Arrange the following fractions in order
from least to greatest.
7 15 3 11 13
5 4 2 4 3

So x → T(S(x)) satisfies homogeneity.

x → T(S(x)) is a linear transformation from P to M.

The completed statement is: "T maps n onto m if and only if A has pivot columns in every row."

One theorem that explains why this is true is the Rank-Nullity Theorem, which states that the rank of a matrix plus the nullity of the matrix (the dimension of the nullspace) equals the number of columns. If A has pivot columns in every row, then the rank of A is equal to the number of rows, which means that the nullity is 0, and therefore T is onto. Conversely, if T is onto, then the range of T has dimension equal to the number of rows, which means that the rank of A is equal to the number of rows, so A has pivot columns in every row.

To show that the mapping x → T(S(x)) is a linear transformation, we need to show that it satisfies the two properties of linearity: additivity and homogeneity.

Additivity: Let x and y be vectors in P. Then we have:

T(S(x + y)) = T(S(x) + S(y)) (by definition of + in P)

= T(S(x)) + T(S(y)) (since T is linear)

= (x → T(S(x))) + (y → T(S(y))) (by definition of the mapping)

= (x + y) → (T(S(x)) + T(S(y))) (by definition of + in M)

So x → T(S(x)) satisfies additivity.

Homogeneity: Let x be a vector in P and let c be a scalar. Then we have:

T(S(cx)) = T(cS(x)) (by definition of scalar multiplication in P)

= cT(S(x)) (since T is linear)

= c(x → T(S(x))) (by definition of the mapping)

So x → T(S(x)) satisfies homogeneity.

x → T(S(x)) is a linear transformation from P to M.

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All possible fourth corners if  the following three points are corners of a parallelogram:(1,2,3),(3,4,7),(2,1,2) is (2, 3, 5) and  (3, 5/2, 9/2)

Let the corners be A(1,2,3);B(3,4,7);C(2,1,2)

Let the fourth vertex D =(x,y,z)

We know that the diagonals of a parallelogram bisect each other. So, the midpoint of AC is same as the midpoint of BD.

Mid point of two points (x 1,y 1,z1) and (x 2,y 2,z2)​  is calculated by the formula ( x 1+x 2/2 , y 1+y 2/2, z1+z2/2 ).

So, midpoint of AC= Mid point of BD

⇒( 1+3/2, 2+4/2, 3+7/2) =(2, 3, 5)

Hence, D=(2, 3, 5).

Same if,

Mid point of two points (x 1,y 1,z1) and (x 2,y 2,z2)​  is calculated by the formula ( x 1+x 2/2 , y 1+y 2/2, z1+z2/2 ).

So, midpoint of AC= Mid point of BD

⇒( 3+2/2, 4+1/2, 7+2/2) = (3, 5/2, 9/2)

Hence, D=  (3, 5/2, 9/2)

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93 chocolate chip cookies

Yes, the given figure is a parallelogram.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Given is a parallelogram as shown in the image.

We have -

S(0, 0), T(3, 0), U(4, 3), V(1, 3)

For the figure to be parallelogram, we will have to prove -

ST = VU   &   SV = TU

We can calculate -

ST = 3

VU = 3

SV = 3.1

TU = 3.1

So -

ST = VU   &   SV = TU

Hence, it is a parallelogram.

Therefore, yes, the given figure is a parallelogram.  

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The binomial distribution is solved as

a) The probability that no more than 2 students out of the random 5  plan to go out on vacation is P ( X ≤ 2 ) = 0.0579

b) The probability that more than 2 students out of the random 5  plan to go out on vacation is P ( X > 2 ) = 0.9421

The binomial distribution is a type of probability distribution that predicts the likelihood of obtaining one of two outcomes given a set of inputs. It summarizes the number of tries where each trial has the equal chance of producing the same result.

The formula for Binomial Distribution is given by

P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ

where

n = number of trials

x = number of successes

p = probability of getting a success in one trial

q = probability of getting a failure in one trial

q = 1 - p

Given data ,

Let the probability be represented as P

Now , the total number of trials = 5

The number of students going for vacation be represented as n

Now , the probability of success p = 0.8

So , the value of q = 0.2

a)

The probability that no more than 2 students out of the random 5  plan to go out on vacation is P ( X ≤ 2 ) = P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ

Substituting the values , we get

The probability that no more than 2 students out of the random 5  plan to go out on vacation is P ( X ≤ 2 ) = 0.0579

The probability that no more than 2 students out of the random 5  plan to go out on vacation is P ( X ≤ 2 ) = 5.79 %

b)

The probability that more than 2 students out of the random 5  plan to go out on vacation is P ( X > 2 ) = P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ

Substituting the values , we get

The probability that more than 2 students out of the random 5  plan to go out on vacation is P ( X > 2 ) = 0.9421

The probability that more than 2 students out of the random 5  plan to go out on vacation is P ( X > 2 ) = 94.21 %

Hence , the binomial distribution is solved

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Answer:

A. The shirt at Store "A".

Step-by-step explanation:

How to find 10% of 28.

First, we need to convert 10% into a decimal.

To do that, we just divide the number by 100.

[tex]\frac{10}{100}[/tex] [tex]= 0.1[/tex]

Now, we take the original number (28) and multiply it by the decimal

[tex]28 x 0.1 = 2.8[/tex]

Finally, we subtract.

[tex]28.00 - 2.80 = 25.20[/tex]

[tex]25.20[/tex] > [tex]25.00[/tex]

Therefore, Store "A" Has the cheapest shirt

Answer:

Below

Step-by-step explanation:

You COULD calculate the lengths of the three sides and then use Heron's Formula to calculate the area.....

 Here is perhaps an easier way (see image)

  calculate the entire area of the rectangle then subtract the 3 smaller RIGHT triangles from the total

Area of rectangle =   6 x 7 = 42 units^2

  triangles    1/2 ( 3 x 7    +    3 x 3    +    4 x 6 ) = 27 units^2

42 - 27 = 15 units^2   = area of given triangle

Answer:

15 square units

Step-by-step explanation:

i am using Heron's formula for this question

Firstly, lets calculate the lengths of the triangle. We can do this by using the formula:

[tex]length=\sqrt{(y_{2}\\-y_{1}\\)^{2}+(x_{2}\\-x_{1}\\)^{2} }[/tex]

Calculating the length between D (3,-9) and E (9,-5):

[tex]length(A)=\sqrt{(-9-(-5))^{2}+(3-9)^{2} } \\length(A)=2\sqrt{13}[/tex]

Calculating the length between F (6,-2) and E (9,-5):

[tex]length(B)=\sqrt{(-2-(-5))^{2}+(6-9)^{2} }\\length(B)=3\sqrt{2}[/tex]

Calculating the length between D (3,-9) and F (6,-2):

[tex]length(C)=\sqrt{(-9-(-2))^{2}+(3-6)^{2} }\\length(C)=\sqrt{58}[/tex]

Now, we can find the semi-perimeter with the formula:

[tex]s=\frac{A+B+C}{2}[/tex]

where A, B and C are the lengths

The semi-perimeter is:

[tex]s=\frac{2\sqrt{13}+3\sqrt{2}+\sqrt{58} }{2}\\s=9.534758... (store \, the \, full \, value \, in \, your \, calculator)[/tex]

The formula for the area of the triangle:

[tex]A=\sqrt{s(s-A)(s-B)(s-C)}\\A=\sqrt{9.534758...(9.534758...-2\sqrt{3})(9.534758...-3\sqrt{2})(9.534758...-\sqrt{58} ) }\\A=15[/tex]

The correct statement about the ordered pair (-4,0) and the system of equations is given as follows:

The ordered pair (-4,0) is a solution to the system because it makes both equations true.

The system of equations for this problem is defined as follows:

The ordered pair (-4,0) means that when x = -4, y = 0.

Hence we verify if the first equation is satisfied, as follows:

2(-4) + 0 = -8

-8 = -8 -> Satisfied.

For the second equation, we have that:

-4 - 0 = -4

-4 = -4 -> Satisfied.

As both equations are satisfied, the ordered pair is a solution for the system of equations.

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The solution of the system of equations by adding method is equal to :

option A. Solution is ordered pair (x ,y) = ( 2.00 , 20.3 ) representing decimal rounded to one decimal place.

System of equations are :

0.9x +0.7y  = 16  ___(1)

-0.3x - 3.5y = - 71.6 ___(2)

To get the solution of the system of equations are:

Multiply (2) by 3 and add it to (1)

0.9x  +0.7y  = 16

-0.9x - 10.5y = -214.8

0x - 9.8y = - 198.8

⇒ y = 20.3

⇒ x = 1.9966

⇒ x = 2.00

Therefore, the value of (x, y ) in the system of equations is given by :

option A. Type of solution is written as ordered pair (x ,y) = ( 2.00 , 20.3 ) having decimal rounded to one decimal place.

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The equation of the straight line would be -

y = 2x.

Given is that a straight line passes through the points (2, 4) and (3, 6).

Refer to the graph of the function attached. We can see that the function that represents the graph is -

[tex]$y=\sqrt[3]{x+6} \;+1[/tex]

Therefore, the function representing the graph is -

[tex]$y=\sqrt[3]{x+6} \;+1[/tex]

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The area of the given polygon will be 10 square units.

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

here, we have,

In other meaning, if we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.

Given the polygon with vertices

N(-2,1), P(3, 1),\ Q(3,-1), R(-2,-1)

If we draw the points in coordinate then it will become a rectangle with side lengths 5 and 2.

Area of rectangle = length × width

Area of rectangle = 5 × 2 = 10 square units.

Hence "The area of the given polygon will be 10 square units".

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The area of the resulting two-dimensional cross-section is 480 inch².

The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.

Given:

The Resulting Cross section will Have the Size

= 20 inch by 14 inch

So, Area of two dimensional Cross section

=  20 x 14

= 240 inch²

As prism is Sliced so this cross section will on the face of two prism.

Then, the Total cross section area

= 2 x 240

= 480 inch²

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The total number of juice bottles is given by the equation J = 3400 bottles

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as a : b : c

Now , the ratio of mango juices to tomato juice to passion fruit be 4 : 4 : 3

The total number of mango juice = 4x

The total number of tomato juice = 4x

The total number of passion fruit juice = 3x

The total number of passion fruit juice = 1020

Substituting the values in the equation , we get

3x = 1020

Divide by 3 on both sides of the equation , we get

x = 340 bottles

Now , the total number of bottles = 4x + 3x + 3x = 10x bottles

So , substituting the value of x in the equation , we get

The total number of juice bottles = 340 ( 10 ) = 3400 bottles

Hence , the proportion is 40 : 40 : 30

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Answer:

.534

Step-by-step explanation:

add, then convert meters to kilometers

Ratio of false positives to true positives is 1/7 .

In statistics, when performing multiple comparisons, the false positive rate is the probability of incorrectly rejecting the null hypothesis for a particular test.

Given In the table,

Number of patient test positive, but not have diabetes = 5%

Number of false positives = 5%

Number of patient test positive, and have diabetes = 35%

Number of true positive = 35%

Ratio of false positives to true positives

= 5%/35%

= 1/7

Hence, 1/7 is the ratio of false positives to true positives.

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The vertex form of the equation is,

⇒ y = (d - 4)² - 26

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The equation is,

⇒ y = d² - 8d - 10

Now, We can change in vertex form as;

⇒ y = d² - 8d - 10

⇒ y = d² - 8d + 16 - 16 - 10

⇒ y = (d - 4)² - 16 - 10

⇒ y = (d - 4)² - 26

Thus, The vertex form of the equation is,

⇒ y = (d - 4)² - 26

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Despite its age, the 15 puzzle remains a popular game today, and it has been adapted into many different variations, including digital versions and physical puzzles with different grid sizes and configurations.

15 puzzle is a sliding puzzle game with numbered squares arranged in 4x4 grid with one tile missing. the puzzle is solved when the numbers are arranged in order. the actions are defined in terms of direction where empty square can be moved to up (u), down(d), left(l), right(r)

The 15 puzzle is a classic sliding puzzle game that has been popular for over a century. The game was invented in the late 1800s by Noyes Chapman, and it quickly became a favorite pastime of people all over the world. The puzzle is sometimes called the "Gem Puzzle" or the "Boss Puzzle," and it has also been used as a tool for studying permutation groups and artificial intelligence algorithms.

Solving the 15 puzzle requires a combination of strategy, planning, and spatial reasoning. While the game is relatively simple to learn, it can be quite challenging to master, especially if you're trying to solve it in the minimum number of moves. In fact, there are over 1 trillion possible configurations of the 15 puzzle, and only a fraction of those can actually be solved.

Despite its age, the 15 puzzle is still widely played today. It has been transformed into a variety of games, including digital and physical puzzles with various grid sizes and arrangements.

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The region bounded by[tex]x=3√3y,x=0,y=5[/tex] is rotated about the y-axis to form a solid. The volume of this solid is V. The region, the solid and a typical disk or washer can be sketched using the given curves.

To calculate the volume V of the solid obtained by rotating the region bounded by [tex]x=3√3y,x=0,y=5[/tex]about the y-axis, we will use the equation [tex]V=π∫a b[(R)^2-(r)^2]dy,[/tex] where R is the outer radius, r is the inner radius, a is the lower limit of the integral and b is the upper limit of the integral. Substituting the given values, we get

[tex]V=π∫0 5[(3√3y)^2-(0)^2]dy[/tex]

This simplifies to [tex]V=π∫0 5[9y^2]dy.[/tex] Integrating this expression, we get [tex]V=π(5^3-0^3)[/tex]. Substituting the limits, we get [tex]V=π(5^3-0^3)[/tex]. This simplifies to V=125π. Hence, the volume of the solid is 125π.

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Answer:

3 over 18 puppies per litter

Step-by-step explanation:

usually, you want to go with the smaller number first, it's like a fraction.

The probability of having i children, i = 1,2,3,4,5 is 0.2, 0.4, 0.25, 0.1, 0.05 respectively. The probability that a randomly chosen child comes from a family with i children are 0.0741, 0,2963, 0.2773, 0.1481, 0.0926.

The probability that a randomly chosen family has i children is given by the ratio of the number of families with i children to the total number of families. Therefore:

P(1 child) = 4/20 = 0.2

P(2 children) = 8/20 = 0.4

P(3 children) = 5/20 = 0.25

P(4 children) = 2/20 = 0.1

P(5 children) = 1/20 = 0.05

(b) To calculate the probability that a randomly chosen child comes from a family with i children, we need to take into account the different numbers of children in each family. There are a total of 4+8x2+5x3+2x4+1x5=54 children in the community organization. Therefore, the probabilities are:

P(child from 1-child family) = 4/54 ≈ 0.0741

P(child from 2-child family) = 2x8/54 ≈ 0.2963

P(child from 3-child family) = 3x5/54 ≈ 0.2778

P(child from 4-child family) = 4x2/54 ≈ 0.1481

P(child from 5-child family) = 5/54 ≈ 0.0926

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____The given question is incomplete, the complete question is given below:

A small community organization consists of 20 families, of which 4 have one child, 8 have two children, 5 have three children,2 have four children, and 1 has five children.

(a) If one of these families is chosen at random, what is the probability it has i children, i = 1,2,3,4,5?

(b) If one of the children is randomly chosen, what is the probability this child comes from a family having i children, i =1,2,3,4,5?

Answer:

There are 3.28542 months in 100 days.

Step-by-step explanation:

For every 100 days, there are approximately 3.28542 months. To solve for any given number of days, divide the time value by 30.417.

For example, to solve for 200 days:

Therefore, 100 days make approximately 3.28542 months.

Answer:

Step-by-step explanation:

Value in months = value in days × 0.0328542

Value in months = 100 × 0.0328542 = 3.28542 (months)

The average normal stress in the links connecting:

(a) points B and D is:

|σ_max| = 13.7 MPa

(b) points C and E is:

|σ_max| = 13.0 MPa

To determine the maximum value of the average normal stress in the links connecting points B and D, we need to calculate the bending moment and the axial force in the link. Assuming the links are in pure bending, we can use the bending stress formula to calculate the maximum normal stress:

σ_max = Mc / I

where M is the bending moment, c is the distance from the neutral axis to the outer fiber, and I is the moment of inertia of the cross-sectional area.

The bending moment in the link BD can be calculated as the sum of the moments due to the applied loads and the reactions at the pins. The axial force can be calculated as the sum of the forces in the link due to the applied loads.

M = 4kN * 80mm - 8kN * 120mm = -640 Nm

F = 4kN - 8kN = -4kN

        I = bh³ / 12

        I = (8mm) * (36mm)³ / 12 = 186624 mm⁴

       σ_max = (-640 Nm) * (4mm) / 186624 mm⁴ = -13.7 MPa

        |σ_max| = 13.7 MPa

       M = 4kN * 40mm + 8kN * 80mm = 800 Nm

        F = 4kN + 8kN = 12kN

I = bh³ / 12 = (36mm) * (8mm)³ / 12 = 24576 mm⁴

       σ_max = (800 Nm) * (4mm) / 24576 mm⁴ = 13.0 MPa

       |σ_max| = 13.0 MPa

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By using the unitary method, 28 students in the school band play woodwind instruments.

Unitary method, which involves finding the value of a single unit and then using that value to find the value of multiple units. In this case, the single unit represents the percentage of students who play woodwind instruments.

Here we need to find the value of a single unit

To find the value of a single unit, we need to divide the given percentage by 100. So, 35% can be written as 0.35.

Therefore, the value of a single unit is 0.35.

Now use the unitary method to find the number of students who play woodwind instruments

Now, we can use the value of a single unit to find the number of students who play woodwind instruments. To do this, we multiply the value of a single unit by the total number of students in the band.

So, the number of students who play woodwind instruments is:

0.35 x 80 = 28

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The function (f+g)(-1) is equal to 3.

We can evaluate (f+g)(-1) by first finding f(-1) and g(-1), and then adding them together.

To find f(-1), we substitute -1 for x in the expression for f(x):

f(-1) = 5(-1)^2 + 7 = 5 + 7 = 12

To find g(-1), we substitute -1 for x in the expression for g(x):

g(-1) = 3(-1) - 6 = -3 - 6 = -9

Now we can add f(-1) and g(-1) together:

(f+g)(-1) = f(-1) + g(-1) = 12 + (-9) = 3

Therefore, (f+g)(-1) is equal to 3.

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The function which represents the value of the car is [tex]y = 11000(0.85)^x[/tex].

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

From the table, we can conclude the function of the car as:-

[tex]y = 11000(0.85)^x[/tex]

At x = 0, the value of y is,

[tex]y = 11000(0.85)^0[/tex].

y = 11000

At x = 1 the value of y is,

[tex]y = 11000(0.85)^1[/tex]

y = 11000 x 0.85

y = 9350

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First we multiply 9 and 15, which is 135cm. 100cm = 1m so the plant will grow 1.35m, so the plant is now 9.35m

Answer:

The number in standard form is 304.014.

Answer:

The Standard form of the number is 44,410.

What is Multiplication?

To multiply means to add a number to itself a particular number of times.

 Multiplication can be viewed as a process of repeated addition.

Here, given number(3 X 100) + (1 X 110) + (4 X 11000)(300) + (110) + (44000)300 + 110 + 44000410 + 4400044410

Thus, the Standard form of the number is 44,410.