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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<span>46, 37, 16, 24, 47, 23, 19, 31, 25
put in order</span>
16, 19, 23, 24, 25, 31,37, 46, 47
mean = 25
LOWER QUARTILE = (16+ 19+ 23+ 24) / 4 = 20.5
answer
Lower IQR = 20.5
Answer:
Step-by-step explanation:
The student hasn't finished the factoring yet.
<u>He still needs the step:</u>
<u>The next step:</u>
- 0 = 2x + 5, 0 = x + 1
- x = - 2.5, x = - 1
Let
be the number of rides Chandler takes in a month. Then the cost with the MetroCard is still $81, but the cost without the MetroCard is
. So we can set up an equation representing what we want: "The cost with a MetroCard of r rides in a month is less than the cost without a MetroCard." In equations,
Thus, at a minimum, Chandler must take 41 rides for his MetroCard to be cheaper than not having it.
Answer:
The functions given are:
f(x) = x²
g(x) = f(-4x-3) + 1
First, find f(-4x-3):
f(x) = x²
f(-4x-3) = (-4x-3)²
Find g(x):
g(x) = f(-4x-3) + 1
g(x) = (-4x-3)² + 1
g(x) = (-1)² (4x+3)² + 1
g(x) = (4x+3)² + 1
First take
y = (x)²
Compress the graph along x axis by multiplying x with 4
y = (4x)²
Shift the graph left by 0.75 units, by adding 3 to x term.
y = (4x+3)²
Shift the graph up by 1 unit by adding 1 to the total terms.
y = (4x+3)² +1
