Answer:
the answer is c
Step-by-step explanation:
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.
Learn more about Sequences on:
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Answer:
(x + 2)(x - 5)
Step-by-step explanation:
Here are the steps:
700 because the 9 in the tenth place is larger than 5
9514 1404 393
Answer:
7 cm, 4.4 cm
Step-by-step explanation:
The side lengths can be found from the law of cosines. Each triangle has legs 3 cm and 5 cm. The angle between these will be 60° or 120°. Then the two sides of the parallelogram are ...
s = √(a² +b² -2ab·cos(C))
s = √(3² +5² -2·3·5·(±1/2)) = √(34 ±15) = {√49, √19}
The two side lengths are 7 cm and about 4.4 cm.
