Answer:
Step-by-step explanation:
The given sequence is:
The first term of this sequence is
There is a common difference of d=½
The recursive formula is:
We substitute the common difference to get:
Answer:
0.00111
Step-by-step explanation:
Since the modem receiver takes a majority vote of the five
received bits to estimate the input signal, it will only make a wrong decision if 3, 4 or 5 of the 5 bits received are wrong.
Given that the channel changes an input bit to its complement with probability p =1/10 and it does so independently of its treatment of other input bits, the probability of changing 3 bits out of five is 0.1*0.1*0.1 = 0.001, of changing 4 is 0.0001 and of changing 5 is 0.00001
So, the probability that the modem makes a wrong decision is 0.001+0.0001+0.00001 = 0.00111
Let 
be the number of cows and ducks, respectively.
So, 4 times the number of cows is 4c, and 2 times the number of ducks is 2d. Together, they are 
This has to equal 20, so the equation is
Let x represent the full area if Mary's garden.
Mary plants roses in 1/4 of her garden. This means that the portion of the garden on which she planted roses would be 1/4 × x = x/4
She also plants some tulips in her garden. She has 1/12 of the garden left to plant more flowers. This means that the portion if the garden that she has left to plant more flowers would be 1/12 × x = x/12
The portion of the garden on which she planted tulips would be
x - (x/4 + x/12) = x - (3x + x)/12 = x - 4x/12
x - x/3 = (3x - x)/3 = 2x/3
Therefore, the fraction of Mary's garden that has tulips would be
(2x/3) /x = 2/3
