This is a True statement that both the matrix equation and the augmented matrix translate into the same system of linear equations.
What are Linear equations?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.
A rectangular matrix is a grouping of numbers into rows and columns. Systems of equations can be solved using matrices. But first, we need to understand how to use matrices to represent systems.
An augmented matrix can be used to express a set of equations. Each column in an augmented matrix represents a variable or the constant terms, and each row in an augmented matrix represents one equation in the system. As a result, it is clear that augmented matrices provide a convenient approach to express systems of equations.
Therefore it is true that the solution set of the equation's equation is the same as the solution set of the linear system whose augmented matrix is.
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The beginning balance on the monthly bank statement for Dorsey's checking
account was $452.76, and the ending balance was $197.59. What can be said
about Dorsey's transactions for the month?
A. He had $650.35 more in credits than in debits.
B. He had $255.17 more in credits than in debits.
C. He had
$650.35 more in debits than in credits.
OD. He had $255.17 more in debits than in credits.
SUBMIT
He has 255.17 more in debits than in credits. Thus, option D is correct.
How to Dorsey's transaction for the month?Debits and credits in double-entry bookkeeping are entries made in account ledgers to reflect changes in value brought on by business transactions. A debit entry, not a credit entry, is used to show the amount of money that has been transferred into or out of an account. Value is exchanged with each transaction from credited to debited accounts.
Let's call B the amount in credit that Ignatius had, and C the amount in debits that Ignatius had during the month.
We know that the initial amount in his account was 124.82, while the final balance was 659.27.
Final amount = the initial amount + amount of credits - the amount of debits
$255.17= $255.17 (B-C)
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Height vs. Age
Height (cm)
160
160
160
160
160
160
160
Function? (Yes or No)
no
If it is a Function what is the:
Domain
Range
****
Age (years)
20
25
30
35
40
45
We can see that height is the dependent variable and age is independent.
Therefore the graph of the relation, if connected, is a line segment parallel to the x-axis.
If we prove it with the vertical line test it will pass the test. Hence we can state it is a function.
The domain is:
x ∈ {20, 25, 30, 35, 40, 45}The range is:
y = 160CHOSE THE LETTER of the correct equation for the graph PLS HELP
The trigonometric function that represent the equation in the graph is y = sin(x + π/2).
What is the trigonometric function?The period of a function is the distance between the repetitions of any function. A period is the length of one complete cycle of a trigonometric function.The graph of y = sin(x) is like a wave that oscillates between -1 and 1, repeating itself every 2 units.The key components visible on the graph are:
y = π/2 is the midpoint.
We can conclude that the correct answer is either b or d.
at x = 0, f(x) = 0.
Function y = sin(x + π/2)
Therefore the correct answer is option d that is y = sin(x + /2) is the trigonometric function that represents the equation in the graph.
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2.1.3 Quiz: What Is a Function?
Question 2 of 10
If f(x) = 2x² +5√(x-2), complete the following statement:
f(6) =_______
A statement, rule, or legislation that establishes the link between the independent variable and the dependent variable (the dependent variable). f ( 6 ) = 82 .
What is the definition of a function?Domain of [tex]$2 x^2+5 \sqrt{x-2}:\left[\begin{array}{cc}\text { Solution: } & x \geq 2 \\ \text { Interval Notation: } & {[2, \infty)}\end{array}\right]$[/tex]
Range of [tex]$2 x^2+5 \sqrt{x-2}:\left[\begin{array}{cc}\text { Solution: } & f(x) \geq 8 \\ \text { Interval Notation: } & {[8, \infty)}\end{array}\right]$[/tex]
Interception zones on the axis [tex]$2 x^2+5 \sqrt{x-2}$[/tex] : None .
Asymptotes of [tex]$2 x^2+5 \sqrt{x-2}$[/tex] : None .
Points of Extremity [tex]$2 x^2+5 \sqrt{x-2}$[/tex] : Minimum (2,8) .
[tex]f(x) = 2x^{2} +5\sqrt{(x-2} \\f (6) = 2 *(6^{2} ) + \sqrt{6 - 2} \\ = 82[/tex]
the type of conduct or activity appropriate to a person, thing, or institution; the reason why something is made or existing; role. any formal event or occasion that is held in public or among friends. a component that affects or is influenced by other components: Availability and demand determine price.
As a set of inputs with one output for each, a function is defined as a relationship between them. A function, expressed simply, is an association between inputs where each input is connected to one and only one output. Each function has a range or codomain. f(x), where x is the input, is a common way to refer to a function.
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anyone know this ? please
The artist needs 78,835.2 cm² of metal to make the sculpture.
How much metal does the artist need to make the sculpture?The artist needs to calculate the total volume of the sculpture in order to determine how much metal is required to make the sculpture.The volume of a rectangular prism can be calculated by multiplying the length, width, and height. In this case, the length is 21.8 cm, the width is 24.4 cm, and the height is 39.6 cm. Multiplying these three measurements gives a total volume of 25,942.56 cm3 (cubic centimeters).Now that the artist knows the total volume of the sculpture, they can calculate how much metal they need to make it.To do this, they need to know the density of the metal they want to use. Let’s assume they are using steel, which has a density of 7,860 kg/m3 (kilograms per cubic meter).To find out how much metal the artist needs, they need to convert the volume of the sculpture from cm3 to m3, by dividing it by 1,000,000.This gives a volume of 0.02594256 m3. Multiplying this by the density of steel gives a total mass of 206.48 kg of steel required to make the sculpture.Therefore, the artist needs 206.48 kg of steel to make their rectangular prism sculpture.To learn more about the total volume of the sculpture refer to:
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Write 0.15 as a fraction in simplest form. 0.15 =
Answer:
3/20
Step-by-step explanation:
3/20 is .15 in the simplest fraction form
e) A student spent 50 minutes doing her homework. She spent m minutes doing Geography. 2m minutes doing Mathematics and the remaining (m + 7) minutes studying History. How many minutes did she spend doing Mathematics?
Answer: 22 minutes
Step-by-step explanation: m + 2m + m + 7 = 4m + 7
4m + 7 = 50
4m = 44
m = 11
2m = 11 x 2 = 22 minutes
Please answer this question for me
The given two triangles are similar to each other by the postulate called SAS.
What is triangle ?
Triangle can be defined as in which it consists of three sides, three angles and sum of the three angles are 180 degrees always.
Given,
The triangles are RST and UVT
So
From the given figure we can say that,
RT = TU
RS = VU
As two sides are already equal and vertically opposite angles are always equal .
so we can say that By postulates SAS we can say that they are similar to each other.
Hence, The given two triangles are similar to each other by the postulate called SAS.
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Let y = πx + π. For what value of x is y = π^3?
The value of the variable is; x = π³ - π/π
What are algebraic expressions?Algebraic expressions are described as mathematical expressions that are comprised of variables, factors, constants, terms and coefficients.
These algebraic expressions are also comprised of arithmetic operations, such are; Division
Multiplication, Subtraction, Floor division, Addition, Bracket, Parentheses
From the given information, we have that;
y = π³
y = πx + π
Substitute the values, we have;
π³ = πx + π
Collect like terms
π³ - π = πx
Divide both sides by the coefficient of x
x = π³ - π/π
Thus, the value is x = π³ - π/π
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a circle is circumscribes around an isosceles triangle whose two congruent angles have degree measure x
The circumference of the circle is equal to the sum of the 3 sides of the triangle, multiplied by pi. The formula for the circumference is:
[tex]C = (2x + (2 (sqrt(2*x^2 - x^2))) * pi[/tex]Calculating the Circumference of a Circle Circumscribing an Isosceles TriangleThe circumference of the circle circumscribing an isosceles triangle with two congruent angles of degree measure x can be calculated using the above formula. The formula takes into account the two congruent angles of the triangle, which have a degree measure of x, as well as the third side of the triangle.
The circumference of the circle is then calculated by multiplying the sum of the three sides of the triangle by pi.
This formula allows us to calculate the circumference of the circle regardless of the size of the triangle or the degree measure of the two congruent angles.
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I need this answer ASAP please answer
Answer: (-2) + 22 + (-30) = (-10)
Step-by-step explanation:
I'm not too sure, I hope this works
Determine the order of the given differential equation and state whether the equation is linear or nonlinear: d^4u/dr^4 + du/dr + 5u = cos(r + u) You have only one attempt for credit. (a) The order of this differential equation is 4 (b) The equation is Linear
Which statements about the figure are true? Select all that apply
Answer:
1st and 2nd ones
Step-by-step explanation:
39 + 3(17) = 90 degrees
Supplementary angles add up to 180
What are the domain and range of this relation?
Please help
Use the FOIL method to find the terms of the following multiplication problem
(4 + 4i) • (5 - 4i)
Using the FOIL method, the product of the first terms is the product of the outside terms is and the product of the inside terms is The product of the last terms in terms of i^2 is _ which simplifies to _
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Show and explain how to find the equation of the plane which contains the point P(1,1,3) and the line x=3t,y=5ât,z=1+2t.
The equation of the plane is:-6x + 0y + 6z - 18 = 0
The equation of a plane containing a point P(x1, y1, z1) and a line defined by x = x0 + at, y = y0 + bt, z = z0 + ct, is given by:
Ax + By + Cz + D = 0
Where:
A = (y1 - y0)a - (x1 - x0)b
B = (z1 - z0)a - (x1 - x0)c
C = (z1 - z0)b - (y1 - y0)c
D = -(A*x1 + B*y1 + C*z1)
Plugging in the given values, we have:
A = (1 - 5)3 - (1 - 3)5 = -6
B = (3 - 1)3 - (1 - 3)2 = 0
C = (3 - 1)5 - (1 - 5)2 = 6
D = -(-6*1 + 0*1 + 6*3) = -18
Therefore, the equation of the plane is:
-6x + 0y + 6z - 18 = 0
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Containers of gochujang, a Korean chili sauce, are sold at a market. The scatter plot shows the relationship between the cost of different containers and the amount of sauce in each container. A line of best fit is drawn through the data. Based on the line of best fit, what is the approximate cost per ounce of a container of gochujang at the market?
The cost per ounce of a container of gochujang at the market can be calculated using the equation of the line of best fit.
The line of best fit is given by the equation y = 0.14x + 1.3, where y is the cost of the container and x is the amount of sauce in the container (in ounces). To calculate the approximate cost per ounce of a container of gochujang, we can use this equation. We set y = 1, since we want the cost of one ounce of sauce. The equation of this line is y = 0.25x + 3.2, where x is the amount of sauce in the container and y is the cost of the container. To find the cost per ounce, we need to divide the y-intercept, 3.2, by the slope, 0.25. This gives us 12.8. Therefore, the approximate cost per ounce of a container of gochujang at the market is $12.8.
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A furniture maker cut a wooden log shaped like a cylinder and sanded the entire surface of it. The log had a radius of 2 in. and a volume of 96π in.^3 How many square inches of the log did the furniture maker sand in terms of π? PLEASE THANKUUUSM
Enter the correct answer in the box in terms of π.
____________ in^2
The amount of square inches of the log that the furniture maker sanded in terms of π is; 288π in²
How to find the surface area of a cylinder?The formula for volume of a cylinder is;
V = πr²h
where;
V is volume
h is height
r is radius
Now, we have the parameters as;
r = 2 in
V = 96π in³
Thus;
96π = π(2)²h
h = 96/4
h = 24 in
Formula for surface area of a cylinder is;
S.A = 2πr²h + 2πrh
S.A = 2(π(2)²*24) + 2(π * 2 * 24)
S.A = 192π + 96π
S.A = 288π in²
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A division of Chapman Corporation manufactures a pager. The weekly fixed cost for the division is $23,000, and the variable cost for producing x pagers/week in dollars is represented by the function V(x). $ V(x) = 0.000001x^3 - 0.01x^2 + 50x $ The company realizes a revenue in dollars from the sale of x pagers/week represented by the function R(x). $ R(x) = -0.02x^2 + 150x \; \quad \; (0 \leq x \leq 7500) $ (a) Find the total cost function C. C(x) = (b) Find the total profit function P. P(x) = (c) What is the profit for the company if 1,900 units are produced and sold each week? $
The total cost function C is T(x) = 0.000001x³ - 0.03x² + 200x + 15,000, the total profit function P is P(x) = 0.000001x³ - 0.01x² + 50x + 15,000 and the profit for the company if 1,900 units are produced and sold each week is $80,759
The term function in math is written as a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables.
Here we have given that the division of Chapman Corporation manufactures a pager.
Here we also know that the weekly fixed cost for the division is $15,000, and the variable cost for producing x pagers/week in dollars is represented by the function V(x).
Then the function is written as,
=> V(x)= 0.000001x³ - 0.01x² + 50x.
Here we have given that company realizes a revenue in dollars from the sale of x pagers/week represented by the function R(x).
Then the function is written as,
=> R(x)= -0.02x² + 150x Where the value of x lies between (0<x<7500)
Then the total cost is calculated as,
=> T(x) = Total Cost + fixed cost + variable cost
Then apply the values on it, then we get,
=> T(x) = 15,000 + 0.000001x³ - 0.01x² + 50x - 0.02x² + 150x
=> T(x) = 0.000001x³ - 0.03x² + 200x + 15,000
And the total profit function is written as,
=> P(x) = 0.000001x³ - 0.03x² + 200x + 15,000 - (-0.02x² + 150x)
=> P(x) = 0.000001x³ - 0.01x² + 50x + 15,000
If the is the profit for the company if 1,900 units are produced and sold each week, then the profit is calculated as,
=> P(1900) = 0.000001(1900)³ - 0.01(1900)² + 50(1900) + 15,000
=> P(1900) = 80759
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Use the Spider Tool located on page 1 of this activity to recreate the eight-pointed logo. Start by asking the spider to move 50 units, rotate 135 degrees, and repeat the sequence until she returns to her starting point. Remember that you can use "Zoom out" or "Fit to window" if the spider leaves the viewing area. In the space below,
sketch the eight-pointed logo you created with the Spider Tool. (4 points)
PLEASE HELP
the star of the mentioned, figure is attached below.
What is a star?
A polygon, which is a form with many sides, is a type of star. In fact, five-pointed stars are categorised as decagons or polygons with ten sides, although the number of sides changes depending on the number of points on the star, such as six, ten, etc. An equilateral and equiangular polygon that self-intersects is referred to as a regular star shape or regular star polygon. It was made by connecting the vertices of a straightforward, regular, n-sided polygon to one another in a nonadjacent direction until the original vertices were once again reached.
How are stars with five points made?
All stars are formed by lines at particular angles. The basic pattern is as follows in the case of five-pointed stars, which are the most prevalent:
Use lines of the same length and rotate 135° each time.
Hence the star of the mentioned figure is attached below.
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A _____ is a statistical technique for combining results from multiple studies in order to identify overall patterns in the studies as a whole.
A meta-analysis is a statistical method for combining the findings average of several research to find overarching trends in the studies as a whole.
A statistical method known as meta-analysis is used to aggregate data from various research in order to find overall trends across all of the investigations. Finding patterns in research that have been carried out using various methods and in various contexts is a specialty of this strategy. Researchers can determine the overall impact of a specific intervention or treatment by performing a meta-analysis, which combines the findings of various studies into a single effect size or summary statistic. This method is employed in a variety of fields, such as psychology, education, and medicine. Meta-analysis is an effective method that may be used to pinpoint larger study trends and to bolster the body of evidence supporting any given hypothesis or course of action.
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Worth 100 points and person who gets it right gets brainliest!
Answer:
6% = $4000
Step-by-step explanation:
6%x + 7%(8500 - x) [tex]\geq[/tex] 555
0.06x + 0.07(8500 - x) [tex]\geq[/tex] 555
0.06x + 595 - 0.07x [tex]\geq[/tex] 555
-0.01x + 595 [tex]\geq[/tex] 555
-0.01x [tex]\geq[/tex] -40
x [tex]\leq[/tex] 4000
distribute (-3u⁴+4u+6) (-5u²v)
NEED HELP ASAP
Answer: 4(u−2)−3u=2(u−6)
Step-by-step explanation:
Here is work Daniela did to solve y=3x+b
For x. Explain why this is incorrect
The value that Daniela got is wrong because she should have divided through by 3 to get x instead of subtracting
How to solve for x in the equation
We have y = 3x + b
We are to find the value of x from the equation that we have above
But first we are to take the other terms to one part of the equation so that x can stand on its own
3x = y - b
divide through the equation by 3
3x / 3 = y - b / 3
x = y - b / 3
This is the solution Daniela should have gotten
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XYZ is located on the coordinate plane below. If the triangle is transformed following the rule (x, y) to (x, -y), will congruence be maintained? Why or why not?
Answer: yes
Step-by-step explanation: because it will stay the same
In the 30-60-90 triangle below, side s has a length of________ and side q has a length of_______
A. 16√3, 5
B. 8-5, 16
C. 4, 8√3
D. 4√2, 4√2
E. 4, 4.5
F. 16√3, 16√3
In the 30-60-90 triangle below, side s has a length of 4 and side q has a length of [tex]4\sqrt{3}[/tex] (Option E).
RIGHT TRIANGLEA triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem. The Pythagorean Theorem says (hypotenuse)²= (leg1)²+(leg2)². And the main trigonometric ratios are: sin (x) , cos (x) and tan (x) .
The question asks the value of sides s and q of the given right triangle. If you have the value of the hypotenuse and all angles of the triangle, you can solve this exercise by applying the trigonometric ratios. See below.
[tex]sin 30\° = \frac{opposite \; leg}{hypotenuse}\\ \\ \frac{1}{2}=\frac{s}{8} \\ \\ 2s=8\\ \\ s=4[/tex]
[tex]cos 30\° = \frac{adjacent\; leg}{hypotenuse}\\ \\ \frac{\sqrt{3} }{2}=\frac{q}{8} \\ \\ 2q=8\sqrt{3} \\ \\ q=4\sqrt{3}[/tex]
Therefore, the solution to this question is the letter E.
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A company that ships glass for a glass manufacturer claimed that its shipping boxes are constructed so that no more than 8 percent of the boxes arrive with broken glass. The glass manufacturer believed the actual percent is greater than 8 percent. The manufacturer selected a random sample of boxes and recorded the proportion of boxes that arrived with broken glass. The manufacturer tested the hypotheses H0:p=0.08 versus Ha:p>0.08 at the significance level of α=0.01. The test yielded a p-value of 0.001. Assuming all conditions for inference were met, which of the following is the correct conclusion?
A
The p-value is greater than α, and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.
B
The p-value is greater than α, and the null hypothesis is rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.
C
The p-value is greater than α, and the null hypothesis is not rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.
D
The p-value is less than α, and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.
E
The p-value is less than α, and the null hypothesis is not rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.
The correct answer is D. the proportion of boxes with broken glass is greater than 0.08.
The p-value is 0.001 which is less than the significance level of α = 0.01; therefore, the null hypothesis (H0: p = 0.08) can be rejected. We can conclude that there is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.
To calculate the p-value, we can use the formula: p-value = P(x ≥ X|H0)
Where X is the sample mean, and H0 is the null hypothesis that the proportion of boxes with broken glass is equal to 0.08.
Using this formula, we get: p-value = P(x ≥X|H0) = P(x ≥ 0.08) = 0.001
Since the p-value is less than the significance level of 0.01, the null hypothesis can be rejected and we can conclude that there is convincing evidence that the proportion of boxes with broken glass is greater than 0.08.
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In a statistics class containing 250 students, each student is instructed to toss a coin 20 times and record the value of , the sample proportion of heads. The instructor then makes a histogram of the 250 values of obtained. In a second statistics classcontaining 200 students, each student is told to toss a coin 40 times and record the value of , the sample proportion of heads. The instructor then makes a histogram of the 200 values of obtained. Which of the following statements regarding the two histograms of -values is true? A.The first class’s histogram is more biased since it is derived from a smaller number of tosses per student.B.The first class’s histogram has greater spread (variability) since it is derived from a smaller number of tosses per student.C.The first class’s histogram has less spread (variability) since it is derived from a larger number of students
B.The first class’s histogram has greater spread (variability) since it is derived from a smaller number of tosses per student.
The question is asking which statement is true regarding the two histograms of -values. The first class has 250 students and they are each instructed to toss a coin 20 times. The second class has 200 students and they are told to toss a coin 40 times. The first class is tossing the coin less times than the second class, so the spread (variability) is greater for the first histogram since it is derived from a smaller number of tosses per student.
The first class has 250 students and they are each instructed to toss a coin 20 times. The second class has 200 students and they are told to toss a coin 40 times.
The first class is tossing the coin less times than the second class, so the spread (variability) is greater for the first histogram since it is derived from a smaller number of tosses per student.
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on a variable ratio schedule, reinforcement is given for the . group of answer choices first correct response after varying amounts of time have passed next correct response after a varying number of responses have been made next correct response after a fixed number of responses have been made
On a variable ratio schedule, reinforcement is given for the next correct response after varying numbers of responses have been made.
What is variable ?
A variable is a value or quantity that can change or take on different values in a given context or system. In mathematics and science, variables are often used to represent unknown or changing values in an equation or model. In programming, a variable is a named container or storage location that holds a value that can be modified during the execution of a program.
On a variable ratio schedule, reinforcement is given for the group of correct responses that occur after varying amounts of time have passed. This means that the reinforcement is not given after a fixed number of responses or after a fixed amount of time has passed. Instead, the reinforcement is given after a varying number of correct responses have been made, making it unpredictable for the individual or organism being reinforced. This type of schedule is often used in gambling and other situations where the reinforcement is desired to be unpredictable and maintain the individual's interest or motivation.
On a variable ratio schedule, reinforcement is given for the next correct response after varying numbers of responses have been made.
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If someone tells us that a random variable is described by a Binomial or Poisson distribution, it becomes a very simple matter (presuming we know the key parameters) to be able to then predict the likelihood that any particular combination of values will be seen in a dataset containing that variable. Sometimes, though, we don’t know what kind of distribution our variable will fit, or we don’t know enough to be able to identify the key parameters needed to make accurate predictions.
The binomial distribution has one possible outcome, success, and two possible outcomes, failure. In contrast, the Poisson distribution has an infinite number of potential outcomes.
What are the distribution about?The distribution of binary data from a finite sample is described by the binomial distribution. As a result, it provides the likelihood that r events will occur in n trials. The distribution of binary data from an infinite sample is described by the Poisson distribution. It provides the likelihood that r events will occur in a population. Two discrete probability distributions are the Poisson distribution and the Binomial distribution.
In discrete trials, the binomial distribution counts discrete occurrences. In a continuous domain, the poisson distribution counts discrete occurrences. The poisson should ideally only be used when success could happen anywhere in a domain.
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