Answer:
The rate at which the total personal income was rising in the Richmond-Petersburg area in 1999 is $1.627 billion per year
Step-by-step explanation:
Let 
be the number of years after 1999.
From the information given:
- In 1999, the population in this area was 961400, and the population was increasing at roughly 9200 people per year.
- The average annual income was 30593 dollars per capita, and this average was increasing at about 1400 dollars per year.
The population growth can be modeled with a linear equation. The initial population was 
is 961400 and it grows by 9200 people per year.
The population in time t can be written
The average annual income can be modeled with a linear equation. The initial average annual income was 30593 dollars per capita and it grows by 1400 dollars per year.
If we multiply both together gives the total personal income at time t.
The rate at which the total personal income was rising in the Richmond-Petersburg area is the derivative 
We need to use the Product Rule that says
If f and g are both differentiable, then:
![\frac{d}{dx}[f(x)g(x)]=f(x)\frac{d}{dx}[g(x)] +g(x)\frac{d}{dx}[f(x)]](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28x%29g%28x%29%5D%3Df%28x%29%5Cfrac%7Bd%7D%7Bdx%7D%5Bg%28x%29%5D%20%2Bg%28x%29%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28x%29%5D)
Applying the Product Rule
![\frac{d}{dt}T(t)=\frac{d}{dt} [(9200t+961400)\cdot (1400t+30593)]\\\\T(t)'=\frac{d}{dt}\left(9200t+961400\right)\left(1400t+30593\right)+\frac{d}{dt}\left(1400t+30593\right)\left(9200t+961400\right)\\\\T(t)'=9200\left(1400t+30593\right)+1400\left(9200t+961400\right)\\\\T(t)'=12880000t+281455600+12880000t+1345960000\\\\T(t)'=25760000t+1627415600](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7DT%28t%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%20%5B%289200t%2B961400%29%5Ccdot%20%281400t%2B30593%29%5D%5C%5C%5C%5CT%28t%29%27%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%289200t%2B961400%5Cright%29%5Cleft%281400t%2B30593%5Cright%29%2B%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%281400t%2B30593%5Cright%29%5Cleft%289200t%2B961400%5Cright%29%5C%5C%5C%5CT%28t%29%27%3D9200%5Cleft%281400t%2B30593%5Cright%29%2B1400%5Cleft%289200t%2B961400%5Cright%29%5C%5C%5C%5CT%28t%29%27%3D12880000t%2B281455600%2B12880000t%2B1345960000%5C%5C%5C%5CT%28t%29%27%3D25760000t%2B1627415600)
For 1999, t = 0.
The raising is
The rate at which the total personal income was rising in the Richmond-Petersburg area in 1999 is $1.627 billion per year.
The parent. function shifted down by 2 units to produce x² and to the right by 3 units to produce y = x^2 + 3
<h3>What is translation?</h3>
This is a way of changing the position of an object on an xy-plane.
Given the parent function expressed as y = (x + 2^)2
From the resulting image after translation, we can see that the parent. function shifted down by 2 units to produce x² and to the right by 3 units to produce y = x^2 + 3
Learn more on translation here; brainly.com/question/12861087
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(a) Sea level is 0 , therefore the elevation of city (A) is -96 , and the elevation of city (C) is -24 For this part we do not need the elevation of city (A). The elevation of city (D) is 1/4 of city (C). The key word is OF! Of means to multiply. Therefore we have the expression 24 · 1/4 = -6. As for explaining why it's negative we go back to how a negative times a positive is a negative.
So all 4 bags of sugar yielded 5 and 1/2 cups..... well.. how many in each one? well, let's split the 5 and 1/2 evenly in 4 pieces.
180
Explanation:
Set a equation of a ratio 120/90=x/135
And calculate!
90x=(120)(135)
90x=16200
x=180
