65 sequences.
Lets solve the problem,
The last term is 0.
To form the first 18 terms, we must combine the following two sequences:
0-1 and 0-1-1
Any combination of these two sequences will yield a valid case in which no two 0's and no three 1's are adjacent
So we will combine identical 2-term sequences with identical 3-term sequences to yield a total of 18 terms, we get:
2x + 3y = 18
Case 1: x=9 and y=0
Number of ways to arrange 9 identical 2-term sequences = 1
Case 2: x=6 and y=2
Number of ways to arrange 6 identical 2-term sequences and 2 identical 3-term sequences =8!6!2!=28=8!6!2!=28
Case 3: x=3 and y=4
Number of ways to arrange 3 identical 2-term sequences and 4 identical 3-term sequences =7!3!4!=35=7!3!4!=35
Case 4: x=0 and y=6
Number of ways to arrange 6 identical 3-term sequences = 1
Total ways = Case 1 + Case 2 + Case 3 + Case 4 = 1 + 28 + 35 + 1 = 65
Hence the number of sequences are 65.
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80 has 9 factor because 1×80=80. 2×40-80. 4×20=80. 5×16=80. 8×10=80 . 10 ×8=80. 20×4=80. 40×2=80. and 80×1=80 80 is greater than 20 and that has 9 factors
Answer:
is there a pic?
Step-by-step explanation:
we are able to see
Answer:
1st odd = 57
2nd odd = 59
3rd odd = 61
Step-by-step explanation:
Suppose the numbers to be:
1st odd = x -2
2nd odd = x
3rd odd = x +2
Now according to given conditions:
1st odd + 2nd odd + 3rd odd = 177
x - 2 + x +x + 2 = 177
By add -2 and + 2 will be cancelled
Adding all x
3x = 177
Dividing both sides by 3 we get
x = 177 / 3
x = 59
Now putting x = 59 to get three consecutive odds:
1st odd = x -2 = 59 - 2 = 57
2nd odd = x = 59
3rd odd = x +2 = 59 + 2 = 61
Proof:
1st odd + 2nd odd + 3rd odd = 177
57 + 59 + 61 = 177
177 = 177
hence proved
I hope it will help you!
9514 1404 393
Answer:
70 -91i
Step-by-step explanation:
Collect terms the same way you would if i were a variable.
(3 -91i) +67 = (3 +67) -91i = 70 -91i
