Final answer:
Exponential growth occurs when a population increases at an increasing rate, whereas exponential decay involves a decrease at a rate proportional to the current size. Logistic growth, adding the concept of carrying capacity, more accurately reflects natural populations with initial exponential increase followed by a plateau as resources become limited.
Explanation:
The key difference between exponential growth and exponential decay lies in the direction and rate at which a quantity changes over time. Exponential growth occurs when a population grows at an increasing rate as time passes, often depicted as a J-shaped curve, whereas exponential decay describes a process of decrease at a rate proportional to the current value, leading to a rapid reduction in size or quantity over time.
In the context of biology and population growth, exponential growth describes how populations can grow dramatically when there are no limits to resources or space. This type of growth can be formalized as a mathematical model where the population after n time periods has increased by a factor of 2n when the base growth rate is 2. In natural populations, this is idealized and does not usually last long as resources become depleted and other limiting factors come into play. On the other hand, exponential decay in biology might refer to the rapid loss of a population due to harsh conditions, lack of resources, or other negative impacts.
Giving Brainliest! Use graphs and numerical summaries to help you describe how the following three datasets are similar and how they are different (think mean, median, range, and sample standard deviation).
A: 5, 7, 9, 11, 13, 15, 17
B: 5, 6, 7, 11, 15, 16, 17
C: 5, 5, 5, 11, 17, 17, 17
Which of the following equations has the solution x= all real numbers?
a. 4(3−x)+6x=x+12−3x
b. 4(3−x)+6x=3x+12+2x
c. 4(3−x)+6x=3x+12−x
d. 4(3−x)+6x=3x+10−x
Option (b) 4(3-x)+6x=3x+12+2x is the equation that has the solution x = all real numbers because it simplifies to an identity, which is true for any value of x.
Among the given equations, the one that has the solution x = all real numbers is essentially an identity, meaning that for any value of x you plug into the equation, the equation will hold true. To determine which equation is an identity, each equation must be simplified.
Let's take option (b) as an example:
4(3−x)+6x=3x+12+2x
4∙3 - 4∙x + 6∙x = 3∙x + 12 + 2∙x
12 - 4∙x + 6∙x = 3∙x + 12 + 2∙x
12 + 2∙x = 5∙x + 12
12 - 12 + 2∙x - 2∙x = 5∙x - 2∙x + 12 - 12
0 = 3∙x - 3∙x
After simplifying, we end up with 0 = 0, which is an identity and is true for all values of x, hence this is the equation where x is all real numbers.
What is the average speed of a person that travels 40 miles to their grandmothers house and then 40 miles back home in 6 hours?
What is an equivalent expression for 1.5(3x + 4) + 0.25(6x + 8)?
An expression is defined as a set of numbers, variables, and mathematical operations. An equivalent expression for 1.5(3x+4)+0.25(6x+8) is 7x+8.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression can be simplified as,
1.5(3x + 4) + 0.25(6x + 8)
= 4.5x + 6 + 2.5x + 2
= 7x + 8
Hence, an equivalent expression for 1.5(3x+4)+0.25(6x+8) is 7x+8.
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Use the graph of the function to find its average rate of change from
=x−3
to
=x3
.
PLEASE HELP NO ONE EVER ANSWERS!
The average rate of change of the function over the interval is 2
Finding the average rate of change
From the question, we have the following parameters that can be used in our computation:
The graph
The interval is given as
From x = -3 to x = 3
The function is a quadratic function
This means that it does not have a constant average rate of change
From the graph
y = -8, when x = -3
y = 4, when x = 3
This means that
f(-3) = -8
f(3) = 4
The average rate is calculated using
Rate = (Change in y values)/(Change in corresponding x values)
So, we have
Rate = (4 + 8)/(3 + 3)
Evaluate
Rate = 2
Hence, the average rate of change is 2
Isosceles triangle ABC has a perimeter of 96 centimeters. The base of the triangle is and measures 24 centimeters.
What is the measure of ?
12 cm
36 cm
48 cm
72 cm
Answer:
The measure of length of equal side is 36 cm each.
B is correct.
Step-by-step explanation:
Isosceles triangle ABC has a perimeter of 96 centimeters.
The base of the triangle is BC and measures 24 cm
We need to find the length of equal side of triangle.
AB=AC
The perimeter of triangle is 96 cm
AB + AC + BC = 96
AB + AB + 24 = 96 ( ∵ AB=AC)
2AB = 96-24
2AB = 72
AB = 36
Hence, The measure of length of equal side is 36 cm each.
If AB= BC and BC= CD, then AB= CD
Kite WXYZ is graphed on a coordinate plane.
What is the area of the kite?
a.7 square units
b.8 square units
c.14 square units
d.16 square units
Answer-
Area of the kite is 14.0 sq.units
Solution-
[tex]\text{Area}_{WXYZ}=\text{Area}_{WXY}+\text{Area}_{WZY}[/tex]
From the graph, in the triangle WXY
Base = WY=4 units,
Height = 3 units
[tex]\text{Area}_{WXY}=\dfrac{1}{2} \cdot base\cdot height=\dfrac{1}{2} \cdot 4\cdot 3=6\ sq.unit[/tex]
From the graph, in the triangle WZY
Base = WY=4 units,
Height = 4 units
[tex]\text{Area}_{WZY}=\dfrac{1}{2} \cdot base\cdot height=\dfrac{1}{2} \cdot 4\cdot 4=8\ sq.unit[/tex]
[tex]\therefore \text{Area}_{WXYZ}=6+8=14\ sq.units[/tex]
The Yoga class you wish to take is offering two price quotes: $108 for 5 weeks as (15 classes) or $125 for 8 weeks (24 classes). How much per class would you save by taking the 8 week class?
A $2.10
B $2.05
C $1.99
D $1.89
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we have given that
Cost for 5 weeks i.e. 15 classes = $108
Cost of per class is given by
[tex]\frac{108}{15}=7.2[/tex]
Cost for 8 weeks i.e. 24 classes = $125
Cost of per class is given by
[tex]\frac{125}{24}=5.21[/tex]
Amount of saving of per class by taking the 8 week class is given by
[tex]7.2-5.21=\$1.99[/tex]
Hence, Option 'C' is correct.
11.) suppose the correlation between two variables r=0.23. What will the new correlation be if 0.14 is added to all values of the x-variable, every value of the y-variable is double, and the two variables are interchanged?
The correlation coefficient r=0.23 will remain unchanged at 0.23 even after adding a constant to all x-variable values, doubling the y-variable values, and swapping the x and y variables, because the correlation coefficient is unaffected by such transformations.
The correlation between two variables is denoted by the symbol, r, and it measures the strength and direction of a linear relationship between two quantitative variables. When we add a constant to all values of the x-variable or multiply all values of the y-variable by a constant, the correlation coefficient does not change. However, interchanging the x and y variables also does not change the value of r since correlation is symmetrical. Therefore, if r=0.23 initially, after adding 0.14 to all values of x, doubling the y-variable values, and interchanging the two variables, the new correlation will still be 0.23.
What are the x and y-intercepts of the line described by the equation? 3x−9y=10.8 Enter your answers, in decimal form, in the boxes.
Answer: The x-intercept and y-intercept of the given line are (3.6, 0) and (0, -1.2) respectively.
Step-by-step explanation: We are given to find the x-intercepts and y-intercepts of the line described by the following equation :
[tex]3x-9y=10.8~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the x-intercept of a line is the point where the y co-ordinate is 0. Similarly, y-intercept is the point where the x co-ordinate is 0.
Substituting y = 0 in equation (i), we get
[tex]3x-9\times0=10.8\\\\\Rightarrow 3x-0=10.8\\\\\Rightarrow 3x=10.8\\\\\Rightarrow x=\dfrac{10.8}{3}\\\\\Rightarrow x=3.6.[/tex]
So, x-intercept is (3.6, 0).
And substituting x = 0 in equation (i), we get
[tex]3\times 0-9y=10.8\\\\\Rightarrow 0-9y=10.8\\\\\Rightarrow 9y=-10.8\\\\\Rightarrow y=-\dfrac{10.8}{9}\\\\\Rightarrow y=-1.2.[/tex]
So, y-intercept is (0, -1.2).
Thus, the x-intercept and y-intercept of the given line are (3.6, 0) and (0, -1.2) respectively.
I NEED THIS ANSWERED ASAP! PLEASE!!
The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equation h = -16t^2 + h0, where h0 is the initial height of the object. Suppose a small rock dislodges from a ledge that is 255 ft above a canyon floor. Solve the equation h = -16t^2 + 255 for t, using the quadratic formula to determine the time it takes the rock to reach the canyon floor.
The time it takes the rock to reach the canyon floor is after 3.99seconds
Application of intercept to a functionThe intercept is the point where the axis is equal to zero. Give the quadratic equation that represents the height h (in feet) of an object t seconds after it is dropped expressed as:
h = -16t² + 255
The rock reaches the ground when h(t) = 0. Substitute
h = -16t² + 255
h = -16t² + 255 = 0
16t² = 255
t² = 255/16
t² = 15.9375
t = 3.99seconds
Hence the time it takes the rock to reach the canyon floor is after 3.99seconds
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What is the first step of adding 12.65 + 30.75?
LM = JK then JK = LM
What property is this?
The principle being demonstrated is known as the Symmetric Property, which holds that if an equation or statement is valid, then its switched or flipped version will also be true.
Explanation:The question refers to a fundamental property in mathematics called the Symmetric Property. The Symmetric Property states that if an equation or statement is true, then its mirror or flipped version will also hold true. In this case, if LM = JK, then under Symmetric Property, it must be true that JK = LM.
For instance: If 5 = 2 + 3, then 2 + 3 = 5.
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Write the point-slope form of the line that passes through (-8, 2) and is parallel to a line with a slope of -8. Include all of your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
A student is reading his book at a rate of 15 pages per day.
a. Write the rate in pages per week.
b. Write the rate in pages per hour.
Consider the following equation, bh+hr=25 when solving for r
Answer:
[tex]r=\frac{25-bh}{h}[/tex]
Step-by-step explanation:
Given : Consider the following equation, [tex]bh+hr=25[/tex]
To find : Solving for r ?
Solution :
The equation is [tex]bh+hr=25[/tex] solve for r,
Subtract 'bh' both side,
[tex]bh+hr-bh=25-bh[/tex]
[tex]hr=25-bh[/tex]
Divide both side by 'h',
[tex]\frac{hr}{h}=\frac{25-bh}{h}[/tex]
[tex]r=\frac{25-bh}{h}[/tex]
Therefore, [tex]r=\frac{25-bh}{h}[/tex]
Rewrite 1/x^-3/6 in simplest radical form. show each step of your process
Which of the following options represents the graph of the function shown below?
ƒ(x) = (x - 3)^3 1 1
ƒ(x) = (x - 3)^3 + 1
ƒ(x) = (x + 3)^3 - 1
ƒ(x) = (x + 3)^3 + 1
The function that best represents the graph of the function which is given is:
[tex]f(x)=(x-3)^2+1[/tex]
Step-by-step explanation:From the graph that is provided to us we observe that the graph passes through the point (3,1).
Hence, we will check which of the following function satisfies this point.
a)
[tex]f(x)=(x-3)^3-1[/tex]
when x=3 we see that:
[tex]f(x)=(3-3)^3-1\\\\i.e.\\\\f(x)=-1\neq 1[/tex]
Hence, option: a is incorrect.
c)
[tex]f(x)=(x+3)^3-1[/tex]
when x=3 we have:
[tex]f(3)=(3+3)^3-1\\\\i.e.\\\\f(3)=9^3-1\\\\i.e.\\\\f(3)=729-1\\\\f(3)=728\neq 1[/tex]
Hence, option: c is incorrect.
d)
[tex]f(x)=(x+3)^3+1[/tex]
when x=3 we have:
[tex]f(3)=(3+3)^3+1\\\\i.e.\\\\f(3)=9^3+1\\\\i.e.\\\\f(3)=729+1\\\\f(3)=730\neq 1[/tex]
Hence, option: d is incorrect.
Now we are left with option: b)
i.e.
b)
[tex]f(x)=(x-3)^2+1[/tex]
Also, when x=3 we have:
[tex]f(3)=(3-3)^2+1\\\\f(3)=0+1\\\\f(3)=1[/tex]
Hence, it passes through the point (3,1)
Also, when we will plot this function we observe that it matches the given graph.
1. At the grocery store checkout, you watch at the register as it rings up your purchases and coupons. The prices were as follows:
$2.95
$1.19
$4.61
$1.74
$3.04
$8.83
$1.16
– $0.75 (coupon)
– $1.00 (coupon)
The register gives your total bill as $21.77. Estimate the total amount of the bill and use your answer to determine whether the total on the register is reasonable.
Answer:
estimate by rounded to the nearest dollars
2 +1 +5 +2 +3 +9 +1 = $23
-2
23-2 = 21
yes the amount is reasonable
Answer: 3+1+5+2+3+9+1-1-1=22
The total on the register is reasonable because if you estimate $21.77 to the nearest dollar you would get $22.00.
Step-by-step explanation:
True or false: f(x) is a function
Answer:
False
Step-by-step explanation:
If f(x) is a function , then for each value of x there should be a single y values
For input 0 there is a output 0
for input 10, the output is 2
for input 15, output is 3
For input 5, we have two output 1 and 3
for single input 5, the function cannot have two outputs 1 and 3
So this f(x) is not a function
The number of sides of a polygon that has n vertices is what?
The total number of sides in a polygon with n vertices is = n sides.
We have a Polygon with n vertices.
We have to determine the number of sides of this polygon.
What is Polygon?In geometry, a polygon can be defined as a plane, two-dimensional closed shape bounded with straight sides.
According to the question, we have -
A polygon with n vertices.
The total number of sides in a polygon with n vertices is = n sides.
The sides of the polygon are connected end to end in a cyclic order. The side with endpoints as nth and (n - 1)th vertices is connected to the side with endpoints as (n - 1)th and (n - 2)th vertices and so on.
Hence, the total number of sides in a polygon with n vertices is = n sides.
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Predict the number of students out of 400 that would pick science(3) as their favorite subject
Math=6
Science=3
English=4
History=7
Factor a 2 bc + ab 2 c + abc 2
A. a2b2c2(a + b + c)
B. a2bc(a + b + c)
C..abc(a + b + c)
Answer:
abc(a + b + c)
That's your answer!!!
What is the converse of the statement? "If you wash the dishes today, then I will wash the dishes tomorrow." Question 5 options: If I wash the dishes tomorrow, then you will wash the dishes today. If I will not wash the dishes tomorrow, then you will not wash the dishes today. If you wash the dishes today, I will dry the dishes today. If you do not wash the dishes today, then I will not wash the dishes tomorrow.
Answer:
Step-by-step explanation:dhdjdbfbd
A van travels 150 miles on 5 gallons of gas. how many gallons will it need to travel 630 miles?
What is the difference between a plane (in geometry) and a piece of paper?
there are 8 boxes, which contain a total of 56 sweaters, in a store warehouse. If the store needs 35 sweaters, how many boxes should they take. can you explain please thank you
Which type of angles could be used as a counterexample for the argument all angles are either right obtuse or acute
Answer: You could use straight angles as a counterexample for the argument all angles are either right obtuse or acute .
Which state of matter has neutral particles that bounce off one another as they collide?
Gas
Liquid
Plasma
Solid
The answer is gas because gas particles move so fast they bounce off one another when they collide. Plasma has Negatively AND Positively charged particles within it.
Gases are the state of matter where neutral particles bounce off one another as they collide. This is due to their constant, random motion and the elastic nature of their collisions.
Explanation:The state of matter that has neutral particles that bounce off one another as they collide is a Gas. This is due to the fact that gases are composed of a large number of particles that are in constant, random motion. These particles collide with each other and with the walls of their container. Importantly, these collisions are perfectly elastic, meaning they conserve both momentum and kinetic energy.
In Liquids and Solids, the particles are held together with stronger intermolecular forces which restrict their motion. In Plasma, the particles are ionized and hence, are not neutral.
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