Four friends are sitting at a table together at the prom. What is the probability that a particular one of them will sit in the chair closest to the dance floor?

The postulate of equality or inequality that is illustrated is the transitive postulate of equality

The illustrated expression is given as

If 1/4 + 1/4 = 2/4 and 2/4 = 1/4 then 1/4 + 1/4 = 1/2

In the above expression, we do not have any inequality sign

This means that the expression is an equation i.e. equality

The transitive postulate of equality states that

if a = b and b = c, then a = c

The given equality expression illustrates the transitive postulate of equality

i.e.

If 1/4 + 1/4 = 2/4 and 2/4 = 1/4 then 1/4 + 1/4 = 1/2

if      a = b            and b = c,     then a = c

Hence, the postulate of equality or inequality that is illustrated is the transitive postulate of equality

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Answer:  [tex]\frac{8}{4}[/tex] = 2

Step-by-step explanation:

5 - 3 = 2

2 x 2 x 2 x 2 = 16

24 - 16 = 8

[tex]\frac{8}{4}[/tex]

Simplify

[tex]\frac{8}{4}[/tex] = 2

Molly's earning increased by 25%

Percentage increase formula is

Increase/ original value × 100

The first step is to calculate the increase by subtracting 120 from 160

160 -120

= 40

Therefore the percentage increase can be calculated as follows

= 40/160 × 100

= 0.25 × 100

= 25

Hence Molly's earnings increased by 25%

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A triangle is dilated with the center of dilation at point U. Point E is a vertex of the triangle and point E ’ is the corresponding vertex of the image. If UE = 2 centimeters and UE ’ = 10 centimeters, the scale factor is 5 cm

Scale Factor Definition

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller.

By definition, a Dilation is a transformation in which the image has the same shape as the pre-image but size changes.

The center of dilation is a fixed point in the plane, and the scale factor is the ratio of the corresponding sides of the image to the pre-image.

Scale Factor In Geometry

Scale is used in geometry to make accurate reproductions of figures; they are different sizes, but same proportions. Figures are similar but to scale.

Based on the information provided in the exercise, you know that:

UE = 2 centimeters

UE ’ = 10 centimeters

Therefore, you can determine that the scale factor is:

The scale factor for scaling up is a ratio greater than 1

The scale factor for scaling down is a ratio of less than 1

.

Scale factor :  10/2 = 5

Scale factor = 5 cm

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The center of dilation for a triangle is located at point U. The image's point E' corresponds to point E, which is the vertex of the triangle. The scale factor is 5 cm if UE = 2 centimeters and UE'= 10 centimeters.

Define Scale Factor

The ratio between comparable measurements of an object and a representation of that object is known as a scale factor in mathematics. The copy will be larger if the scaling factor is a whole number. A fractional scaling factor means that the duplicate will be smaller.

A dilation is, by definition, a transformation in which the size of the image changes but the shape remains the same as the pre-image.

The scale factor is the ratio of the corresponding sides of the image to the pre-image, and the center of dilatation is a fixed point in the plane.

Considering Scale in Geometry

In geometry, scale is utilized to create correct figures that have varying sizes but the same proportions. Similar but scaled figures are shown.

You are aware of the following thanks to the material in the exercise:

2 centimeters equals UE.

10 centimeters equals UE'.

Therefore, you can determine that the scale factor is:

The scale factor for scaling up is a ratio greater than 1

The scale factor for scaling down is a ratio of less than 1

Scale factor :  10/2 = 5

Scale factor = 5 cm

The density of the rock is 25g.

1ml=1 cc

If the water rose 7 ml−2ml=5ml then the stone had a volume of 5 ml or 5cc

With a mass of 25 g it must have a density of = 25 g

5 cc= 5 g/cc

Density is the substance's mass per unit of volume. The symbol most often used for density is ρ although the Latin letter D can also be used. For example, a block of the heavier element lead (Pb) will be denser than the softer, lighter element gold (Au).

A block of Styrofoam is less dense than a brick. It is defined as mass per unit volume.

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Answer:

The measure of angle F is 74°.

Step-by-step explanation:

[tex]9x - 38 + 2x + 42 = 180[/tex]

[tex]11x + 4 = 180[/tex]

[tex]11x = 176[/tex]

[tex]x = 16[/tex]

For angle F: 2(16) + 42 = 32 + 42 = 74°

A triangle cannot be both right-angled and obtuse-angled. Because a right-angled triangle has only one right angle, its other two are acute.

The sum of all triangle angles (of all types) equals 180°. The total of the lengths of a triangle's two sides is higher than the length of something like the third side. Similarly, the length of something like the third side is less than the differences between two sides of a triangle.

Triangles are categorized in two ways: thus according to internal angles and based on the side length. There are three sorts of triangles based on internal angles: acute, right, and obtuse-angled triangles. Triangles are categorized into three types based on the length of its sides: Scalene, Isosceles, and Equilateral triangles.

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Look at the expression.

3x  -8y  +2x^2  +3y  -8x

Add up all the x-squareds . . . there are 2 of them

Add up all the Xs . . . 3x - 8x  =  -5x

Add up all the Ys . . .   -8y + 3y  =  -5y

Add up the collection:  2x^2 -5x -5y

Answer:

The next three terms is -2,-4,-6

The probability is 1.38.

Probability is the possibility of an event occurring. We can scale the probability of an event between 0 and 1. 0 refers to an improbable event, and one refers to an event with the highest possibility. The type of probability we will use to solve this problem is the geometric distribution.

The geometric distribution is defined as a discrete probability distribution representing the probability of consecutive failures before success in a Bernoulli trial. There could be only two possible outcomes; either True (1) or False (0).

Bernoulli's trial is an experiment in which we have only two possible outcomes, success or failure. In other words, the geometric distribution repeats Bernoulli trials until it succeeds, then stops. So, achieving success is the ultimate goal and is the point that stops Bernoulli's trials from happening further.

Geometric distribution, the class of probability distributions, is based on three key assumptions, and these assumptions are defined as:

The studies conducted are independent. Each event is independent of the other.

Each attempt has only two outcomes: success or failure. If an event has any other possible output other than 0 and 1, it can not be classified as a Bernoulli trial.

The probability of success, indicated by p, is the same for each trial.

After understanding the concepts stated above now, we will move towards the actual statement of the problem. So, a scenario is given to us that tells us that the variable is from a geometric distribution setting, which means that all of the assumptions for geometric distribution will be applied. The given probability that Anita makes is,

Given = 0.46

So, to find the probability that she will get a hit on her 3rd try, we will add one possibility three times,

p = 0.46 + 0.46 + 0.46

p = 1.38

Or we can also do it like this,

p = 0.46 * 3

p = 1.38

Both ways will provide us with the correct answer.

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Answer: 0 and 1

Step-by-step explanation:

The statement "If ∠ 1 ≅ ∠ 5 , then lines p and q are skew lines" is false because "If ∠ 1 ≅ ∠ 5 , then lines p and q are parallel lines"

Given,

The statement " If ∠ 1 ≅ ∠ 5 , then lines p and q are skew lines"

Here,

Two lines are cut by a transversal.

If ∠ 1 ≅ ∠ 5  we can say that two parallel line cut by transversal and both are corresponding angles

So,  If ∠ 1 ≅ ∠ 5 , then lines p and q are parallel lines

Hence, the statement "If ∠ 1 ≅ ∠ 5 , then lines p and q are skew lines" is false,  because "If ∠ 1 ≅ ∠ 5 , then lines p and q are parallel lines"

The complete question is :

State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.

If ∠ 1 ≅ ∠ 5 , then lines p and q are skew lines.

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Answer:

2$!$! jdnznwi bdbejsn uebeij737 y

The equation in slope intercept form is y = -4 / 5 x - 8  / 5

The slope intercept equation can be represented as follows:

y = mx + b

where

Therefore, using (-2, 0)(3, -4) let's find the slope

m = -4 - 0 / 3 - (-2)

m = - 4 / 3 + 2

m = - 4 / 5

Hence, the y = mx + b can be defined as follows:

let's find b, the y-intercept using (-2, 0)

y = -4 / 5 x + b

0 = - 4 / 5(-2) + b

0 = 8 / 5 + b

b = - 8 / 5

Therefore, the equation in slope intercept form is y = -4 / 5 x - 8  / 5

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Answer:

f^-1 (x)= ^3√(x-5)

Step-by-step explanation:

the inverse of this function would be ^3 and x-5 inside the radical

Answer:

9

Step-by-step explanation:

-2- -9 - -2

this means

-2-(-9)-(-2)

then - times - is equal to +so...

-2+9+2

-2+11

9

the final answer is 9

The equation of point slope form of (1,10) and (5,42) is -2.7x + y - 3 = 0.

A straight line is represented using its slope and a point on the line using point slope form. In other words, the point slope form is used to determine the equation of a line whose slope is "m" and passes through the point (x1, y1).

given that

the coordinates points are (0,3) and (3,11)

(x1,y1) = (0,3)

(x2, y2) = (3,11)

The formula of point-slope is

(y - y1) = m(x - x1)

Here,

x1 = 0 and y1 = 3 but we don't know the value of m.

now,find the value of m using the following formula

[tex]m = \frac{(y2 - y1)}{(x2 - x1)}[/tex]

now, substitute the values, we get

[tex]m = \frac{(11 - 3)}{(3 - 0)}[/tex]

[tex]m = \frac{8}{3}[/tex]

m = 2.7

so, the value of m is 2.7.

substitute these values into the point-slope formula

(y - 3) = 2.7(x - 0)

y - 3 = 2.7x - 0

-2.7x + y - 3 = 0

Hence, the equation of point slope form of (1,10) and (5,42) is -2.7x + y - 3 = 0.

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If it is suggested that people of age, less than or equal to 18 years and of age, greater than or equal to 50 years, should be the first to get a flu vaccine, then we can define a variable "A" to the age group suggested to be prioritized for to vaccinate with the flu vaccine, and the compound inequality to describe the situation can be written as [(A ≤ 18) or (A ≥ 50)].

As per the question statement, it is suggested that people of age, less than or equal to 18 years and of age, greater than or equal to 50 years, should be the first to get a flu vaccine.

We are required to define a variable to the age group suggested to be prioritized for to vaccinate with the flu vaccine, and describe the question mentioned situation in the form of a compound inequality.

To start with, let us first determine the variable. It is as simple as assuming any alphabet, say "A", to be the age group, suggested to be prioritized for to vaccinate with the flu vaccine.

Since, suggested that people of age, less than or equal to 18 years should be amongst the the first to get a flu vaccine, thus "A" must be less than equal to 18, i.e., [tex][A\leq 18][/tex]...(1)

Similarly, suggested that people of age, greater than or equal to 50 years should be amongst the the first to get a flu vaccine, thus "A" must be greater than equal to 50, i.e., [tex][A\geq 50][/tex]...(2)

Now, combining (1) and (2), we get our required compound inequality to be [(A ≤ 18) or (A ≥ 50)].

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If my explanation seems confusing please refer to the images

Answer:

Step-by-step explanation:

4. To answer questions 4,5 and 6 you would apply the same steps for question 3. Your final answer for question 4 is x = 10.

5. The only difference for question 5 is that the measure of the angles combine is not explicitly given and it is a right angle (from the square in the corner) which means the total is 90⁰ and the final answer is for question 5 is 51⁰

6. For question 6 you need to know that the total is 180⁰. The final answer is 128⁰

7. Steps to solve questions 7,8,9 and 10 (question 7 is the demonstration) :

8. Apply the same step for question 7: the final answer is x = 5

9. Apply the same steps for step 7 however you substitute x in m < JGH which is 4x + 1 which is 57⁰

10. Apply the same steps for step 7 however you substitute x in m < GEF (11x) which is 33⁰

The general form of a linear equation is y - y1 = m(x - x1) then the  point-slope form exists y - 5 = 3(x - 9)

The general structure of a linear equation exists y - y1 = m(x - x1). It draws attention to the line's slope and one of the line's points (that exists not the y-intercept).

Given: (x1, y1) = (9, 5) and (x2, y2) = (8, 2)

The point-slope form exists given by,

y - y1 = m(x - x1)

m = (y2 - y1)/(x2 - x1)

substitute the values in the above equation, we get

m = (2 - 5)/(8 - 9)

m = 3

The value of m = 3.

y - 5 = 3(x - 9)

Therefore, the point-slope form exists y - 5 = 3(x - 9).

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Answer:

x=7

Step-by-step explanation:

3x-3x=11-4

x=7....

Answer:

Step-by-step explanation:

3x+4=3x+11

-3x      -3x

x+4=11

   -4  -4

x=7

the answer is 7 at the end

Greetings from Brasil...

Just take the cross product of the vectors EF and EH. The result will be a vector n. This vector (n) will help in the equation of the plane

vector EF = point F - point E

vector EH = point H - point E

check the attachment

according to the example in the annex, we notice that the points E, F and G are in the plane whose equation will be:

π : 6X + 9Y + 5Z + 1 = 0

The ray, line, or line segment that divides an angle into two congruent angles is known as an angle bisector.

There are 4 important elements to notice about two-column proofs.

1) The first column exists utilized to write math statements.

2) The second column exists utilized to write the reasons you make those statements.

3) The statements are numbered and follow a logical order.

The angle bisector theorem in geometry is concerned with the relative lengths of the two segments of a triangle's side that are divided by a line that bisects the opposite angle. It compares their lengths to the lengths of the other two sides of the triangle.

The ray, line, or line segment that divides an angle into two congruent angles is known as an angle bisector.

Let CB bisects [tex]\angle[/tex] ABD and [tex]\angle[/tex] ACD

[tex]\angle[/tex] ABC ≅ [tex]\angle[/tex] DBC (Definition of angular bisector)

[tex]\angle[/tex] BC ≅ [tex]\angle[/tex] BC  (Reflexive Property)

[tex]\angle[/tex]  ACB ≅ [tex]\angle[/tex] DCB (Definition of angular bisector)

[tex]\triangle[/tex] ABC ≅ [tex]\triangle[/tex] DBC (ASA)

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Answer:

2x + y= 6 y= 3x +4

Step-by-step explanation:

2x + (3x + 4) = 6(3x + 4)

Answer:

Here,

x+(-5) = 4

x = 4+5

x = 9

Therefore, 9+(-5) = 4

The equation of line is y = 3

Given the points:

(x₁, y₁) = (-1, 3)

(x₂, y₂) = (7, 3)

The slope-intercept form:

y = mx + b

Where m is the slope and b is the y-intercept.

The formula for slope is,

m = (y₂ – y₁) / (x₂ – x₁)

We have given,

x₁ = -1

x₂ = 7

y₁ = 3

y₂ = 3

So,

m = (3 – 3) / ( 7-(-1)) = 0/8 = 0

Slope intercept form,

y = mx + b

Considering y as 3, then

3 = 0(x) + b

3 = 0 + b

b = 3

Therefore, the equation of line is

y = 3

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The span between the towers is 1732 feet.

A suspension bridge has two support towers. Each tower is 1152 feet from the end of the bridge. The total length of the bridge is 4036 feet.

and, find the span between the towers?

Now, According to the question:

The total length of the bridge is 4036 feet.

and, each tower length is 1152 feet

The span between the tower is

=> 4036 -1152 - 1152

= 1732 feet.

Hence, The span between the towers is 1732 feet.

What do towers do on bridges?

A long - span suspension bridge usually has tall towers. The height of the Bridge's towers directs the tensile (pulling) forces in the main cables upward, so that the cables can efficiently do their job of holding up the roadway deck.

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AB = CA This triangle comprises two sides that are congruent. As a result, it is isosceles.

A coordinate system is a method of determining the position of points or other geometric components on a manifold, such as Euclidean space, by using single or more numbers, or coordinates.

Use the Distance Formula to find the lengths of AB ,BC and CA.

AB has endpoints A(–2, –1) and B(–1, 3).

AB = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the values we get:

AB = √((-1 - (-2))² + (3 - (-1))²)

     = √((1)² + (4)²)

     = √(1 + 16)

    = √(17)

BC has endpoints B(–1, 3) and C(2, 0).

BC = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the values we get:

BC = √((2 - (-1))² + (0 - 3)²)

      = √((3)² + (-3)²)

       = √(9 +9)

       = √(18)

CA = has endpoints C(2, 0) and A(–2,–1).

CA = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the values we get:

CA = √((-2  - 2)² + (-1 - 0)²)

     = √((-4)² + (-1)²)

     = √(16 +1)

    =  √(17).

AB = CA. This triangle comprises two sides that are congruent. As a result, it is isosceles.

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Answer:

Simplify 4x√3x-x√3x-2x√3x

x√3x

x√9x

2x√6x

2x√6x³

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