Triangle abc was dilated using the rule do,4. Triangle a'b'c' is the result of the dilation. Point o is the center of dilation. Triangle a b c is dilated to create triangle a prime b prime c prime. The length of o b is three-fourths. What is ob'?.

Serena's company implemented the process of Delayering.

To improve operational efficiency, delayering is the act of removing levels of hierarchy between the top and bottom levels of staff.

Delayering often involves the removal of intermediate managers, giving top managers better access to the business as a whole and fostering the necessary openness.

The delayering process has benefits and drawbacks of its own. Although the employer can lower pay costs, the company's ability to make decisions may suffer as a result of top managers' diminished visibility.  

Delayering is helpful for reducing bureaucracy and increasing flexibility in the organizational structure. Additionally, it enhances internal communication and participation. Other advantages include increased drive and empowerment.

Given that

Serena's company decided to reduce the number of levels within the job structure and as a result, she has 20 more people who report to her. her company implemented.

By the given observation about Delayering, we can conclude that the company implemented the process of Delayering.

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The point F lies on 4.5 in the number line.

What is the number line?

The number line is a One dimensional representation of point referring by a number only.

We know that if a point divides a line joining the points at x, y in the number line respectively in m:n ratio then that point lies on

= (my+nx)/(m+n) in the number line.

Here in the given problem that,

Point D lies on -6 in the number lin

Point E lies on 8 in the number line

And F lies between D and E points and DE:EF = 3:1

So the point F clearly divides the staright line DE joining the point D at -6 and E at 8 in 3:1 ratio.

So the point F lies on = (1*(-6)+3*8)/(3+1) = (-6+24)/4 = 18/4 = 4.5

Hence, the point F lies on 4.5 in the number line.

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Answer:

The answer is A

Step-by-step explanation: I'm so smart

Answer:

x = 9

Step-by-step explanation:

(7x + 7) + 60 = 13x + 13 (exterior angle)

7x + 67 = 13x + 13

6x = 54

x = 9

The expected value of the random variable is 5.37, the variance of the random variable is 0.8531 and the standard deviation of the random variable is 0.9236.

Given that,

The number of days it takes for packages to arrive from an online shop, together with the probability that it will happen, are provided in the table below.

The table is

Number of days           Probability

A-3                                    0.01

B-4                                    0.14

C-5                                    0.46

D-6                                    0.25

E-7                                     0.14

We have to find the expected value of the random variable, the variance of the random variable and the standard deviation of the random variable.

We know that,

The random variable's predicted value is now shown.

Expected value = summation (x ×P(x))

= 3×0.01+4×0.14+5×0.46+6×0.25+7×0.14

= 5.37

Now the variance of the random variable

Variance =summation ((x - mean)² ×P(x))

= (3-5.37)² × 0.01 + (4-5.37)² × 0.14 + (5-5.37)² × 0.46 + (6-5.37)² × 0.25 + (7-5.37)² × 0.14

= 0.8531

The random variable's standard deviation is now available.

σ  = √(0.8531)

= 0.9236

Therefore, the expected value of the random variable is 5.37, the variance of the random variable is 0.8531 and the standard deviation of the random variable is 0.9236.

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Answer: x= 27/5

Step-by-step explanation:

This equation can rewrite as -2/3x + 4 = 2/5

We separate x by subtracting 4 from both sides

-2/3x = -20/5 +2/5

-2/3x = -18/5

Then we divided both sides by -2/3

Ad we will get x= 27/5

The two true statements about these are,

The volume of both the tennis ball and squash ball is proportionate to the

the scale factor of the radii.

The scale factor of the volume of the tennis ball to the volume of the

squash ball is approximately 8.

In geometry, a sphere is a three-dimensional solid figure, which is round in shape.

The surface area is 4πr².

The volume is (4/3)πr³.

The diameter is 2×radius of the sphere.

Given, A tennis ball is a sphere with a radius of 1.56 inches. A squash ball is also a sphere with a radius of 0.78 inches.

So, The volume of the tennis ball is (4/3)π(1.56)³ = 16 cubic inches.

The volume of the squash ball is (4/3)π(0.78)³ = 2 cubic inches.

The volume of both the tennis ball and squash ball is proportionate to the

the scale factor of the radii.

The scale factor of the volume of the tennis ball to the volume of the

squash ball is approximately 8.

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Answer:

the answer is no

Step-by-step explanation:

Answer:75

Step-by-step explanation:

Since the total angle in the rhombus adds to 360, we minus the 2 110 and get 140. The 65 degrees is reflected on the other side, so we subtract 65 from 140, leaving 75.

The value of [y] will be 1.

Given is the following expression -

y = 2 x (2/4)

We can write the value of [y] as -

y = 4/4 = 1

y = 1

Therefore, the value of [y] will be 1.

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The total number of people at the stadium was 6800 people .

A Percent in mathematics is defined as a number or ratio that is expressed as a fraction of 100 , it is denoted by sign "%" .

For Example : 2% is = 2/100   .

In the question ,

it is given that ,

percent of teenagers fans in the stadium is = 5%

number of teenagers present at the football stadium is = 340

which means 5% represents 340 people ,

So , 1% will be 340/5 = 68 people .

the total percent of people present in the stadium is = 100% ,

multiplying both sides by 100 ,

we get ,

So , 100%  = 68 × 100 = 6800 people

Therefore , The total attendance at the football stadium was 6800 people .

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Answer: $7

Step-by-step explanation:

We know that $28 for four people.

So we take 28 divided by 4 and we get $7 per people

The tax on a car that sells for $16,500 at the rate of  6.7%  is $195.5 higher.

What is the percentage?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

We have,

First car price is  =  $13,500

and tax of the first car is = $910

Second car price is  =  $16,500

and tax of the second car is = ?

so,

 $13,500 -----    100,

  $910      -----    x

x = 910 * 100 / 13500

x =  6.7

therefore, the rate of tax is 6.7%

so, we will calculate the tax for the second car,

$16,500 -----    100,

    y        -----    6.7

y = 6.7 * 16,500 / 100

y = $1105.5

difference of tax price between two cars = $1105.5 - $910 = $195.5

Hence, the tax on a car that sells for $16,500 at the rate of  6.7%  is $195.5 higher.

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The equation -7(8x + 5) = 5x+10 has one solution of x which satisfies the equation. The solution is x = -45/61.

What is solution of system of equation?

A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously. In order to solve a system of equations, one must find all the sets of values of the variables that constitutes solutions of the system.

According to the given question:

Given equations is -7(8x + 5) = 5x+10

Simplifying both sides to get value of x

-7(8x + 5) = 5x+10

-56x - 35 = 5x + 10

-61x = 45

x = -45/61

Therefore x has one solution which is -45/61

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The values that make the inequality, h < 3h < 3, true are the values of h in the range 0 < h < 1. The values -5, -2, 0, 2, 2.9, 2.99, 2.999, 3, 3.001, 3.01, 3.1, 4, 6, 8, 11, are larger or smaller than the values make the inequality true.

An is a comparison between two expressions, using non equal expressions, such as ≥, >, ≠,  <, or ≤ symbols.

The specified inequality is; h < 3·h < 3

When h < 3·h, we get;

h is a positive number larger than 0, such that we get;

When h < 0, 3·h < h

Therefore; h > 0

The inequality, 3·h < 3, indicates;

3·h < 3

h < 3/3 = 1

h < 1

Which indicates that we get;

0 < h < 1

Therefore, non of the values make the inequality, h < 3·h < 3

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Answer:

Step-by-step explanation:

4,505 tickets were sold 219 times.

4,505 x 219

The answer is 986,595

4300 workers are there in all.

What is algebra?

One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for using these symbols in formulas.

Here, we have

In a company, 90% of the workers are women.

430 people work for the company who aren’t women.

% of male = 10%

Now,

10% of x = 430

10÷100 × x = 430

x = 4300

Hence, 4300 workers are there in all.

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The measure of angle RPT is 122° if the measure of an angle RST is 64°.

In Euclidean geometry, an angle is the figure formed by two rays, known as the sides of the angle, that have a common termination, known as the vertex of the angle. These are referred to as dihedral angles. An angle can also be defined by two intersecting curves, which is the angle of the rays lying tangent to the respective curves at their point of intersection.

Angle can also refer to a rotation or the measurement of an angle. This measurement is the ratio of the length of a circular arc to its radius.

The total of a triangle's angle measurements is 180°. Because ∠RST = 64°, the other two angles must equal to  180-64 = 116°.

The diagram shows that RST is an isosceles triangle. This suggests that the basis angles, SRT and STR, are equivalent, with each equaling 116/2 = 58°.

RP will cut RST, and PT will cut STR.

PTR = 58/2 = 29° and PRT = 58/2 = 29°.

This suggests that the base angles are 29+29 = 58°, leaving RPT at 180-58 = 122°.

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The correct option which represents  sum expressed in sigma notation is A.

What is sigma notation?

A series is represented in an exceedingly compact type, referred to as summation or sigma notation. The greek capital letter, ∑ , is employed to represent the total.

The series 4+8+12+16+20+24 is expressed as ∑n= 4n . The expression is browse because the total of 4n as n goes from one to six . The variable n is termed the index of summation.

The geometric series.

Main body:

∑ 125 (1/5)ⁿ⁻¹ ; where, n = 1 to 4.

Now, Calculate the partial sum of the geometric series as;

The geometric series = ∑ 125 (1/5)ⁿ⁻¹

Substitute n = 1, 2, 3, 4, we get;

= 125 (1/5)¹⁻¹ + 125 (1/5)²⁻¹ + 125 (1/5)³⁻¹ + 125 (1/5)⁴⁻¹

= 125 (1/5)⁰ + 125 (1/5)¹ + 125 (1/5)² + 125 (1/5)³

= 125 + 25 + 125/25 + 125/125

= 125 + 25 + 5 + 1

Thus, The partial sum of the geometric series is;

⇒ 125 + 25 + 5 + 1

Option A is true.

The correct question is in the figure.

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The sum of decimals 4.2 and 466.99​ evaluates to 471.19

Decimals are numbers that consist of two parts namely, a whole number part and a fractional part separated by a decimal point e.g 2.35

Given:  4.2 and 466.99​

To evaluate the sum of 4.2 and 466.99​, you simply need to add the two numbers. Arrange the numbers as shown below and add as you would add other numbers.

    4.2

466.99

.................

  471.19

................

Therefore, the sum 4.2 and 466.99​ is  471.19

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Answer:

2

Step-by-step explanation:

The y-intercept is the point at which the graph crosses the y-axis.

(I have marked it in blue on the attached graph).

From inspection of the given graph, the line crosses the y-axis at point (0, 2). So the y-intercept is 2.

Answer:

200*1-0.95-0.95+0.9025

200*1-1.9+0.9025

200*0.0025

0.5

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The expressions that are simplified are:

[tex]n^{4}[/tex]

[tex]\frac{1}{n^{-5}}[/tex]

[tex]\frac{1}{n^3}[/tex]

Options A, B, and E are the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

[tex]n^{4}[/tex]

This is already simplified.

[tex]\frac{1}{n^{-5}}[/tex]

This is already simplified.

[tex]n^6 . n^{-8}[/tex]

= [tex]n^{6 - 8}[/tex]

= [tex]n^{-2}[/tex]

[tex]n^7 . p^8[/tex]

= [tex]n^{7 + 8}[/tex]

= [tex]n^{15}[/tex]

[tex]\frac{1}{n^3}[/tex]

This is already in simplified form.

Thus,

The expressions that are simplified are:

[tex]n^{4}[/tex]

[tex]\frac{1}{n^{-5}}[/tex]

[tex]\frac{1}{n^3}[/tex]

Options A, B, and E are the correct answer.

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The expression which is equivalent to the given expression as in the task content by virtue of the laws of indices is; ( 3 )^2n.

It follows from the task content that the expression which is equivalent to the given expression is to be determined.

Since the given expression is;

( 3^4n ) ^(1/2)

However, it follows from the power of power law of indices that the expression above can be written as follows;

( 3 ) ^ (4n × 1/2)

= ( 3 )^2n

Therefore, the required equivalent expression is; ( 3 )^2n.

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The best treatment for this patient's acute blood pressure control is to administer an intravenous (IV) antihypertensive medication such as labetalol or nitroprusside. Additionally, it is important to assess for underlying causes of her elevated blood pressure such as infection, kidney disease, or heart failure.

What is blood pressure?
Blood pressure (BP) is indeed the force exerted by moving blood against blood vessel walls. The heart's action of trying to pump blood through the blood vessels is largely responsible for this pressure. The pressure in the major arteries is meant when the term "blood pressure" is used without qualification. Systolic pressure, or the highest pressure during one heartbeat, is typically expressed as the ratio of diastolic pressure, or the lowest pressure between two heartbeats, in blood pressure measurements. It is expressed as a millimetre of mercury (mmHg) just above atmospheric pressure in the immediate vicinity. Along with respiratory rate, pulse rate, oxygen levels, and body temperature, blood pressure is among the vital signs that medical professionals consider when assessing a patient's health.

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The Trigonometric ratios are:

P/H = Sinθ

B/H = Cosθ

P/B = Tanθ

H/P = Cosecθ

H/B = Secθ

B/P = Cotθ

Where,

'P' represents the perpendicular

'B' represents the base

'H' = represents the hypotenuse

P/H = Sinθ

B/H = Cosθ

P/B = Tanθ

A. As the values of p, b or h are not given.

Pythagoras Theorem states that:

h² = p² + b² or h = [tex]\sqrt{p^2 + b^2}[/tex]

Altitude of a triangle is usually given by the perpendicular,

So,

h² = p² + b²

h² - b² = p²

p² = h² - b²

p  = [tex]\sqrt{h^2 - b^2}[/tex]

B. The trigonometric ratios for θ = 60°

Sin 60 = √3/2

Cos 60 = 1/2

Tan 60 = √3

C. The trigonometric ratios for θ = 30°

Sin 30 = 1/2

Cos 30 = √3/2

Tan 30 = 1/√3

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T|=|S|⟹ there is bijection F:S→T.

A bijection is a function between the elements of two sets in mathematics that is also referred to as a one-to-one correspondence, an invertible function, or a bijective function.

In this function, each element of one set is paired with exactly one element of the other set, and each element of the second set is paired with exactly one element of the first set.

No elements are left unpaired. A one-to-one (injective) and onto (surjective) mapping of a set X to a set Y is known as a bijective function, or f: X Y in mathematics.

One-to-one function (an injective function; a bijection from the set X to the set Y has an inverse function from Y to X) should not be confused with one-to-one correspondence. X and Y must be finite if.

According to our question-

The function f:ST |S||T| has an injective and not a surjective nature.

Assume an injective function exists: g:TS|T||S|. |T|=|S|

(this follow from the Cantor-Bernstein theorem).

|T|=|S|⟹ F:S:T has a bijection.

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Main answer: mean = 23

supporting answer: Agraphical representation of a normal distribution is sometimes called a bell curve because of its flared shape. The precise shape can vary according to the distribution of the population but the peak is always in the middle and the curve is always symmetrical. In a normal distribution, the mean, mode and median are all the same.

body of the answer: given total number of samples=15

 percentage of failure stain=25 percent=0.25

 standard deviation=3.5

a. formula used=z=x- mean/standard deviation

p(0.25<x<0)

z=25-mean  /3.5

0.6*3.5=25-mean

mean=25-0.6*3.5

           =22.9

since A(0.25)=0.6

b. for 15 adults the mean is 23

for one adult =23/15

                     =1.533

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The mean for the given statistic problem is 23.

The strain for a single adult in a way that conveys information about precision and reliability is 1.533.

What is normal distribution?

A graphical representation of a normal distribution is sometimes called a bell curve because of its flared shape. The precise shape can vary according to the distribution of the population but the peak is always in the middle and the curve is always symmetrical. In a normal distribution, the mean, mode and median are all the same.

Given total number of samples=15

percentage of failure stain=25 percent=0.25

standard deviation=3.5

a. formula used=z=x- mean/standard deviation

p(0.25<x<0)

z=25-mean  /3.5

0.6*3.5=25-mean

mean=25-0.6*3.5

          =22.9

since A(0.25)=0.6

b. For 15 adults the mean is 23

For one adult =23/15

                    =1.533

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At the end of the sale, there were a total of 196 customers in the store for the given function.

The earliest known attempt to the notion of function may be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were initially the idealization of how a variable quantity depended on another quantity.

The total number of shoppers in the store is the number of shoppers present at the start of the sale Plus the number of shoppers who entered the store minus the number of shoppers who left.

Given that there were no shoppers in the store before the sale began, the number of shoppers in the store at the start of the sale is 0.

It is assumed that the number of customers who have entered the store is represented by S(t)=0.5t⁴-16t³+144t².

So, at t=12, the number of shoppers in the store is S(12)=

0.5(12)⁴-16(12)³+144(12)²

S(12)=3456 shoppers.

L(t)= -80+(4400/t²-14t+55)

At t=12,

[tex]\int\limits^{12}_0 {L(t)} \, dt[/tex]=[tex]\int\limits^{12}_0[/tex]( -80+(4400/t²-14t+55))dt

At the end of the sale, there were a total of 196 customers in the store.

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a) T( K₁A₁+K₂A₂)= K₁T(A₁)+K₂T(A₂). So, T is a linear transformation.

b) T(A)=B, if B be any element of M₂

c) Range of T=={A∈ [tex]M_{ 2*2}[/tex]/[tex]A^{T}[/tex]=-A}

A matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions arranged in rows and columns that is used to represent a mathematical object or an attribute of such an item.

A square matrix's determinant is a number connected with the matrix that is crucial for studying a square matrix; for example, a square matrix is invertible if and only if it has a nonzero determinant, and a square matrix's eigenvalues are the roots of a polynomial determinant.

Define T: [tex]M_{ 2*2}[/tex] ⇒ [tex]M_{ 2*2}[/tex] by T(A)=A+[tex]A^{T}[/tex]

a) Let T is a linear transformation

Consider K₁A₁+K₂A₂ ∈  [tex]M_{ 2*2}[/tex]

T( K₁A₁+K₂A₂)= K₁A₁+K₂A₂+( K₁A₁+K₂A₂)[tex]( K₁A₁+K₂A₂)^{T}[/tex]

= K₁T(A₁)+K₂T(A₂)

T( K₁A₁+K₂A₂)= K₁T(A₁)+K₂T(A₂)

Therefore, T is a linear transformation.

b) Let B∈ [tex]M_{ 2*2}[/tex] such that [tex]B^{T}[/tex]=B

Therefore, B is a symmetric matrix.

Let A=(1/2)B∈ [tex]M_{ 2*2}[/tex]

T(A)=A+[tex]A^{T}[/tex]

=(1/2)B+[tex](1/2B)^{T}[/tex]

T(A)=B

A=(1/2)B such that T(A)=B

c) Range of T is the set of B in  [tex]M_{ 2*2}[/tex], [tex]B^{T}[/tex]=B

T( [tex]M_{ 2*2}[/tex])={B∈ [tex]M_{ 2*2}[/tex]/ [tex]B^{T}[/tex]=B}

d) Kernel of T={A∈ [tex]M_{ 2*2}[/tex]/T(A)=0)

={A∈ [tex]M_{ 2*2}[/tex]/A+[tex]A^{T}[/tex]=0}

={A∈ [tex]M_{ 2*2}[/tex]/[tex]A^{T}[/tex]=-A}

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Three points Assuming M22 is the vector space containing all 22 matrices, T: M22 M22 is defined as T(A) = A + AT.

T is a linear transformation, therefore demonstrate it.

b) Assume that B is any element from M22 where BT = B. In M22, look for an A such that T(A) = B.

c) Explain the T kernel.

a) Verifying that T preserves sums and multiplication by scalars—which implies that T(0) = 0 in particular—is sufficient to determine if T is linear.

Additions: T(A+B) = A+B+A+B T = A+B+A T +B

T = (A + A T ) + (B + B T ) = T(A) + T (B).

Scalar multiplication

T(c · A) = (c · A)

T = c · A

T = c · T(A) (A).

b) Calculate A = 1 2B. Since AT = 1 2BT = 1 2B, T(A) = A + A.

T = \s1 \s2 \sB + \s1 \s2 \sB = B.

c) If 0 0 0 0 = A + A, then and only if A = a b c d, A is in the kernel of T.

If and only if 2a = b + c = 2d = 0, i.e., a = d = 0 and c = b, then T = a b c d + a c b d = 2a b + c b + c 2d. Therefore, the set ker(T) = 0 b b 0 : b R is the kernel of T.

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