Population Growth Using 20th-century U.S. census data,
the population of Ohio can be modeled by
12.79
P(1) =
1 + 2.402,-0.0309
where P is the population in millions and r is the number of
years since April 1, 1900. Based on this model, when was the
population of Ohio 10 million?
Answers
The population of Ohio will be 10 million in the year 1970
The population growth of Ohio is represented by the function:
[tex]P(t)=\frac{12.79}{1+2.402e^{-}0.0309t}[/tex]
P is the population in millions
t is the number of years since 1900
To find the year that the population of Ohio will be 10 million, substitute P = 10 into the function P(t) and solve for t
[tex]10=\frac{12.79}{1+2.402e^{-}0.0309t}\\\\10(1+2.402e^{-}0.0309t)=12.79\\\\1+2.402e^{-}0.0309t=\frac{12.79}{10} \\\\1+2.402e^{-}0.0309t=1.279\\\\2.402e^{-}0.0309t=1.279-1\\\\2.402e^{-}0.0309t = 0.279\\\\e^{-}0.0309t =\frac{0.279}{2.402} \\\\e^{-}0.0309t =0.116\\\\-0.0309t=ln0.116\\\\-0.0309t=-2.154\\\\t=\frac{-2.154}{-0.0309} \\\\t=69.7[/tex]
t = 70 years (to the nearest whole number)
70 years after 1900 will be 1970
Therefore, the population of Ohio will be 10 million in the year 1970
Learn more here: https://brainly.com/question/25504185
Related Questions
Is -3/4 greater than -0.25
Answers
Answer: No
Step-by-step explanation:
you should know that 3/4 is the same as 0.75. -0.75 is smaller than -0.25 because when dealing with negative numbers, what would be the “smaller” number in positive negative integers is actually the larger number as it is closer to 0.
Answer:
-0.25 is greater than -0.75
Step-by-step explanation:
usually if they were positive 0.75 would be bigger but since there negative decimals, -0.25 is greater. By the way, -0.75 is -3/4.
Please help me quickly
Answers
Step-by-step explanation:
a full circle (turning around a point a full turn) is 360°.
so, all these angles together must be 360°.
90 + 33 + 165 + 20 + x = 360
308 + x = 360
x = 52°
the weight in pounds of a newborn baby t months after birth can be modeled by the equation W=t+7. what is the y-intercept of the equation and what is its interpretation in the context of the problem
Answers
Answer:
y intercept = (0,7) , it is the weight of a newborn at birth/ before any months have passed
Step-by-step explanation:
in this equation:
weight= t(months) + 7
this is an equation written as y=mx +b
in a line equation like this b is the y intercept , or the y value when x=0
in this problem when x=0 it means that 0 months have passed , i.e. the baby is a newborn
f(x)={x+4….
for f(x)
Answers
Answer:
3f=5
Step-by-step explanation:
f(x) = x+4
3f=4x
x<5
5<_x<7
7<_x<_10
Slope between (6,-11) and (2,-1)
Answers
terrell is going to the salem fair. it costs $5 to get into the fair and $.75 per ride. if he only has $20, how many rides can terrell ride?
Answers
Find the value of a.
х
409
0.
a
y
O A. 60
OB. 80
OC. 40
Answers
Answer:
50°
Hope you could understand.
If you have any query, feel free to ask.
What is the area (what is the height)
Answers
Answer:
5 i think
Step-by-step explanation:
The trapezoid's height (h) is 4 mm(millimeters).
Formula to calculate a trapezoid's height;
2 x Area ÷ by A(short base) + B(large base)
Lena is asked to write an explicit formula for the graphed geometric sequence. On a coordinate plane, 3 points are plotted. The points are (1, 1), (2, 2. 5), (3, 6. 25). What value, written as a decimal, should Lena use as the common ratio? 1. 0 1. 5 2. 5 2. 0.
Answers
Answer:
r = 2.5
Step-by-step explanation:
Consider the y- coordinates of the plotted points
1 , 2.5 , 6.25
The common ratio r is calculated as
r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex] = [tex]\frac{2.5}{1}[/tex] = [tex]\frac{6.25}{2.5}[/tex] = 2.5
are the lines in the figure parallel, perpendicular, or neither?
Answers
Answer:
Perpendicular
Step-by-step explanation:
perpindicular
Step-by-step explanation:
Perpindicular has multiple sides and has a 90 degree plane
A radar station is 2000 ft from the launch site of a rocket. If the rocket is launched vertically at the
rate of 500 ft/sec, how fast is the distance between the radar station and the rocket changing 10 seconds
later?
Answers
Answer: f 500 Ft./sec
Step-by-step explanation:
By evaluating the derivate of the distance in t = 10s, we will see that at t = 10s the distance is changing at a rate of 464.2 ft/s
We can think of the situation as in a right triangle, one cathetus is equal to 2000ft, and the other cathetus increases at a rate of 500ft/sec.
The hypotenuse would be the distance between the radar and the rocket.
Then the distance function is:
[tex]D(t) = \sqrt{(2000ft)^2 + (500ft/s*t)^2}[/tex]
Now we need to get the rate of change, this is given by:
[tex]\frac{dD(t)}{dt} = (1/2)*\frac{2*(500ft)^2*t}{\sqrt{(2000ft)^2 + (500ft/s*t)^2} }[/tex]
Now we evaluate this in t = 10s to get:
[tex]\frac{dD(10s)}{dt} = (1/2)*\frac{2*(500ft/s)^2*10s}{\sqrt{(2000ft)^2 + (500ft/s*10s)^2} } = 464.2 ft/s[/tex]
If you want to learn more, you can read:
https://brainly.com/question/18904995
Which statements are true? Check all that apply.
3
1
-2.5=-2
2.
2.
-1.5 > -0.5
0.5 <0
-2.5 <-2
1
0
UD
1>15
-1
-2
-3
Answers
Answer:
3is the answer because t
s apply
Step-by-step explanation:
Write the equation of the line from the graph.
Answers
Answer: y = 4x + 2
Step-by-step explanation:
A linear equation is usually in y= mx + b form, where m is the slope and b is the y-intercept.
In order to calculate the slope, we choose two-point from the graph. (-1 ,-2) and (0, 2).
slope = [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]
= (2 - (-2)) / (0 - (-1))
= (2 + 2) / (0 + 1)
= 4 / 1
= 4
y-intercept means the y value when x is 0, according to the graph, the y value when x at 0 was 2. So the y-intercept is 2.
Plug both slope and y-intercept in, we get the equation:
y = 4x + 2
Answer: y = 4x + 2
Step-by-step explanation:
-4 + (-3) – 8 + (-2) =
Answers
a series of 1125 consecutive integers has a sum which is a perfect cube find the smallest possible positive sum for this series?
please show your work :)
Answers
If zero is considered to be positive, the answer is zero (0).
otherwise
562 negative consecutive integers, then 0, then 562 positive consecutive integers has a sum of zero (0).
Moving the start, the smallest integer up 1 adds 1125 to the sum.
1125 = 9 * 125
1125 = 9 * 5³
= 9³ * 5³ is the smallest sum
= 45³
= 91125
Therefore the smallest possible sum is 91125
for more questions like this see, https://brainly.com/question/19261165
please help me with this. I will give brainliest to whoever gets the question right. attachment below.
Answers
Answer:
22100
Step-by-step explanation:
First you would add the truckloads of concrete for both playgrounds (3 5/8 + 3 5/8 + 1 9/10). Then you would divide that by 1/2. Finally multiply that number by 2000. (Pls mark me the brainliest)
please help! thanks!
Answers
2(3) - 3(2) = 0
2(3) + 2 = 8
A line passes through the points (-4,5) and (1,-5). Write the equation of the line in slope-
intercept form.
A. y = - 2x - 3
B.y = - 2x +3
C. y=2x-3
D. y = 2x + 3
Answers
Answer:
y = -2x - 3
Step-by-step explanation:
Slope: (5 - - 5)/(-4 -1) = 10/-5 = -2
y-intercept: 5 - (-2)(-4) = -3
I do this do y'all can get extra point and complete challenges!
What is 4 + 4
Answers
8 is the correct answer. By the way, Thank you for the few extra points.. It is very appreciated.
Look at the screen shot and answer the question. Please Explain !!
Answers
Answer:
see explanation
Step-by-step explanation:
- 4x + 3 < 23 ( subtract 3 from both sides )
- 4x < 20
x < - 5 ← Her error is on this step
When dividing by a negative quantity the symbol is reversed, that is
Divide both sides by - 4 and reversing the symbol gives
x > - 5
A computer virus infects files very quickly. The number of files triples every minute. After the first minute, five files are infected. (pls answer)
Options in the pic
Answers
Answer:
C
Step-by-step explanation:
The answer is C because r =3 I got that because it says triples. a=5 it comes from when it says five files are infected. an=3an-1. an=5(3)n-1. Hope this helps!
Jasmine got a new puppy for her birthday. He's full of energy, so she takes him for a walk along a 1.2-mile loop in a nearby park. If they walked a total of 3.6 miles, how many loops did they do?
Answers
Answer:
3 loops
Step-by-step explanation:
1.2x = 3.6 [Setting up an equation]
x = 3 [dividing both sides by 1.2]
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
What is -2(3x+12y-5-17x-16y+4) simplified?
A) -40x+8y+2
B) 28x+8y+2
C) 28x+6y+2
D) -28x-8y+2
Answers
Answer: B
Step-by-step explanation:
Multiply everything in the bracket by -2 and combine like terms
Answer:
It's B
Step-by-step explanation:
Write an explicit rule and recursive rule for a geometric sequence with a 2nd term of 6 and a 3rd term of 12.
Answers
this is my attachment answer hope it's helpful to you
Solve the quadratic by factoring.
4x^2 – 2x – 3 = 2x
PLS HELP ASAP!!!
Answers
Answer: X = -(1/2) AND X = (3/2)
Step-by-step explanation:
4x^2 – 2x – 3 = 2x
4x^2 – 4x – 3 = 0
(2x+1)(2x-3) = 0
1. (2x+1) = 0
2x = -1
X = -(1/2)
2. (2x-3) = 0
2X = 3
X = (3/2)
Using the area model divide, true or false, 79/7 is equal to 11 R 1.
Answers
Area models are used to evaluate products and divisions
[tex]\mathbf{79 \div 7 = 11\ R\ 1}[/tex] is false
The division equation is given as:
[tex]\mathbf{79 \div 7 = 11\ R\ 1}[/tex]
Express 79 as 77 + 2
[tex]\mathbf{(77 + 2) \div 7 = 11\ R\ 1}[/tex]
Split the expression on the left-hand side
[tex]\mathbf{77 \div 7+ 2 \div 7 = 11\ R\ 1}[/tex]
Divide 77 by 7
[tex]\mathbf{11+ 2 \div 7 = 11\ R\ 1}[/tex]
2 divided by 7 is 0 with a remainder of 2
So, we have:
[tex]\mathbf{11\ R 2 = 11\ R\ 1}[/tex]
The equations above are not equal.
This is represented as:
[tex]\mathbf{11\ R 2 \ne 11\ R\ 1}[/tex]
Hence, [tex]\mathbf{79 \div 7 = 11\ R\ 1}[/tex] is false
Read more about area models at:
https://brainly.com/question/18701102
Find the term of the arithmetic sequence in which a 27=-1/2 and the common difference is 2.
Answers
Step-by-step explanation:
arithmetic sequence means that every new term is created by adding a certain constant (here 2) to the previous term.
a27 = -1/2 = a1 + (n-1)×2 = a1 + 26×2 = a1 + 52
a1 = -52 1/2 = -105/2
an = -105/2 + (n-1)×2
If it takes 7 people 8 days to dig a ditch, how many people would it take to dig the ditch in 1/2 day
Answers
Answer:
112
Step-by-step explanation:
8 days when fitted into a half (1/2) gives you 16
7 times 16 gives the answer of 112 (people needed)
Answer:
112 people to do it in 1/2 of a day
Step-by-step explanation:
7 · 8 = 56
56 ÷ ½ = 112 people to dig a ditch in 1/2 of a day
i need the solution to this problem pls!
Answers
Answer:
FE = 43.2
Step-by-step explanation:
FE/36 = 24/20
multply both sides by 36
FE = 24/20 * 36
FE = 43.2
How many solutions does 3(x + 5) - 3 = 2(3x + 1) - 3x have? Show your work.
2noop
no
ordon
dos
SOLUTION I don’t want the answer I just wanna know how to solve it cause I’m bad at math
Answers
Answer:
No solution
Step-by-step explanation:
1.Simplify
3(x+5)-3 = 2(3x+1) -3x
3x+15-3=6x+2-3x
2.Simplify
3x+12=3x+2
3. Combine like terms
3x-3x+12-2=3x-3x+-2
10 does not equal 0
No solution
Answer:
[tex]\boxed{\boxed{\sf No\:Solution}}[/tex]
Step-by-step explanation:
[tex]\sf 3\left(x+5\right)-3=2\left(3x+1\right)-3x[/tex]
Expand: Apply distributive property:
[tex]\sf 3(x+5)-3[/tex]
[tex]\sf 3x+15-3[/tex] [tex]\sf 3x+12[/tex][tex]\sf 2(3x+1)[/tex]
[tex]\sf 3x+2[/tex][tex]\sf 3x+12=3x+2[/tex]
Subtract 12 from both sides:
[tex]\sf 3x+12-12=3x+2-12[/tex]
[tex]\sf 3x=3x-10[/tex]
Subtract 3x from both sides:
[tex]\sf 3x-3x=3x-10-3x[/tex]
[tex]\sf 0=-10[/tex]
Sides are not equal, so therefore there is no Solution.
___________________________________________