Independent trials, each resulting in a success with probability p, are performed until k consecutive successful trials have occurred. let x be the total number of successes in these trial, and let pn = p(x = n). (a) find pk . (b) derive a recursive equation for the pn, n k, by imagining that the trials continue forever and conditioning on the time of the first failure. (c) verify your answer in part (a) by solving the recursion for pk . (d) when p = .6, k = 3, find p8.

b. would be the answer : )

step-by-step explanation:

step 1: add -16x to both sides.

16x−4y+−16x=64+−16x  

−4y=−16x+64

step 2: divide both sides by -4.

−4y /-4 = -16x + 64/-4

answer:   y=4x−16

hope i'm right

this is the formula: v = the value of investment at the end of the time period

p = the principal amount (the initial amount invested)

r = the annual interest rate

n = the annual frequency of compounding (how many times a year interest is added)

t = the number of years the money is invested

^ means raise to the power of

he has 140 chickens because he has 10 times more chickens than ducks and he has 14 ducks so 14*10=140

you estimate that the angle of elevation to the top of the 86th floor (the observatory) is 82 .the total height of the building is another 123 meters above the 86th floor.

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