of the third piece is 12 inches.

.

CHECK:

F+S+T=24in

4in+8in+12in=24in

24in=24in

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