Answer:
39 years
Step-by-step explanation:
Adapt the formula A = P(1 + r)^n, letting P represent the original population, r the growth rate as a decimal fraction, and n the number of years.
Solve this for n:
2 billion = (1.353 billion)(1 + 0.01)^n
After simplification, we have:
2
--------- = 1.01^n
1.353
Taking the log of both sides, we get:
log 2 - log 1.353 = n log 1.01, or
log 2 - log 1.353 0.1697
------------------------ = -------------- = 39 years (rounded off from 39.28)
log 1.01 0.0043
Answer:
Yes, no two ordered pairs in this list has the same second element.
Step-by-step explanation:
The function is a relation that associates to different elements 
and 
different elements 
and 
Given K = {(-3, -3), (-4, -4), (-5, -5), (-6, -6)}
So,
Since different x have different image points y, this relation is the function. The correct answer is "Yes, no two ordered pairs in this list has the same second element."
Answer:
See below.
Step-by-step explanation:
I will assume that 3n is the last term.
First let n = k, then:
Sum ( k terms) = 7k^2 + 3k
Now, the sum of k+1 terms = 7k^2 + 3k + (k+1) th term
= 7k^2 + 3k + 14(k + 1) - 4
= 7k^2 + 17k + 10
Now 7(k + 1)^2 = 7k^2 +14 k + 7 so
7k^2 + 17k + 10
= 7(k + 1)^2 + 3k + 3
= 7(k + 1)^2 + 3(k + 1)
Which is the formula for the Sum of k terms with the k replaced by k + 1.
Therefore we can say if the sum formula is true for k terms then it is also true for (k + 1) terms.
But the formula is true for 1 term because 7(1)^2 + 3(1) = 10 .
So it must also be true for all subsequent( 2,3 etc) terms.
This completes the proof.
Answer:
Russell family's sprinkler: 40 hours
Gonzales family's sprinkler: 20 hours
Step-by-step explanation:
Let's call the amount of time the Russell family's sprinkler was on by X, and the Gonzales family's sprinkler by Y.
We can then formulate the equations:
X + Y = 60
X*35 + Y*40 = 2200
We can solve this system multiplying the first equation by 35, and then subtracting the result from the second equation:
35*X + 35*Y = 2100
5*Y = 100
Y = 20
from the first equation:
X + 20 = 60
X = 40
Russell family's sprinkler: 40 hours
Gonzales family's sprinkler: 20 hours
