How do you do this? Please give explanation

  2, 1, 3, 4, 6, 5

Step-by-step explanation:

The rate of change of function f(x) on an interval [a, b] is defined as ...

  average rate of change = (f(b) -f(a))/(b -a)

For the function h(x) = 2^-x, this will be ...

  arc = (h(b) -h(a))/(b -a) = (2^-b -2^-a)/(b-a) = (2^-a)(2^(a-b) -1)/(b -a)

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1. For the interval [0, 2], the average rate of change is ...

  arc = (2^-0)(2^(0-2) -1)(2 -0) = (1/4 -1)/2 = -3/8 = -0.375

  1 goes in the 2nd answer blank

2-6. For the other intervals, it is convenient to let a calculator or spreadsheet compute the values. The average rates of change are shown in the attachment.

answer: 0.64

step-by-step explanation:

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