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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If 7 > 2, then explain why -7 < -2.
A. The above statement is false.
B. Because the sign changed.
C. Because -7 is more negative and further to the left on the numberline than
-2.
D. Because 7 is an odd number and 2 is even, which flips when they become
negative, where -7 becomes even and -2 becomes odd.
Answer:
C
Step-by-step explanation:
Hope it can help you lovelots
If 7 > 2, then explain why -7 < -2.
Answer =》C. Because -7 is more negative and further to the left on the numberline than
-2.
______
RainbowSalt2222 ☔
Which graph represents x ≥ 2?
Answer:
...
Step-by-step explanation:
Please help me please help mee
Answer:
1.-profit
2.-$300
3.-25%
Step-by-step explanation:
1.- 1500-1200=300+
2.-(1)
3.-1200/100= 12
300/12= 25
A right triangle has legs that are 10. 1 inches and 12. 2 inches long. What is the approximate length of the hypotenuse? 6. 8 inches 15. 8 inches 22. 3 inches 125. 5 inches.
Answer:
A^2 + B^2 = C^2 for a right triangle
C^2 = (10.1^2 + 12.2^2)^1/2 = 250.85^1/2 = 15.8 in
Helpppp!!
Drag each image to the correct location on the graph. Each image can be used more than once.
The following list shows the grams of fiber per serving for each flavor of oatmeal at a grocery store.
3, 6, 3, 4, 2, 4, 4
3, 5, 2, 1, 4, 1, 2
Create a histogram that correctly displays the data.
Answer:
The answer is 2, 6, 5, 1 for the Grams of Fiber.
Step-by-step explanation:
With a population standard deviation of 10 and a sample size of 4, what is the standard error of the mean
With a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the meanWith a population standard deviation of 10 and a sample size of 4, what is the standard error of the mean
Step-by-step explanation:
Will give brainly crown (if shown step by steps I'll give half of my entire points)
Felix and Oscar applied for the same credit card from the same bank. The bank checked both of their FICO scores. Felix had an excellent credit rating, and Oscar had a poor credit rating.
a. Felix was given a card with an APR of 14%. What was his monthly percentage rate? Round to the nearest hundredth of a percent.
b. Oscar was given a card with an APR of 21%. What was his monthly percentage rate? Round to the nearest hundredth of a percent.
c. If each of them had an average daily balance of $800 for a specific month, and had to pay a finance charge, how much more would Oscar pay than Felix?
A) The monthly percentage rate of Felix is;
B) The monthly percentage rate of Oscar is;
C) The amount that Oscar will pay more than Felix is; $0.96
Annual Percentage Rate
A) Felix was given a card with APR of 14%.
Thus;
Monthly percentage rate = 14%/12 = 1.63%
B) Oscar was given a card with an APR of 21%. Thus;
Monthly percentage rate = 21%/12 = 1.75%
C) We are told that each of them had an average daily balance of $800 for a specific month.
Thus;
Amount paid by Felix = 800 * 1.63%
Amount paid by Felix = $13.04
Amount paid by Oscar = 800 * 1.75%
Amount paid by Oscar = $14
Difference in Payments = $14 - $13.04 = $0.96
Thus, Oscar pays $0.96 more than Felix.
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a. felix: 14/12 = 1.167% (round to nearest hundredth = 1.17%)
b. oscar 21/12 = 1.75% (no need to round here)
c.
felix: (1.17/100) x 800 = 9.36
oscar: (1.75/100) x 800 = 14.00
14.00 - 9.36 = 4.64
oscar will pay $4.64 more than felix.
Does someone have this answer???? Thank you so much
Answer: 3
Step-by-step explanation:
We know that p(t) = 11:
11=2t+5
11-5=2t
6=2t
6/2 = t
3 = t
- 3< t <2
t is an integer.
Write down all the possible values of t.
Answer:
-2, -1, 0, 1
Step-by-step explanation:
-2
-1
0
1
All the possible values of t in the inequality - 3 < t < 2 is,
t = - 2, - 1, 0, 1
Used the concept of inequality that states,
A relation by which we can compare two or more mathematical expressions is called an inequality.
Given that;
The inequality is,
- 3 < t < 2
Here the given inequality means all the values of t are lies between - 3 and 2.
That is,
t = - 2, - 1, 0, 1
Therefore, the value of t are t = - 2, - 1, 0, 1
To learn more about inequality visit:
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Solve for x
9(x + 5) = -9
Answer:
x = -6
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
9(x+5)=−9
(9)(x)+(9)(5)=−9(Distribute)
Step 2: Subtract 45 from both sides.
Step 3: Divide both sides by 9.
Hello there! :)
9(x+5)=-9
Use the Distributive Property:
9(x+5)=-9
9x+45=-9
9x=-9-45
9x=-54
Divide both sides by 9:
x=-6
Hope it helps you! :) Feel free to ask me if you have any questions.
~A smiley teen who adores helping others
[tex]MagicalNature[/tex]
What is this symbol??
Answer:
plus and minus
Step-by-step explanation:
example : 3 ± 5 = 8 or -2
Hello!
The symbol + means "plus or minus"
It means we either add or subtract 4.
Example: 2+4=6 or -2
Hope it helps!
~Just a felicitous teen
#CarryOnLearning
[tex]SilentNature :-)[/tex]
5
8. The frequency distribution below summarizes employee years of service for Alpha Corporation. Determine the width of each class.
Years of service Frequency
1-5
6-10
20
11-15
25
16-20
10
21-25
5
26-30
The required class widths are 3, 8, 13, 18, 23 and 28
Given the frequency distribution that summarizes employee years of service for Alpha Corporation as shown below:
[tex]1-5 \ | \ 6-10\ | 11-15 \ | \ 16-20 \ | 21-25 \ | 26 - 30\ \\ 0\ \ \ \ \ \ \ \ 20 \ \ \ \ \ \ \ \ 25 \ \ \ \ \ \ \ \ \ \ 10 \ \ \ \ \ \ \ \ \ \ 5[/tex]
The width of each class is calculated by taking the midpoints of each of the class intervals as shown:
For the class interval 1 - 5
width = 1+5/2 = 3
For the class interval 1 - 5
width = 6+10/2 = 8
For the class interval 11 - 15
width = 11+15/2 = 13
For the class interval 16 - 20
width = 16+20/2 = 18
For the class interval 21 - 25
width = 21+25/2 = 23
For the class interval 26 - 30
width = 26+30/2 = 28
Hence the required class widths are 3, 8, 13, 18, 23 and 28
Learn more on class width here: https://brainly.com/question/24326240
What is the median?
And why
? Do you think so
Answer:
32 seconds
Step-by-step explanation:
The median is the exact middle of the data after putting the data in order. In this example, it would be 32 seconds.
23, 23, 28, 31, 32, 34, 47, 49, 56
What's the length of an arc with a central angle of 100° and a radius of 2 inches?
A) 10pi/9 inches
B) 5pi/3 inches
C) 100pi/3 inches
D)40pi/3 inches
Will make brainly who answers correctly.
Laura wants to place a flowerpot every 3/4 meters along the path from the gate to the main entrance of her home the path is 12 meters long how many flowerpots will she need
Answer:
16 pots
Step-by-step explanation:
Laura wants to place a pot every 3/4 (0.75)m
The length she wants to cover is 12m
So all we must do is divide
1) 12/0.75 (I converted the fraction to a decimal cause its easier)
2) 12/0.75 = 16
3) which means for each 3/4 there will be one pot so there is 16 pots in total
Add the following fractions answer in lowest terms.
1) 9/10+4/5+5/6=
2) 14/15+2/9+1/5=
please give me Right answers please.
Answer:
1) 9/10 + 4/5 + 5/6 = 2 8/15
2) 14/15 + 2/9 + 1/5 = 1 16/45
==============================================
Solution:
[tex] \bold{1)} \: \tt \frac{9}{10} + \frac{4}{5} + \frac{5}{6} \\ \\⟹ \tt \frac{9}{10} + \frac{4}{5} \\ = \tt \frac{9 \times 1}{10 \times 1} + \frac{4 \times 2}{5 \times 2} = \frac{9 + 8}{10} = \frac{17}{10} \\ \\ ⟹\tt \frac{17}{10} + \frac{5}{6} \\ = \tt \frac{17 \times 3}{10 \times 3} + \frac{5 \times 5}{6 \times 5} = \frac{51 + 25}{30} = \frac{76}{30} \: or \: 2 \frac{16}{30} = 2 \frac{8}{15} \\ \\ \\ \\ \bold{2)} \tt \: \: \frac{14}{15} + \frac{2}{9} + \frac{1}{5} \\ \\⟹ \tt \frac{14 \times 3}{15 \times 3} + \frac{2 \times 5}{9 \times 5} = \frac{42 + 10}{45} = \frac{52}{45} \\ \\⟹ \tt \frac{52}{45} + \frac{1}{5} \\ = \frac{52 \times 1}{45 \times 1} + \frac{1 \times 9}{5 \times 9} = \frac{52 + 9}{45} = \frac{61}{45} = 1 \frac{16}{45} [/tex]
plz help asap
Find the length X
Answer:
x=8 that's the answer for the question
b/4 + 2 = -1
Please help, I’ll give brainliest to whoever answers correct first.
Answer:
[tex]\frac{b}{4}+2=-1[/tex]
Subtract 2 from both sides:
[tex]\frac{b}{4}+2-2=-1-2[/tex]
[tex]\frac{b}{4}=-3[/tex]
Multiply 4 to both sides:
[tex]4*\frac{b}{4} =-3*4[/tex]
[tex]b=-12[/tex]
A Science book has 428 pages, of which 47% are on biology, 28% on Chemistry and the remainder on Physics. How many pages on Physics are there?
Answer:
107 pages.
Step-by-step explanation:
100 - 47 - 28 = 25% are on Physics.
Number of pages on physics = 0.25 * 428
= 107.
Answer:
There are 107 pages devoted to physics.
Step-by-step explanation:
The number of pages on bio is 0.47(428) = 201 (rounded up from 201.16);
the number of pages for on chem is 0.28(428) = 120 (rounded up from 119.84), and so the total number of pages devoted to bio and chem is
201 + 120, or 321.
Subtracting this subtotal from the book's 428 pages yields 107.
There are 107 pages devoted to physics.
Do you know what the variables could be
Answer:
5, 7, and 12
Step-by-step explanation:
First we can make and equation
x + z + y = 24
we can plug in the numbers you gave us giving us
y = x + z
z = y - x
x = (y - 2) ÷ 2
Once, were done we get that x = 5 ≈ smallest number
z = 7 ≈ second largest number
y = 12 ≈ largest number
(Pythagorean theorem) do the following lengths form a right triangle? Show steps
Answer:
8^2+6^2=10^10?
64+36=100
Yes
Hope This Helps!!!
Answer:
Yes,
Step-by-step explanation:
8^2 +6^2=100
[tex]\sqrt 100\\[/tex]= 10
Which number is a zero of the given function?
g(x) = (x^2– 36) (x + 7)
The zeros of the function g(x) = (x² - 36)(x + 7) are x = 6 and x = -6.
To find the zeros of the function g(x) = (x² - 36)(x + 7), we need to identify the values of x that make the entire function equal to zero.
For a function to be equal to zero, at least one of its factors must be zero. Therefore, we set each factor to zero and solve for x:
Setting the first factor, x² - 36, to zero:
x² - 36 = 0
Now, add 36 to both sides of the equation:
x² = 36
Next, take the square root of both sides:
x = ±√36
x = ±6
Setting the second factor, x + 7, to zero:
x + 7 = 0
Now, subtract 7 from both sides of the equation:
x = -7
The zeros of the function g(x) = (x² - 36)(x + 7) are x = 6 and x = -6.
Learn more about zeros of the function from the link given below.
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The flywheel on a steam engine rotates 60 revolutions every 15 seconds. What is the flywheel's rate of revolutions per second?
Answer:
It is 4
Step-by-step explanation:
Find the measure of
Answer:
120° , 80° , 90°
Step-by-step explanation:
The sum of the inner angles of a triangle is one hundred and eighty degrees. and as the diagram shows, The AB is equal to AC so angle ABC is equal to angle ACB so Angle A is 180°-(30°×2)=120°
you can get the second follow the above steps
and the third one is 2x+x+x=180°
so 4x=180°
so x=45°
so 2x=90°
Q.17) Given info:- In ∆ABC , AB = AC where, angle A = x°, angle B = 30°and angle C = ?°. Find the value of X in triangle ABC ?
Explanation:
Given that
ABC is a triangle
angle A = x°
angle B = 30°
angle C = ?°
And
AB =AC
We know that
In a triangle Angles opposite to equal sides are equal.
⇛Opposite angle to AB = Opposite angle to AC
⇛angle B = angle C
⇛angle B & C = 30°
We know that
The sum of all angles in a triangle is 180°
⇛ angle A + angle B + angle C = 180°
⇛30° + x° + 30° = 180°
⇛60° + x° = 180°
⇛x° = 180°÷60 = 180°:60
⇛x° = 180°/60
⇛x° = 3°
Now,
⇛angle A = x = 3°
⇛angle B = 30°
⇛angle C = 30°
Answer: The value of x for the given problem is 3°
Q.18) Given info:- In ∆ABC , AB = AC where, angle A = x°, angle B = 50°and angle C = ?°. Find the value of X in triangle ABC ?
Explanation:
Given that
ABC is a triangle
angle A = x°
angle B = 50°
angle C = ?°
And
AB =AC
We know that
In a triangle Angles opposite to equal sides are equal.
⇛Opposite angle to AB = Opposite angle to AC
⇛angle B = angle C
⇛angle B & C = 50°
We know that
The sum of all angles in a triangle is 180°
⇛ angle A + angle B + angle C = 180°
⇛ x° + 50°+50° = 180°
⇛x° + 100 = 180°
⇛x° = 180°÷100° = 180°:100°
⇛x° = 180°/100
⇛x° = 18°
Now,
⇛angle A = x = 18°
⇛angle B = 50°
⇛angle C = 50°
Answer: The value of x for the given problem is 18°
Q.19) Given info:- In ∆ABC , AB = AC and angle A = 2x°, angle B = x°, angle C = x°. Find the value of X in triangle ABC ?
Explanation:
Given that
ABC is a triangle
angle A = 2x°
angle B = x°
angle C = x°
And
AB =AC
We know that
In a triangle Angles opposite to equal sides are equal.
⇛Opposite angle to AB = Opposite angle to AC
⇛angle B = angle C
⇛angle B & C = x°
We know that
The sum of all angles in a triangle is 180°
⇛ angle A + angle B + angle C = 180°
⇛x° + 2x° + x° = 180°
⇛2x° + 2x° = 180°
⇛4x° = 180°
⇛x° = 180°÷4 = 180°:4
⇛x° = 180°/4
⇛x° = 45°
Now,
⇛angle A = 2x = 2(45) = 90°
⇛angle B = 45°
⇛angle C = 45°
Answer: The value of x for the given problem is 45°
Solve for x using
multiplication.
Cross
-
3x - 3
5
=
2x - 2
4.
x = [?]
Answer:
x = 1
Step-by-step explanation:
[tex]\frac{3x-3}{5}[/tex] = [tex]\frac{2x-2}{4}[/tex] ( cross- multiply )
4(3x - 3) = 5(2x - 2) ← distribute parenthesis on both sides
12x - 12 = 10x - 10 ( subtract 10x from both sides )
2x - 12 = - 10 ( add 12 to both sides )
2x = 2 ( divide both sides by 2 )
x = 1
In figure BC = CA and ∠A = 40°. Then ∠ACD is...
a)40° b) 80° c) 120° d) 60°
Answer:
B
Step-by-step explanation:
The size of the exterior angle in a triangle is the sum of interior opposite angles. In this case, it's
Angle ACD=40+40=80° (Exterior angle=sum of int. opp. angles)
Answer:
b. 80°
Step-by-step explanation:
B is 40°
A triangle has 180°
40 + 40 + x = 180
80 + x = 180
x = 100
Since it's a supplementary angle...
180 - 100 = 80
Solve for x
………………..
I need help with these questions. Thanks!
Answer:
47.27°44.22°Step-by-step explanation:
Q1)The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
cos(x) = 57/84
The inverse function is used to find the angle.
x = arccos(57/84)
x ≈ 47.27°
__
Q2)The relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(x) = 53/76
The inverse function is used to find the angle.
x = arcsin(53/76)
x ≈ 44.22°
if pepsi Bottles 8-pack or cans 12-pack 3 for $12.88 how much for 1 pack?
explain
Answer: $4.29?
Step-by-step explanation:
3 pack /3 = $12.88 /3
1 pack = 4 22/75 or approx $4.29
Find the value of x and y and each labeled
angle.
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The required values are ~
[tex]\fbox \colorbox{black}{ \colorbox{white}{x} \: \: \: \: \: \: \: \: \colorbox{white}{=} \: \: \: \: \: + \colorbox{white}{40 \degree}}[/tex]
[tex]\fbox \colorbox{black}{ \colorbox{white}{y} \: \: \: \: \: \: \: \: \colorbox{white}{=} \: \: \: \: \: + \colorbox{white}{80 \degree}}[/tex]
[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]
From the given figure, we can infer that ~
3x - 20° + 2x = 180°(by linear pair)
now, let's solve for x ~
[tex]5x - 20 \degree = 180 \degree[/tex][tex]5x = 180 \degree + 20 \degree[/tex][tex]5x = 200 \degree[/tex][tex]x = 200 \degree \div 5[/tex][tex]x = 40 \degree[/tex]And, we can see that 2x = y (by alternate interior angle pair)
So, let's find the value of y ~
[tex]2x[/tex][tex]2 \times 40 \degree[/tex][tex]80 \degree[/tex]Answer:
x = 40
3x - 20 = 100
2x = 80
y = 80
2x - 15 = 65
Step-by-step explanation:
The angles 3x - 20 and 2x are a linear pair, so they are supplementary. Their measures has a sum of 180°.
Angles 2x and y are alternate interior angles, so they are congruent.
Once we find the value of x, we can find the measure of angle 2x - 15.
3x - 20 + 2x = 180
5x = 200
x = 40
3x - 20 = 3(40) - 20 = 120 - 20 = 100
2x = 2(40) = 80
y = x = 80
2x - 15 = 2(40) - 15 = 80 - 15 = 65