Answer:
common ratio: 1.155
rate of growth: 15.5 %
Step-by-step explanation:
The model for exponential growth of population P looks like: 
where 
is the population at time "t",
is the initial (starting) population
is the common ratio,
and 
is the rate of growth
Therefore, in our case we can replace specific values in this expression (including population after 12 years, and initial population), and solve for the unknown common ratio and its related rate of growth:
![P(t)=P_i(1+r)^t\\13000=2300*(1+r)^{12}\\\frac{13000}{2300} = (1+r)^12\\\frac{130}{23} = (1+r)^{12}\\1+r=\sqrt[12]{\frac{130}{23} } =1.155273\\](https://tex.z-dn.net/?f=P%28t%29%3DP_i%281%2Br%29%5Et%5C%5C13000%3D2300%2A%281%2Br%29%5E%7B12%7D%5C%5C%5Cfrac%7B13000%7D%7B2300%7D%20%3D%20%281%2Br%29%5E12%5C%5C%5Cfrac%7B130%7D%7B23%7D%20%3D%20%281%2Br%29%5E%7B12%7D%5C%5C1%2Br%3D%5Csqrt%5B12%5D%7B%5Cfrac%7B130%7D%7B23%7D%20%7D%20%3D1.155273%5C%5C)
This (1+r) is the common ratio, that we are asked to round to the nearest thousandth, so we use: 1.155
We are also asked to find the rate of increase (r), and to express it in percent form. Therefore we use the last equation shown above to solve for "r" and express tin percent form:
So, this number in percent form (and rounded to the nearest tenth as requested) is: 15.5 %
Answer:
20/9
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 80 and 36 is 4
Divide both the numerator and denominator by the GCD
80 ÷ 4
36 ÷ 4
Reduced fraction: 20/9
Let us say that:
a = black kittens
b = white kittens
We know that:
a = 5 b
a + b = 25
Therefore:
5 b + b = 25
6 b = 25
b = 4.17
But we cannot have a fraction value for the number of
kittens, so round off:
b = 4
So a is:
a = 25 – 4 = 21
<span>Hence Zoe counts additional 1 black kitten.</span>
Step-by-step explanation:
75×1=75
75×2=150
75×3=225
75×4=300
75×5=375
75×6=450
75×7=525
75×8=600
75×9=675
75×10=750
Answer:
<h2>There are 3,921,225 ways to select the winners.</h2>
Step-by-step explanation:
This problem is about combinations with no repetitions, because the same person can't win four times. It's a combinaction because the order of winning doesn't really matter.
Combinations without repetitions are defined as
Where 
and 
.
Replacing values, we have
Therefore, there are 3,921,225 ways to select the winners.
Additionally, as you can imagine, the probability of winning is extremely low, it would be 3,921,225 to 1.
