What is the explicit formula for this sequence?
1 answer:
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Answer:
The answer to your question is: (3x + 5)(9x² - 15x + 25)
Step-by-step explanation:
Data
G(x) = 27x³ + 125
This is a sum of cubes
Process
27x³ + 125 = (3x)³ + (5)³ = (3x + 5)(9x² - 15x + 25)
A) 
B) 1/4 = 25%
C) 1/8 = 12.5%
Explanation
A) Let x = the number of yellow blocks. Then x+4 = the number of red blocks, and x+x+4=2x+4 is the total number of blocks.
The probability of choosing a red block first would be
since there are x+4 red blocks out of 2x+4 total blocks.
The probability of choosing a yellow block after the red block would be
since there are x yellow blocks, and after 1 is chosen, there are 2x+3 total blocks remaining.
This gives the total probability of
B) If there are 6 yellow blocks, there are 6+4=10 red blocks, and 10+6=16 total blocks.
The probability of getting a red block first would be 10/16, and the probability of getting a yellow block after the red block would be 6/15. Together this gives us
10/16(6/15) = 60/240 = 1/4 = 0.25 = 25%
C) If there are 6 yellow blocks, there are 6+4=10 red blocks, and 10+6=16 total blocks.
The probability of getting a yellow block first is 6/16, and the probability of getting a second yellow block after the first one is 5/15. Together this gives us
6/16(5/15) = 30/240 = 1/8 = 0.125 = 12.5%
B) 1/4 = 25%
C) 1/8 = 12.5%
Explanation
A) Let x = the number of yellow blocks. Then x+4 = the number of red blocks, and x+x+4=2x+4 is the total number of blocks.
The probability of choosing a red block first would be
since there are x+4 red blocks out of 2x+4 total blocks.
The probability of choosing a yellow block after the red block would be
since there are x yellow blocks, and after 1 is chosen, there are 2x+3 total blocks remaining.
This gives the total probability of
B) If there are 6 yellow blocks, there are 6+4=10 red blocks, and 10+6=16 total blocks.
The probability of getting a red block first would be 10/16, and the probability of getting a yellow block after the red block would be 6/15. Together this gives us
10/16(6/15) = 60/240 = 1/4 = 0.25 = 25%
C) If there are 6 yellow blocks, there are 6+4=10 red blocks, and 10+6=16 total blocks.
The probability of getting a yellow block first is 6/16, and the probability of getting a second yellow block after the first one is 5/15. Together this gives us
6/16(5/15) = 30/240 = 1/8 = 0.125 = 12.5%