Adilation with a scale factor of 4 is applied to the three line segments shown. the resulting images are p′q′ , a′b′ , and m′n′ .

P'Q' ⇔ 8 cm

A'B' ⇔ 6 cm

M'N' ⇔ 12 cm

Step-by-step explanation:

A dilation with a scale factor of 4 is applied to the three line segments PQ, AB and MN.

The length of PQ is given as: 2 cm.

The length of line segment AB is given as: 1.5 cm

The length of line segment MN is given as: 3 cm.

Now as there is a dilation with a scale factor of 4 to all the line segments this means that the resulting image will have length 4 times the length of these line segments.

PQ → P'Q'

⇒ Length of P'Q'= 8 cm.   ( since 4×2=8)

AB → A'B'

⇒ Length of A'B'= 6 cm.   ( since 1.5×4=6)

MN → M'N'

⇒ Length of M'N'= 12 cm.   ( since 4×3=12)

Hence,

P'Q' ⇔ 8 cm

A'B' ⇔ 6 cm

M'N' ⇔ 12 cm

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