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.
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Find the perimeter. Simplify your answer.
Answer:
3a+ 16
Hope this helps!
1) 9 × 0 + (-80) + 8 = ?
9 × 0 + (-80) + 8 = ?
= 0 - 80 + 8
= -80 + 8 <==> 8 - 80
= -72
~bilbul
9 × 0 + (-80) + 8
= 0 + (-80) + 8
= (-80) + 8
= -72 ✔️
:)
Find the vertices of the dilated figure whose original coordinates are A (0, 0), B (0, 9), C (8, 8) and D (10, 0) which is dilated by a scale factor of 6.
A' (0, 0), B' (0, 54), C' (48, 48), and D' (60, 0)
A' (0, 0), B' (0, -54), C' (-48, 48), and D' (60, 0)
A' (0, 0), B' (0, 54), C' (48, -48), and D' (60, 0)
A' (0, 0), B' (0, 54), C' (48, 48), and D' (-60, 0)
Answer:
A
Step-by-step explanation:
when dilating by a scale factor of 6, you are starting at the origin and just making it larger by a factor of 6, so you multiply the coordinates by 6 and get A
Measure these angles.
a)
b)
Ruth wants to purchase a new video game that costs $59.00 and several bags of chips that sell for $1.99 each. She can spend no more than $75.00. Which inequality and its solution represents her possible purchase?
Answer:
1.99c + 59 ≥ 75, where c ≥ 8.04
Step-by-step explanation:
you have $5.88. You buy 8 items that cost $0.44 each How many items much money do you have left?
Answer:
$2.36
Step-by-step explanation:
0.44 x 8 = 3.52
5.88 - 3.52 = 2.36
$2.36
-Chetan K
7.
Fit a quadratic function to these three points:
(−1, −11), (0, −3), and (3, −27)
y = −4x^2 − 4x + 3
y = −4x^2 − 4x − 3
y = −4x^2 + 4x − 3
y = 4x^2 − 4x − 3
Answer:
y = −4x^2 + 4x − 3
Step-by-step explanation:
I built a toy model of my car that is 15 inches long.If my actual car is 20 feet long.What is the scale distance between the toy model and the actual car?
If I built a toy model of my car for the given condition the scale distance between the toy model and the actual car will be 225 inches.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
The term PEMDAS describes the sequence in which arithmetic operations must be carried out in an equation.
It is given that the length of the toy model car is 15 inches and the actual car is 20 feet
As we know 1 foot consists of 12 inches as a result 20 feet has 240 inches.
The scale distance between the toy model and the actual car is the difference between the actual length and the model length.
Scale distance = 240 inches - 15 inches
Scale distance =225 inches
Thus, if I built a toy model of my car for the given condition the scale distance between the toy model and the actual car will be 225 inches.
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what is the gcf of 8 and 11?
To find the greatest common factor, line both numbers up and continue adding that specific number until you find two factors that correlate with both numbers.
With that being said, let's begin.
8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88
Simply add 8.
11: 11, 22, 33, 44, 55, 66, 77, 88
Simply add 11.
The greatest common factor of 8 and 11 is 88.
Solve pls brainliest
Answer:
The answer is 60%
Step-by-step explanation:
To solve that, just divide 24 by 40
24 ÷ 40 = 0.6
Now turn 0.6 to fraction.
0.6 = 60%
What is the value of a? Enter the answer in the box.
Answer:
a = 25°
Step-by-step explanation:
60° and 3a - 15° are congruent because they are corresponding.
60 = 3a - 15
75 = 3a
a = 25°
-Chetan K
the height of mont blanc is 4810 m correct to the nearest 10 meters. what is its least possible height
Subtraction is a mathematical operation that reflects the removal of things from a collection. The least possible height of the mont blanc is 4800 meters.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
Given the height of mont blanc is 4810 m correct to the nearest 10 meters. Therefore, the least possible height of the mont blanc can be written as,
Least height = 4810m - 10m = 4,800 meters
Hence, the least possible height of the mont blanc is 4800 meters.
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What is 5,000 x 1,000
Answer:
The Answer is 5,000,000
Hope this helps!!
In a 30 minute show 12 minutes of airtime are spent on commercials. Determine what percent of the television show air time is spent on commercial
Belvedere goes to the store and buys a garden statue for $30. The store has a sales tax rate of 7.8%. How much tax will Belvedere have to pay?
Answer:
$2.34
Step-by-step explanation:
30x0.078=2.34
Find the nth term of this sequence
-3 -5 -7 -9 -11 ...
Answer:
Step-by-step explanation:
Answer:
2n-1
Step-by-step explanation:
-5 ---> -3 = 2
-3 -2= -1
i dont get it can u guy help me
Answer:
y = x + 8
Step-by-step explanation:
Let's build the equation:
There are 8 entries to start
y = 8
Adding 1 entry every day
y = x + 8
Shamika earns $25.75 one week. The next week she earns $37.80, and she spends $32.How much money does Shamika have from these two weeks?
Answer: $31.55
Step-by-step explanation:
$25.75 + 37.80 - 32.00 = $31.55
How long did it take a jet to accelerate from 200 m/s to 300 m/s with a constant acceleration of 50 m/s?
It will take 2 seconds a jet to accelerate from 200 m/s to 300 m/s with a constant acceleration of 50 m/s.
What is division?One type of operation in mathematics is division. We divide the phrases or numbers into the same number of components during this operation.
Given:
A constant acceleration is of 50 meter per second.
A jet to accelerate from 200 m/s to 300 m/s.
Acceleration is 100 meters per 2 seconds.
That means,
it will take = (300 - 200)/ 50 m/s
= 2 seconds.
Therefore, it will take 2 seconds.
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solve pls brainliest
Answer:
95%
Step-by-step explanation:
19/20=0.95
0.95x100=95%
-6(2v)+3a(3); v=1/3 a=2/3
Answer:
0
Step-by-step explanation:
-6(2(1/3)+3(2/3(3))=
Starting with pedmas (parenthesis, exponents, division, mulitplication, addition, subtraction).
We look at 2*1/3 and 2/3*3
[tex]2*\frac{1}{3}=\frac{2}{3}[/tex] and [tex]\frac{2}{3}*3=2[/tex]
[tex]-6(\frac{2}{3})+3(2)[/tex]=-6+6=0
[tex]v = \dfrac 13 ,~ a = \dfrac 23\\\\-6(2v) +3a(3)\\\\=-12v + 9a\\\\=-12\left(\dfrac 13 \right) + 9 \left( \dfrac 23 \right)\\\\=-4+ 3 \cdot 2 = -4 +6 = 2[/tex]
PLEASE HELP ME AND NOT JUST ANSWER FOR POINTS!!!
I'm confused on if it's 3 or 2
Answer:
it's 3 cause if u do 1 2 3 there are 3 hearts and they are broke up in half so 6
Can you figure out if the slopes are parallel, perpendicular or neither and type the correct code? Please remember to type in ALL CAPS with no spaces.
Answer:
1. C, 2. A, 3. C, 4. B
Step-by-step explanation:
Parallel: slopes are equal. In problem 2, the slopes appear to be 2 ("rise over run") One line passes through points (2, 1) and (3, 3) -- y increases by 2 if x increases by 1. The other line passes through points (0, 3) and (1, 5) -- y increases by 2 if x increases by 1. The lines have the same slope.
Perpendicular: slopes are opposite reciprocals (they have opposite signs). In problem 4, that happens: 2/3 and -3/2. That is not the relationship between slopes in problem 3. 1/3 and 3 are not opposite reciprocals.
Corrected! #4 is B (perpendicular)
What is the equation of this line?
A y= 6x - 4
B y= 1/4 x -6
C y=6x - 1/4
D y= 4x - 6
Answer:
the answer is D pls brainliesttt
What is the slope of the graph of the given line?
Answer:
slop = 2/3
Step-by-step explanation:
slope = rise/run
Start at the lower left point (-2, -1).
We need to go to the upper right point (4, 3) by going only vertically (rise) and horizontally (run).
First we go up 4. The rise is 4.
Then we go right 6. The run is 6.
slope = m = rise/run = 4/6 = 2/3
slope = 2/3
multiply 4 (-52/3) in simplest form
Answer:
Should be -69 1/3
Step-by-step explanation:
Let X equal the decimal number
Equation 1:
X=69.3333333333¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
With 10 digits in the repeating decimal group,
create a second equation by multiplying
both sides by 1010 = 10000000000
Equation 2:
10000000000X=693333333333.3333333333¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Subtract equation (1) from equation (2)
10000000000XX9999999999X===693333333333.3333333333...69.3333333333...693333333264
We get
9999999999X=693333333264
Solve for X
X=6933333332649999999999
Find the Greatest Common Factor (GCF) of 693333333264 and 9999999999, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 3333333333,
693333333264÷33333333339999999999÷3333333333=2083
Simplify the improper fraction,
=6913
In conclusion,
−69.3333333333¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯=−6913
Gina Wilson all things algebra unit 4 homework 3 questions 12-15
Step-by-step explanation:
the essential thing to remember here (and please, burn this into your brain for life) : the sum of all angles in a triangle is always (really always) 180 degrees.
therefore, in 12 and 13 we only need to add all 3 angles, and their sum must be 180.
from there we get really all 4 answers.
the next thing to consider is when a triangle had two equal angles, then it is an isoceles triangle (the 2 sides leading away from these 2 angles are equally long). that gives us the answers for 14 and 15.
12.
3x + 18 + 7x - 58 + 2x - 8 = 180
12x - 48 = 180
12x = 228
x = 19
angle A = 3x+18 = 3×19 + 18 = 57+18 = 75 degrees
angle B = 7x-58 = 7×19 - 58 = 133-58 = 75 degrees
angle C = 2x-8 = 2×19 - 8 = 38 - 8 = 30 degrees
13.
8x - 17 + 19x + 4 + 5x + 1 = 180
32x - 12 = 180
32x = 192
x = 6
angle Q = 8x-17 = 8×6 - 17 = 48-17 = 31 degrees
angle R = 19x+4 = 19×6 + 4 = 114+4 = 118 degrees
angle S = 5x+1 = 5×6 + 1 = 30+1 = 31 degrees
14.
KL = 9x - 14
LM = 7x - 37
KM = 3x + 23
angle K = angle L
so, the sides LM and KM must be equally long. that gives us
7x - 37 = 3x + 23
4x = 60
x = 15
KL = 9x-14 = 9×15 - 14 = 135-14 = 121
LM = 7x-37 = 7×15 - 37 = 105-37 = 68
KM = 3x+23 = 3×15 + 23 = 45+23 = 68
15.
XY = 13x - 21
YZ = 8x - 6
XZ = x + 4
angle X = angle Z
so, the sides XY and ZY (or YZ) must be equally long. that gives us
13x - 21 = 8x - 6
5x = 15
x = 3
XY = 13x-21 = 13×3 - 21 = 39-21 = 18
YZ = 8x-6 = 8×3 - 6 = 24-6 = 18
XZ = x + 4 = 3+4 = 7
Due to delays, a company had to extend a project from 26 days to 42
days. What was the percentage increase in time to complete the
project? Round your answer to the nearest tenth.
Answer:
It should be 38.1
PLEASE HELP ME !! ILL MARK U BRAINIEST
hope you like my answer its 17