The first differences are 8, 14, 20.
The second differences are 6.
Half of 6 is 3, so the first term of the sequence is 3n^2.
If you subtract 3n^2 from the sequence you get 0,-1,-2,-3 which has the nth term of -n + 1.
Therefore your final answer will be 3n^2 - n + 1
A: (x + 5i)^2
= (x + 5i)(x + 5i)
= (x)(x) + (x)(5i) + (5i)(x) + (5i)(5i)
= x^2 + 5ix + 5ix + 25i^2
= 25i^2 + 10ix + x^2
B: (x - 5i)^2
= (x + - 5i)(x + - 5i)
= (x)(x) + (x)(- 5i) + (- 5i)(x) + (- 5i)(- 5i)
= x^2 - 5ix - 5ix + 25i^2
= 25i^2 - 10ix + x^2
C: (x - 5i)(x + 5i)
= (x + - 5i)(x + 5i)
= (x)(x) + (x)(5i) + (- 5i)(x) + (- 5i)(5i)
= x^2 + 5ix - 5ix - 25i^2
= 25i^2 + x^2
D: (x + 10i)(x - 15i)
= (x + 10i)(x + - 15i)
= (x)(x) + (x)(- 15i) + (10i)(x) + (10i)(- 15i)
= x^2 - 15ix + 10ix - 150i^2
= - 150i^2 + 5ix + x^2
Hope that helps!!!
Answer:
Step-by-step explanation:
y = -2x + 2/2.....slope = -2, y int = 2/2(or just 1)
y = -2x + 3/2....slope = -2, y int = 3/2
when the equations have the exact same slope, but different y intercepts.....and this one does....then there is no solution because these are parallel lines....they never cross each others path.
Answer:
17.5%
Step-by-step explanation:
First of all, see this situation as a cumulative binomial distribution. You have isolated trials with a probability of success. This makes it binomial. The wording of the question "what is the probability of at least half..." makes this cumulative.
There are a few ways to calculate this, and I'm not quite sure which way you're familiar with. I'll show the cumbersome way and use wolfram to make the calculation.
First, I'll calculate the probability for 15 success, given 30 trials.
30c15*0.4^15*0.6^15
Since the question asks for the probability of at least 15 success, I'll have to make a calculation for the probability of 16 successes, then 17, and so on. Then I'll have to add all the probabilities together. So, I'll use wolfram for that (see attached)
