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 %
A table which shows a possible ratio table for ingredients X and Y for the given number of servings is table 4.
<h3>What is a proportion?</h3>
A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
Mathematically, a direct proportion can be represented the following equation:
y = kx
<u>Where:</u>
- y and x are the variables.
- k represents the constant of proportionality.
Since the recipe ingredients remain in a constant ratio, we have:
k = y/x
For table 1, we have:
k = 2/1 = 2.
k = 3/2 = 1.5.
k = 4/3.
For table 2, we have:
k = 2/1 = 2.
k = 4/2 = 2.
k = 8/3.
For table 3, we have:
k = 2/1 = 2.
k = 3/2 = 1.5.
k = 5/3.
For table 4, we have:
k = 2/1 = 2.
k = 4/2 = 2.
k = 6/3 = 2.
In conclusion, a table which shows a possible ratio table for ingredients X and Y for the given number of servings is table 4 as shown in the image attached below.
Read more on proportionality here: brainly.com/question/12866878
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Answer:
APC is 90 degrees
Step-by-step explanation:
When lines intersect and are perpendicular. that means the angle of intersection is 90 degrees.
APC is 90 degrees
Using the properties of arcs and inscribed angles, B is 110/2=55.
quadratic formula:
x = <u>-b ± √(b² - 4ac)</u>
2a
7x² - x = 7
subtract 7 from both sides:
7x² - x - 7 = 0
plug values into the quadratic formula:
x = <u>-(-1) ± √((-1)²- 4(7)(-7))</u>
2(7)
simplify:
x = <u>1 ± √(197)</u>
14
