four players pick a real number from [0,1]. the players with the middle two numbers are paired together, while the players with the two extreme numbers are paired together. the pair with a lower sum has to each pay the difference to the pair with a higher sum. if you are allowed to choose your number (while everyone else draws uniformly at random), which number should you choose?

Answer: Since AFGH is a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. We can use this property, known as the triangle inequality theorem, to determine the angles of AFGH in order from largest to smallest.

We are given that the perimeter of AFGH is 87, so we know that:

FG + GH + FH = 87

6x + 7 + 8x - 5 + 10x - 11 = 87

24x + 1 = 87

24x = 86

x = 3.5

Now that we know that x = 3.5, we can use the given lengths of the sides to find the values of the sides:

FG = 6x + 7 = 6(3.5) + 7 = 23

GH = 8x - 5 = 8(3.5) - 5 = 25

FH = 10x - 11 = 10(3.5) - 11 = 29

We can now use these values to determine the angles of AFGH in order from largest to smallest.

We can use the triangle inequality theorem to determine that:

FH>FG+GH

29>23+25

Therefore, the angle that is opposite to side FH is the largest angle in the triangle, and the angles opposite to FG and GH are the smaller angles.

So, the angles in the triangle AFGH are ordered from largest to smallest:

The angle opposite to side FH, angle A, is the largest.

The angles opposite to side FG and GH are the smaller angles.

Step-by-step explanation:

Answer:

16.281 rounded to the nearest whole number is 16.

This is because since 2 in the tenths place is bellow 5, the 16 will not round up to 17, and remain the same.

Step-by-step explanation:

Hope it helps! =D

The expression 16t-3t is not equivalent to 3t-16t because the negative sign belongs to the term 3t

For t = 2, 16t - 3t is equal to 26 and 3t - 16t is equal to -26

We know that an expression is nothing but a mathematical sentence with a minimum of two numbers or variables and at least one algebraic operation.

Also,  if two expressions are equivalent expression , then the two expressions must have the same value when we substitute the same values for the variables.

Here we have been given two mathemtical expressions:

16t - 3t and 3t - 16t

For t = 2,

16(2) - 3(2)

= 32 - 6

= 26

and 3(2) - 16(2)

= 6 - 32

= -26

This means, 16t - 3t ≠ 3t - 16t

We can oberve that 16t - 3t = -(-16 + 3t)

= -(3t - 16)

This means, 16t-3t is not equivalent to 3t-16t because the negative sign belongs to the term 3t

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Using the congruency of the top-right angles, it is found that the value of y is of 130.

What are parallel lines ?

Parallel lines can be defined as the lines which are equi distant from each other and they never intersect.

When two parallel lines are cut by a transversal, the top-right angles are congruent, that is, they have the same measure.

In this question, their measures are of (2x + 18)º and (4x - 14)º. Thus, with this, we can find x:

4x-14 = 2x+18

4x-2x = 18+14

2x = 32

x = 32/2

x = 16

Thus, the measure of the top right angles is given by, in degrees:

4x-14 = 4*16 - 14 = 64 - 14 = 50

The top-right and the bottom-right angles are supplementary, that is, the sum of their measures is 180º.

The measure of the top-right angle is of 50º.

The measure of the bottom-right angle is of y.

Thus:

y + 50 = 180

y = 180 - 50

y = 130

Hence, The value of y is of 130.

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Answer: 167.7

Step-by-step explanation:

Step 1:

Substitute

11.5(7) + 10.9(8)

Step 2:

Multiply:

80.5 + 87.2

Step 3:

Add:

167.7

167.7

Variables are letters within math that represent numbers.

The Expression

The question above is written as an expression. An expression is a mathematical statement that does not contain an equal sign. This is an expression because it's an addition statement without an equal sign.

Within the expression, there are 2 variables. Both x and y are variables because they're letters within the expression that are intended to represent numbers.

Solving the Expression

Now, to solve the expression we can plug the numbers we were given for each variable.

So, the answer to the expression 167.7.

The value of g(-6) is 42

A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2.

For example if f(x) = 3x-2, the value of f(3) is derived by substituting 3 for x In the function. Therefore f(x) = 3(3) -2 = 9-2 = 7

Similarly to solve g(-6) we substitute -6 for x in the function

g(-6) = -6² -(-6)

g(-6) = 36 + 6

g(-6) = 42

therefore the value of g(-6) = 42

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Answer:

Step-by-step explanation:

35368

Given that a = 8 cm and b = 21 cm, the value of A is 20.9 degrees

The complete question is added as an attachment

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

a = 8 cm and b = 21 cm

Using the tangent function, we have

tan(A) = a/b

So, we have

tan(A) = 8/21

Evaluate

tan(A) = 0.3810

Take the arctan of both sides

A = 20.9 degrees

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Answer:

Step-by-step explanation:

-Hope this helps!

Answer: x = 16

Step-by-step explanation:

To solve for x, add 5 and 11.

5 + 11 = 16

16 - 5 = 11

x = 16

[tex]\overline{AB}[/tex]1) The proof for to show that ΔJKN ≅ΔMKL is given as follows:

Given:

∠N≅∠L

[tex]\overline{JK}[/tex] ≅ [tex]\overline{MK}[/tex]

Thus,

ΔJKN ≅ΔMKL:

Reason: Angle - Angle - Side Theorem

Note that Vertical ∡s are ≅ (Congruent)

2) Given:

[tex]\overline{DE}[/tex] || [tex]\overline{FG}[/tex]

∠E ≅ ∠G

Since

[tex]\overline{DE}[/tex] || [tex]\overline{FG}[/tex], it means that ∠EDF ≅ ∠GFD, is because Alternate Angles of parallel lines are ≅ (Congruent). Given that ∠E ≅ ∠G. On the basis of reflexive property, [tex]\overline{DF}[/tex] ≅ [tex]\overline{FD}[/tex].

Hence, by the rule of Angle - Angle - Side, ΔFDE ≅ΔDFG.

In geometry, the reflexive property of congruence asserts that every angle, line, and figure/shape is congruent to itself.

This characteristic is commonly utilized in proofs such as establishing two triangles are congruent and parallel lines are parallel.

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Using the information in the issue and the formulas for the total surface area and volume of a rectangular solid, we can determine the volume of the rectangle solid in detail.

First, we calculate the rectangular solid's overall surface area using the following formula:

2(lw + lh + wh) = 972

Where the rectangular solid's dimensions are l for length, w for width, and h for height.

We can describe the three sides in terms of x, so that l = 10x, w = 4x, and h = x, since the ratio of the length to the breadth to the height is 10:4:1.

Now, we change the variables in the equation for the total surface area to match these values:

The formula is 2(lw + lh + wh) = 2(10x * 4x + 10x * x + 4x * x) = 972.

The equation will become more precise and give us:

80x^2 = 972

x^2 = 12.15

x = 3.5

Now that we have one side's value (height), we can use the following formula to get the solid's volume:

V = lwh

V = (10x)(4x)(x)

V = 40x^3

V = 40 * (3.5)^3

V = 40 * 42.875

V = 1715 cubic units

As a result, the rectangular solid has a volume of 1715 cubic units.

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If the plant is n inches then,

the actual plant = 2n feet.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Given:

The garden club at central middle school is planting a flower bed.

A scale drawing of the flower is shown.

The scale 1 in:2 ft

The scale factor,

the model = 1 inch

Then the actual plant = 2 feet.

If the plant is n inches then,

the actual plant = 2n feet.

Therefore, If the plant is n inches then, the actual plant = 2n feet.

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The scale of the drawing is given as follows:

1 : 4.5.

The scale of the drawing is obtained applying the proportions in the context of this problem.

The scale is defined as the division of the drawn length by the actual length.

The lengths are given as follows:

90/20 = 4.5, hence the scale of the drawing is given as follows:

1 : 4.5.

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The analysis of the data in the table, which is a linear relationship between the pages Jake reads to the number of days is as  follows;

1. Please find attached the graph of the data in the table created with MS Excel

a. The variable x represents the number of days Jake reads the book

b. The variable y represents the number of pages Jake reads

c. The slope is the rate of change of the pages Jake reads to the number of days he has been reading the book

d. The slope is 27 pages per day

A linear relationship is a relationship that has a straight line graph when plotted on the coordinate plane.

1. The data in the table are presented as follows;

Days[tex]{}[/tex]             Pages Read

0[tex]{}[/tex]                   0

2[tex]{}[/tex]                   54

4[tex]{}[/tex]                   108

6[tex]{}[/tex]                   162

8[tex]{}[/tex]                   216

Please find attached the graph created with the above data in the table for the Days and the number of Pages Jake read, created with MS Excel.

a. The input variable is normally represented by x, while the output variable is normally represented by y.

The input variable, which is the variable that determines or indicates the number of pages Jake reads is the number of days, therefore;

The value of x represents the number of days

b. The output variable obtained from the input variable which is the number of days is the number of books Jake reads, therefore;

The output variable, y, represents the number of books Jake reads

c. The slope is the rate of change of the number of pages Jake reads per unit time. Therefore, the slope represents the number of pages Jake reads per day.

d. The graph of the data in the table indicates that the relationship is a straight line relationship,the slope can therefore be obtained using two points as follows;

Slope, m = (108 - 0)/(4 - 0) = 27

The slope of the line is 27 pages per day

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If Candidate A received 36 votes, the number of votes that Candidate B received is 60 votes. (third option)

The first step is to determine the relationship between the number of votes of Candidate A and B. This can be determined by expressing the number of votes in its simplest form.

12 : 20 in its simplest form is 3 : 5

18 : 30  in its simplest form is 3 : 5

27 : 45  in its simplest form is 3 : 5

Now, determine the factor second factor of 36 if the first factor is 3.

36 / 3 = 12

Now multiply 12 by 5: 12 x 5 = 60

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Book 2 with 4 kg weight has the higher gravitational pull and the  pull decreases with increase in distance.

In Physics, the gravitational force is one of the types of forces. It is a force that attracts any two objects with mass. The gravitational force is also known as the attractive force, as it always pulls the masses of two objects together. Newton’s gravitational law states that every object in the universe is pulled by other objects. The other types of forces are electromagnetic force, strong force, weak force, and so on. The formula to calculate the gravitational force is given by Gravitational Force = (Gravitational Constant × Mass of first object × Mass of the second object) / (Distance between the centre of two bodies)².

Given here:

Book 1 has 2 kg textbook and Book 2 weighs 4 kg.

In the first case The gravitational pull when they were 2 cm apart is

F₁=    Gm₁m₂  / 2cm

  =0.00000133486 N

While if the two books are 8 cm apart we have

F₂= Gm₁m₂  / 8

  =0.0000000834288 N

clearly the gravitational pull decreases with the increase in distance.

And owing to Book 2's higher weight it has the superior gravitational pull.

Hence, Book 2 with 4 kg weight has the higher gravitational pull and the  pull decreases with increase in distance.

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As per the unitary method,

(a) The amount earned by the sales​ rep's orders in​ May is $42 600

(b) The amount did her orders​ decrease is $8520

in math the term unitary method is known as the process of how to find the value of a unit from the value of a multiple and the value of a multiple from the value of a unit.

Here we have given that a sales representative’s orders for May were 16 2/3% less than her April orders, which amounted to $51 120.

By using the unitary method as we all know that the May order is decreased, then it can be calculated as,

=> 51120 – 16 2/3% of $51120

When we simplify this one then we get,

=> 51120 – 1/6 × 51120 = 51120 – 8520

Therefore the earning is $42 600

Similarly, through the calculation we have identified that  the decreased amount is $8520.

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Answer:

C=5Q

Step-by-step explanation:

The possible outcomes are the sample space of the game

The number of possible outcomes in the game is 3

Now, According to the question:

In the domain of Statistics, the number of possible outcomes for a given event help in determining the overall size of the universe of outcomes. From such a universe, one can ascertain the probability or likelihood of desirable outcomes in terms of percentage or fraction.

How to determine the possible outcomes

The number of games is given as:

n = 2 i.e. 2 games to finish the season

In each game, the soccer team can either win, lose or tie.

So, we have the outcome of each game to be:

Outcome = {Win, Lose, Tie}

Count the outcomes

Count = 3

Hence, the number of possible outcomes in the game is 3.

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The given question is incomplete , complete question is:

Assume your favorite football team has two games left to finish the season. the outcome of each game can be win, lose, or tie. the number of possible outcomes is in the game ____

Answer:

9/10

Step-by-step explanation:

90/100

is 9/10 simplified

Answer:

it 9/10 becuse nvm

Step-by-step explanation:

The value of the expression is 28

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

2 square root 98 times square root 2

Express properly

So, we have the following representation

2√98 * √2

Evaluate the products

This gives

2√196

Take the square root of 196

2 * 14

So, we have

28

hence, the solution is 28

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Part A) According to the the scatter plot r = 0.01 is not an accurate value for this data

Part B) We have to describe a scenery where a variable is the cause of the number of strawberries picked.

The term scatter plot in math is known as  a horizontal and a vertical axis in the attempt to show how much one variable is affected by another

As we all know that the correlation coefficients r and it measure the strength of the correlation of two variables and they can have values from - 1 to  1.

Here we have know that r = - 1 is  a perfect negative correlation and the points will adjust perfectly to a line with negative slope.

Where as r =  + 1 is a perfect positive correlation and the points will adjust perfectly to a line with positive slope.

Where as r = 0 means that the variables are not correlated at all.

Hence the calculated value of r = 0.01 is not accurate for t his scatter plot.

As we all know that the causal relationship means that the explanatory variable is the cause of the dependent variable.

Therefore here we know we have to find a reasonable variable that can be the cause of the number of strawberries picked.

As the amount of rainfall is the cause of the number of strawberries picked, and you could find a model that relates both variables.

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The solution to the equation is 23

From the question, we have the following parameters that can be used to solve the question

7 - 5p + 3q

Also, we have the following values

p = 1 and q = 7

Substitute the know values in the given expression, so we have the following representation

7 - 5(1) + 3(7)

Evaluate the products

This gives

7 - 5 + 21

Evaluate the like terms

23

Hence the solution is 23

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Answer:

To find an equation of the line that passes through the point (-2, -3) and is parallel to the line 4x-y = 1, we know that the slope of the line we are looking for must be the same as the slope of the line 4x-y = 1. We can find the slope of 4x-y = 1 by rearranging it to the slope-intercept form y = mx + b.

4x - y = 1

y = -4x + 1

The slope of this line is -4

Now that we know the slope of the line we are looking for is -4, we can use the point-slope form of a linear equation, which is:

y - y1 = m (x - x1)

where (x1, y1) is a point on the line, and m is the slope.

We know that the point (-2, -3) is on the line we are looking for, so we can substitute these values into the point-slope form:

y - (-3) = -4 (x - (-2))

y + 3 = -4x + 8

y = -4x + 5

So an equation of the line that passes through the point (-2, -3) and is parallel to the line 4x-y = 1 is y = -4x + 5.

The z-score is greater in the case of Amber than in Roger so Amber had a better year relative to their peers.

First for Roger:

We have

Mean, μ = 4.371

Standard deviation, s = 0.787

so z-score for X = 3.14 will be

z = (X-μ)/s = (3.14 - 4.371)/0.787

or z = -1.564

Now In the case of Amber:

We have

μ = 4.363

s = 0.869

X = 3.38

so z = (X-μ)/s =  (3.38 - 4.363)/0.869

or z = -1.131

Therefore, The z-score is greater in the case of Amber than Roger so Amber had a better year relative to their peers.

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a. The scale factor is: 3/2

b. The pairs of corresponding angles are, <J and <P; <K and <Q; <L and <R.

c. The ratios are: JK/PQ = KL/QR = JL/PR.

The scale factor, also known as the ratio of similitude, is used to describe the relationship between the size of two similar figures. It is the ratio of the corresponding measurement of the new figure to the original figure.

a. scale factor from triangle JKL to triangle PQR = PQ/JK

= 9/6

= 3/2

b. The pairs of corresponding angles are:

<J and <P

<K and <Q

<L and <R

c. The ratios of the corresponding side lengths in a statement of proportionality will be: JK/PQ = KL/QR = JL/PR.

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Form the given five quadratics , the one representing the repeated roots is equal to option d. 25x² - 30x + 9 and repeated roots are 3/5 or 3/5.

Quadratics representing repeated roots has discriminant equals to zero.

Standard quadratic equation is:

ax² + bx + c = 0

Discriminant 'D' = b² - 4ac

option a. -x²+ 18x + 81

Discriminant

'D' = 18² - 4(-1)(81)

      = 324 + 324

      = 648

D>0 has distinct roots.

option b. 3x²- 3x - 168

Discriminant

'D' = (-3)² - 4(-3)(-168)

      = 9 - 2016

      = -2007

D< 0 has distinct roots.

option c. x²- 4x -  4

Discriminant

'D' = (-4)² - 4(1)(-4)

      = 16 + 16

      = 32

D>0 has distinct roots.

option d. 25x²- 30x + 9

Discriminant

'D' = (-30)² - 4(25)(9)

      = 900 - 900

      = 0

D = 0 has repeated roots.

Repeated roots are:

x = ( -b ±√D ) / 2a

  = [-(-30)±√0 ]/ 2(25)

  = 30/ 50

  = 3/5.

option e.  x² - 14x + 24

Discriminant

'D' = (-14)² - 4(1)(24)

      = 196 - 96

      = 100

D>0 has distinct roots.

Therefore, the quadratics which represents the repeated roots are given by option d. 25x² - 30x + 9 and its repeated roots are 3/5 or 3/5.

The above question is incomplete, the complete question is:

One of the five quadratics below has a repeated root. (There other four have distinct roots.) What is the repeated root?

a. -x²+ 18x + 81

b. 3x² - 3x - 168

c. x² - 4x - 4

d. 25x² - 30x + 9

e. x² - 14x + 24

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Answer:

72.8

Step-by-step explanation:

52*1.4=72.8

Answer: $70.80

Step-by-step explanation:

This is a two-step equation. First, you need to find what 40% of 52 is. You do this by multiplying 52 by 0.40. Then you would get the answer 20.8, but that isn't the final answer. Next, you add 52 and 20.8 together to get the final solution.

The probability of scoring more than 45 ixe is 0.91. P(X<=45) = (240C0 * (1/2)^0 * (1/2)^240) + (240C1 * (1/2)^1 * (1/2)^239) + (240C2 * (1/2)^2 * (1/2)^238) + ... + (240C45 * (1/2)^45 * (1/2)^195)

P(X<=45) = 0.0909

The probability of scoring more than 45 ixe can be calculated by using the Binomial Probability formula.

The formula is:  P(X>45) = 1 - P(X<=45)

Where P(X<=45) is the probability of scoring 45 or less ixe.

P(X<=45) = (240C0 * (1/2)^0 * (1/2)^240) + (240C1 * (1/2)^1 * (1/2)^239) + (240C2 * (1/2)^2 * (1/2)^238) + ... + (240C45 * (1/2)^45 * (1/2)^195)

P(X<=45) = 0.0909

Therefore, P(X>45) = 1 - 0.0909 = 0.9091

The probability of scoring more than 45 ixe is 0.91 (to 2 d.p.).

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The first diagram is the equation represented by 5 . 2 = 10 and the second diagram is the one with the equation represented by 2 + 5 = 7.

Tape diagrams are diagrams which are used to understand about the relationship between quantities and also they describe how those relationships has been described by operations.

Given are two tape diagrams.

First take the equation 2 + 5 = 7.

This means that 2 is just added to 5 to get 7.

One part contains 2 and the other part contains 5.

Length of it is 7.

Consider the second equation 5 × 2 = 10.

5 × 2 actually means that 5 is added to itself two times or 2 is added to itself five times.

Either 5 + 5 = 10 or 2 + 2 + 2 + 2 + 2 = 10

We have a diagram with 5 equal parts of 2.

Length is 10.

Hence the length of the first diagram is 10 and the length of second diagram is 7.

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