Step-by-step explanation:
1/x^24 is the correct expression
The function P(t) = 4000(1.2) represents
the population of a small island
a. Does the function represent exponential
growth or decay?
b. what is the yearly percentage change in
population?
c. estimate how many people will be living on the island after 5 years.
Given:
Consider the given function is:
[tex]P(t)=4000(1.2)^t[/tex]
To find:
a. The type of exponential function (growth or decay).
b. Percentage change in population.
c. Population after 5 years.
Solution:
a. The general exponential function is:
[tex]P(t)=P_0(1+r)^t[/tex] ...(i)
Where, [tex]P_0[/tex] is the initial population and r is the rate of change in decimal.
If r<0, then the function represents exponential decay and if r>0, then the function represents exponential growth.
We have,
[tex]P(t)=4000(1.2)^t[/tex]
It can be written as:
[tex]P(t)=4000(1+0.2)^t[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]P_0=4000[/tex]
[tex]r=0.2[/tex]
Since r>0, therefore the given function represents exponential growth.
b. From part (a), we have
[tex]r=0.2[/tex]
So, the rate of change in the population is 0.2. Multiply is by 100 to get the percentage change in population.
[tex]r\%=0.2\times 100[/tex]
[tex]r\%=20\%[/tex]
Therefore, the yearly percentage change in population is 20%.
c. We have,
[tex]P(t)=4000(1.2)^t[/tex]
Substitute [tex]t=5[/tex] in the given function to find the population living on the island after 5 years.
[tex]P(5)=4000(1.2)^5[/tex]
[tex]P(5)=4000(2.48832)[/tex]
[tex]P(5)=9953.28[/tex]
[tex]P(5)\approx 9953[/tex]
Therefore, the estimated population living on the island after 5 years is 9953.
hi please answer me asap I will mark brainlist
Answer:
for No1 answer is 0. for no 2 answer is 9.
Step-by-step explanation:
for no 3 answer is 14. no 4 =5,no 5 = 0 ,no 6= -16/3 ,no 7 =-3 ,no 8=180 and no 9 = 3
Help pls and thank uu
Answer:
[tex]for~x=3[/tex]
[tex]f(x)=-5[/tex]
[tex]So,f(3)=-5[/tex]
--------------------------hope it helps...have a great day!!Find area of shaded regioni in pi T):
3 in
120°
area of sector:
pi
Submit
Answer:
A = 2π in2
Step-by-step explanation:
See the image I have shared
What minus 12 equals 12
Answer:
24-12
Step-by-step explanation:
Find the sum. Express your answer in simplest form. 9a^2-5/b^2+2 + -2a^2+4/b^2+2
Answer:
Step-by-step explanation:
[tex]\frac{9a^{2}-5}{b^{2}+2}+\frac{-2a^{2}+4}{b^{2}+2}=\frac{9a^{2}-5-2a^{2}+4}{b^{2}+2}\\\\=\frac{9a^{2}-2a^{2}-5+2}{b^{2}+2}\\\\=\frac{7a^{2}-3}{b^{2}+2}[/tex]
Kevin is doing a puzzle. He has completed 89/100 of the puzzle. Which decimal represents how much of the puzzle Kevin has left to do?
Answer:
100-89/100=11/100
=0.11
A cylinder and a sphere both have the same radius, 4. The height of the cylinder is equal to the diameter of the sphere. Select the expression that describes the volume of the cylinder that is not occupied by the sphere.
Answer:
134.04 cubic units
Step-by-step explanation:
Step 1
Find the Volume of the Sphere
Formula = 4/3πr³
r= radius = 4
Hence,
Volume = 4/3 × π × 4³
= 268.08 cubic units
Step 2
Find the Volume of the cylinder
Formula = πr²h
r = radius = 4
h = Height = Diameter of the sphere
Radius of a sphere = 4
Diameter = Height of cylinder = 2 × r = 2 × 4 = 8
Hence: π × 4² × 8
= 402.12 cubic units
Step 3
The expression that describes the volume of the cylinder that is not occupied by the sphere = Volume of Cylinder - Volume of sphere
= 402.12 cubic units - 268.08 cubic units
= 134.04 cubic units
The expression that describes the volume of the cylinder that is not occupied by the sphere is 134.04 cubic units
We have given radius of sphere is 4
What is the formula for volume of the Sphere?[tex]V= 4/3\pi r^3[/tex]
r= radius
We have given that r=4
[tex]Volume = 4/3 \times \pi \times 4^3[/tex]
V= 268.08 cubic units
What is the formula for volume of the cylinder?[tex]Formula = \pi r^2h[/tex]
r = radius = 4
h = Height = Diameter of the sphere
Radius of a sphere = 4
Diameter = Height of cylinder
= 2 × r
= 2 × 4
= 8
Therefore we get
[tex]V=\pi \times 4^2 \times 8[/tex]
V= 402.12 cubic units
The expression that describes the volume of the cylinder that is not occupied by the sphere = Volume of Cylinder - Volume of sphere
= 402.12 cubic units - 268.08 cubic units
= 134.04 cubic units
Therefore the expression that describes the volume of the cylinder that is not occupied by the sphere is
(402.12 - 268.08) cubic units.
To learn more about the volume visit:
https://brainly.com/question/1972490
Evaluate the expression 4q(q + 3w)^2 when q = 2 and w = 3
What is the length of the diagonal of the square shown below?
5√2
Step-by-step explanation:
By the Pythagorean theorem,
A² + B² = C²
5² + 5² = C²
25 + 25 = C²
C² = 50
C = √50
C = √(2 • 25)
C = √2 x √25
C = √2 • 5
C = 5√2
Answer:
5[tex]\sqrt{2\\}[/tex]
Step-by-step expla
chọn tam giác ==> cạnh huyền là đường chéo của hình vuông ảg
sin(∝)= đối / huyền
⇒huyền= đối /sin(45°)
⇒huyền= 5/ sin(45°)
⇒huyền= 5[tex]\sqrt{2}[/tex]
5/12,3/8,6,14in ascending or
der
what is the correct answer
===================================================
Explanation:
Focusing on triangle ACD, we see that AC = 20 is the hypotenuse and AD = 20/2 = 10 is the short leg. The short leg is half that of the hypotenuse when working with 30-60-90 triangles.
Also, for these types of triangles, the long leg is sqrt(3) times that of the short leg. That makes CD = AD*sqrt(3) = 10*sqrt(3)
The opposite sides are the same length, meaning BC = AD and AB = CD.
-----------
The perimeter of rectangle ABCD is
P = AB+BC+CD+AD
P = 10*sqrt(3) + 10 + 10*sqrt(3) + 10
P = 20 + 20*sqrt(3)
P = 54.6410161513776
P = 54.6 cm is the approximate perimeter
Answer:
54.64 cm
Step-by-step explanation:
The perimeter of a rectangle is the total length of all the sides of the rectangle. Hence, we can find the perimeter by adding all four sides of a rectangle. Perimeter of the given rectangle is a + b + a + b.
Length of CD = 17.32 cm from :
[tex] \sin(60) = \frac{cd}{20} \\ then \: x = 17.32 \: cm[/tex]
now CD = BA
Now we must determine length of AD :
[tex] \sin(30) = \frac{ad}{20} \: then \: ad \: = 10 \: cm[/tex]
Now :
perimeter = 17.32 + 17.32 +10+10 = 54.64 cm
47 randomly selected students were asked how many siblings were in their family. Let X represent the number of pairs of siblings in the student's family. The results are as follows:
# of Siblings 0 1 2 3 4 5 6
Frequency 4 11 8 10 6 5 3
Round all your answers to 4 decimal places where possible.
The mean is:
The median is:
The sample standard deviation is:
The first quartile is:
The third quartile is:
What percent of the respondents have at least 4 siblings?
%
94% of all respondents have fewer than how many siblings?
Identifying the Input Value of a Function
The tiles on the left contain functions written using function notation. Match each function with its input.
h(g) = -4+9
The input is f.
f(h) = h - 7
The input is h.
g(t) = 21
The input is g.
Done
Intro
✓
Match each function with its impact
Answer: g(f)= 2f - The input is f
h(g)=-4+g - The input is g
f(h)=h-7 - The input is h
Step-by-step explanation:
The matches are:
h(g) = -4 + 9 corresponds to input g.
f(h) = h - 7 corresponds to input h.
g(t) = 21 corresponds to input t.
We have to given that,
To Match each function with its input.
h(g) = -4+9
The input is f.
f(h) = h - 7
The input is h.
g(t) = 21
The input is g.
Now, We get;
h(g) = -4 + 9 corresponds to input g.
f(h) = h - 7 corresponds to input h.
g(t) = 21 corresponds to input t.
So the matches are:
h(g) = -4 + 9 corresponds to input g.
f(h) = h - 7 corresponds to input h.
g(t) = 21 corresponds to input t.
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ7
Help is appreciated:)
Answer:
Step-by-step explanation:
(-1, 3)
y=3
15. Identify the slope of the line graphed below? *
Answer:
[tex]\displaystyle m = 2[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Reading a coordinate planeCoordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Identify points from graph
Point (0, -1)
Point (1, 1)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{1--1}{1-0}[/tex][Fraction] Subtract: [tex]\displaystyle m = \frac{2}{1}[/tex][Fraction] Divide: [tex]\displaystyle m = 2[/tex]Answer:
Step-by-step explanation:
Please help this is done today at 11:59 PM tonignt
Answer:
should be 359.18876
Step-by-step explanation:
if you round it to the nearest hundredth it will give you your answer in units
Will give BRAINLIST,
the bottom one... i think
Answer:
∠ 1 = 53°, ∠ 2 = 37°
Step-by-step explanation:
let ∠ 2 be x then ∠ 1 = x + 16
Complementary angles sum to 90° , then
x + 16 + x = 90
2x + 16 = 90 ( subtract 16 from both sides )
2x = 74 ( divide both sides by 2 )
x = 37
Then
∠ 2 = 37° and ∠ 1 = 37 + 16 = 53°
Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
C = 32π
Step-by-step explanation:
The circumference (C) of a circle is calculated as
C = 2πr ( r is the radius ) , then
C = 2π × 16 = 32π units
The area of a planned garden can be modeled by the equation A= -4w2 + 64w,
where w is the width of the garden in feet. Someone please help
Answer:
8 feet, 256 ft^2
Step-by-step explanation:
The function of the area can be graphically rapresented with a parabola that opens downwards
in this specific case the vertex is the maximum point of the parabola.
(X) Vertex = -64/-8 = 8 feet
(Y) Vertex = -4(64) + 512 = -256 + 512 = 256 ft^2
Answer:
Maximum Width = 8 feet.
Maximum area = 256 ft^2.
Step-by-step explanation:
Part A.
A = -4w^2 + 64w
Finding the derivative:
dA/dw = -8w + 64 = 0 for maxm/minm, so
-8w = -64
w = 8
The second derivative is -8 so w = 8 gives a maximum.
Part B.
The maximum area = -4(8)^2 + 64*8
= -256 + 512
= 256 ft^2.
If I can travel 35 miles on 1 gallon of fuel and my tank holds 8 gallons, how many miles can I travel on a tank of fuel?
Answer:
can can travel 280 miles
Step-by-step explanation:
A force of 68 N is applied to an area of 540 cm2. Calculate the pressure in N/m2. Give your answer to the nearest integer.
Answer:
[tex]P=1259.26N/m^2[/tex]
Step-by-step explanation:
From the question we are told that:
Force [tex]F=68N[/tex]
Area [tex]A=540cm^2=0.054m^2[/tex]
Generally the equation for Pressure is mathematically given by
[tex]P=\frac{F}{A}[/tex]
[tex]P=\frac{68}{0.054}[/tex]
[tex]P=1259.26N/m^2[/tex]
can you guys help me please!
Answer:
Step-by-step explanation:
What is 2y+5 = 3y+2 ?
2y + 5 = 3y + 2
=> 5 - 2 = 3y - 2y
= 3 = y
Answer:
y = 3
Step-by-step explanation:
2y + 5 = 3y + 2
2y - 3y + 5 = 3y - 3 y + 2 [ subtract both sides by 3y ]
- y + 5 = 0 + 2 [ 3y - 3y = 0 ]
- y + 5 - 5 = 2 - 5 [ subtract by 5 on both sides ]
- y + 0 = - 3 [ -5 + 5 = 0 ]
- y = - 3
y = 3 [ divide by - 1 on both sides ]
Correct answer gets brainliest!
Answer:
D
Step-by-step explanation:
YD and TH
TH is in HOT and YD is in DAY
They go from end to the front in the same way
Making a straight line from left to right that are on the same place
H. E. L. P. ! ! ! !
Answer:
(D) $1 050
Step-by-step explanation:
Simple interest = 7000 × 3 × 5/100 =
70 x 15 = 1 050
NECESITO AYUDA URGENTE...
1- Ordena en forma descendente el siguiente polinomio con respecto a la
variable n. Luego identifica el término independiente:
6n 3 + 7n 4 -2n 2 -5 + 9n 5
2- Completa el polinomio para que cada término tenga el mismo grado
absoluto:
5x 4 y 3 – 3x 6 ___ + 5x 2 4__ + 7___ y 2 + 8y 7 - 6
3- Observa el siguiente polinomio e identifica cuáles son los términos
semejantes:
-8 + 3m 3 n – 4m 2 n + 7mn 2 -11nm 3 + 5 + 6m 2 n
4- Evalúa la veracidad de cada afirmación de la siguiente afirmación:
El grado absoluto de un polinomio no puede ser 1: ___________
5- El grado absoluto de un polinomio se obtiene sumando los grados relativos
de las variables: _________
_
6- El grado absoluto de un binomio puede ser cero: _________
_
7- Si el grado relativo de una variable es tres, entonces, el grado absoluto es
un número mayor que tres: __________
8- Si el grado absoluto de un término es uno. Entonces, el polinomio tiene una
sola variable: ___________
9- Completa el polinomio, luego ordénalo en forma descendente:
15x 4 + 5x 6 + 3x 3 + 2x 2 + 8 + +
10- Cuál es el valor numérico del siguiente polinomio cuando la x = -2 ; y= -3
: 3x 2 y – 5xy 2 + x -3y + 2
Answer:
Step-by-step explanation:
1- Order in descending order the following polynomial with respect to the
variable n. Then identify the independent term:
[tex]6n^3 + 7n^4 - 2n^2 - 5 + 9n^5[/tex]
The independent term is - 5.
3- Look at the following polynomial and identify what the terms are
similar:
[tex]- 8 + 3m^3 n - 4m^2n + 7mn^2 - 11nm^3 + 6 m^2 n[/tex]
The similar terms are + 3m^3 n and - 11 nm^3 and
- 4 m^2 n and 6 m^2 n
Pls help me with this!
Answer:
5 ÷ 1/3
5 × 3/1
5 × 3
=15
Step-by-step explanation:
the answer is 15
Worth 12 points and actually help me with the question plz
Answer:
(x + 1, y - 3)
Step-by-step explanation:
The translation is 1 unit right and 3 units down.
Answer:
x+1 y-3
Step-by-step explanation:
Because with any of the points it goes to the right 1 and down 3
State if the triangles in each pair are similar. If so, state how you know they are similar and complete the similarity statement. *
Answer:
please give me brainliest for quest
Step-by-step explanation: