Answer:
a: (x + 3)(x + 4)
Step-by-step explanation:
assuming x^2 + 7x + 12 is the equation you are factoring
you would first multiply a * c
a is 1
b is 7
c is 12
1 * 12 = 12
then you take b and find what adds up to b but multiplies to ac
what adds up to 7 but multiplies to 12
3 and 4
so
you split the equation up like this
x^2 + 3x + 4x + 12
then you factor
x(x + 3) + 4(x + 3)
because x + 3 and x + 3 are the same we can do this
(x + 4)(x + 3)
that is your equation
so a is your answer
it doesnt matter if you have the (x + 3) or (x + 4) in the front
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Option A, (x + 3)(x + 4)}[/tex]
-------------------------------------------------------------------------------------------------------------
In order to factor the polynomial we need to first split the middle term so it add up to 7 but multiplies to 12. We know that 3 and 4 can do that. We would the factor by grouping which would give us our final answer.
[tex]x^2 + 7x + 12[/tex]
[tex]x^2 + 4x + 3x + 12[/tex]
[tex]x(x + 4) + 3(x + 4)[/tex]
[tex](x + 3)(x + 4)[/tex]
Answer: [tex]\textsf{Option A, (x + 3)(x + 4)}[/tex]
Complete the number pattern
Answer:
137,131
Step-by-step explanation:
The time it takes a person to wash the dishes is uniformly distributed between 6 minutes and 14 minutes. What is the probability that a randomly selected event of washing dishes will take a person between 8 and 13 minutes? Round your answer accurate to two decimal places.
The probability that a randomly selected event of washing dishes will take a person between 8 and 13 minutes is 66.66%.
It is given that the time it takes a person to wash the dishes is uniformly distributed between 6 minutes and 14 minutes.
That means that the number of possible minutes it will take will be 6, 7, 8 ,9, 10, 11, 12, 13, 14 That's a total of 9 separate minutes or intervals.
If it takes between 8 and 13 minutes, that is only 8 ,9, 10, 11, 12, 13 that's only 6 separate minutes or intervals.
The probability of it taking between 8 and 13 minutes is therefore [tex]\frac{6}{9} = \frac{2}{3}[/tex]
Or 0.6666666667 x 100 is 66.66%.
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According to the table, which ordered pair is a local maximum of the function, f(x)?
(0, 64)
(3, –35)
(5, 189)
(2, 0)
The local maximum of the function f(x) is (0,64)
Given,
From the table we can notice that when ₋2<x<0, f(x) is increasing
And in case of when 0<x<3, f(x) is decreasing progressively.
we know that a local maximum is present on the graph of the function y=f(x) at the location where the graph shifts from increasing to decreasing. The tangent has zero slope at this location. And at the point when the graph shifts from declining to increasing, a local minimum is present.
Therefore, a local maximum also known as relative maximum, is a maximum that exists in a certain area and is not necessarily(but could be) a global maximum.
Hence f(0) is a local maximum of the ordered pair (0,64)
Hence we get the local maximum pair as (0,64)
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Answer:
it is 0,64
which is C for me but looks like A for you
In the following exercises, multiply the binomials. Use any method.
241. (x + 8)(x + 3)
Answer:
Hence the expression [tex]$(x+8)(x+3)=x^{2}+11 x+24$[/tex].
Step-by-step explanation:
- The given expression is (x+8)(x+3).
- We have to multiply the given expression.
- Multiply the (x+8) by 3 , multiply the (x+8) by x then add like terms.
[tex]$$\begin{array}{r}x+8 \\\underline {\times \quad x+3} \\3 x+24 \\\underline {x^{2}+8 x+24} \\x^{2}+11 x+24\end{array}$$[/tex]
34. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.
34. Passes through (-1, 4) and (5, 2)
Answer:
The linear equation for the line which passes through the points given as (-1,4) and (5,2), is written in the point-slope form as [tex]$y=\frac{1}{3} x-\frac{13}{3}$[/tex].
Step-by-step explanation:
A condition is given that a line passes through the points whose coordinates are (-1,4) and (5,2).
It is asked to find the linear equation which satisfies the given condition.
Step 1 of 3
Determine the slope of the line.
The points through which the line passes are given as (-1,4) and (5,2). Next, the formula for the slope is given as,
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Substitute 2&4 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and [tex]$5 \&-1$[/tex] for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,
[tex]m=\frac{2-4}{5-(-1)}$\\ $m=\frac{-2}{6}$\\ $m=-\frac{1}{3}$[/tex]
Step 2 of 3
Write the linear equation in point-slope form.
A linear equation in point slope form is given as,
[tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]
Substitute [tex]$-\frac{1}{3}$[/tex] for m,-1 for [tex]$x_{1}$[/tex], and 4 for [tex]$y_{1}$[/tex] in the above equation and simplify using the distributive property as follows,
[tex]y-4=-\frac{1}{3}(x-(-1))$\\ $y-4=-\frac{1}{3}(x+1)$\\ $y-4=-\frac{1}{3} x-\frac{1}{3}$[/tex]
Step 3 of 3
Simplify the equation further.
Add 4 on each side of the equation [tex]$y-4=\frac{1}{3} x-\frac{1}{3}$[/tex], and simplify as follows,
[tex]y-4+4=\frac{1}{3} x-\frac{1}{3}+4$\\ $y=\frac{1}{3} x-\frac{1+12}{3}$\\ $y=\frac{1}{3} x-\frac{13}{3}$[/tex]
This is the required linear equation.
On a coordinate plane, triangle T V W has points (negative 4, 8), (0, 4), and (4, 4).
What are the coordinates of the endpoints of the segment T'V'?
T'(-3, 6) and V'(0, 3)
T'(-3, 6) and V'(0, 1)
T'(-1, 2) and V'(0, 3)
T'(-1, 2) and V'(0, 1)
The coordinates of the endpoints of line segments T'V' are; T'(-1, 2) and V'(0, 1).
What are the coordinates of the endpoints of the segment T'V'?It follows from the task content that the transformation involved in the formation of the image from the pre-image is dilation by a scale factor of 1/4.
It follows therefore that, given the coordinates of T and V from the task content are; (-4, 8) and (0,4), it follows that the coordinates of the endpoints as required are; T'(-1, 2) and V'(0, 1).
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-a(4a5 + 9a + 6)
Find the product and simplify the answer.
If
sin
x
=
2
9
, x in quadrant I, then find (without finding x) :
sin
(
2
x
)
=
cos
(
2
x
)
=
Incorrect
tan
(
2
x
)
=
Answer:
Step-by-step explanation:
Right triangle ABC is on a coordinate plane. Segment AB is on the line y=2 and is 6 units long. Point C is on the line x=-3. What is the y value of point C is the area of ABC is 9 units squared
The y-coordinate of point C may have a value of 5 or -1.
What is a right-angle triangle?If any of its inner angles is 90 degrees, the triangle is said to be right-angled. Another term for this triangle is the right triangle or 90-degree triangle.
The given data in the problem is;
A coordinate plane contains the right triangle ABC.
AB = 6 units
Surface area, A= 9 square units
The AB symbol is located on the x-axis parallel line y=2.AB will thus be perpendicular to the x-axis.
As a result, AB will be parallel to the side that contains point C. (BC or AC). As a result, the triangle's area should be justified by the length of the side or leg containing point C, which is the point's y-coordinate.
The other triangle leg's length should be,
BC = AC = 9/3
BC = AC = 3
Therefore, the point C's y-coordinate can be,
2±3 = 5,-1
Hence, the y-coordinate of point C may have a value of 5 or -1.
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Find the value of x in Figure 7 (pictured below):
Answer:
x = 10
Step-by-step explanation:
Interior angles of a triangle sum to 180°
Therefore, to find the value of x, sum the given angles, equal them to 180, then solve for x:
⇒ 6x + 8x + 4x = 180
⇒ (6 + 8 + 4)x = 180
⇒ 18x = 180
⇒ 18x ÷ 18 = 180 ÷ 18
⇒ x = 10
a lily pad is growing in a pond and it doubles in size every day. after 30 days it covers the entire pond. on what day does it cover half the pond?
The growth of the lily pad is in geometric progression, and it covers half the pond in 29 days.
In the question, we are given that the size of the lily pad doubles itself every day.
If we assume the size of the lily pad on the first day as a, then on the second day its size will be 2a, on the third day it will be 2(2a) = 4a, and on the fourth day, it will be 2(4a) = 8a, and so on.
This makes a geometric progression, with the first term as a, and the constant ratio as 2.
We are given that on the 30th day, the size of the lily pad, covers the entire pond.
The size on the 30th day can be shown as the 30th term of this geometric progression
Therefore, size of the pond = a(2)³⁰⁻¹ = a.2²⁹. {Using the formula, aₙ = arⁿ⁻¹, where aₙ is the n-th term, a is the first term, and r is the constant ratio}.
We are asked the day on which the pond is half covered.
The size of the pond in this case = (a.2²⁹)/2 = a.2²⁸.
The day can be calculated as follows:
a.2ⁿ⁻¹ = a.2²⁸,
or, 2ⁿ/2 = 2²⁸,
or, 2ⁿ = 2²⁹,
or, n = 29.
Thus, the lily pad covers half the pond on the 29th day.
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Gasoline is pouring into a vertical cylindrical tank of radius 55 feet. When the depth of the gasoline is 66 feet, the depth is increasing at 0.30.3 ft/sec. How fast is the volume of gasoline changing at that instant
The volume of gasoline in the cylindrical tank is increasing at 23.56 ft.³/sec when the depth of the gasoline in the tank is 6 feet. Computed using differentiation.
Since the tank is cylindrical in shape, its volume can be written as:
V = πr²d,
where V is its volume, r is the radius, and d is the depth.
The radius is constant, given r = 5ft.
Thus the volume can be shown as:
V = π(5)²d,
or, V = 25πd.
Differentiating this with respect to time, we get:
δV/δt = 25πδd/δt ... (i),
where δV/δt, represents the rate of change of volume with respect to time, and δd/δt represents the rate of change of depth with respect to time.
Now, we are given that when the depth increases at 0.3 ft./sec when the depth of the gasoline is 6 feet.
Thus, we can take δd/δt = 0.3 ft./sec, in (i) to get:
δV/δt = 25πδd/δt = 25π(0.3) ft.³/sec = 23.56 ft.³/sec.
Thus, the volume of gasoline in the cylindrical tank is increasing at 23.56 ft.³/sec when the depth of the gasoline in the tank is 6 feet. Computed using differentiation.
The question written correctly is:
"Gasoline is pouring into a vertical cylindrical tank of radius 5 feet. When the depth of the gasoline is 6 feet, the depth is increasing at 0.3 ft./sec. How fast is the volume of gasoline changing at that instant?"
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The steps to derive the quadratic formula are shown below:
I need help pls
Step 1 ax2 + bx + c = 0
Step 2 ax2 + bx = − c
Step 3 x2 + b over a times x equals negative c over a
Step 4 x2 + b over a times x plus b squared over 4 times a squared equals negative c over a plus b squared over 4 times a squared
Step 5 x2 + b over a times x plus b squared over 4 times a squared equals negative 4 multiplied by a multiplied by c, all over 4 multiplied by a squared plus b squared over 4 times a squared
Step 6
Provide the next step to derive the quadratic formula. (1 point)
x plus b over 2 times a equals plus or minus b squared minus 4 times a times c all over the square root of 4 times a squared
x plus b over 2 times a equals plus or minus b minus 2 times a times c all over square root of 2 times a
x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 4 times a squared
x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 2 times a
Answer:
(c) x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 4 times a squared
Step-by-step explanation:
The next step is to take the square root of both sides of the equation. It can help to show the intermediate steps.
Result so farThe last step shown in the derivation so far is ...
[tex]x^2+\dfrac{b}{a}x+\dfrac{b^2}{4a^2}=-\dfrac{4ac}{4a^2}+\dfrac{b^2}{4a^2}[/tex]
Next stepThe left side of the above expression can be written as a square, and the right side can be written over one denominator. Then the square root is taken as the next step.
[tex]\left(x+\dfrac{b}{2a}\right)^2=\dfrac{b^2-4ac}{4a^2}\\\\\sqrt{\left(x+\dfrac{b}{2a}\right)^2}=\sqrt{\dfrac{b^2-4ac}{4a^2}}\\\\\boxed{x+\dfrac{b}{2a}=\pm\dfrac{\sqrt{b^2-4ac}}{\sqrt{4a^2}}}\qquad\text{"next step"}[/tex]
Answer: [tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}[/tex]
Step-by-step explanation:
We can rewrite the left hand side as a perfect square, more specifically
[tex]\left(x+\frac{b}{2a} \right)^2[/tex]
So, taking the square root of both sides,
[tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}[/tex]
Which statement is true about function f, which is shown in the graph? The graph shows a cubic function. The curve is drawn using the points (minus 1, 8), (minus 1, minus 3.5), (0, 0), (1, 3.5), and (1, minus 8) which intercepts (1, 0), and (minus 1, 0) A. Function f is odd. B. Function f is even. C. Function f is neither even nor odd. D. Function f is both even and odd.
We conclude that f(x) is odd, so the correct option is A.
Which statement is true?
f(x) is an odd function if:
f(-x) = -f(x).
f(x) is an even function if:
f(x) = f(-x).
In this case, we know that the function f(x) has the points:
{ (-2, 8), (-1, -3.5), (0, 0), (1, 3.5), (2, -8)}
As you can see:
f(-2) = 8
f(2) = -8
Then:
f(-2) = -f(2)
Also:
f(-1) = -3.5
f(1) = 3.5
Then:
f(-1) = -f(1).
So we conclude that this is an odd function, and the correct option is A.
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The product of two consecutive positive even integers is 8. Find the value of the greater integer.
Answer:
4
Step-by-step explanation:
n and (n + 2)
Therefore,
n × (n + 2) = 8
n^2 + 2n = 8
n^2 +2n - 8 = 0
n^2 + 4n - 2n -8 = 0
n (n + 4) -2 ( n + 4)
(n - 2 ) ( n + 4)
Therefore,
n = -4 or + 2
But since n can't be negative, n = 2
substituting
(n+2) = 2+2 = 4
Therefore, the value of the greater integer is 4
find the square by multiplying the polynomial
(4c + 4)²
Answer:
16c² + 32c + 16
Step-by-step explanation:
(4c+4)² =
(4c+4)(4c+4) =
16c² + 16c + 16c + 16 =
16c² + 32c + 16
I think this is the answer you are looking for.
Hope this helped and have a good day
Ten six graders will each eat 1/4 of a pizza. How many whole pizza pies need to be
ordered for the ten students? Show your work
Answer:
3 whole pizzas
Step-by-step explanation:
[tex]10 \times \frac{1}{4} = \frac{10}{4} = \frac{5}{2} = 2 \frac{1}{2} [/tex]
So 3 whole pizzas will need to be ordered.
Answer:
2 and a half pies
Step-by-step explanation:
ten sixth graders eat 1/4 each, therefore 4 kids eat 1 whole pie. similarly, 8 kids eat two whole pies, since two kids are remaining they eat 2/4 of a pie.
which can also be put in as 1/2. this means they eat half a pie. and that is how altogether it is 2 and a half pies.
hope this helps!
Find the value of x. in this triangle lol
ffffffffffffffffffffffffffff
Can someone help me out with these questions ?
Answer:
See attached image
Step-by-step explanation:
Questions in the picture
By constructing and solving the profit equation for the cuckoo clock sales, we conclude that the sales of 30 clock will make a profit of $ 4250
How to determine the monthly profit by the cuckoo clock sales
The profit (P) is the result of subtracting costs from sales (S). Cost (Cp) is the sum of rent (C) and production cost (C'). Now we proceed to create and solve the expression:
P = S - C - C'
P = 500 · x - 275 · x - 2500
P = 225 · x - 2500
P = 225 · 30 - 2500
P = 4250
By constructing and solving the profit equation for the cuckoo clock sales, we conclude that the sales of 30 clock will make a profit of $ 4250.
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which of the following is a fifth root of the given complex number?
Answer: D
This result is true by De Moivre's theorem.
Refer to Table 24-1. If Year 1 is the base year, then the inflation rate in Year 2 was
a. 2.10 percent.
b. 1.40 percent.
c. –3.90 percent.
d. –1.40 percent.
Answer:
c
Step-by-step explanation:
If Year 1 is the base year, then the inflation rate in Year 2 was 2.10 percent. The correct option is a.
What is inflation rate?Inflation rate is the rate at which the general level of prices for goods and services in an economy is increasing over a certain period of time, typically one year.
To calculate the inflation rate, we need to compare the price level in Year 2 to the price level in Year 1.
Using the data from Table 24-1, we can see that the price index in Year 2 is 102.1 and the price index in Year 1 is 100.0.
The inflation rate can be calculated using the following formula:
Inflation rate = (Price index in Year 2 - Price index in Year 1) / Price index in Year 1 * 100%
Plugging in the values, we get:
Inflation rate = (102.1 - 100.0) / 100.0 * 100%
Inflation rate = 2.1%
Therefore, the correct answer is (a) 2.10 percent.
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Triangle XYZ is a right triangle with ZQ¯¯¯¯¯⊥XY¯¯¯¯¯¯ .
Drag and drop a correct answer into each box to complete the proof of the Pythagorean theorem.
(See images for details.)
The correct answer is. Proportional.
2. ce
3. Segment Addition Postulate.
By the angle-angle similarity postulate, △YXZ∼△YZQ, and △YXZ∼△ZXQ.
The corresponding sides of two similar triangles are proportional.
What is the proportional side of a similar triangle?Since similar triangles have proportional sides, therefore
[tex]\frac{a}{c}=\frac{f}{a}[/tex] and [tex]\frac{b}{c}=\frac{b}{e}[/tex]
Solving the equation for a² and b² gives
[tex]a^2=cf[/tex] and [tex]b^2=ce[/tex]
The value of a² is cf and the value b² is ce.
Adding these together gives
[tex]a^2+b^2=cf+ce[/tex]
Factoring out the common segment gives
[tex]a^2+b^2=c(f+e)[/tex]
From the given figure it is clear that
[tex]c=f+e[/tex]
(Segment Addition Postulate)
Using the Segment Addition Postulate, we get
[tex]a^2+b^2=c(c)[/tex]
On simplification, we get
[tex]a^2+b^2=c^2[/tex]
Therefore the required answers are 1. Proportional, 2. ce, 3. Segment Addition Postulate.
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Answer:
1. Angle-Angle similarity Postulate 2.Proportional 3. C
Step-by-step explanation:
By the Angle-Angle similarity Postulate, △YXZ~ △YZQ and △YXZ~ △ZXQ. Since similar Triangles have Proportional sides, a/c= f/a and b/c= e/b. Solving the equation for a² and b² gives a² = cf and b² =ce. Adding these together gives a²+b²=cf+ce. Factoring out the common segment gives a²+b²=c(f+e). Using the segment addition postulate gives a²+b²=c(c)
, which simplifies to a²+b²=c² (Look at image for proof)
.
A person invested $690 in an account growing at a rate allowing the money to double
every 7 years. How much money would be in the account after 3 years, to the nearest
dollar?
Rachel is now 11 years old. Five years ago, Lily was twice as old as Rachel. How old is Lily now?
Lily present age now 17 years old.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Here, Unit means 'single entity', the fundamental constructing block. Usually, it is 1 in mathematics and science.
Thus, unit price of something is price of 1 thing.
Thus, suppose we're taking about price of mangoes, then unit price will denote the price of 1 mango.
We have been given that Rachel is now 11 years old. Five years ago, Lily was twice as old as Rachel.
We want to find the present age of lily.
Since five years ago rachel was 6, we know that Lily was twice as old as Rachel makes lily 12 years old.
For five years ago so 12 + 5 = 17.
Therefore, Lily is now 17 years old.
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Simplify the following expression as a
monomial:
-60b8
————
-2065
Answer:
3b^3
Step-by-step explanation:
I assume the 6 in the denominator should be b.
-60 / -20 = 3
b^8/b^5 = b^(8 - 5) = b^3
Answer: 3b^3
If f(x) = -3x - 5 and g(x) = 4x - 2, find (f+ g)(x).
Answer:
(f + g)(x) = x - 7
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= - 3x - 5 + 4x - 2 ← collect like terms
= x - 7
Transportation problem is an example of a category of problems that can be modeled as __________ problems. a. Nonlinear. b. Simple. c. Network flow. d. Complex.
The transportation problem is an example of a category of problems that can be modeled as c. Network flow problems.
A transportation problem is a special kind of alignment that aims to calculate the cost of transporting a particular product from a set of sources or origins (factories, manufacturing facilities, etc.) to a set of destinations (warehouses, businesses, etc.). It's a planning issue. Minimize.
The transport problem is one of the models of linear programming problems. Its main purpose is to handle situations where goods are shipped from multiple sources to different destinations and to minimize overall shipping costs.
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What is a severe limitation of using the Internet for primary research? The data on the Internet are usually outdated. The educational qualifications of the respondents of surveys on the Internet cannot be identified accurately. A sample universe composed solely of Internet respondents represents a potential bias. Secondary data cannot be accessed on the Internet for conducting research. Using the Internet for primary research is the most expensive way of conducting primary research.
The severe limitation of using the internet for primary research is that a sample universe composed solely of internet respondents represents a potential bias.
Given options 1)The data on the Internet are usually outdated.
2) The educational qualifications of the respondents of surveys on the Internet cannot be identified accurately.
3) A sample universe composed solely of Internet respondents represents a potential bias.
4)Secondary data cannot be accessed on the Internet for conducting research.
5) Using the Internet for primary research is the most expensive way of conducting primary research.
We have to choose most appropriate option which shows the severe limitation of using internet for primary research.
The most appropriate option is option third which is that a sample universe composed solely of internet respondents a potential bias
There is biasness because on internet people gives their own opinion and reviews and don't think about reality. The data may have been collected for the research according to researcher's priority. The data may be outdated but it is of our choice whether we use that data or not because generally the date is given on the internet. We can also access secondary data on the internet. Using internet in research is not so expensive because some organisation provides study materials to researchers themselves.
Hence the limitation of using the internet for primary research is that a sample universe composed solely of internet respondents a potential. bias.
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What is the value of the Pearson coefficient of skewness for a distribution with a mean of 17, a median of 12, and a standard deviation of 6
The distribution value's skewness Pearson coefficient is 2.5.
Given that the median is 12 and the standard deviation is 6, the mean value is 17.
The difference between the mean and median is multiplied by three to determine Pearson's coefficient of skewness. By dividing the outcome by the standard deviation, A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance.
To determine Pearson's coefficient of skewness, use the following formula:
Skewness=(3(Mean-Median))÷standard deviation
Replace the values there with,
Skewness=(3(17-12))÷6
Skewness=(3×5)÷6
Skewness=5÷2
Skewness=2.5
Therefore, for a distribution with a mean of 17, a median of 12, and a standard deviation of 6, the value of the Pearson coefficient of skewness is 2.5.
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