Answer:
Answer:
x = 12
Step-by-step explanation:
m∠S + m∠T = 180
8x + 7x = 180
15x = 180
x = 12
does this help?
F(x)=x^2.what is g(x) ?
Answer:
Option C. [tex]g(x)=(\frac{1}{3}x)^2[/tex]
Step-by-step explanation:
Stretch transformations of functionsIn which direction is the transformation happening?Given a function to start with, extra operations that are done outside of the given function, cause vertical transformations, whereas operations that are done inside of the function cause horizontal transformations.
Transformations on the outside
Ex. [tex]g(x)=(x^2)-3[/tex] is subtracting 3 outside, so its transformation is vertical.
Transformations on the inside
Ex. [tex]g(x)=(x-7)^2[/tex] is subtracting 7 inside, so its transformation is horizontal.
Stretch/compression transformationsFor any function, stretches or compressions occur by multiplying by positive numbers larger or smaller than 1.
Multiplying by numbers larger than one, quantities get larger, and multiplying by a positive number less than one, quantities get smaller.
For example, [tex]\$10*2 = \$20[/tex], but [tex]\$10*\frac{1}{2} = \$5[/tex]
For transformations, this intuition needs a small modification:
Operations outside: transformations happen "normally" as you would expect.Operations inside: transformations happen "backwards" from the natural way one might expect.Multiplying on the outside
When multiplying outside of the function, things outside happen normally, and since it is happening outside, it is in a vertical direction.
Ex. Multiplying outside by 3, things get larger (stretch) vertically to 3 times as much as (300% of) normal (away from a height of zero).
Multiplying outside by [tex]\frac{1}{2}[/tex] , things get smaller (compress) vertically down to [tex]\frac{1}{2}[/tex] as much as (50% of) normal (toward a height of zero).
"g" is lower than "f", so it may have been compressed vertically (see alternative solution at end).
Looking at the only options with multiplication outside (A & B), option B multiplies by 3 (greater than 1), so it would stretch "f" even taller.
Option A, does compress "f" vertically (by 1/3), but doesn't compress it enough to arrive at the point (3,1) defined on function "g". Note ordered pair (3,1) on "g", meaning when you input "3", you get out "1".
Putting 3 into the "f" function, f(3)=9. Since one-third (the transformation in Option A) of 9 is 3, not 1, Option A doesn't compress "f" enough.
Multiplying on the inside
When multiplying inside, transformations happen horizontally, and inside things happen "backwards".
So, if multiplying inside by 4, (...normally things get bigger...) things actually get smaller (compressed) horizontally, reduced to 1/4 (the reciprocal of 4) the size (toward a horizontal distance of zero).
If multiplying by a number less than one (but positive), like [tex]\frac{1}{3}[/tex] , (...things normally get smaller...) things will actually get larger (stretch) in the horizontal direction out to triple (the reciprocal of [tex]\frac{1}{3}[/tex]) as much as normal.
Looking options C & D (where multiplication happens inside), both have multiplication by a positive number less than one (... normally would make things smaller...), which will stretch "f" out horizontally.
How far has the function been stretched out horizontally?Looking at the red point (3,1), the blue function does have a height-matched point at (1,1).
Measuring horizontal distances, (3,1) is 3-units from the y-axis, whereas (1,1) is only 1-unit away. Thus, the "g" is 3 times as far as "f", meaning a horizontal stretch outward by 3.
Answer C multiplies inside by [tex]\frac{1}{3}[/tex], so it actually makes things 3 times bigger horizontally.
The correct answer is option C.
Verifying algebraicallyTo verify, from (3,1), put 3 into the option C g(x) -- it gives "1" as an output.
[tex]g(x)=(\frac{1}{3}x)^2\\g(3)=(\frac{1}{3}(3))^2\\g(3)=(1)^2\\g(3)=1\\[/tex]
An alternative solutionThis function could have been compressed vertically to obtain the red graph.
Note that f(3)=9.
The point (3,1), on the red function, is only at a height of 1 ... 1/9th the height of the blue function. We could compress the "f" vertically by 1/9th to transform the blue function into the red function.
Vertical transformations come from operations outside, and outside things behave "normally", so to vertically compress by 1/9th, just multiply on the outside by 1/9th.
Thus, an alternative answer to transform f(x) to g(x) is [tex]g(x)=\frac{1}{9}(x^2)[/tex]
Two last things:
Simplifying this function we just obtained we get [tex]g(x)=\frac{1}{9}x^2[/tex]
Returning to the function that we chose for our answer in option C, [tex]g(x)=(\frac{1}{3}x)^2[/tex]
[tex]g(x)=(\frac{1}{3}x)(\frac{1}{3}x)[/tex]
[tex]g(x)=\frac{1}{9}x^2[/tex]
Note that the transformation answer for this problem (Option C) and our alternative solution both simplify and match perfectly, so they both represent the same end result.
A pyramid has a square base with sides of length s. The height of the pyramid is equal to 1/2 of the length of a side on the base. Which formula
represents the volume of the pyramid?
A. V = 1/12 s ^3
B. V=1/6 s ^3
C. V=1/3s ^3
D. V=3s³
E. V=6s³
Answer:
V = (s^3)/6 (Answer B )
Step-by-step explanation:
If the length of a side of the base is s, then the height of the pyramid is half that, or s/2.
The volume of a pyramid with a square base and base side length S and height H is V = (1/3)(S^2)(H).
In this case, the formula is V = (1/3)(s^2)(s/2), or V = (s^3)/6 (Answer B)
Translate each English phrase in the following problem into an algebraic expression and set up the related equation. Let z be the unknown number. The difference between a number and −23 − 23 is equal to the product of the number and 13 13 . Step 2 of 3 : Translate "the product of the number and 13 13 ".
The English phrase of the obtained equation is 12 times z subtracted by 3. The obtained equation after solving is 12z -23
What exactly is simplification?Simplifying means making something easier to do or comprehend, as well as making something less difficult.
Given data;
z be the unknown number
Given conditions;
1. The difference between a number and −23.
2.−23 is equal to the product of the number and 13.
The mathematical form of the given phrase is;
⇒ z - (-23) = z × 13
⇒z+23 = 13z
⇒12z -23
The English phrase of the obtained equation is 12 times z subtracted by 3.
Hence the simplification of the given expressions is 12z -23.
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The price of an item has dropped to 27$ today. Yesterday it was 90. Find the percentage decrease
The percentage decrease would be 70 percent.
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
The price of an item has dropped to 27$ today. Yesterday it was 90.
90 - 27 = 63
The percentage decrease;
63 / 90 x 100= 70%
Hence, The percentage decrease would be 70 percent.
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What is the lowest value of the range of the function
shown on the graph?
O -∞
O -2
0 0
03
The question is incomplete. Below you will find the missing graph.
The lowest value of the range of the function shown on graph is (B) -2.
A graph is the pictorial representation of the function or mathematical relation (Equation or Inequality etc).
The lowest value of the graph is the value of y when y=f(x) gives the least value.
From the given graph we can clearly see that at x=3 the graph of the given function approaches the least value which is -2.
So the lowest value of the range of the function shown on the graph is -2.
Hence the correct option is (B).
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In formula P = 2L + 2W
A. solve for L
B. solve for W
C. Find P if L=12 and W=8
Answer:
P=2l+2W
if l=12 and W=8
then,
P=2L+2W
=2.18+2.8
=36+16
=52
The graph shown below expresses a radical function that can be written in the form F(x) = a(x+ k)^1/n+ C. What does the graph tell you about the value of a in this function?
For the function F(x)=[tex]a(x+k)^{1/n}+C[/tex] the value of a is less than zero and the correct option is option d.
Given the value of function F(x)=[tex]a(x+k)^{1/n}+C[/tex].
We have to put the function equal to 0 for finding the nature of a and C is a fixed number in the function :
a[tex](x+k)^{1/n}[/tex]+C=0
a[tex](x+k)^{1/n}[/tex]=-C
a=-C/[tex](x+k)^{1/n}[/tex]
Since negative sign is coming before a and the value of rest of the expression cannot be negative so the value of a should b negative which means less than 0. The rest of the expression cannot be negative because it has a power of 1/n which only gives positive values like modulas.
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Eduardo and his friends want to start a band, so he decides to take guitar lessons. He purchases a 6-lesson package at Sharp Notes music store, which comes out to $22.50 per lesson.
Which is the domain and range of the parabola with the equation y = 0.5(x2 – 8x – 6)?
D: (–∞, ∞); R: (–∞, –11]
D: (–∞, ∞); R: [–11, ∞)
D: (–∞, –11]; R: (–∞, ∞)
D: [–11, ∞); R: (–∞, ∞)
Answer:
D: (–∞, ∞); R: [–11, ∞)
Step-by-step explanation:
The domain of a quadratic function is all real numbers, so eliminate the third and fourth options.
Also, since the coefficient of [tex]x^2[/tex] is positive, we know the graph opens up and thus has a minimum.
This means that the first option must be wrong since the range has a maximum, not a minimum.
Therefore, the correct answer is Option 2.
Answer:
D: (–∞, ∞); R: [–11, ∞)
Step-by-step explanation:
I honestly don't know the answer but the other person said this so I'm putting it as my answer ill update this answer when i find out if its right or not.
update I GOT A 100% woop woop
In the figure below, lines I and mare parallel. What is the value of x?
1
(4x13)
X=
m
(2x + 37)
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: x = 25°[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 4x - 13 = 2x + 37[/tex]
[ Alternate Exterior Angle ]
[tex]\qquad \tt \rightarrow \: 4x - 2x = 37 + 13[/tex]
[tex]\qquad \tt \rightarrow \: 2x = 50[/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{50}{2} [/tex]
[tex]\qquad \tt \rightarrow \: x = 25 \degree[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Help please I need it asap and thank you
Answer: 2.5
Step-by-step explanation:
The altitude of an equilateral (or isosceles) triangle bisects the side to which it is drawn.
i needs help with it
Answer:
a) initial height = 0 m
b) 8 s
c) vertex = (4, 32)
maximum height = 32 m
Step-by-step explanation:
Given equation:
[tex]h=-2t^2+16t[/tex]
where:
h is the height of the arrow about the ground (in metres)t is the time (in seconds)Part (a)The initial height of the arrow will be at the beginning of its journey, so when t = 0
Substitute t = 0 into the equation and solve for h:
[tex]\implies h=-2(0)^2+16(0)[/tex]
[tex]\implies h=0[/tex]
Therefore, the initial height of the arrow is 0 m.
Part (b)The arrow will hit the ground when the height is 0 m.
Substitute h = 0 into the given equation:
[tex]\implies -2t^2+16t=0[/tex]
Factor out -2t:
[tex]\implies -2t(t-8)=0[/tex]
Therefore:
[tex]\implies -2t=0 \implies t=0[/tex]
And:
[tex]\implies t-8=0 \implies t=8[/tex]
Therefore, the arrow will hit the ground at 8 seconds.
Part (c)The vertex is the turning point of a parabola - it's minimum or maximum point.
As the leading coefficient for the given equation is negative, the parabola opens downwards and so its vertex is its maximum point.
There are different ways to find the vertex of a parabola. The easiest way to find the x-coordinate is by calculating the midpoint of the x-intercepts.
We have determined that the arrow has a height of 0 m at 0 seconds and 8 seconds. Therefore, t = 0 and t = 8 are the x-intercepts. The midpoint is halfway between zero and 8, so the midpoint is t = 4
To find the y-coordinate, substitute t = 4 into the equation and solve for h:
[tex]\implies h=-2(4)^2+16(4)[/tex]
[tex]\implies h=-32+64[/tex]
[tex]\implies h=32[/tex]
Therefore, the coordinates of the vertex are (4, 32)
The maximum height is the y-coordinate of the vertex.
Therefore, the maximum height is 32 m
Mama bear wants to bake a cake with chocolate frosting for her twins birthday party. She uses a package containing 495 grams of coco powder for the frosting. What will be the weight of the chocolate frosting if it is 55% cocoa powder?
The weight of the chocolate frosting if it is 55% cocoa powder will be 272.25 grams.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred.
Mama bear wants to bake a cake with chocolate frosting for her twin's birthday party.
She uses a package containing 495 grams of cocoa powder for the frosting.
Then the weight of the chocolate frosting if it is 55% cocoa powder will be
⇒ 0.55 × 495
⇒ 272.25 grams
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Over which interval is the graph of the parent absolute value function decreasing?
(–∞, ∞)
(–∞, 0)
(–6, 0)
(0, ∞)
The graph of the parent absolute value function decreases over Option B(–∞, 0) interval.
What is the parent absolute value function?An absolute value function is defined as a function that contains an algebraic expression within absolute value symbols.
The absolute value function is f(x) = |x| is defined as,
f(x )
x = x < x = 0 < x = -x
Observe that the graph is V-shaped.
The vertex of the graph is (0,0).
The domain is the set of all real numbers.
The x-intercept and the y-intercept are both 0.
Hence, The graph of the parent absolute value function decreases over Option B(–∞, 0) interval.
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Sandra owns a rectangular pice of farmland that is 2/3 miles wide and has an area 5/9 square mile what is the leght of sandras farmalnd
Answer:
5/6 mile
Step-by-step explanation:
The formula for the area of a rectangle can be used with the given values to write an equation for the length of the farmland.
__
Here is the equation for the area of a rectangle.
A = LW . . . . . area is the product of length and width
When we fill in the area and width, we have ...
5/9 mi² = L(2/3 mi) . . . . . equation for the length of the farmland
Solving this equation gives ...
L = (5/9)/(2/3) mi . . . . . . . . divide by the coefficient of L
L = (5/9)/(6/9) mi = 5/6 mi . . . . . perform the division
The length of Sandra's farmland is 5/6 mile.
find the slope of the line on the graph write your answer as a whole number or a fraction not a mixed number or decimal
Answer: 3/4
Step-by-step explanation:
7 of 9 For each 48 mm of coloured fabric Fiona uses to make her curtains, she also uses 1.2 cm of white fabric. Express the amount of white fabric to coloured fabric as a ratio in its simplest form. 7 of 9 For each 48 mm of coloured fabric Fiona uses to make her curtains , she also uses 1.2 cm of white fabric . Express the amount of white fabric to coloured fabric as a ratio in its simplest form
Answer:
amount of coloured fabric in mm = 48
amount of white fabric in mm = 12
ratio = white fabric : coloured fabric = 12 : 48 = 1:4
if a polyhedron has a volume of 35 cm^3 and is dilated by a factor of 5/2, what will be the volume of the dilated polyhedron? Round your answer to the nearest thousandth if necessary.
If a polyhedron has a volume of 35 cm cube and is dilated by a factor of 5/2 then the volume of dilated polyhedron will be 50.6 cm cube.
Given Volume of polyhedron=35 cm cube . Factor from which is dilated 5/2.
If the polyhedron is dilated by factor 5/2 then the volume of the polyhedron will change by the cube of that factor because when it is dilated by factor its material also increases.
Volume =35[tex]cm^{3}[/tex]
After dilation
Volume=35+[tex](5/2)^{3}[/tex]
=35+15.625
=50.625
After Rounding nearest to thousand we will get 50.6 [tex]cm^{3}[/tex].
Hence after dilation the volume which is 35 cm cube will change from 35 to 50.6[tex]cm^{3}[/tex].
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Select the graph that represents the correct answer to the equation.
5y = 3x - 5
Given:
The given equation is 5y=3x-5
Find: Draw the graph
Explanation:
It is given that 5y=3x-5. Substitute x=0 into the given equation we have
[tex]5y = 3x - 5[/tex]
[tex]5y = 3(0) - 5[/tex]
[tex]5y = - 5[/tex]
[tex]y=-1[/tex]
Now, substitute x=5 into the given
equation we have
[tex]5y = 3(5)-5[/tex]
[tex]5y = 15-5[/tex]
[tex]5y = 10[/tex]
[tex]y = 2[/tex]
The points are (0,-1) and (5,2).
Therefore, the required graph is
Hence, the required graph is obtained.
Would it be
A.
B.
C.
D.
Answer:
A. is the answer
pls help how do i solve for x in this equation??
Answer:
x = -2
Step-by-step explanation:
1. Square both sides
x^2 +3x + 6 = x^2
2. Subtract x^2 from both sides
3x + 6 = 0
3. Subtract 6 from both sides and divide by 3
x = -2
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 20 13 7 40
Female 9 2 8 19
Total 29 15 15 59
If one student is chosen at random,
Find the probability that the student got an A.
20
29
29
59
20
59
The grades and gender is 29/59
What is probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given:
A B C Total
Male 20 13 7 40
Female 9 2 8 19
Total 29 15 15 59
Total candidates who have A grade = 20+9 = 29
So, the probability that the student got an A
= 29/59
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AB and CD intersect at point E if measure angle AED equals 6x-24 and measure angle CEB equals 4y+32 find the values of x and y such that AB is perpendicular to CD
The values of x and y such that AB is perpendicular to CD will be 19 and 14.5.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
AB and CD intersect at point E.
If measure angle AED equals 6x – 24 and measure angle CEB equals 4y + 32.
Then the values of x and y such that AB is perpendicular to CD will be
6x – 24 = 90
6x = 114
x = 19
Then we have
4y + 32 = 90
4y = 58
y = 14.5
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NEED ASAP !!!!!
Which table represents a linear function?
in the game of roulette, a player can place a $ 7 bet on the number 28 and have a 1/38 probability of winning. if the metal ball lands on 28, the player gets to keep the $7 paid to play the game and the player is awarded $245. otherwise, the player is awarded nothing and the casino takes the player's $7. what is the expected value of the game to the player? if you played the game 1000 times, how much would you expect to lose?
Answer: The player expects to lose 184.21 dollars.
=========================================================
Explanation:
X = net winnings in dollars
Ignore the "28" because it's really not that relevant here. All we care about is the probability 1/38 which is the probability of winning money. The probability of losing money is 1 - (1/38) = 37/38. Put another way: there's 1 way to win, and 37 ways to lose.
If the player wins, then they walk away with 7+245 = 252 dollars
If the player loses, then their "winnings" is -7
So either X = 252 or X = -7 are the only two options.
Let's form a table showing those options with their corresponding probabilities.
[tex]\begin{array}{|c|c|} \cline{1-2}X & P(X)\\\cline{1-2}252 & 1/38\\\cline{1-2}-7 & 37/38\\\cline{1-2}\end{array}[/tex]
Now multiply each X value and P(X) value across the rows.
252*(1/38) = 6.631579
-7*(37/38) = -6.815789
These values are approximate.
[tex]\begin{array}{|c|c|c|} \cline{1-3}X & P(X) & X*P(X)\\\cline{1-3}252 & 1/38 & 6.631579\\\cline{1-3}-7 & 37/38 & -6.815789\\\cline{1-3}\end{array}[/tex]
Add up the results of the third column
6.631579 + (-6.815789) = -0.18421
This represents the net winnings for any average spin of the wheel. The player unfortunately expects to lose, on average, about $0.18421 or 18.421 cents per spin.
Do this 1000 times and the player should expect to lose about
1000*(0.18421) = 184.21 dollars
Keep in mind that due to the random nature of roulette wheel, the player may get lucky or their luck may be worse than what is described. The idea is that over the long run, the average should be somewhat close to losing 184.21 dollars.
Another way to think of it could be to have 1000 players doing the same game (rather than have 1 person play the same game 1000 times). Some players may get lucky, while others may not get so lucky. But their collective average should be losing that $184.21
Which expression is modeled by this arrangement of tiles?
40 positive tiles are broken up into 10 groups of 4 positive tiles.
The answer is 40/10 because the total number of square units is 40 option second 40/10 is correct.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The question is incomplete.
The complete question is:
Which expression is modeled by this arrangement of tiles? 40 positive tiles are broken up into 10 groups of 4 positive tiles.
40/(-10) 40/10 40/40 40/(-40)Please refer to the attached picture.
We have a rectangular shape as shown in the picture.
Total number of square units = 40
Each row has 10 units cube.
Each cube = 40/10
Thus, the answer is 40/10 because the total number of square units is 40 option second 40/10 is correct.
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In a recent year, 17.7% of all registered doctors were female. If there were 54,400 female registered doctors that year, what was the total number of registered doctors?
Answer:
The total number of registered doctors in this year are 307345.
Step-by-step explanation:
Let the total number of doctors who registered in this year are x
Given that the total number of female doctors in total registered doctors are 54400
According to the question 17.7 percent of the total registered doctors are the female doctors
Hence the total number of registered doctors who are females are 17.7% of x
which is written as 17.7*x÷100
According to the question 17.7x÷100= 54400
as we are given that the total number of female doctors are 54400
now
17.7x = 54400×100
x= 54400×100÷17.7
x= 307344.633 ≈ 307345
Therefore there are 307345 doctors who registered that year.
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2) An electronic gadgets distributor distributes various brands of mobiles to retailers.
The data for the number of smartphones distributed in nine months (Jan-Sep) are
collected to make a box-and-whisker plot. Read the plot and answer the questions.
H
20
30
40
a) Write the median from the above given plot.
b) What is the least number of smartphones distributed?
c) Write the third quartile from the given plot.
50
t>
60
The median is 40, the least number of smartphones distributed is 33, and the third quartile is 48.
What is the box and whisker plot?A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a box and whisker plot shown in the picture.
From the box plot, the line between the box ends represents the median of the data.
The median = 40
The least number of smartphones distributed = 33
Q3 = 48
Thus, the median is 40, the least number of smartphones distributed is 33, and the third quartile is 48.
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find the value of the hypotenuse for each of the following right triangles.
Answer:
I have done the 1st 2 sums in proper systematic manner. The remaining sums I'll be writing only the main formula and substitution. I hope you will write the missing sentences .
Step-by-step explanation:
Hope you will understand the sums..Also I would appreciate it if you could marke my answer as BRAINLIEST and THANK ME.｡◕‿◕｡
Answer:
Step-by-step explanation:
1. hypotenuse = 89
2. hypotenuse = 85
3. hypotenuse = 97
4. hypotenuse = 153
5. hypotenuse = 34
6. hypotenuse = 113
7. hypotenuse = 916
8. hypotenuse = 170
9. hypotenuse = 394
10. hypotenuse = 61
question is attachment
The degree of dispersion in your data collection is indicated by variance.
It is given by the formula:
[tex]\overline{d}= \sum_{i=1}^{i=n}\frac{|x_i-\overline{x}|^2}{n}[/tex]
To determine the values of a certain set of scattered data, the standard deviation formula is utilized. The dispersion of the quantities or data from the mean is how the standard deviation is simply defined. The conclusion drawn from a lower standard deviation is that the results are fairly near to the average. Higher values, on the other hand, indicate a significant dispersion from the mean. The standard deviation number can never be negative, it should be positive.
It is given by the formula:
[tex]s_d = \sqrt{\sum_{i=1}^{i=n}\frac{|x_i-\overline{x}|^2}{n}} =\sqrt{\overline{d}}[/tex]
We have that the mean of the values is:
at 8 AM [tex]\overline{x}=\frac{97.9+99.3+97.9+97.6+97.4}{5}=98.02[/tex]
at 12 AM [tex]\overline{x}=\frac{98.5+99.7+98+97.4+97.6}{5}=98.24[/tex]
Using the above definitions we have that
at 8 AM [tex]\overline{d}=\frac{(98.02-97.9)^2+(98.02-99.3)^2+(98.02-97.9)^2+(98.02-97.6)^2+(98.02-97.4)^2}{5}=0.4456[/tex]
[tex]s_d=\sqrt{\overline{d}}=\sqrt{0.4456}=0.6675[/tex]
at 12 AM
[tex]\overline{d}=\frac{(98.24-98.5)^2+(98.24-99.7)^2+(98.24-98)^2+(98.24-97.4)^2+(98.24-97.6)^2}{5}=0.6744[/tex]
[tex]s_d=\sqrt{\overline{d}}=\sqrt{0.6744}=0.8212[/tex]
In general, [tex]\mu_d[/tex] represents the mean of the differences from the population of matched data.
Learn more about the variance and standard deviation here-
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