Evaluate. 2 1/6 - (8/3) + (-4 7/9) write the fraction in simplest form. I need this ASAP plzzzzzz

A) Find a recurrence relation for the number of bit strings of length n that contain a pair of consecutive 0s.

Fed [463]

Answer:

A) $a_{n} = a_{n-1} + a_{n-2} + 2^{n-2}$

B) $a_{0} = a_{1} = 0$

C) for n = 2

$a_{2}$ = 1

for n = 3

$a_{3}$ = 3

for n = 4

$a_{4}$ = 8

for n = 5

$a_{5}$ = 19

Step-by-step explanation:

A) A recurrence relation for the number of bit strings of length n that contain a pair of consecutive Os can be represented below

if a string (n ) ends with 00 for n-2 positions there are a pair of consecutive Os therefore there will be : $2^{n-2}$ strings

therefore for n ≥ 2

The recurrence relation for the number of bit strings of length 'n' that contains consecutive Os

$a_{n} = a_{n-1} + a_{n-2} + 2^{n-2}$

b ) The initial conditions

The initial conditions are : $a_{0} = a_{1} = 0$

C) The number of bit strings of length seven containing two consecutive 0s

here we apply the re occurrence relation and the initial conditions

$a_{n} = a_{n-1} + a_{n-2} + 2^{n-2}$

for n = 2

$a_{2}$ = 1

for n = 3

$a_{3}$ = 3

for n = 4

$a_{4}$ = 8

for n = 5

$a_{5}$ = 19

7 0

3 years ago

The area of a square mat is 125 square inches. The best approximation of its length is inches. If the length of each side is inc

gtnhenbr [62]

The area of a square is simply the side length squared and we are given that the area is 125 so:

s^2=125

s=√125

s=5√5

Now using the area equation again, and adding 1 inch to s we have:

A=(s+1)^2, and using s found above we have:

A=(5√5+1)^2

A=125+10√5+1

A=126+10√5 in^2

A≈148.36 in^2 (to nearest hundredth of a square inch)

4 0

3 years ago

Read 2 more answers

What are the next three terms of the sequence below?

vichka [17]

Answer:

64, 256, 1024 (D)

Step-by-step Explanation:

The sequence is following some rule. And the rule is: Multiplying the term with 4 to get the next term. Like:

$1 × 4 = 4$
$4 \times 4 = 16$

Similarly, the next terms are:

$16 \times 4 = 64$
$64 \times 4 = 256$
$256 \times 4 = 1024$

The terms are 64, 256, 1024 which matches with Option D. And that's the correct answer

4 0

2 years ago

Read 2 more answers

Which fraction is equivalent to -7/8? A) 8 /- 7 b)7 /-8 c)-7/-8 d)7/ 8

lozanna [386]

Answer:

im pretty sure b

Step-by-step explanation:

because i took a test

6 0

3 years ago

A card is selected at random from a standard deck of 52 playing cards. find each probability.(a) randomly selecting a club or a

vodka [1.7K]

A) 17/52
B) 15/26
C) 4/13

A) The probability of getting a club is 13/52; the probability of getting a 3 is 4/52; the probability of a club or 3 is

13/52+4/52 = 17/52

B) The probability of a red card is 26/52; the probability of a King is 4/52; the probability of a red card or King is

26/52+4/52=30/52 = 15/26

C) The probability of a 9 is 4/52; the probability of a face card is 12/52; the probability of a 9 or a face card is 4/52+12/52 = 16/52 = 4/13

7 0

3 years ago