Exponential functions model growth patterns such as population growth under ideal conditions, while the logistic model accounts for resource limits. The standard exponential equation is Y=abˣ, while logistic growth has a more complex form that includes the carrying capacity.
Exponential functions model various real-world phenomena in which growth occurs at a rate proportional to the current amount. For example, in natural populations, exponential growth is observed when resources are abundant and organisms can reproduce without constraints.
The standard form of an exponential function is Y = abx, where 'a' is the initial amount, 'b' is the growth factor, and 'x' represents time or another independent variable. In the context of population growth, 'a' would be the initial population size, 'b' is the growth rate per time period, and 'x' is the time elapsed.
Logistic growth is another pattern that is observed when resources become limited. It starts off similar to exponential growth but eventually slows down as the population reaches the carrying capacity of the environment.
Environmental conditions represented by the exponential growth model imply unlimited resources and space, whereas the logistic growth model includes the effects of limiting factors such as space, food, and other resources.
Which inequality is shown above?
Which of the following correctly describes the variation in the equation h= V/lw
Answer:
It shows that h varies directly with V and inversely with l and w.
Step-by-step explanation:
The given equation is:
h = V/lw
It shows that h varies directly with V and inversely with l and w.
Inversely means if the value of one entity increases, the value of second entity decreases or vice versa. Directly related means as one quantity increases, another quantity increases at the same rate
We can show it as h=1/lw which means h is in inverse relation with l and w and in direct relation with V....
NEED HELP QUICK! WILL GIVE BRAINLIEST AND 25 POINTS!!!!
Show the formula for finding the area of a parallelogram. Then find the area of the parallelogram pictured:
Answer:
611.04 mm³
Step-by-step explanation:
The area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
here b = 30.4 and h = 20.1, hence
A = 30.4 × 20.1 = 611.04 mm³
Answer:
611.04 mm³
Step-by-step explanation:
Formula for finding the area of a parallelogram: A = B * H
B is base, H is height, * is multiply.
_________________________________________________
The area of the parallelogram pictured: 611.04 mm³
A=bh=30.4·20.1=611.04
_________________________________________________
Slade draws triangle PQR. He then constructs a perpendicular bisector from vertex P that intersects side QR at point T. What can Slade conclude, based on his drawing? QT = RT TP = RQ PQ = PR PT = PQ
Answer:
QT = RT
Step-by-step explanation:
When drawing triangle PQR the perpendicular bisector cuts the triangle in half, which results in two sides that are congruent. This makes QT and RT congruent.
Based on the triangle QPR option C) PQ = PR and A) QT = RT
A) QT = RT B) TP = RQC) PQ = PR D) PT = PQWhat is congruent triangle?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
In QPR
∠Q = ∠R (∵ PT is a bisector)
∴QT = RT (∵ PT is a bisector of QR)
PT is a common between PQT and RQT
∴PQ = PR ( by congruent part of congruent triangle)
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What is an equation of the line that is perpendicular to y- 4 = 2(x-6) and
passes through the point (-3,-5)?
O A. y + 5 = 2(x+3)
O B. y-5=-2(x-3)
O C. v-5-x-3)
OD. y +5 - -}(x+3)
Answer:
D. Y+5=-(1/2)*(x+3)
Step-by-step explanation:
Perpendicular Lines are those with the following condition:
y=a*x+b (1)
y=c*x+d (2)
Where 'a' and 'c' are the respective slope
If These two lines are perpendicular, then
a=- 1/c
Equation (1) for our case is written as y=2x-8, meaning that a=2 and b = -8
Using those principles we have that the slope for our needed line ('c') has to be -(1/2).
Now we most use the given point to find the remaining term of the equation (d) so, evaluate (-3,-5) in eq (2) to have this:
-5=(-1/2)*(-3)+d
resulting that d=-5-(3/2)
Eq (2) is written now as the following: y= (-1/2)*x - (5+3/2)
Rearranging terms, we have the following:
y+5=(-1/2)*x-(3/2)
where you can obtain a more pretty expression:
y+5=(-1/2)*(x+3)
ASAP PLS: #11-8: At a local restaurant, the waiter earn a 7% commission on any dessert they sell. The average customer bill is $42, of which 10% is dessert. How much commission is earned on an average sale?
solve the equation, 3x^2+5x+2=0 using the quadratic formula
Given a quadratic equation [tex]ax^2+bx+c=0[/tex], the two solution (if they exist) are given by the formula
[tex]x_{1,2}=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In your case, the coefficients are
[tex]a=3,\quad b=5,\quad c=2[/tex]
So the quadratic formula becomes
[tex]x_{1,2}=\dfrac{-5\pm\sqrt{25-24}}{6} = \dfrac{-5\pm 1}{6}[/tex]
So, the two solutions are
[tex]x_1 = \dfrac{-5+1}{6}=-\dfrac{4}{6}=-\dfrac{2}{3}[/tex]
[tex]x_2 = \dfrac{-5-1}{6}=-\dfrac{6}{6}=-1[/tex]
solve this inequality-3(2x-5)<5(2-x)
[tex]
-3(2x-5)<5(2-x) \\
-6x+15<10-5x \\
-x<-5 \\
\boxed{x>5}
[/tex]
Hope this helps.
r3t40
In a survey, 4 out of 30 students reported that they walk to school. If there are 900 students in the school, how many walk to school?
Answer: 120 people
Step-by-step explanation: To do this problem, you want to find common denominators. The lowest common denominator is 900. So to get the denominator to 900 from 30, multiply it by 30. 30 x 30=900. Multiply 4 by 30. 4 x 30=120. Another way to do this is to set up a proportion. It would be 4/30=x/900. Cross multiply and solve for x. 3600=30x. X=120.
What is the sum of the rational expressions below? 3x/x+9 + x/x-4
Answer:
[tex]\frac{4x^2-3x}{(x+9)(x-4)}[/tex]
Step-by-step explanation:
The sum of two rational expressions is done in the following way:
[tex]\frac{a}{b}+\frac{c}{d} = \frac{a*d + c*b}{b*d}[/tex]
In this case we have the following rational expressions
[tex]\frac{3x}{x+9} + \frac{x}{x-4}[/tex]
So:
[tex]a=3x\\d=(x+9)\\c=x\\d=(x-4)[/tex]
Therefore
[tex]\frac{3x}{x+9} + \frac{x}{x-4}=\frac{3x(x-4)+x(x+9)}{(x+9)(x-4)}[/tex]
simplifying we obtain:
[tex]\frac{3x(x-4)+x(x+9)}{(x+9)(x-4)}=\frac{3x^2-12x+x^2+9x}{(x+9)(x-4)}\\\\\frac{3x^2-12x+x^2+9x}{(x+9)(x-4)}=\frac{4x^2-3x}{(x+9)(x-4)}[/tex]
Answer:
[tex]\frac{4x^2-3x}{(x+9)(x-4)}[/tex]
Step-by-step explanation:
We are given the following expression and we are to find the sum of this rational expression below:
[tex] \frac { 3 x } { x + 9 } + \frac { x } { x - 4 } [/tex]
Taking LCM of it to get:
[tex]\frac{3x}{x+9} =\frac{3x(x-4)}{(x+9)(x-4)}[/tex]
[tex]\frac{x}{x-4} =\frac{x(x+9)}{(x-4)(x+9)}[/tex]
[tex]\frac{3x(x-4)}{(x+9)(x-4)}+\frac{x(x+9)}{(x-4)(x+9)}[/tex]
[tex]\frac{3x(x-4)+x(x-9)}{(x+9)(x-4)}[/tex]
[tex]\frac{4x^2-3x}{(x+9)(x-4)}[/tex]
if two cylinders are similar and the ratio between the lengths of the radii is 3:4 what is the ratio of their surface area
Answer:
that the linear scale factor is 4:3 which can be written as 4/3
the volume scale factor will be:
(4/3)^3
D. 64:27
Step-by-step explanation:
Add the polynomials 6a-4b+c and 4a+c
Answer:
10a-4b+2c
Step-by-step explanation:
Answer:
10a -4b +2c
Step-by-step explanation:
6a-4b+c and 4a+c
6a-4b+c + 4a+c
Combine like terms
6a+4a + (-4b) + c+c
10a -4b +2c
Use the Quadratic Formula to solve the equation 4x^2−7=4x.
Select one:
a. x=−1/2+√2 or x=−1/2−√2
b. x=7/8+√133/8 or x=7/8-√133/8
c. x=1/2+√2 or x=1/2−√2
d. x=2+4√2 or x=2−4√2
Answer:
[tex]\large\boxed{x=\dfrac{1}{2}-\sqrt2\ or\ x=\dfrac{1}{2}+\sqrt2}[/tex]
Step-by-step explanation:
[tex]\text{The quadratic formula of}\ ax^2+bx+c=0:\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\text{We have:}\\\\4x^2-7=4x\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\4x^2-4x-7=0\\\\a=4,\ b=-4,\ c=-7\\\\b^2-4ac=(-4)^2-4(4)(-7)=16+112=128\\\\\sqrt{b^2-4ac}=\sqrt{128}=\sqrt{64\cdot2}=\sqrt{64}\cdot\sqrt2=8\sqrt2\\\\x=\dfrac{-(-4)\pm8\sqrt2}{(2)(4)}=\dfrac{4\pm8\sqrt2}{8}\qquad\text{simplify by 4}\\\\x=\dfrac{1\pm2\sqrt2}{2}\to x=\dfrac{1}{2}\pm\sqrt2[/tex]
The moon forms a right triangle with the Earth and the Sun during one of its phases, as shown below:
A scientist measures the angle x and the distance y between the Sun and the moon. Using complete sentences, explain how the scientist can
use only these two measurements to calculate the distance between the Earth and the moon.
Answer:
The distance between the Earth and the Moon is equal to the distance between the Sun and the Moon multiplied by the sine of angle x
Step-by-step explanation:
Let
EM -----> the distance between the Earth and the Moon.
y -----> the distance between the Sun and the Moon.
we know that
In the right triangle of the figure
The sine of angle x is equal to divide the opposite side to angle x (distance between the Earth and the Moon.) by the hypotenuse ( distance between the Sun and the Moon)
so
sin(x)=EM/y
Solve for EM
EM=(y)sin(x)
therefore
The distance between the Earth and the Moon is equal to the distance between the Sun and the Moon multiplied by the sine of angle x
What is the equation of the following line written in general form? (The y-intercept is 7.)
Answer:
3x - y + 7 = 0Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
Put the given y-intercept b = 7 and the coordinates of the point (-2, 1) to the equation:
[tex]1=-2m+7[/tex] subtract 7 from both sides
[tex]-6=-2m[/tex] divide both sides by (-2)
[tex]3=m\to m=3[/tex]
We have the equation:
[tex]y=3x+7[/tex]
Convert it to the general form [tex]Ax+By+C=0[/tex]:
[tex]y=3x+7[/tex] subtract 3x and 7 from both sides
[tex]-3x+y-7=0[/tex] change the signs
[tex]3x-y+7=0[/tex]
Two mechanics worked on a car. The first mechanic charged $95 per hour, and the second mechanic charged $60 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $1375 . How long did each mechanic work?
Answer:
Mechanic A worked for 5 hours and Mechanic B worked for 15 hours
I hope my answer and explanation helped!
okay to get started you need to make a system of equations:
x= number of hours worked by mechanic A
y= number of hours worked by mechanic B
x + y= 20
95x + 60y= 1375
substitute in an equation:
x + y= 20
y= 20- x
95x + 60(20-x)=1375
Solve for x
95x + 1200 - 60x=1375
35x =175
x= 5
plug in x to solve for y
x + y= 20
5 + y= 20
y=15
Check work
then you're done :D
This is a cross-sectional view of candy bar ABC. A candy company wants to create a cylindrical container for candy bar ABC so that it is circumscribed about the candy bar. If segment AD = 3 cm, what is the smallest diameter of wrapper that will fit the candy bar?
a.3
b.4
c.5
d.6
Answer:
6
Step-by-step explanation:
Because AD and BC Are congruent so when you add them that would equal the diameter of the rapper.
Option D is correct. The smallest diameter of wrapper that will fit the candy bar is 6
According to the attached figure - the cross-sectional view of candy bar ABC. If a cylindrical container is created from the cross-section, then the diameter of the cylindrical container formed from the cross-section will be the side AC.
From the figure, AD = DC and AC = AD + DC
Given the segment AD = 3cm
AC = AD + AD (Since AD = DC)
AC = 2AD
AC = 2(3)
AC = 6
This shows that the smallest diameter of wrapper that will fit the candy bar is 6. Option D is correct
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Evaluate f(x) = 1/4 x for x =-5.
Answer:
f(x) = -1.25
Step-by-step explanation:
Substitute x with -5, so our equation would look this:
Note: We were already given the value of x
f(x) = 1/4(-5)
Multiply 1/4 and -5:
1/4 * -5 = -1.25
So, our answer would be -1.25
-1.25
Step-by-step explanation:In order to find the answer to your question, we're going to need to plug in a number to the variable x.
We know that x = -5
This means that whenever you see x, you would replace it with what it equals to. In this case, we would plug in -5 to x, since that's what it equals to.
Your equation would look like this:
[tex]\frac{1}{4}( -5)[/tex]
Now, you would solve to get your answer.
[tex]\frac{1}{4} (-5)=-1.25\\\\\text{1/4 is the same as 0.25} \\\\0.25(-5)=-1.25[/tex]
Once you're done solving, you should get -1.25
This means that f(x) = -1.25
I hope this helps you out.Good luck on your academics.Have a fantastic day!I need help with #63
Step-by-step explanation:
Given that line a is parallel to line b
∠6 = ∠2 = 36.5° (property of corresponding angles)
∠8 = 180° -∠6 (property of adjacent angles on a straight line)
∠8 = 180° - 36.5° = 143.5°
Determine the factors of x^2 − 12x − 20. (5 points)
For this case we must factor the following expression:[tex]x ^ 2-12x-20[/tex]
We have that the expression cannot be factored with rational numbers.
On the other hand, we can find the zeros, applying the quadratic formula we have:[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]
Where:
[tex]a = 1\\b = -12\\c = -20[/tex]
[tex]x = \frac {- (- 12) \pm \sqrt {(- 12) ^ 2-4 (1) (- 20)}} {2 (1)}\\x = \frac {12 \pm \sqrt {144-4 (1) (- 20)}} {2 (1)}\\x = \frac {12 \pm \sqrt {144 + 80}} {2}\\x = \frac {12 \pm \sqrt {224}} {2}\\x = \frac {12 \pm \sqrt {16 * 14}} {2}\\x = \frac {12 \pm4 \sqrt {14}} {2}[/tex]
Thus, the roots would be:
[tex]x_ {1} = 6 + 2 \sqrt {14}\\x_ {2} = 6-2 \sqrt {14}[/tex]
Answer:
the expression cannot be factored with rational numbers.
The factors of the given quadratic expression are: (x - 2) and (x - 10)
What are the factors of the quadratic expression?The quadratic expression is given as:
x² - 12x - 20
Now, to get the factors, we need to write as follows:
x² - 10x - 2x + 20
This can be factorized to get:
x(x - 10) - 2(x - 10)
= (x - 2)(x - 10)
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Which describes the difference between the two sequences?
First Sequence: 5, 10, 20, 40..
Second Sequence: 8, 15, 22, 29, ...
The first sequence is geometric because there is a common ratio of 2. The second sequence is arithmetic because there
is a common difference of 7.
The first sequence is geometric because there is a common difference of 2.
The second sequence is arithmetic because there is a common ratio of 7
The first sequence is geometric because there is a common difference of 7. The second sequence is arithmetic because
there is a common ratio of 2.
The first sequence is arithmetic because there is a common difference of 2. The second sequence is geometric because
there is a common ratio of 7.
NEEDD THE ANSWER ASAP IMA MARK BRAINLIS! 1st one answer
Answer:
its a)the first sequence is geometric bc of the common ratio of 2. the second sequence is arithmetic bc of the common difference of 7.
Option (A) the first sequence is geometric because there is a common ratio of 2 and the second sequence is arithmetic because there is a common difference of 7 is the correct answer.
What is a number pattern?Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers. A recursive pattern rule is a pattern rule that tells you the start number of a pattern and how the pattern continues.
For the given situation,
First sequence: 5, 10, 20, 40..
Second sequence: 8, 15, 22, 29, ...
Now consider the first sequence: 5, 10, 20, 40..
Here, when we divide the second number by first number, we get the common ratio as 2.
⇒ [tex]\frac{10}{5}=2[/tex]
⇒ [tex]\frac{20}{10}=2[/tex]
⇒ [tex]\frac{40}{20}=2[/tex]
Thus the first sequence follows a geometric progression with common ratio 2.
Now consider the second sequence: 8, 15, 22, 29, ...
Here, when we subtract the first term is subtracted from the second term, the common difference is 7.
⇒ [tex]15-8=7[/tex]
⇒ [tex]22-18=7[/tex]
⇒ [tex]29-22=7[/tex]
Hence we can conclude that option (A) the first sequence is geometric because there is a common ratio of 2 and the second sequence is arithmetic because there is a common difference of 7 is the correct answer.
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You are one of 34 people entering a contest. What is the probability that your name will be drawn first?
Answer:
1/34 or 2.94%
Step-by-step explanation:
There is only one paper that has your name on it out of 34 papers. So there is a 1 out of 34 chance your name is drawn.
You have write this as a fraction 1/34 or as a percentage 2.94%
Final answer:
The probability that your name will be drawn first in a contest with 34 entrants is 1 in 34, based on the principle of equally likely outcomes in a random selection process.
Explanation:
The probability of any one person being chosen first in a random draw from a group of 34 people is based on the principle that each person has an equal chance of being selected. To determine this probability, we use the concept of equally likely outcomes, which suggests that each person has 1 chance in the total number of people competing. Therefore, the probability that your name will be drawn first from a group of 34 people is 1 in 34.
I WILL MARK BRIANLIEST!!
Find the approximate area of a circle that has a diameter of 11 inches. Round your answer to the nearest hundredth.
A = ___ in.2
Answer:
A = 95.03in² or 95.03 ( rounded to the nearest hundredth )
Step-by-step explanation:
The approximate area of a circle that has a diameter of 11 inches, rounded to the nearest hundredth is 95.03.
Formula: A=1/4πd²
A=1
4πd^2=95.03.
4·π·11^2≈95.03318in²
which of the following could be the equation of the graph below? See graph below select the answer
ANSWER
[tex]y = 2( {x - 4)}^{2} - 3[/tex]
EXPLANATION
The function equation of a parabola that opens up in vertex form is given by
[tex]y = a( {x - h)}^{2} + k[/tex]
where (h,k) is the vertex and 'a' is the leading coefficient.
The given graph is a parabola that opens up and has its vertex at (4,-3).
This implies that, h=4 and y=-3
We substitute these values into the vertex form to obtain,
[tex]y =a( {x - 4)}^{2} + - 3[/tex]
This simplifies to,
[tex]y =a( {x - 4)}^{2} - 3[/tex]
The graph also contains (3,-1). We plug x=3 and y=-1 into the equation to find the value of 'a'.
[tex] - 1=a( {3 - 4)}^{2} - 3[/tex]
[tex] - 1 + 3 = a( { - 1})^{2} [/tex]
[tex]2 = a[/tex]
We substitute this value to get:
[tex]y = 2( {x - 4)}^{2} - 3[/tex]
The last choice is correct.
Figure ABCD is a parallelogram.
What are the lengths of line segments AB and BC?
○ AB=4; BC=16
○AB=4; BC=8
○AB=10; BC=20
○AB=10; BC=28
Answer:
○ AB = 10; BC = 28Step-by-step explanation:
In each parallelogram opposite sides have the same length.
Therefore we have the equations:
2x - 4 = x + 12 and 3y - 2 = y + 6
2x - 4 = x + 12 add 4 to both sides
2x = x + 16 subtract x from both sides
x = 16
3y - 2 = y + 6 add 2 to both sides
3y = y + 8 subtract y from both sides
2y = 8 divide both sides by 2
y = 4
AB = 3y - 2 → AB = 3(4) - 2 = 12 - 2 = 10
BC = x + 12 → BC = 16 + 12 = 28
Answer:
D
Step-by-step explanation:
i need help asap thank you marking brainliest
Answer:
[tex]a_{20} = 12+3(20-1)[/tex]
Step-by-step explanation:
Question 11 (5 points)
The digestive system ends at the
Ocolon
Olarge intestine
Oanus
O small intestine
Answer:
C. anus
Step-by-step explanation:
The digestive system ends at the anus.
Therefore, it does not end in the colon, large intestine, or small intestine.
The digestive system starts when you take in food and ends in the anus.
8. Factor 12y2 + 5y - 2 completely.
A. (6y - 1)(2y + 2)
B. (4y - 2)(3y + 1)
C. (4y - 1)(3y + 2)
D. (4y + 1)(3y - 2)
Answer:
C. (4y -1)(3y+2)
Step-by-step explanation:
12 y^2 + 5 y - 2
12 y^2 + (-3+8) y - 2
12 y^2 - 3y + 8y - 2
3y(4y-1)+2(4y-1)
(4y-1)(3y+2)
From a window, the angle of elevation of the top of a flagpole is 25°, and the angle of depression of the base of the
flagpole is 12°.How high is the flagpole if the window is in a building at a distance of 185 feet from the flagpole?
Answer:
125.59 feet
Step-by-step explanation:
(see attached)
Which quadratic equation is equivalent to (x^2-1)^2-11(x^2-1)+24=0
Answer:
The correct answer is first option
u² - 11u + 24 = 0
When u = (x² - 1)
Step-by-step explanation:
It is given that,
(x² - 1)² - (x² - 1) + 24 = 0
To find the correct answer
Substitute u = x² - 1
The equation becomes,
u² - 11u + 24 = 0 Where u = (x² - 1)
Therefore the correct answer is first option
u² - 11u + 24 = 0
When u = (x² - 1)
Answer:
u² - 11u + 24 = 0 is equivalent to (x²-1)² - 11(x²-1) + 24 = 0
Step-by-step explanation:
(x²-1)² - 11(x²-1) + 24 = 0
Evaluate each equation by substituting the value of u to match the equation above.
1) u² - 11u + 24 = 0 where u = (x² - 1)
(x²-1)² - 11(x²-1) + 24 = 0
This equation matches (x²-1)² - 11(x²-1) + 24 = 0
2) (u²)² - 11(u²) + 24 where u = (x² - 1)
[(x²-1)²]² - 11(x²-1)² + 24
This equation does not match (x²-1)² - 11(x²-1) + 24 = 0
3) u² + 1 - 11u +24 = 0 where u = (x² - 1)
(x² - 1)² + 1 - 11(x²-1) + 24 = 0
This equation does not match (x²-1)² - 11(x²-1) + 24 = 0
4) (u² - 1)² - 11(u² - 1) + 24 where u = (x² - 1)
[(x²-1)²-1]² - 11(u² - 1)² + 24
This equation does not match (x²-1)² - 11(x²-1) + 24 = 0
Therefore, the first quadratic equation is equivalent to (x²-1)² - 11(x²-1) + 24 =0.
!!