The value of a³b for the value of a=3 and b=-5-2i is -135-54i for the given complex number that defines "Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and 'i' is an imaginary number called “iota”."
What is complex numbers?Complex numbers are those that are expressed as a+ib, where a and b are real numbers and I is a fictitious number called a "iota." I has the value (√-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im). In the 19th century, the term "complex numbers"—which denotes that they have both real and imaginary components—became widely used. Occasionally, the term "imaginary number" is used to describe a complex number that is not real or, more commonly, a number whose real part is zero (a.k.a "pure imaginary").
Here,
The value of a³b
=3³(-5-2i)
=27(-5-2i)
=-135-54i
For the given complex number that defines "Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and I is an imaginary number called "iota," the value of a³b is -135-54i.
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The average price of a certain model of pickup truck in 1992 was $12,500. In 2013, the average price of the pickup truck was $22,000. What is the percentage increase in the average price of the pickup truck?
The average price in 1992 and 2013 was given. It is required to find the percentage increase in the average price over these years.
Recall that the formula for Percentage Increase is:
[tex]\text{percent increase}=\frac{\text{final price-initial price}}{\text{initial price}}\times100\%[/tex]Substitute initial price=12500 and final price= 22000 into the formula:
[tex]\begin{gathered} \text{percent increase}=\frac{22000-12500}{12500}\times100\%=\frac{9500}{12500}\times100\%=0.76\times100\% \\ \Rightarrow\text{percent increase}=76\% \end{gathered}[/tex]Hence, the percent increase in the average price is 76%.
Answer:
depends on whether or not the dealerships are scammers
Step-by-step explanation:
Paul biked 7 miles on Saturday and 15 miles on Sunday. What was the total distance, in miles, Paul biked during those 2 days?
We have that:
Paul biked 7 miles on Saturday.
Paul bike 15 miles on Sunday.
The total distance, in miles, the Paul biked during Saturday and Sunday is:
[tex]T=7+15=22[/tex]-1/5 = -1/2w - 1/7 solve for w and simplify your answer as much as possible
Answer:
w = (4/35)
Step-by-step explanation:
-1/5 = -1/2w - 1/7
+1/7 +1/7
-----------------------------
-2/35 = -1/2w
÷-1/2 ÷-1/2
-----------------------
4/35 = w
Extra:
-1(7) 1(5)
------- + -------
5(7) 7(5)
-7 5 -2
------- + ------- = -------
35 35 35
------------------------------------------------------------
-2 -1
------- ÷ -------
35 2
-2 -2 4
------- × ------- = -------
35 1 35
I hope this helps!
Which is greater 12.5 or |-13|?
From the question, we are asked to find which is great between 12.5 or |-13|
recall:
|-13|
The absolute value is the distance between a number and zero. The distance between -13 and 0 is 13.
The absolute symbol makes any number positive.
So, |-13| is the greater because |-13| = 13.
So, between 12.5 and |-13|, |-13| is greater since it is same as 13.
URGENT DUE TODAY!!!!!
49. Which of the following is the solution of
0.125x +1 -0.25x < -3?
a. x < -0.5
b. x < 0.5
C. x > 0.5
d. x < 32
e. x > 32
The solution of 0.125x +1 -0.25x < -3 is x > 32
Difference between equality and inequality equations
Both mathematical phrases, equations and inequalities, are created by connecting two expressions.The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols show that the two expressions in an inequality are not always equal: >, <, ≤ or ≥. Or in simple words the equation which has '=' sign is an equality equation while the inequality equation has the signs are >, <, ≤ or ≥.
The given expression is,
0.125x +1 - 0.25x < -3
subract the x value,
0.125x - 0.25x + 1 < -3
-0.125x + 1 < -3
-0.125x < -3 - 1
-0.125x < -4
Now, if on both the sides the signs are -ve then change the inequality sign, like this
x > 4 / 0.125
x > 32
Hence, The solution of 0.125x +1 -0.25x < -3 is x > 32
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Which inequality statements are true? Select all that apply.-0.7<-0.40.5 -0.6-0.8<-0.70.6 > 0.4
Answer:
-0.7 < -0.4
0.5 > -0.6
-0.8 < -0.7
0.6 > 0.4
Explanation:
The symbol < means less than and the symbol > means greater than.
On the other hand, if we identify each number on a number line, we get:
Therefore, the true statements are:
-0.7 < -0.4
0.5 > -0.6
-0.8 < -0.7
0.6 > 0.4
Because, for example, -0.7 is on the left of -0.4 which means that -0.7 is less than -0.4.
0.5 in on the right of -0.6 which means that 0.5 is greater than -0.6.
Which equation is true when x=10 but not when x= – 10? Select all that apply.
Applying power rules, the equations that is true when x = 10 but false when x = -10 is given as follows:
x³ = 10000.
Exponents of 10The behavior of the exponents of 10 is different for even and for odd exponents, as follows:
Even exponents generate even functions, that is, 10^n = (-10)^n if the exponent n is even.Odd exponents generate odd functions, that is 10^n = -(-10)^n if the exponent is odd.In this problem, we have two exponents, as follows:
Exponent 2 is even.Exponent 3 is odd.We want different results for the power when x = 10 and when x = -10, hence the correct option will involve the odd exponent 3.
The third power of 10 is calculated as follows:
10³ = 10 x 10 x 10 = 100 x 10 = 1000.
Hence the equation that is true for x = 10 and false for x = -10 is:
x³ = 10000.
As when x = -10, the result is:
(-10)³ = (-10) x (-10) x (-10) = 100 x (-10) = -1000.
Missing informationThe options are given by the image at the end of the answer.
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determine the measure of angle j.
The measure of the value of ∠j is 10°.
What are a few properties of a triangle considering its angles?
A triangle's outer angle is the sum of its internal angles' two opposite sides.
The sum of two linear angles is supplementary.
Given, the three angles of the triangle are measured as (5x - 3)°,
(4x - 2)° and j°.
Also, the exterior angle of the triangle is (10x - 20)°.
Following the literature established above, considering that a triangle's outer angle is the product of its internal angles' two opposite sides, we have: (5x - 3) + (4x - 2) = 10x - 20 ⇒ 9x - 5 = 10x - 20 ⇒ 10x - 9x = 20 - 5
⇒ x = 15 --(i)
Again, since the sum of two linear angles is supplementary, we have using (i):
j + (10x - 20) = 180 ⇒ j + 150 - 20 = 180 ⇒ j = 10°
Therefore, the measure of the value of ∠j is 10°.
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The image of the point (1, 1) under a translation is (0, 3). Find the coordinates of the image of the point (-4, "-1) under the same translation.
The image of the point (-4, -1) after the translation is:
(-3, 1)
How to identify the translation?
A translation:
Tᵃ'ᵇ applied to a point (x, y) gives:
Tᵃ'ᵇ(x, y) = (x + a, y + b).
In this case, we know that:
Tᵃᵇ(1, 1) = (1 + a, 1 + b) = (0, 3)
Then:
1 + a = 0
1 + b = 3
Solving these we get:
a = 1
b = 3 - 1 = 2
The translation is:
T¹'²
Applying this to the point (-4, -1) gives:
T¹'²(-4, -1) = (-4 + 1, -1 + 2) = (-3, 1)
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Which of the following is TRUE for every polynomial P with degree = n ?a) The highest power of x in P(x) is n-1b) There are at most n-1 solutions to P(x) = 0c) The graph of P has at most n-1 turning pointsd) The graph of P has at most n-1 x-intercepts
We need to identify the true statement for every polynomial P with degree n.
The degree n of a polynomial is the exponent of the highest power of x in that polynomial. For example, the polynomial
[tex]x³+3x²+3[/tex]has degree 3, since the highest power of x has exponent 3.
Thus, if the degree is n, then the highest power is n (not n-1). Therefore, (a) is False.
About the number of solutions to P(x) = 0, it can equal the number of the polynomial degree. For some polynomials, the solutions can repeat, so the number of solutions will be less than n. For some of them, the solutions may not belong to the real numbers.
As an example, for P(x) = x²+4, we have:
[tex]\begin{gathered} x²+4=0 \\ \\ x²=-4 \\ \\ x=\pm\sqrt{-4} \\ \\ x=\pm2\sqrt{-1} \\ \\ x=\pm2i \\ \\ x_1=-2i \\ \\ x_2=2i \end{gathered}[/tex]The above polynomial has degree 2 and 2 solutions. Therefore, (b) is False.
Each turning point is where the graph of the polynomial P(x) changes from decreasing to increasing or vice versa. The graph of any polynomial of degree n has at most n-1 turning points.
Therefore, (c) is True.
We can see that (d) is False from the following example:
the line P(x) = x+1 has degree n = 1 and n = 1 x-intercept, which is its zero x = -1.
Answer:
c) The graph of P has at most n-1 turning points
3. 40 ounces of granola costs $6.52
a. How much does granola cost per ounce? (Give your answer to the nearest cent.) pleasee help
Answer: $0.2
Step-by-step explanation:
To find the answer you divide 6.52 by 40 which will get 0.163. To check the answer and make sure its correct you can multiply 0.163 by 40 to get 6.52 making the answer correct so 0.2 is the answer to the nearest cent. Hope this helps :)
Here is the answer again
The boxplot displays the arm spans for 44 students.
Which of the following is not a true statement?
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
The statements The range of the distribution is around 60 cm and
the center of the distribution is around 180 cm are true.
What is statistics?Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data.
In the given statements
There are no outliers in this distribution.
The shape of the boxplot is fairly symmetric.
The range of the distribution is around 60 cm.
The center of the distribution is around 180 cm.
The statement "The range of the distribution is around 60 cm" is true.
The range is the spread of your data from the lowest to the highest value in the distribution.
In the given graph
Range=200-140
=60
So it is true.
The center of the distribution is around 180 cm is also true.
Hence the statements The range of the distribution is around 60 cm and
the center of the distribution is around 180 cm are true.
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Nick was thinking of a number. Nick adds 11 then divides by 11 to get an answer of 28. Form an equation with
x
from the information.
Answer:
??
Step-by-step explanation:
In Exercises 1 and 2, find m/1 and m<2
1.
Answer:
m/1 = 87
m/2 = 93
Step-by-step explanation:
m1 and m2 need to have an angle of 180
so 180-87 = 93
Last year, Milan had $10,000 to invest. He invested some of it in an account that paid 9% simple interest per year, and he invested the rest in an account that
paid 7% simple interest per year. After one year, he received a total of $780 in interest. How much did he invest in each account?
Answer:
$4000 at 9% and $6000 at 7%Step-by-step explanation:
Let the amount invested at 9% be x.
Then the amount invested at 7% is 10000 - x.
The amount of interest after one year is $780.
Set up equation to represent this:
0.09x + 0.07(10000 - x) = 7800.09x + 700 - 0.07x = 7800.02x = 780 - 7000.02x = 80x = 80/0.02x = 4000Amount invested at 7% is:
10000 - 4000 = 6000Answer:
Milan invested:
$4,000 into the account earning 9% interest.$6,000 into the account earning 7% interest.Step-by-step explanation:
Given information:
Total amount invested = $10,000.Account A = 9% simple interest per year.Account B = 7% simple interest per year. Total interest earned after one year = $780.Let x be the amount invested in Account A.
Therefore, the amount invested in Account B is (10000 - x).
Simple Interest Formula
I = Prt
where:
I = Interest earned.P = Principal invested.r = Interest rate (in decimal form).t = Time (in years).Create two equations using the given information:
[tex]\begin{aligned}\textsf{Interest: Account A} &= x \cdot 0.09 \cdot 1\\& = 0.09x\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Interest: Account B} &= (10000 - x) \cdot 0.07 \cdot 1 \\& = 0.07(10000 - x)\\& = 700-0.07x\end{aligned}[/tex]
As the total interest earned was $780, set the sum of the two found equations to 780 and solve for x:
[tex]\begin{aligned}\implies 0.09x+700-0.07x&=780\\0.02x+700&=780\\0.02x&=80\\x&=4000\end{aligned}[/tex]
Therefore, Milan invested:
$4,000 into the account earning 9% interest.$6,000 into the account earning 7% interest.HELP ME PLEOPLE THIS IS SO CONFUSING HELP ME I WILL GET SUSPENDED IF I DON"T ANSWER THIS HELP ME PLEASE HELP I WILL GET A 0 AND SUSPENDED HELP HELP
Kala earns 45 dollars each week working part-time at a bookstore. She earns one additional dollar for each book that she sells.
Let A be the amount (in dollars) that Kala earns in a week if she sells
B books.
Write an equation relating to A to B Then use this equation to find the amount of money Kala earns if she sells 21 books.
The equation relating to A to B is A = 45 + b and the amount is $66.
What is an equation?An equation is used to show the relationship between the variables that are illustrated.
In this case, Kala earns 45 dollars each week working part-time at a bookstore and she earns one additional dollar for each book that she sells.
Let the books be represented as b. The equation will be:.
A = 45 + 1b
A = 45 + b
where A = amount earned.
The amount earned when 21 books are sold will be:
A = 45 + b
A = 45 + 21
A = 66
The amount is $66.
This illustrates the concept of equations.
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Jan uses 78 yard of fabric for one quilt square and 17 yard in another. how much fabric has jan used? responses 914 of a yard 9 over 14 of a yard 618 yards 6 and 1 eighth yards 756 of a yard 7 over 56 of a yard 1156 yards
Based on the yards of fabric used by Jan for the quilt squares, the total fabrics used by Jan was 1 ¹ / ₅₆ yards
How to find the number of yards used?The yards of fabric used by Jan were 7 / 8 of a yard and 1 / 7 of another yard.
The total yards used by Jan can be found by adding these fractions up. To add both fractions, you first need to find the common denominator of 8 and 7 which is 56.
Then the numerators can be found by dividing 56 by the denominator and then multiplying the numerator by the result.
Fraction 7 / 8 yards:
= 56 / 8 x 7
= 49 / 56
Fraction 1 / 7:
= 56 / 7 x 1
= 8 / 56
The total number of yards used is:
= 49 / 56 + 8 / 56
= 57 / 56
= 1 ¹ / ₅₆ yards
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Ten bags of oranges were sold to a family of eight.each family member ate six oranges, what fraction of the oranges were eaten?
The fraction of oranges eaten by the family is 3/5
Given,
Number of oranges in a bag = 8 oranges
Number of bags sold to a family = 10 bags
Number of members in the family = 6 members
Number oranges ate by each member of the family = 6 oranges
We have to find the fraction of the oranges eaten by the family members;
Here,
8 oranges in 1 bag and 10 bags sold.
So, total number of oranges sold = 8 x 10 = 80 oranges
Each member ate 6 oranges and there are 8 members.
So, total number of oranges eaten by them = 6 x 8 = 48 oranges
Now,
The fraction of oranges eaten by the family = 48/80 = 6/10 = 3/5
That is,
3/5th of oranges were eaten by the family.
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ashley’s house and the public Library are plotted on the coordinate plane as shown.What is the distance between Ashely’s house and the public library to the nearest tenth
The distance between Ashely’s house and the public library is of 7.8 miles.
What is the distance between two points?Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between these two points is given by the following rule:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the Cartesian plane, with the hypotenuse representing the distance between them.
In the context of this problem, the coordinates of her house and of the library are given as follows:
House: (4,2).Library: (10,7).Hence the distance is calculated as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]D = \sqrt{(10 - 4)^2+(7 - 2)^2}[/tex]
D = sqrt(61)
D = 7.8 miles, as each unit on the plane represents one mile.
Missing informationThe problem states that each unit on the plane represents one mile and the image gives their position on the plane.
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2/7×7/10 reduced to the smallest fraction
Answer:
1/5
Step-by-step explanation:
I multiplied 2 * 7, which is 14. Then, I multiplied 7 * 10 which equals 70. Then, I divided 14/70 by 14. The answer is 1/5.
Anna is computing 266 - 39. To do so, she first says that 266 is close to 270 and 39 is
close to 40, so she starts out computing 270 - 40 = 230. She then computes 230 - 3 =
227, and declares that 227 is her final answer. Is Anna's strategy correct? If yes, explain
why. If no, explain why not. Be mathematically specific, and support your reasoning
with a number-line model.
Yes, her strategy was correct.
What is BODMAS?When compared to operations involving just two numbers, solving an arithmetic expression that includes multiple operations like addition, subtraction, multiplication, and division is more difficult. A two-number operation is simple, but how do you work out an expression with brackets as well as multiple operations, as well as how to make a bracket simpler? Let's review the BODMAS rule as well as discover how brackets can be made simpler. For Bracket, Order, Division, Multiplication, Addition, and Subtraction, the acronym BODMAS is used. The acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication, Division, Addition, as well as Subtraction, is also known as BODMAS in some areas. Thus, the following figure illustrates the order in which BODMAS and PEMDAS operate.
Simplification is done following BODMAS rule.
266-39 gives 227.
Hence, her strategy was correct.
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Write the sentence as an equation.
y decreased by 283 is equal to 48
Answer:
y - 283 = 48
Step-by-step explanation:
y decreased by 283 means that 283 is subtracted from y. All set equal to 48.
I m struggle with this problem can someone help me
Check below, please
1) The way to tackle this problem, is by dividing those numerators by the denominators so we can get the decimal form of each fraction, and count the marks to plot them.
2) Let's divide them:
[tex]\begin{gathered} -\frac{5}{6}=-0.83 \\ \frac{17}{6}=2.83 \end{gathered}[/tex]So now, we can plot them:
Thus, this the answer.
Hakeem is the oldest of three siblings who ages are consecutive integers. If the sum of their ages are 69, find Hakeem age
Answer:
24
Step-by-step explanation:
Hakeem is the oldest of three siblings who ages are consecutive integers. If the sum of their ages are 69, find Hakeem age.
It should be noted that:
= 22 + 23 + 24
= 69
Hakeem's age is 24
What is the solution to the inequality?
17<9+x
OA. x<8
OB. x>8
OC. x > 26
OD. x< 26
SUBMIT
Answer:
B) x > 8
Step-by-step explanation:
1-Step: Combine like terms by subtracting 9 on both sides : 17-9 < X
8 < X
2- Step: flip the signs (Since 8 is less than X, Then X is greater than X)
X > 8
A boy bought some pencils for N60.00. If he had paid N1 less for each pencil, he could have bought 5 more pencils. How many pencils did he pay for?
The number of pencils he paid for is 15.
How to find the number of pencil he paid for?He bought some pencils for N60.00.
If he had paid N1 less for each pencil, he could have bought 5 more pencils.
Let
x = cost of each pencil that amount to N60.00
y = number of pencil
Therefore,
xy = 60
y = 60 / x
(y + 5)(x - 1) = 60
(60 / x + 5)(x - 1) = 60
60 - 60 / x + 5x - 5 = 60
- 60 / x + 5x + 55 = 60
- 60 / x + 5x = 60 - 55
- 60 / x + 5x = 5
- 60 + 5x² / x = 5
5x = -60 + 5x²
5x² - 5x - 60 = 0
x² - x - 12 = 0
x² + 3x - 4x - 12 = 0
x(x + 3) - 4(x + 3) = 0
(x - 4)(x + 3)
Hence,
x = 4 and x = -3
We can only use positive value.
xy = 60
y = 60 / 4
y = 15
Therefore, he paid for 15 pencils.
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if square one is the largest of the three squares in the model,which statement is true?
_______________
I'm reading your question
___________________
According to the Pythagorean theorem
Hypotenuse ^2 = Side 1 ^2 + Side 2 ^2
The hypotenuse is the case (Square 1 )
area of the sqaure= side of the square^2
________________________
That means the area of 1 is = area of square 2 + area fo square3 (J is false)
_______________________________
We are not sure about the relation between square 2 and 3 just the addition is the square 1 (F and H we have no certainty)
______________________________
G is true
______________________________
Answer
G
A candy box is made from a piece of cardboard that measures by inches. Squares of equal size will be cut out of each corner. The sides will then be folded up to form a rectangular box. What size square should be cut from each corner to obtain maximum volume?.
Using the concept of Application of Derivatives(A.O.D),we got 4.79 inches will be the square size for making the volume of candy box maximum.
A candy box is made from a piece of a cardboard that measures 43 × 23 inches.
Let squares of equal size will be cut out of each corner with the measure of x inches.
Therefore, measures of each side of the candy box will become
Length = (43 - 2x)
Width = (23 - 2x)
Height = x
Now we have to calculate the value of x for which volume of the box should be maximum.
Volume (V) = Length×Width×Height
=>V = (43 -2x)×(23 - 2x)×(x)
=>V= [(43)×(23) - 46x - 86x + 4x²]×x
=>V= [989 - 132x + 4x²]×x
=>V= 4x³- 132x² + 989x
Now we find the derivative of V and equate it to 0
[tex]\frac{dV}{dx}[/tex]= [tex]12x^{2} -264x+989[/tex]=0
Now we get values of x by quadratic formula
x=(264±[tex]\sqrt{264^{2}-4.12.989 }[/tex] )/24
=>x=(264±[tex]\sqrt{69696-47472}[/tex])/24
=>x=(264+√22224)/24, and x=(264-√22224)/24
=>x=(264+149.07)/24 and x=(264-149.07)/24
=>x=17.212 and x=4.79
Now we test it by second derivative test for the maximum volume.
[tex]\frac{d^{n}V }{dx}[/tex]=24x-264
For x = 17.212
[tex]\frac{d^{n}V }{dx}[/tex]=(24×17.212)-264=413.088-264=149.088
This value is > 0 so volume will be minimum.
For x = 4.79
[tex]\frac{d^{n}V }{dx}[/tex]=(24×4.79)-264= -149.04
-149.04 < 0, so volume of the box will be maximum.
Therefore, for x = 4.79 inches volume of the box will be maximum.
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(Complete Question) is
A candy box is made from a piece of cardboard that measures 43 by 23 inches. Squares of equal size will be cut out from each corner. The sides will then be folded up so that to form a rectangular box. What size square should be cut from each corner so that to obtain maximum volume?
Find the mean for the data set. 6, 14, 7, 4, 12, 8, 13, 4, 18, 14
Answer:
Concept:
Mean is just another name for average. To find the mean of a data set, add all the values together and divide by the number of values in the set. The result is your mean!
The values are given below as
[tex]6,14,7,4,12,8,13,4,18,14[/tex]The image below shows how to calculate the mean
By substituting values, we will have
[tex]\begin{gathered} \bar{x}=\frac{\sum ^{}_{n\mathop=0}x}{n} \\ n=10 \end{gathered}[/tex][tex]\begin{gathered} \bar{x}=\frac{6+14+7+4+12+8+13+4+18+14}{10} \\ \bar{x}=\frac{100}{10} \\ \bar{x}=10 \end{gathered}[/tex]Hence,
The mean = 10
To calculate the variance, we will use the formula below
[tex]^{}\sigma^2=\frac{\sum ^{\infty}_{n\mathop=0}(x-\bar{x})^2}{n}[/tex][tex]\begin{gathered} \sigma^2=\frac{\sum ^{\infty}_{n\mathop{=}0}(x-\bar{x})^2}{n} \\ (x-\bar{x})^2=(6-10)^2+(14-10)^2+(7-10)^2+(4-10)^2+(12-10)^2+(8-10)^2+(13-10)^2+(4-10)^2+(18-10)^2+(14-10)^2 \\ (x-\bar{x})^2=16+16+9+36+4+4+9+36+64+16 \\ (x-\bar{x})^2=210 \end{gathered}[/tex][tex]\begin{gathered} \sigma^2=\frac{\sum ^{\infty}_{n\mathop{=}0}(x-\bar{x})^2}{n} \\ \sigma^2=\frac{210}{10} \\ \sigma^2=\frac{210}{10} \\ \sigma^2=21 \end{gathered}[/tex]Hence
The variance = 21
To calculate the standard deviation,
[tex]\begin{gathered} \sigma=\sqrt[]{variance} \\ \sigma=\sqrt[]{21} \\ \sigma=4.58 \end{gathered}[/tex]Hence,
The standard deviation is = 4.58