Which of the following is NOT an elementary row operation?
A. Delete a row of negative numbers
B. Interchange (swap) two rows
C. Add a multiple of one row to another row
D. Multiply a row by a nonzero constant

The expected length of the piece that we are left with after breaking twice is L/4 and the variance Var(X) is 7L^2/144.

In the given question, consider a stick of length 1.

We break it at a point which is chosen randomly and uniformly over its length and keep the piece that contains the left end of the stick.

We then repeat the same process on the piece that we were left with.

We have to find expected length of the piece that we are left with after breaking twice.

In the same setting as Q7, suppose the length of the piece that we are left with after breaking twice is Y.

We also have to calculate the variance Var(Y).

Following Laws are used in the solution

Law of Iterated Expectations: E[X] = E[ E[X|Y] ]

& Law of total variance: Var(X) = E[Var(X|Y)]+Var(E[X|Y])

Now, Y = Length of the stick after we break it the first time

and X = length of the stick after we break it the second time

As both the distribution is uniformly distributed.

Now, E[Y] = L/2 and Var(Y)= l^2/12

E(x|y)[X|Y=y] = y/2 and Var(x|y)[X|Y=y] = y^2/12

As the expectation of uniform distribution over {a,b} is (b-a)/2 and variance is (b-a)^2/12

Using Law of Iterated Expectations

E[X] = E[ E[X|Y] ]

E[X] = E[ y/2 ]

E[X] = \int_{L}^{0}

E[X] = L/4

Now using Law of Total Variance

Var(X) = E[Var(X|Y)]+Var( E[X|Y] )

Var(X) = E[y^2/12]+Var(y/2)

Var(X) = (1/12)*E[Y^2]+(1/4)*Var(Y)

Var(X) = (1*12)*(Var[Y] + (E[Y])^2) + (1/4)*Var(Y)

Var(X) = (1/12)*(L^2/12+L^2/4) + (1/4)*(L^2/12)

Var(X) = 7L^2/144

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Answer:

\(11\)

because \(5 + 6 = 11\)

Answer:

the answer is 11

Step-by-step explanation:

the answer is 11 because 6 plus 5 equals 11

For the competition of project ,  5.75 quarts of paint is required .

Usually one quart of paint cover 100 square feet

Since, a gallon covers 250 square feet, it means that

 one gallon of paint is equal to \(\frac{250}{100} =2.5\) quarts of paint.

Number of gallon required to paint 575 square feet,

                                                                                        \(=\frac{575}{250} \\=2.3 gallons\)

So, 2.3 gallons is equal to,

                                                \(=2.3*2.5\\=5.75 quarts\)

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Answer: 44%

Step-by-step explanation:

100 - 49 - 7 = 44 people who preferred Soda B

44 of a 100 = 44%

Answer: 44%

Step-by-step explanation:

Since we have 100 people, each person is one percent.

49 people preferred A, so we can subtract 49 from 100.

100 - 49 = 51

7 people didn't have an opinion, so we can subtract 7 from 51.

51 - 7 = 44

That means that 44 people preferred B, which is 44%

The congruent reason for the triangles is (b) HL theorem

From the question, we have the following parameters that can be used in our computation:

Triangles = FGH and JHK

The SSS similarity theorem implies that the corresponding sides of the two triangles in question are not just similar, but they are also congruent

From the question, we can see that the following corresponding sides on the triangles:

Sides GH and HK

Sides FH and JK

These parameters are given in reasons (2) and (3) and it implies that these sides are congruent sides

For the triangle to be congruent by SSS, the following sides must also be congruent

GH must be congruent to HK

The above statement is true because point H is the midpoint of line GK

This is indicated in reason (2)

Hence, the congruent statement is SSS.

However, we can also make use of the HL theorem in (B)

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Answer:

$19.44

Step-by-step explanation:

first you need the conversion for pounds and ounces,

16 oz = 1 lb

therefore the 6 lb package is 6 × 16 = 96 ounces

so the first ounce costs $0.44

the remaining 95 ounces cost .20 per ounce or

.20 × 95 = $19

therefore the total cost is $19 + $0.44 = $19.44

For the function  f(x) = 2x + 3 the third iterate x₃  is 37

To find the third iterate, x3, of the function f(x) = 2x + 3, given an initial value of x₀ = 2,

we can apply the function repeatedly.

Starting with x₀ = 2:

x₁ = f(x₀)

= 2(2) + 3

= 7

x₂ = f(x₁)

= 2(7) + 3 = 17

x₃ = f(x₂)

= 2(17) + 3

= 37

Therefore, the third iterate x₃  is 37.

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Answer:

FH = 35.64

Step-by-step explanation:

(∠A = 360 so the other angle is 40)

By law of cosines,

FH² = AH² + FA² - 2(AH)(FA) * cos(A)

= 30² + 25² - 2(30)(25) * cos(80)

= 900 + 625 - 1500 * 0.17

= 1525 - 255

FH²  = 1270

FH = √1270

FH = 35.64

Answer:

288π inch³

Step-by-step explanation:

V=4

/3πr³

by substituding in formulae

4/3*216π

=288π inch³

hope this helps

plzz mark me brainliest

Actual dimensions of the rectangular stamp is Length = 3.5cm and Width = 4.9cm

perimeter of a rectangle is the sum of the dimensions. This is the sum of the 2 lengths and the 2 widths

Given data

width of a rectangular stamp ( W ) = 1.40cm + L

L = length

perimeter of stamp after increment = 20.8cm

Perimeter p = 2 ( L + W )

20.8 =  2 ( L + 1 + W + 1 )

20.8 =  2 ( L + 1 + 1.4+ L + 1 )

20.8 =  2 ( 2L + 3.4 )

10.4 = ( 2L + 3.4 )

2L = 10.4 - 3.4

L = 7 / 2

L = 3.5cm

Therefore length of the stamp is 3.5 cm

Width of the stamp = 1.4 + L

W = 1.4 + 3.5

W = 4.9 cm

Actual dimensions of the rectangular stamp is Length = 3.5cm and Width = 4.9cm

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Michael drove 1125 miles and paid $295 for renting the truck for 3 days

Rental company charges per day = $70

Rental company charges per mile = $0.20

Number of days truck is rented by Michael = 3 days

The total amount paid by Michael for the truck = $295

Let x be the number of miles Michael drives the truck

Formulating the equation using the information given in the question:

295 = 70 + 0.20(x)

295-70 = 0.20(x)

225 = 0.20(x)

x = 1125 miles

Therefore, the total miles driven by Michael is 1125 miles.

Michael paid $295 for driving the truck for 1125 miles and renting it for 3 days.

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If guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent (E), above average (AA), average (A), below average (BA), or poor (P). The frequency is : 1, 8, 6, 3, 2.

Analysis

E = E =1

AA= AA +AA + AA + AA + AA+ AA + AA +AA = 8

A= A + A+ A+ A+ A+ A = 6

BA = BA + BA + BA =3

P = P + P =2

Hence,

Class     frequency

E                     1

AA                  8

A                     6

BA                   3

P                      2

Total               20

Therefore  1, 8, 6, 3, 2 is the frequency .

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Lucio is 64 meters from the starting point.

The square has four sides of equal length, so Lucio has walked half the length of one side.

To return to the starting point, he needs to walk the other half of the side, which is 64 meters.

The angle Lucio turns is irrelevant, as long as he turns 180 degrees in total.

With this in mind, it can be seen that based on the parameters and the conditions, Lucio is 64 meters from the starting point because the angle to which he turns is irrelevant.

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The question in English:

In a square Lucio walks in straight sections, starting from the flagpole, at one point he changes direction turning 150º to his left, advances 64 meters and stops. To return to the pole you have to turn 75º to the left. How far are you from the starting point?

Step-by-step explanation:

Consuelo Butler

08/07

Homework: Practice

Exam 3

Question 1, 12.1.13

HW Score: 10%, 3 of 30 points

Score: 1 of 1

A professor had students keep track of their social interactions for a week. The

number of social interactions over the week is shown in the following grouped

frequency distribution. How many students had at least 60 social interactions for

the week?

12

Number of Social

Interactions

30-34

35-39

40-44

45-49

50-54

55-59

60-64

65-69

70-74

75-79

Frequency

9

14

11

15

16

8

7

By calculating the greater than cumulative frequency using the given frequency table, 12 students had at least 60 social interactions for the week.

The greater than cumulative frequency is also known as the more than type cumulative frequency. Here, the greater than cumulative frequency distribution is obtained by determining the cumulative total frequencies starting from the highest class to the lowest class.

Class interval     Frequency     Cumulative frequency

30-34                9                   85

35-39                14                   76

40-44                11                   62

45-49                15                   51

50-54                16                   36

55-59                 8                   20

60-64                 7                   12

65-69                 3                    5

70-74                  1                    2

75-79                  1                     1

[We read the cumulative frequencies with respect to the corresponding lower class limits. For example, 85 students had 'more than 30' social interactions, 76 students had 'more than 35 social interactions and so on.]

By reading the greater than cumulative frequency, we find that 12 students had at least 60 social interactions for the week.

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Given:

Required:

Simplify the expression.

Explanation:

The given expression is:

Simplify the expression as:

Apply the addition property.

Final answer:

The simplification of the expression is 3.7

Answer:

1.2 cups of raisins or 1 and 1/5 cups of raisins. (Same thing) :)

Step-by-step explanation:

6/5 is 1.2. So multiply the 1 by 1.2 as well to get 1.2. This was solved by using proportions.

Hope it helps!

Answer:

Step-by-step explanation:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; \frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] --- eq(1)\)

Lets look at the derivative part:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] \\\\= \frac{d}{dx}[cos(3x^2) \sqrt[3]{5x^3 -1} ] + \frac{d}{dx}[sin(4x^3)]\\\\=cos(3x^2) \frac{d}{dx}[ \sqrt[3]{5x^3 -1} ] + \sqrt[3]{5x^3 -1}\frac{d}{dx}[ cos(3x^2) ] + cos(4x^3) \frac{d}{dx}[4x^3]\\\\=cos(3x^2) \frac{1}{3} (5x^3 -1)^{\frac{1}{3} -1} \frac{d}{dx}[5x^3 -1] + \sqrt[3]{5x^3 -1} (-sin(3x^2))\frac{d}{dx}[ 3x^2] + cos(4x^3)[(4)(3)x^2]\)

\(=\frac{cos(3x^2) 5(3)x^2}{3(5x^3 - 1)^{\frac{2}{3} }} -\sqrt[3]{5x^3 -1}\; sin(3x^2) (3)(2)x + 12x^2 cos(4x^3)\\\\=\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)\)

Substituting in eq(1), we have:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; [\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)]\)

Answer:

Step-by-step explanation:

The second pair of points representing the solution set of the system of equations is (-6, 29).

To find the second pair of points representing the solution set of the system of equations, we need to substitute the x-coordinate of the second point into one of the equations and solve for y.

Given the system of equations:

y = x^2 - 2x - 19

y + 4x = 5

Substituting the x-coordinate of the second point (-6) into equation 2:

y + 4(-6) = 5

y - 24 = 5

y = 5 + 24

y = 29

Therefore, the second pair of points representing the solution set of the system of equations is (-6, 29).

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Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

y = x2 − 2x − 19

y + 4x = 5

The pair of points representing the solution set of this system of equations is (-6, 29) and

_________.

we can conclude that the two triangles ABD and ACD are congruent by the SSS criterion.

What is congruent ?

Congruent refers to having the same shape and size. In mathematics, two objects (such as triangles or polygons) are considered congruent if they have the same measurements for all corresponding sides and angles. When two objects are congruent, they can be superimposed on top of each other perfectly without any gaps or overlaps. Congruence is an important concept in geometry and is often used in proofs and problem-solving.

According to the question:
In order to determine whether the triangles are congruent, we can use the SSS (side-side-side) congruence criterion. This criterion states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Let's compare the triangles ABD and ACD. We can see that they share a common side AD. We also know that AB = AC, since C is the foot of the perpendicular drawn from A to AD. Finally, we know that BD = CD, since D is the midpoint of BC. Therefore, the triangles ABD and ACD have three sides that are congruent: AB = AC, BD = CD, and AD = AD.

By the SSS criterion, the triangles ABD and ACD are congruent. We can also conclude that angle ADB is congruent to angle ADC, since they are corresponding angles in congruent triangles. Therefore, the triangles are not only congruent, but also isosceles, with base AD.

Therefore, we can conclude that the two triangles ABD and ACD are congruent by the SSS criterion.

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The interval of the graph at which Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

Given data ,

Susan is running a 5k race. The graph of distance vs. time is shown

So , the slope of the first line is m₁

And , the slope of the second line is m₂

where the points are A ( 0 , 0 ) , B ( 10 , 3 ) , C ( 20 , 4 )

Now , slope of AB is

m₁ = ( 3/10 ) = 0.3

And , m₁ = 0.3 kilometers per minute

And , slope of BC is

m₂ = ( 4 - 3 ) / ( 20 - 10 )

m₂ = 1/10

m₂ = 0.1 kilometers per minute

Therefore , the interval is fastest at second line from B ( 10 , 3 ) , C ( 20 , 4 )

Hence , Susan is running fastest is from point A ( 0 , 0 ) to B ( 10 , 3 )

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Answer:

\(\textsf{a)} \quad T_n=-n^2+n+20\)

\(\textsf{b)} \quad T_{12}=-112\)

\(\textsf{c)} \quad \sf 8th\;term\)

a)  Second difference is 2.

b)  First term is 10.

Step-by-step explanation:

The given number pattern is:

To determine the type of sequence, begin by calculating the first differences between consecutive terms:

\(20 \underset{-2}{\longrightarrow} 18 \underset{-4}{\longrightarrow} 14 \underset{-6}{\longrightarrow}8\)

As the first differences are not the same, we need to calculate the second differences (the differences between the first differences):

\(-2 \underset{-2}{\longrightarrow} -4 \underset{-2}{\longrightarrow} -6\)

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of the n² term is half of the second difference.

As the second difference is -2, the coefficient of the n² term is -1.

Now we need to compare -n² with the given sequence (where n is the position of the term in the sequence).

\(\begin{array}{|c|c|c|c|c|}\cline{1-5}n&1&2&3&4\\\cline{1-5}-n^2&-1&-4&-9&-16\\\cline{1-5}\sf operation&+21&+22&+23&+24\\\cline{1-5}\sf sequence&20&18&14&8\\\cline{1-5}\end{array}\)

We can see that the algebraic operation that takes -n² to the terms of the sequence is to add (n + 20).

\(\begin{array}{|c|c|c|c|c|}\cline{1-5}n&1&2&3&4\\\cline{1-5}-n^2&-1&-4&-9&-16\\\cline{1-5}+n&0&-2&-6&-12\\\cline{1-5}+20&20&18&14&8\\\cline{1-5}\sf sequence&20&18&14&8\\\cline{1-5}\end{array}\)

Therefore, the expression to find the the nth term of the given quadratic sequence is:

\(\boxed{T_n=-n^2+n+20}\)

To find the value of T₁₂, substitute n = 12 into the nth term equation:

\(\begin{aligned}T_{12}&=-(12)^2+(12)+20\\&=-144+12+20\\&=-132+20\\&=-112\end{aligned}\)

Therefore, the 12th term of the number pattern is -112.

To find the position of the term that has a value of -36, substitute Tₙ = -36 into the nth term equation and solve for n:

\(\begin{aligned}T_n&=-36\\-n^2+n+20&=-36\\-n^2+n+56&=0\\n^2-n-56&=0\\n^2-8n+7n-56&=0\\n(n-8)+7(n-8)&=0\\(n+7)(n-8)&=0\\\\\implies n&=-7\\\implies n&=8\end{aligned}\)

As the position of the term cannot be negative, the term that has a value of -36 is the 8th term.

\(\hrulefill\)

Given terms of a quadratic number pattern:

We know the first differences are negative, since the difference between the second and third terms is -7. Label the unknown differences as -a, -b and -c:

\(T_1 \underset{-a}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-b}{\longrightarrow}T_4 \underset{-c}{\longrightarrow} -14\)

From this we can create three equations:

\(T_1-a=1\)

\(-6-b=T_4\)

\(T_4-c=-14\)

The second differences are the same in a quadratic sequence. Let the second difference be x. (As we don't know the sign of the second difference, keep it as positive for now).

\(-a \underset{+x}{\longrightarrow} -7\underset{+x}{\longrightarrow} -b \underset{+x}{\longrightarrow}-c\)

From this we can create three equations:

\(-a+x=-7\)

\(-7+x=-b\)

\(-b+x=-c\)

Substitute the equation for -b into the equation for -c to create an equation for -c in terms of x:

\(-c=(-7+x)+x\)

\(-c=2x-7\)

Substitute the equations for -b and -c (in terms of x) into the second two equations created from the first differences to create two equations for T₄ in terms of x:

\(\begin{aligned}-6-b&=T_4\\-6-7+x&=T_4\\T_4&=x-13\end{aligned}\)

\(\begin{aligned}T_4-c&=-14\\T_4+2x-7&=-14\\T_4&=-2x-7\\\end{aligned}\)

Solve for x by equating the two equations for T₄:

\(\begin{aligned}T_4&=T_4\\x-13&=-2x-7\\3x&=6\\x&=2\end{aligned}\)

Therefore, the second difference is 2.

Substitute the found value of x into the equations for -a, -b and -c to find the first differences:

\(-a+2=-7 \implies -a=-9\)

\(-7+2=-b \implies -b=-5\)

\(-5+2=-c \implies -c=-3\)

Therefore, the first differences are:

\(T_1 \underset{-9}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-5}{\longrightarrow}T_4 \underset{-3}{\longrightarrow} -14\)

Finally, calculate the first term:

\(\begin{aligned}T_1-9&=1\\T_1&=1+9\\T_1&=10\end{aligned}\)

Therefore, the first term in the number pattern is 10.

\(10 \underset{-9}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-5}{\longrightarrow}-11 \underset{-3}{\longrightarrow} -14\)

Note: The equation for the nth term is:

\(\boxed{T_n=n^2-12n+21}\)

Answer:

2p-8

Step-by-step explanation:

Know you're amazing and smart!

Answer:

Step-by-step explanation:

4p+8-2p-16 combine like terms

2p-8

The answer is attached. I hope this helps answer your question!

The amount the women would pay for 2.4 kg of chicken and 2 kg of meat in total is $15.2

The meaning of unit price is a price quoted in terms of so much per agreed or standard unit of product or service

Given that, a woman bought 1.8 kg of chicken and 1.6 kg of meat. The chicken cost $5.40 and the meat cost $6.40,

We need to find, if she had bought 2.4 kg of chicken and 2 kg of meat, how much would she have had to pay,

To find the same, we will first find the unit price of each,

Unit price = total price / total quantity

Since, 1.8 kg of chicken costs $5.40,

Therefore, 1 kg will cost = 5.40 / 1.8 = $3

Similarly,

If 1.6 kg of meat costs $6.40,

Therefore, 1 kg will cost = 6.40 / 1.6 = $4

Now, to find the cost of 2.4 kg of chicken and 2 kg of meat, we will multiply the unit prices to the required quantities,

Therefore,

2.4 kg of chicken will cost = 2.4 x 3 = $7.2

2 kg of meat will cost = 2 x 4 = $8

In total, she had to pay = 8+7.2 = $15.2

Hence, the amount the women would pay for 2.4 kg of chicken and 2 kg of meat in total is $15.2

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Answer:

4.5

Step-by-step explanation:

I did 45/1 I and it's 45 then 45/10

Answer:

On a number line, 1/6 would land in the exact middle between 0 and 2/6

Step-by-step explanation:

Not too sure what your question meant, but I hope my answer helped!

If it wasn't what you were looking for, please let me know and elaborate on your question and I'll be happy to help out! :)

Answer: C

Step-by-step explanation: