The assumption Johnny made is that, none of the residents of the town will live up to 230.7 years.
The given parameters are:
[tex]\mathbf{a =10000}[/tex] --- the initial population
[tex]\mathbf{r =0.3\%}[/tex] -- the declining rate
Population are always modelled using exponential function.
This is represented as:
[tex]\mathbf{y = a(1 - r)^x}[/tex]
Where y represents the population in x years.
So, we have:
[tex]\mathbf{y = 10000(1 - 0.3\%)^x}[/tex]
[tex]\mathbf{y = 10000(1 - 0.003)^x}[/tex]
[tex]\mathbf{y = 10000(0.997)^x}[/tex]
When the population reaches half, then y = 5000.
So, we have:
[tex]\mathbf{5000 = 10000(0.997)^x}[/tex]
Divide both sides by 10000
[tex]\mathbf{0.5 = 0.997^x}[/tex]
Take logarithm of both sides
[tex]\mathbf{log(0.5) = log(0.997)^x}[/tex]
Apply law of logarithm
[tex]\mathbf{log(0.5) = xlog(0.997)}[/tex]
Make x the subject
[tex]\mathbf{x = log(0.5) \div log(0.997)}[/tex]
[tex]\mathbf{x = 230.7}[/tex]
This means that the population will become half the original population in 230.7 years.
The assumption Johnny made is that, none of the residents of the town will live up to 230.7 years.
Read more about exponential function at:
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3. Which of the following is true for a rigid motion?
A The preimage and the image have the same measurements.
B The preimage is larger than the image.
The preimage is smaller than the image.
D The preimage is in the same position as the image.
-4y + 12 = -7y + 24
I’ll give Brain whoever solves
PLEASE DO IT STEP BY STEP
Answer:
y - 4
Step-by-step explanation:
subtract 12 from both sides of the equation
4y+12-12= -7y +24 - 12
-4y = -7y +24 - 12
subtract
-4y +-7y + 12
add 7y to both sides of the equation
-4y + 7y = -7y +12 + 7y
simplify
3y + -7y +12 + 7y
combine like terms.
3y = 12
divide
3y/3
=12/3
simplify
y=12 3
y = 4
Answer:
y = 4
Step-by-step explanation:
Given the algebraic equation, -4y + 12 = -7y + 24, the goal is to solve for the value of y by isolating it to either sides of the equation.
Start by adding 7y to both sides of the equation:
-4y + 7y + 12 = -7y + 7y + 24
3y + 12 = 0 + 24
3y + 12 = 24
Next, subtract 12 from both sides:
3y + 12 - 12 = 24 - 12
3y = 12
Divide both sides by 3 to isolate and solve for y:
[tex]\frac{3y}{3} = \frac{12}{3}[/tex]
y = 4
Double-check whether the value of y will provide a true statement if plugged into the equation:
-4y + 12 = -7y + 24
-4(4) + 12 = -7(4) + 24
-16 + 12 = -28 + 24
-4 = -4 (True statement).
Therefore, the value of y = 4.
Please help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee (thank you :)
(cAt)
x>-6
1st step: 3(x-1)>-15------(3x-3)>-15
2nd step: subtract -3 from -15 which is -18
3rd step: 3x>-18------x>-6
Answer:
x > -4
Step-by-step explanation:
First, distribute the 3 among everything inside the parentheses to get 3x - 3 > -15.
Next, add 3 on both sides to get 3x > -12, then divide 3 on both sides to get x > -4.
Hope this helps :)
Also I love the kitty lol, but what's with the hair tie?
which one is it please do this quick!
Answer:
B
Step-by-step explanation:
The answer is B because Figure JKML is a result of PQRS by a scale factor of 3
You can verify this because the distance from J to K is 6 and the distance from P to Q is 2, from 2 to get to 6 you need to multiply 2 by 3 meaning JKML would be the dilation of figure PQRS by a scale factor of 3
solve the proportion (someone pls help)
There are about 0.15 million people in Barrie, Ontario,
and 0.4 million people in London, Ontario.
a) How many more people live in London than Barrie?
b) How many times as many people live in London as in Barrie?
no links.
Answer:
a)0.11
b) 3.75
Step-by-step explanation:
a) take 4 away from 15
B) do 15 divided by 4
hope this helps bye if right mark brainlest PLEASE
Use the example as a model. Simplify the expressions.
t^37=?
i
-i
1
-1
Answer:
Step-by-step explanation:
[tex](\iota)^{37}=(\iota)^{36} \times \iota=[(\iota)^2]^{18}\times \iota=(-1)^{18} \iota=\iota[/tex]
You jog 623 miles around a track each day. If you jogged that distance 4
times last week, how many miles did you jog? in a fraction
Answer:
6 2/3 miles times 4
Step-by-step explanation:
Convert the fraction 2/3 to a decimal
2/3 = .67
6.67 miles times 4 = 26.68 miles
or 6x4= 24
2/3+2/3+2/3+2/3 =8/3 or 2 2/3
2 2/3 +24 =26 2/3 miles
Hope this helps, have a nice day/night! :D
Raymond frequently dined at his favorite restaurant, Hungry Hippo. At his most recent visit, he paid his bill. If the bill had been half as much, he would have gotten three times as much change. If the bill had been two dollars more, Raymond would have gotten only half as much change as he actually did get. How much was Raymond’s change?
Raymond's change was $ 4.
Since Raymond frequently dined at his favorite restaurant, Hungry Hippo, and at his most recent visit, he paid his bill, and if the bill had been half as much, he would have gotten three times as much change, while if the bill had been two dollars more, Raymond would have gotten only half as much change as he actually did get, to determine how much was Raymond's change the following calculation must be performed:
1 / 2X = 3Y X + 2 = 1 / 2Y X = Y 2 = 1 / 2Y Y = 2 x 2 Y = 4
Therefore, Raymond's change was $ 4.
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Please help will mark brainliest
Answer:
u cant be marked
Step-by-step explanation:
u cant be marked
10.
Identify the vertex of the parabola.
A. (−1, 0)
B. (0, −1)
C. (1, 0)
D. (0, 1)
Answer:
C. (1, 0)
Step-by-step explanation:
1,0 should be the vertex for this parabola
1,0 should be the correct answer
For the problem -4(-5)(9), will the answer be positive or negative?
Answer:
Positive
Step-by-step explanation:
-4(-5)(9)
Negative cancels out negative, so it makes a positive:
20(9)
Simplify normally to get 180 as your final answer.
Make each denominator rational. In other words, rationalize the denominator.
A) (√11-1)/√11
B) (3 + √6 )/√6
The detailed answer is there in the image I have attached.
Hope it helps you....
Please mark as Brainlliest!!!!
Explain what the vertical line test is and how it is used.
Answer:
The vertical line test is a test to determine if a relation or its graph is a function or not. For a relation or graph to be a function, it can have at most a single y-value for each x-value. Thus, a vertical line drawn at any x-position on the graph of a function will intersect the graph at most once.
Step-by-step explanation:
(winks and runs off)
Hailey ordered 12 pizzas for a grade level party. If each person eats 3/8 of a pizza equally, how many people can Hailey feed with 12 pizzas?
Answer:
24
Step-by-step explanation:
Triangle JKL with vertices /(1, -1), K(2, 3), and
L(3,-2) in the line x = 4.
.ب)J
K'.
L'(_
(
The reflection of the triangle JKL across the line x = 4 is equivalent to
equivalent to flipping the preimage across the line x = 4.
The correct coordinates are;
[tex]\underline{J'(7, \, -1)}[/tex]
[tex]\underline{K'(6, \, 3)}[/tex]
[tex]\underline{L'(5, -2)}[/tex]
Reasons:
The given transformation is a reflection about the line x = 4
The points of triangle JKL are J(1, -1), K(2, 3), and L(3, -2), in the line x = 4
The coordinates of the triangle JKL following a reflection across the line x = 4, have the same y-coordinates , while the x-coordinates have the same distance magnitude to the line x = 4, but opposite sign.Distance between x-coordinate of the point J and the line x = 4 is 4 - 1 = 3
Which gives;
Distance between x-coordinate of the point J' and the line x = 4 is 4 + 3 = 7
Therefore, the coordinate of the point J' is [tex]\underline{J'(7, \, -1)}[/tex]
Similarly, we have;
Distance between x-coordinate of the point K and the line x = 4 is 4 - 2 = 2
Distance between x-coordinate of the point K' and the line x = 4 is 4 + 2 = 6
The coordinate of the point K' is [tex]\underline{K'(6, \, 3)}[/tex]
Distance between x-coordinate of the point L and the line x = 4 is 4 - 2 = 2
Distance between x-coordinate of the point L' and the line x = 4 is 4 + 2 = 6
The coordinate of the point L' is [tex]\underline{L'(5, -2)}[/tex]
Learn more here:
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3.
(03.06)
Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form. (2 points)
f(x) = (x −8)2
f(x) = (x −4)2−13
f(x) = (x −4)2 + 3
f(x) = (x −4)2 + 16
Answer: f(x) = (x −8)2
Step-by-step explanation:
Answer number three and four please
Answer:
Yes (both)Step-by-step explanation:
Let's verify using Pythagorean:
#3 1² + 1² = (√2)² ⇒ 1 + 1 = 2 ⇒ 2 = 2, TRUE#40.3² + 0.4² = 0.5² ⇒ 0.09 + 0.16 = 0.25 ⇒ 0.25 = 0.25, TRUEwhat is 7a-7b when a-b=5
Answer:
35
Step-by-step explanation:
7a -7b
Let a-b = 5
Factor
7(a-b)
7(5)
35
Answer:
a=5+7b/7
Step-by-step explanation:
7a-7b
a-b=5
7a-7b=5
7a-7b+7b=5+7b
7a-0=5+7b
7a=5+7b
7a=5+7b/7
a=5+7b/7
Find the slope of the line passing through the points (5,9) and (5, - 7)
Answer:
9/11
Step-by-step explanation:
solve for x
5x - 2 = 6
give your answer as an improper fraction in its simplest form
Answer:
x= 8/5
Step-by-step explanation:
add 2 to both sides
5x=8
divide both sides from 5
x=8/5
How do i find the measure of <2 in this equation?
Answer:
142
Step-by-step explanation:
It is equal to the one above it.
I hope this helps!!
The equation P=4s represents the perimeter P of a square with side length s. What is the perimeter of a square with a side length of 5ft ?
The perimeter is.
Answer:
20 feet
Step-by-step explanation:
s= side
P= 4s
I our case, s is 4, so 4*5 is 20.
Hence,
P=20
Hope this helps!
r(m)r(m)r, left parenthesis, m, right parenthesis models the average monthly rainfall (in millimeters) in Tanzania for the years 190019001900-200920092009 as a function of the month number mmm.
Month # Rainfall (millimeters)
111 145145145
222 135.8135.8135, point, 8
333 179.1179.1179, point, 1
444 171171171
555 64.864.864, point, 8
666 12.612.612, point, 6
777 8.48.48, point, 4
888 8.98.98, point, 9
999 15.715.715, point, 7
101010 29.529.529, point, 5
111111 83.883.883, point, 8
121212 142.6142.6142, point, 6
Which number type is more appropriate for the domain of rrr?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Integers
(Choice B)
B
Real numbers
What's the appropriate domain?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
0\le m\le 179.10≤m≤179.10, is less than or equal to, m, is less than or eq
Answer:
Integers
1</ M </ 12
Step-by-step explanation:
Khan Aacademy
Find x special right triangle
Answer:
This is a 45 45 90 triangle, so v=[tex]\sqrt{2}[/tex]. The side opposite the right angle in a 45 45 90 triangle is equal to the length of the other sides * [tex]\sqrt{2}[/tex].
Therefore, u=2, because [tex]\sqrt{2}[/tex]*[tex]\sqrt{2}[/tex]=2. So, your answer is A, 2.
Step-by-step explanation:
Answer:
2
Hope you could understand.
If you have any query, feel free to ask.
simplify (3x^2y3)^3 / x3
Just need some help with this one
Answer:
y = -2/3x + 10/3
volume of a cube is 343 cm cube . find the edge
Answer:
Edge: 7 cm
Step-by-step explanation:
Cubic root of 343 = 7
I need help pleaseeeeee
ok for the first one says
f(x)= 2 which is our Y, now we see when y is 2 our x = 1
f(x)=0 so when y= 0 , x = 2
f(1) = 2
Could you please help with this
Please find attached photograph for your answer.
Hope it helps.
Do comment if you have any query.