The two lines are perpendicular because the product of their slopes is equal to 1
What is the slope-intercept form of a line?The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line
Given here: The two lines x-3y =15 and y = -3y + 4
Rewriting the given expressions in slop-intercept form we get
y=x/3-5
y = -3y + 4
The respective slopes are given as 1/3 and -3
Thus the product of the two slopes is 1/3×-3=-1
Hence, The given lines are perpendicular.
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The roof shingles are arranged so that each row has 7 fewer shingles than the row below it. If the first row has 75 shingles, how many shingles are in the 6th row?
The shingles are in the 6th row is 110 using arithmetic process.
What is arithmetic process?A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The study of numbers and the operations on those numbers, which are relevant to all other branches of mathematics, is the focus of a branch of mathematics known as arithmetic operations. It includes addition, subtraction, multiplication, and division as its fundamental operations.
Given that A = 75 and d = 7, n = 6
A₆ = A + (n-1)d
A₆ = 75 + (6-1)7
A₆ = 75 + 5 * 7
A₆ = 75 + 35
A₆ = 110
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Answer:
33
Step-by-step explanation:
it starts with 75 and decreases by 7 for each row. on the 6th row youll be at 33!
STARTS AT 75
row one: 68
row two: 61
row three:54
row four: 47
row five: 40
row six: 33
Write an explicit formula for the sequence generated by a1 = 10, an = an − 1 + 7 where n = 2, 3, 4, ….
Group of answer choices
an = n + 7 where n = 1, 2, 3, …
an = 3n + 4 where n = 1, 2, 3, …
an = 7n − 10 where n = 1, 2, 3, …
an = 7n + 3 where n = 1, 2, 3, …
Answer:
= 7n − 3 emde n = 1, 2, 3, ...
Solve this system of linear equations. Separate
the x- and y-values with a comma.
2x + 2y = -8
-13x + 7y = -48
Enter the correct answer.
Answer:
x = 1, y = - 5
Step-by-step explanation:
2x + 2y = - 8 → (1)
- 13x + 7y = - 48 → (2)
multiplying (1) by 7 and (2) by - 2 and adding will eliminate y
14x + 14y = - 56 → (3)
26x - 14y = 96 → (4)
add (3) and (4) term by term to eliminate y
40x + 0 = 40
40x = 40 ( divide both sides by 40 )
x = 1
substitute x = 1 into either of the 2 equations and solve for y
substituting into (1)
2(1) + 2y = - 8
2 + 2y = - 8 ( subtract 2 from both sides )
2y = - 10 ( divide both sides by 2 )
y = - 5
then solution is x = 1, y = - 5
The function f(x) is shown on the graph.
The graph shows a downward opening parabola with a vertex at 3 comma 25, a point at negative 2 comma 0, a point at 8 comma 0, a point at 0 comma 16, and a point at 6 comma 16.What is the standard form of the equation of f(x)?
a) f(x) = x2 − 6x + 16
b) f(x) = x2 + 6x + 16
c) f(x) = −x2 − 6x + 16
d) f(x) = −x2 + 6x + 16
The correct answer is d. The standard form of the equation of f(x) is −x2 + 6x + 16.
What is downward opening parabola?A downward opening parabola is a curve in the shape of a parabola that opens downward and is symmetrical about the x-axis. The equation of a downward opening parabola is y = ax^2 + bx + c, where a is a negative number, and b and c are constants.
The focus of a downward opening parabola is the point on the parabola where the curvature is greatest and is located at the vertex of the parabola.
The directrix of a downward opening parabola is a line parallel to the x-axis and the distance from the focus to the directrix is equal to the length of the latus rectum of the parabola. The equation of the directrix is y = -a(x - h)^2 + k, where h and k are constants.
Downward opening parabolas can be used to graphically represent any type of data that follows a parabolic shape. This includes physical phenomena such as the path of a projectile or the vibration of a string.
Downward opening parabolas can also be used to model economic or financial data, such as the demand for a product or the price of a commodity. They may also be used to describe relationships between two variables in a mathematical equation.
The standard form of a parabola equation is f(x) = ax2 + bx + c, where a, b, and c are real numbers. In this case, the vertex of the parabola is at (3, 25), so the equation is in the form f(x) = a(x - 3)2 + 25. Putting in the other points on the graph to solve for a, b, and c yields the equation f(x) = -x2 + 6x + 16.
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Suppose that X and Y are integer valued random variables with joint probability mass function given by pX, Y(a, b) = {1/4a, for 1 > b > a > 4, otherwise. a. Show that this is indeed a joint probability mass function. b. Find the marginal probability mass function of X and Y. c. Find P(X = Y + 1).
The joint probability mass function given by PX, Y(a, b) = {1/4a, for 1≤ b≤a≤4, otherwise is indeed a joint probability mass function because the sum of all the joint probabilities is equal to 1.
To find the marginal probability mass function of X, we need to sum the joint probabilities over all possible values of Y:
PX(a) = ∑ PX, Y(a,b) = ∑ (1/4a) = 1/4
To find the marginal probability mass function of Y, we need to sum the joint probabilities over all possible values of X:
PY(b) = ∑ PX, Y(a,b) = ∑ (1/4a) = 1/4
To find P(X = Y + 1), we need to find the joint probability of X = a and Y = a-1, where a = 2,3.
P(X = Y + 1) = PX, Y(2,1) + PX, Y(3,2) = (1/42) + (1/43) = 1/4 + 3/12 = 5/12
So the probability that X is one more than Y is 5/12.
It's important to note that the given joint probability mass function is valid as it satisfies the non-negativity and the condition of summing to 1.
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24 of the students in a Biology class passed a Biology test. If these students are 80% of
all the students in the class, how many students are in this Biology class? Round your
answer to the nearest whole number if necessary.
What represents the expression below simplified?
[tex](4x-1) + (-6x+3)[/tex]
suppose that 40% of all adults regularly consume coffee, 60% regularly consume carbonated soda, and 35% regularly consumes both coffee and soda. draw a venn diagram, then answer the following:(a) What is the chance a randomly selected adult regularly drinks coffee but doesn't drink soda?(b) What is the probability that a randomly selected adult consumes coffee, soda or both?(c) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?
The probabilities of adults who drinks only coffee , both/ coffee ,soda and doesn't drink any are 5% , 65% and 35%.
Let A be the event that an adult consumes coffee.
Let B be the event that an adult consumes carbonated soda.
Given probabilities of the events.
P (A) = 0.4
P (B) = 0.6
P(A∩B) = 0.35
(a). P(A) - P(A∩B) = 0.4 - 0.35
= 0.05 OR 5 %
(b). P(AUB) = P (A) + P (B) - P(A∩B)
= 0.4 + 0.6 - 0.35
= 0.65 OR 65%
(c). The given case represents compliment of the event when the adult consumes at least one of the drink. According to probability axiom, the probability is given by:
P ((AUB)') = 1 - P (AUB) = 1-0.65 = 0.35
Therefore,
P ((AUB)') = 0.35 or 35 %.
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What is the answer to this?
Step-by-step explanation:
what is missing is the definition that QS is the height and therefore standing at a right angle (90°) at PR.
then this can be solved.
we use Pythagoras
c² = a² + b²
c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.
let's start with the triangle PQS.
21² = 15² + QS²
441 = 225 + QS²
QS² = 216
QS = sqrt(216) = sqrt(36×6) = 6×sqrt(6) = 14.69693846...
now for triangle QSR
(5x - 16)² = (3x - 4)² + QS²
25x² - 160x + 256 = 9x² - 24x + 16 + 216
16x² - 136x + 24 = 0
2x² - 17x + 3 = 0
the solution to a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (17 ± sqrt(17² - 4×2×3))/(2×2) =
= (17 ± sqrt(289 - 24))/4 = (17 ± sqrt(265))/4
x1 = (17 + 16.2788206...)/4 = 8.319705149...
x2 = (17 - 16.2788206...)/4 = 0.180294851...
but using x2 in side lengths 3x - 4 or 5x - 16 gives us negative side lengths. that does not make any sense for actual side lengths.
so, x1 is our solution :
x = 8.319705149...
Question
This graph shows a proportional relationship.
What is the constant of proportionality?
Enter your answer in the box.
Graph titled Math Test Raw Scores. The vertical axis is labeled Points. The horizontal axis is labeled Correct answers. The horizontal axis ranges from 0 to 24 in increments of 2. The vertical axis ranges from 0 to 120 in increments of 10. A line passes through the origin and the points begin ordered pair 5 comma 30 end ordered pair and begin ordered pair 12 comma 72 end ordered pair and begin ordered pair 18 comma 108 end ordered pair and begin ordered pair 20 comma 120 end ordered pair.
The constant of proportionality is equal to 6.
What is a proportional relationship?In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x represents the correct answers.y represents the points.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) for the relationship between correct answers and points on this graph as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 30/5 = 72/12 = 108/18 = 120/20
Constant of proportionality, k = 6
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Answer:
6
Step-by-step explanation:
120/20 = 6
108/18 = 6
72/12 = 6
30/5 = 6
See the pattern? :)
The probability of picking two black marbles from a box at random without replacement is 10/91 . The probability of drawing a black marble first is 5/14 . What is the probability of picking a second black marble, given that the first marble picked was black?
The probability of picking a second black marble is 4/13
What is probability?Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability helps us know the chance an event has to occur. The closer it gets to zero(0) the less chance it has to occur. The closer it gets to one(1) the more chance it has to occur.
Therefore, The probability of picking a second black marble is 4/13
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The option are :
4/13
85/182
25/637
45/182
Question 4 of 10
The lines shown below are perpendicular. If the green line has a slope of
what is the slope of the red line?
ch
10
KO
1
-10
+0
6
10
16
OA
OB./
OC
OD
Answer:
B
Step-by-step explanation:
Trust
A 2D depiction of what a 3D shape would look like if it was opened out and laid flat is called a
Answer: Net (of a shape)
Step-by-step explanation:
Answer:
Step-by-step explanation:
no need for step by step its called a net
Slope of the line y=29/8x - 2/3
Answer:
The slope of a line is represented by the coefficient of the x-term in the equation, which is also known as the "rise over run" or change in y over change in x.
In this equation y = 29/8x - 2/3
The coefficient of the x-term is 29/8, so the slope of the line is 29/8.
Trapezoid PQRS has vertices P(0, 0), Q(0, 4), R(6, 4), and S(12, 0).
What is the length of the midsegment?
please help me its the last question on this test and i only have 20 mins left of this class
Trapezoid PQRS having vertices P(0, 0), Q(0, 4), R(6, 4), and S(12, 0),
has the length of the midsegment as 11.07 units.
What is a trapezoid?
A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.
The length of the mid segment of trapezoid is half the sum of the lengths of the two parallel sides, PQ and RS.
The points for vertices are given as - P(0, 0), Q(0, 4), R(6, 4), and S(12, 0).
Length of sides PQ and RS is given as -
The line segment PQ = √(x2 - x1)² + (y2 - y1)²
PQ = √(0 - 0)² + (4 - 0)²
PQ = √0² + (4)²
PQ = √0 + 16
PQ = √16
PQ = 4 units
The line segment RS = √(x2 - x1)² + (y2 - y1)²
RS = √(12 - 6)² + (0 - 4)²
RS = √(6)² + (-4)²
RS = √36 + 16
RS = √50
RS = 5√2 units
To find the mid segment add the length of PQ and RS.
So, the equation will be -
Midsegment = PQ + RS
Midsegment = 4 + 5√2
Midsegment = 11.07 units
Therefore, the length of midsegment is 11.07 units.
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Answer: 9
Step-by-step explanation: (6+12) / 2 = 9
really confused please help
The given relationship is such that 1 / z⁴ = z ⁻⁴.
What is the relationship ?When given 1 / z⁴, this can be rewritten in such a way that it becomes z ⁻⁴.
This is because when a denominator is raised to a exponent , it can be transformed to a numerator if the sign on the power is changed to the negative.
This means that when the fraction was 1 / z⁴, it can become the value of z ⁻⁴ because the negative in front of the 4 shows that it is a fraction.
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Need help with question attached below in an image.
Average rate of change for the first 10 minutes after the soup was placed in the bowl is 200 .
How can I determine the graph's average rate of change?To get the slope of a graphed function, use the average rate of change formula. Divide the y-value change by the x-value change to determine the average rate of change. Identifying changes in quantifiable parameters like average speed or average velocity calls for the knowledge of the average rate of change.Measure the temperature change every hour and compute the average rate of change. In order to achieve that, we calculate the temperature difference between 220 and 180 and divide it by the number of hours in that period.220 +180/2 = 200
average rate of change for the first 10 minutes after the soup was placed in the bowl 200.
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a freshly poured cup of coffee from mcdonald’s is measured to be 185 degrees fahrenheit. if left alone in a cup, the temperature of the coffee decreases by about 3.2% each minute. what would be the temperature if left alone in the cup for 20 minutes? round to the nearest degree
The temperature of the cup if it is left alone for 20 minutes, can be found to be 97 degrees Fahrenheit
How to find the temperature of the cup ?To find the tempertature of the cup, the formula would be:
= Beginning temperature x ( 1 - rate of decrease per minute ) ^ number of minutes
Beginning temperature = 185 degrees fahrenheit
rate of decrease per minute = 3.2% each minute
number of minutes = 20 minutes
The temperature is:
= 185 x ( 1 - 3 .2 %) ²⁰
= 97 degrees Fahrenheit
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The U.S. population in 2018 was estimated to be 327,200,000 within that population, there were 30,357,000 people who were 18-29 years old and 52,431,000 people who were 65 years and older
According to the graphic, 85% of the 30,357,000 people who were 18-29 years old tried vaping or electronic cigarettes Approximately how many people ages 18-29 said that they have tried vaping or e-cigarettes? Show your work
We can see here that the people of ages 18-29 that have tried vaping or e-cigarettes is: 25,803,450.
What is population?Population refers to the number of individuals of a particular species living in a particular area or region. In the context of human populations, it refers to the number of people living in a particular geographic area or country.
To find out the number of people ages 18-29 who said they have tried vaping or e-cigarettes, you can use the following calculation:
30,357,000 (the number of people ages 18-29) x 0.85 (the percentage of people who have tried vaping or e-cigarettes) = 25,803,450.
So, approximately 25,743,950 people ages 18-29 said that they have tried vaping or e-cigarettes.
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: AXYZ is located on the coordinate
plane below.
X
4
If the triangle is transformed following
the rule (x, y) → (x, -y), will congruence
be maintained? Why or why not?
If KL
show
When two pairs of corresponding angles and the included pair of sides are likewise congruent, a triangle is said to be congruent.
What is the congruent triangle?When two triangles can be superimposed, have identical side lengths, and equal angles, they are said to be congruent.
Triangles with the same angle measurements and side lengths are said to be congruent. SSS (Side-Side-Side) SAS are the triangle congruence criteria (Side-Angle-Side). When they have, triangles are congruent. There are precisely the same three sides and three angles.
Triangles are said to be congruent if two pairs of corresponding angles and the included pair of sides are also congruent. The triangles are congruent if a pair of sides that are not included and two pairs of comparable angles are congruent.
When the coordinates of XYZ are converted to produce its congruent image, X'Y'Z.
The triangle XYZ's translated picture is X'Y'Z'.
The triangle XYZ's reflected image becomes X'Y'Z'.
The triangle XYZ does not turn into its rotated counterpart, X'Y'Z'.
Therefore, Option I and II are true statements. so D is the correct answer.
The complete question is:
XYZ is transformed on a coordinate plane to obtain its congruent image X'Y'Z. Which of the following statements could be true?
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xplain in words and write mathematically how the fundamental theorem of calculus is used to evaluate definite integrals.
Please help me, I really need this so bad.
Answer:
slope = 1/2
Step-by-step explanation:
rise = 3
run = 6
rise/run
3/6 = 1/2
Answer:
The slope is 1/2
Step-by-step explanation:
The slope is rise over run, from point 1 to point 2 the line rises 3.
The run from point 1 to point 2 is 6.
That means that rise over run is 3/6
Simplify this so that it is in the simplest form to get 1/2.
The image shows the rise and the run.
I hope this helps you out :D
if matrix a is symmetric show that any two eigenvectors of a correspond to different eigenvalues are orthogonal
A symmetric matrix is a square matrix that is equal to transpose of itself. If A is a symmetric matrix, then it satisfies the condition: A = AT. (AT is the inverse of A )
A square matrix with real numbers or elements is said to be an orthogonal matrix if its transpose is equal to its inverse matrix. Or we can say when the product of a square matrix and its transpose gives an identity matrix, then the square matrix is known as an orthogonal matrix.
Suppose λ and μ are 2 distinct values of matrix A.
For the matrix to be Symmetric,
( Ax,y)=(x,Ay)
condition needs to be satisfied.
Here, ( x,y) is dot product between vectors x and y
λ (u,v) = (λu,v)
where u,v are eigen vectors for eigen values λ and μ
λ(u,v) = (Au,v)
λ(u,v) = (u,Av)
λ(u,v) = μ(u,v)
λ(u,v) = μ(u,v)
but λ≠μ
∴ (u,v) = 0.
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The complete question is :
If a matrix is symmetric then show that any two eigenvectors of that matrix corresponding to different eigenvalues are orthogonal. Assume square matrix.
Please help with their question
If f(x) = x⁴ + 2, g(x) = x-6 and h(x) = √x , then the simplified form of f(g(h(x))) is f(g(h(x))) = (√x - 6)⁴ + 2.
What is the polynomial expression?
Any expression which consists of variables, constants, and exponents, and is combined using mathematical operators like addition, subtraction, multiplication, and division is a polynomial expression.
We can simplify f(g(h(x))) by first evaluating h(x), then substituting the result into g(x), and finally substituting the result into f(x).
Starting with h(x) = √x, we can substitute this into g(x) to get:
g(h(x)) = g(√x) = √x - 6
Next, we can substitute g(h(x)) = √x - 6 into f(x) to get:
f(g(h(x))) = f(√x - 6) = (√x - 6)⁴ + 2
Simplifying this expression requires some algebraic manipulation, but we can expand (√x - 6)⁴ using the binomial theorem or by using the method of FOIL (first, outer, inner, last) repeatedly. Either way, we will end up with a polynomial expression in x with terms of various degrees.
Therefore, the simplified form of f(g(h(x))) is f(g(h(x))) = (√x - 6)⁴ + 2.
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Find E(X) and Var(X) for a continuous random variable X with a pdf f(x) = 4x³,0 < x < 1.
Simply multiply each value of the discrete random variable by the probability associated with that value to obtain the expected value, E(X), or mean. E(X)=xP is the formula's notation (x).
How do you find ex and Var X?It is common to refer to the long-term average or mean (symbolized as ) as the expected value of a discrete random variable X, denoted by the symbol E(X). Thus, if you conducted an experiment again throughout time, you could anticipate this average result. If you toss three fair coins, for instance, let X be the number of heads you receive. The expected value of X is the average number of heads you would anticipate receiving after three fair coin tosses if you were to perform this experiment a significant number of times.f(x) = 4x³,0 < x < 1
Domain of f(x) = 4x³,0 < x < 1 : Solution : 0 < x < 1
Interval notation : (0,1)
Range of 4x³ ,0 < x < 1;
Solution : 0 < f(x) < 4
Interval Notation : (0,4)
Axis interception points of 4x³,0 <x <1.
Asymptotes of 4x³. 0 < x < 1;
Extreme Points of 4x³ . 0<x < 1:
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what is the value of 8 divided by 3
Answer:
there's ur answer ...........
Simplify each expression by combining like terms
-9y-10y -2z
By Simplify expression -9y-10y -2z this we get - 19y - 2z.
What is the Simplify expression ?Expression simplification is a crucial skill to master if you want to comprehend algebra. We can convert a complicated expression into one that is more condensed and straightforward by simplifying it.When constants and variables are merged with the help of the operation symbols (+, -, x, and ), the result is an algebraic expression.The process of solving a math problem is simply known as simplifying an expression. An expression is simplified when it is written in the most straightforward way feasible. There should be no more multiplying, dividing, adding, or subtracting to be done once everything is done.Examples :
-9y-10y -2z
Simplify
-9y - 10y - 2z : -19y - 2z
-9y - 10y - 2z
= - 19y - 2z.
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Solve the initial value problem 2yy' + 3 = y^2 + 3x with y(0) = 9. 1. To solve this, we should use the substitution u = _____ With this substitution, y = _____
y' = _____
Enter derivatives using prime notation (e.g., you would enter y' for dy/dx). 2. After the substitution from the previous part, we obtain the following linear differential equation in x, u, u'. 3. The solution to the original initial value problem is described by the following equation in x, y.
The given initial value problem y(0)=8, solution is [tex]y=\sqrt{64e^x-3x}[/tex]
Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation. Assuming that a function's rate of change with regard to x is inversely proportional to y, we may write it down as dy/dx = k/y. An equation involving the derivative (derivatives) of the dependent variable with respect to the independent variable is referred to as a differential equation in calculus (variables). The differential equation assists us in presenting a relationship between the changing quantity with respect to the change in another variable. The derivative represents nothing more than a rate of change. If y is a dependent variable, f is an unknown function, and x is an independent variable, then y=f(x) is a function.
The given differential equation is,
[tex]2yy'+3=y^2+3x\\\\2y\frac{dy}{dx}=y^2+3x-3\\\\(3-y^2-3x)dx+2ydy=0\\\\compare, Mdx+Ndy=0\\\\M=3-y^2-3x\\\\N=2y[/tex]
The given equation is not exact but if we multiplied by [tex]e^{-x}[/tex]
[tex]The D.E.\\(3-y^2-3x)e^{-x}dx+2ye^{-x}dy=0\\\\then M_y=-2ye^{-x}=N_x\\The G.S,=y^2e^{-x}+3xe^{-x}=c\\\\y(0)=8\\c=64\\hence,\\y=\sqrt{64e^x-3x}[/tex]
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whats the solution to the equations
Answer:
A solution of an equation is any value of the variable that satisfies the equality, that is, it makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation the same value. To solve an equation is to find the solution(s) for that equation.
Step-by-step explanation:
given values of median, mean, mode, first and third quartiles for the observations of a numeric feature, what insights can we gain into the statistical distribution of its observations? you may use an example to further illustrate your points. (word limit: 100-150). you must post first before being able to read the responses of others. it is recommended that you respond to your classmates' responses, but not required.
The terms mean median, mode, and range describe properties of statistical distributions.
The statistical distributions' characteristics are described by the terms mean, median, mode, and range. The set of all potential values for terms that indicate predetermined events is known as a distribution in statistics. A term's value stated as a variable is referred to as a random variable.
The two main categories of statistical distributions are as follows. There are discrete random variables in the first category. This indicates that each phrase has a distinct, precise numerical value. A continuous random variable is present in the distribution of the second major kind. An unlimited number of possible values can be represented by a continuous random variable. A term is said to have a probability density function when any value can be assigned to it within an uninterrupted interval or span.
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