(a) When the sequence is arithmetic, sequential terms have a common difference.
... x - 3 = (4x/3) - x . . . . differences of sequential terms are equal
... (2/3)x = 3 . . . . . . . add 3-(1/3)x
... x = 9/2 . . . . . . . . . multiply by 3/2
(The arithmetic sequence is 3, 4.5, 6. The common difference is 3/2.)
(b) When the sequence is geometric, sequential terms have a common ratio.
... x/3 = (4x/3)/x . . . . . ratios of sequential terms are equal
... x^2 = 4x . . . . . multiply by 3x
... x = 4 . . . . . . . . divide by x. (the "solution" x=0 is extraneous)
(The geometric sequence is 3, 4, 16/3. The common ratio is 4/3.)
Answer:
Initial population of Rabbit = 5 rabbit
After 2 months
Population of Rabbit = 10
After 4 months
population of rabbit = 20
Formula for growth is :
G = ![G_{0}[1 + R]^n](https://tex.z-dn.net/?f=G_%7B0%7D%5B1%20%2B%20R%5D%5En)
, where G is final population and 
is initial population, and R is growth rate.
1. 10 = 5 [1 +R]²
Dividing both sides by 5 , we get
2 = (1 + R)²
→ R + 1 = √2 ⇒ taking positive root of 2
→R = √2 -1
Amount of rabbit after 1 year = 
Answer: The value of y is 
.
Explanation:
It is given that the graph of a proportional relationship passes through (12, 16)
and (1, y).
The graph of a proportional relationship means the x and y coordinates are in a proportion k. The equation of the graph is in the form of y=kx. Where k is the proportion factor.
It is given that the graph passing through (12,16).
So the equation of the line is,
put x=1.
Therefore, the value of y is .
So for number there are 6 possible outcomes nad 5 is one of them so 1/6
He next one there are 2 outcomes and heads is 1 outcome so 1/2
For the next one you have to multiply them together so you get 1/12
And the events are independent because whatever you roll on the die won’t affect the coin(it actually does on a very small scale but I don’t think you go into that much detail for high school maths)
