The figure, polygon ABCD is dilated by a factor of 2 to produce A B C D with the origin as the center of dilation

[1] 0.25, 0.25%, or [tex]\frac{1}{4}[/tex]

     We will divide the number of wanted outcomes by possible outcomes.

[tex]\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{5}{3+5+12} =\frac{5}{20} =\frac{1}{4}[/tex]

[2]

     We will follow the same steps as problem 1.

MTHMTCS = 7 consonants

AEAI = 4  vowels

MTHEMTICS = 9 letters that are not A's

MATHEMATICS = total of 11 letters

(a)

[tex]\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{7}{11}[/tex]

(b)

[tex]\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{4}{11}[/tex]

(c)

[tex]\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{9}{11}[/tex]

[3] 0.877

     If the probability that a television is defective is 0.123, then the probability that a television is not defective is:

1 - 0.123 = 0.877

Answer:

1.  25%

2 and 3:  See below.

Step-by-step explanation:

1.  There are 4 letters in the box, all different.  The odds of randomly picking 1 letter is 1/4, or 25%  That is true for any of the letters.

Questions 2 and 3 technically cannot be answered.  In both cases, the selection process involves more than random chance.  The selection of a nurse depends on qualifications such as training and experience.  Winning the math quiz depends on knowledge and practice.  Neither question is a random selection.

If the questions were random, the answers would be:

2.  1/5 or 20% that Eunice gets picked, and

2.  6/10 or 60% that a girl wins

Answer:

  HA congruence postulate

Step-by-step explanation:

In order to show W is equidistant from A and Z, we must demonstrate that WA ≅ WZ. The HA congruence postulate can be used for that purpose.

__

WX bisects AXZ, so ∠WXA≅∠WXZ by the definition of an angle bisector. By the reflexive property of congruence, WX≅WX. The angles at A and Z are given as right angles.

So, we have triangles WAX and WZX that are right triangles with congruent hypotenuse and corresponding angle. These are the preconditions for the application of the HA congruence postulate. That postulate says the triangles WAX and WZX are congruent, so ...

WA ≅ WZ by CPCTC. Hence W is equidistant from the outside rays.

__

Additional comment

The definition of distance from a point to a line is the perpendicular distance from the point to the line. In this geometry, the perpendicular distances from W to the outside rays are the lengths of segments WA and WZ. That is why we need to show those lengths are the same.

Answer: 1.601 × 10^-1

Step-by-step explanation: 1 minute = 60 seconds or 1 second = 1/60 minutes

9.63 seconds = 9.63/60 minutes

9.63/60 = 963/6x1000 = 321/2x1000

=160.1/1000=1.601/10 = 1.601 x 10^-1 minutes :)

The x-intercept of the function [tex]h(x) = 3 * \sqrt[3]{x - 5} +6[/tex] is -3

The function is given as:

[tex]h(x) = 3 * \sqrt[3]{x - 5} +6[/tex]

The x-intercept is when h(x) =0.

So, we have:

[tex]3 * \sqrt[3]{x - 5} +6 = 0[/tex]

Subtract 6 from both sides

[tex]3 * \sqrt[3]{x - 5} = -6[/tex]

Divide both sides by 3

[tex]\sqrt[3]{x - 5} = -2[/tex]

Take the cube of both sides

x - 5 = -8

Add 5 to both sides

x = -3

Hence, the x-intercept of the function is -3

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Answer:

Step-by-step explanation:

^^

Answer:

Step-by-step explanation:

Let the length of shorter sides be x and longer sides be y.

Then we have the system:

Solve it by substitution:

Find the value of y:

Shorter one be x

longer one=x+8

So

Time required for longer side

Answer:

Step-by-step explanation:

It looks like the best option is 3.

Given the equation,

we can make a table. x as input and y as output to get our points to the graph.

I have used the desmos graph as a reference to confirm the equation by graphing also. The table is also there.

Answer: It should look something like this.

Step-by-step explanation:

The graph of f(x) = (x + 3)(x - 2) is a parabolic function that is the product of two linear factors, (x + 3) and (x - 2).

The graph is given below.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

To understand the graph, we can begin by considering the x-intercepts, which are the points where the graph crosses the x-axis.

These occur where the value of f(x) is zero, which happens when either

x + 3 = 0 or x - 2 = 0.

So the x-intercepts are x = -3 and x = 2.

Next, we can consider the leading coefficient, which is 1 in this case.

Since the leading coefficient is positive, the parabola opens upward.

We can also find the vertex of the parabola by completing the square.

We have:

f(x) = x² + x(-2 + 3) - 2(-3)

f(x) = x² + x + 6

Now we can rewrite this in vertex form:

f(x) = (x + 1/2)² + 23/4

So the vertex is (-1/2, 23/4), which is a minimum point on the graph.

Thus,

We can sketch the graph of f(x) = (x + 3)(x - 2) as an upward-opening parabola that crosses the x-axis at -3 and 2 and has a minimum point at (-1/2, 23/4).

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Answer:

You are to write a five paragraph literary essay based on one of the 4 prompts and what you have read and learned in this module. These are your options:

1. How do the events of "The White Umbrella" teach the narrator a lesson about shame and acceptance?

2. What role does creativity play in "The Bat-Poet"?

3. How does the character of Squeaky change over the course of "Raymond's Run"?

4. Discuss the influences of older family members on the protagonists and speakers in the stories and poems of this unit.

You are to write a five paragraph literary essay based on what you have read and learned in this module. Your final submission should meet the following requirements.

• Submit completed pre-writing and outline documents.

• Write an essay that contains an introduction with hook and thesis statement, supporting paragraphs with evidence and at least one quotation, and a conclusion that restates the thesis and reviews main points.

• Use transitions appropriate to the pattern of organization.

• Use vocabulary to create tone and voice.

• Cite primary source (quotation).

• Submit completed revision checklist.

• Vary sentence structure.

• Create sentences with parallel structures.

• Use technology in the writing process.

Step-by-step explanation:

Expand the square. Remember that

(a - b)² = a² - 2ab + b²

With a = 5√3 and b = √27, we have

(5√3 - √27)² = (5√3)² - 2 (5√3) √27 + (√27)²

… = 25•3 - 10√81 + 27

… = 75 - 10√(9²) + 27

… = 102 - 10•9

… = 102 - 90

… = 12

Answer:

Step-by-step explanation:

A.  20

B. 20 (what is the 30 thing)

C. 28

D. 36

E. 20

F. 96

Answer:

2

Step-by-step explanation:

Congruent shapes are 2 shapes that are ewual in size angles and sides, but they can be rotated or moved around in any way

Answer:

The answer is [tex]\frac{3}{10}[/tex]

Step-by-step explanation:

Answer:

68

Step-by-step explanation:

[tex]4+\left(11-3\right)^2\\(11-3)=8\\=4+8^2\\=4+64\\=68[/tex]

The reason for step 4 that is missing is: definition of linear pair.

A line pair are two angles on a straight line whose sum equals 180 degrees.

Angles ANV and ANR line on a straight line and are therefore linear pair. This implies that:

m∠ANV + m∠ANR = 180 degrees

Therefore, the missing reason is: definition of linear pair.

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Answer:

None of these

Step-by-step explanation:

See attached image

So

Like that

f(2)

f(3)

As you can see

It's an geometric progression

So the formula is

None of the above

Answer:

500(10) + 600(2)

Step-by-step explanation:

Answer:

500(10) + 600(2)

Step-by-step explanatio:

500*10+600*2

 5,000+1,200

        6,200

The statement: "Kiley bought a platter for $ 19 and several matching bowls that were $ 8 each. What is the cost before tax?" shows discrete graph.

A discrete graph is one with scattered points. They may or may not show a direction or trend. They don't have data in between the points already given.

Here only first option shows a graph with scattered point.

Thus, the statement: "Kiley bought a platter for $ 19 and several matching bowls that were $ 8 each. What is the cost before tax?" shows discrete graph.

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Point (3,0) is system solution.

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

We have

y> -2

x + y <4

First inequation:

-5> -2 (incorrect)

Second inequality:

1-5 <4 (correct)

First inequation:

0> -2 (correct)

Second inequality:

0+3 <4 (correct)

First inequation:

-2> -2 (incorrect)

Second inequality:

-1-2 <4 (correct)

First inequation:

5> -2 (correct)

Second inequality:

1+5 <4 (incorrect)

Hence, Point (3,0) is system solution.

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Answer:

(x+1)(x-9)

Step-by-step explanation:

x^2+x-9x-9=0
x*(x+1)-9(x+1)=0
(x+1)(x-9)=0
x+1=0
x-9=0
x=-1 and x=9

An event that may occur in the game is you roll a  and get a tail.

The probability that he will roll a 5 and get a head is 1 / 12.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that he will roll a 5 and get a head = (Number of sides with a 5 / number of sides in a cube) x (number of sides with a head / number of sides in a coin)

1/6 x 1/2 =  1 / 12.

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Answer:

Step-by-step explanation:

[tex]\frac{2x+4}{x(x+2)(x-4)} =\frac{a}{x} +\frac{b}{x+2} +\frac{c}{x-4} \\2x+4=a(x+2)(x-4) +bx(x-4)+cx(x+2)\\[/tex]

put x=0

0+4=a(0+2)(0-4)+0+0

-8a=4

a=-4/8=-1/2

put x+2=0 or x=-2

2(-2)+4=0+b(-2)(-2-4)+0

12b=0

b=0

put x-4=0 or x=4

2(4)+4=0+0+c(4)(4+2)

24c=12

c=12/24=1/2

[tex]\frac{2x+4}{x(x+2)(x-4)} =\frac{-1}{2x} +0+\frac{1}{2(x-4)} \\\frac{2x+4}{x(x+2)(x-4)} =\frac{-1}{2x} +\frac{1}{2(x-4)}[/tex]

Answer:

20° and 30°

Step-by-step explanation:

the sum of the 4 angles in a quadrilateral = 360°

given 2 angles are 200° and 110° , then remaining 2 angles sum to

360° - 200° - 110° = 360° - 310° = 50°

sum the parts of the ratio, 2 + 3 = 5 parts , then

1 part = 50° ÷ 5 = 10° , so

2 parts = 2 × 10° = 20°

3 parts = 3 × 10° = 30°

the two angles are 20° and 30°

Answer:

Step-by-step explanation:

As it is a second order equation, it means that it has two possible answers and they are [tex]x_1[/tex] and [tex]x_2[/tex].

The famous quadratic formula for solving any second order equation is the following:

[tex]x_{1} = \frac{-b + \sqrt{b^2 - 4 ac}}{2a}\\x_{2}=\frac{-b - \sqrt{b^2 - 4 ac}}{2a}[/tex]

Where a is the coefficient of [tex]x^2[/tex], b is the coefficient of x, and c is the free term. In other words,

[tex]a = 3\\b=4\\c=-2[/tex]

as the equation should be in the following form:

[tex]a x^2 + bx+c = 0[/tex]

Therefore the possible answer should be the following,

[tex]\frac{-4 + \sqrt{4^2 - 4*3*(-2)}}{2*3}=\frac{-4 +\sqrt{16 + 24}}{6} =\frac{-4 + \sqrt{40}}{6}=\\ \frac{-4 + \sqrt{4*10}}{6} = \frac{-4 + 2\sqrt{10}}{6}[/tex][tex]\frac{2*(-2 + \sqrt{10})}{2*3} = \frac{-2 + \sqrt{10}}{3}[/tex]

by dividing the numerator and denominator by 2, we can deduce the following,

The percentage of Container A that is full after the pumping is complete is; 45.3%

The formula for volume of a cylinder is;

V = πr²h

Volume of Cylinder A is;

V = π × 12² × 13

V = 1872π

Volume of Cylinder B is;

V = π × 8² × 16

V = 1024π

After pumping, volume in container A will be;

V_new = 1872π - 1024π

V_new = 848π

Percentage is;

848π/1872π * 100% = 45.3%

Thus, 45.3% of Container A is full after the pumping is complete.

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Answer:

A B and C

Step-by-step explanation: