2.3.4 In a game between two equal teams; the home team wins with probability p > 1/2_ In a best of three playoff series; a team with the home advantage has a game at home, followed by a game away, followed by a home game if necessary The series is over as soon as one team wins two games. What is P[H], the probability that the team with the home advantage wins the series? Is the home advantage increased by playing a three-game series rather than a one-game playoff? That is, is it true that P[H] > p for all p > 1/2?

3/4 is the lowest form of the given fraction.

if the highest common factor of numerator and denominator if equals to 1. then  that fraction can't be reduced further and is said to be in the lowest form.

so suppose we are having any fraction of the form [tex]\frac{a}{b}[/tex]

the lowest form of the given fraction is  given by   [tex]\frac{x}{y}[/tex]

where x = [tex]\frac{a}{gcd(a,b)}[/tex] , y = [tex]\frac{b}{gcd(a,b)}[/tex]

where gcd is greatest common divisor of a , b

we are given fraction = 3/4

=> a = 3 and b = 4

gcd(3,4) = 1

so x = 3/(gcd(3,4)) = 3

y=  4/(gcd(3,4)) = 4

so the lowest form of 3/4 =  [tex]\frac{x}{y}[/tex]

and x=3 and y=4

and hence lowest form = 3/4

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Answer:

squares : triangles

1:2 or 1/2

Step-by-step explanation:

⭐What is a ratio?

⭐ How can we write a ratio?

For this problem, we can write the ratio of squares to triangles as:

[tex]\frac{2}{4}[/tex], or [tex]2:4[/tex].

But, we can further simplify this ratio.

To simplify the ratio, divide the numerator and denominator or both sides of the colon by the number they are both divisible by.

2 is divisible by 2, and 4 is divisible by 2:

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

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

Simplified is: [tex]\frac{1}{4}[/tex]

[tex]2:4[/tex]

[tex]\frac{2}{2} : \frac{4}{2}[/tex]

Simplified is: [tex]1:4[/tex]

Answer:

adult ticket $16

child ticket $12

Step-by-step explanation:

let x = price of adult tix

y = price of child tix

1)  3x + 4y = $96

2) 2x + 3y = $68

Subtract equation 2 from equation 1 to get:

3) x + y = 28

x = 28 - y  (now substitute this into equation 1)

3(28-y) + 4y = 96

84 - 3y + 4y = 96

y = 96 - 84 = 12 (price of child tickets)

Now that you know the value of y, plug it into equation 3:

x + 12 = 28

x = 28 - 12 = 16 (price of adult tickets)

The preimage of a value z by the function f are all the values for which the function f(x)=z.

What is preimage?

The preimage of a value z by the function f are all the values for which the function f(x)=z.

According to the given question:

As a simple example, consider the function f(x) = √x . The preimage of 5 is 25; for ℕ(the set of natural numbers) it is the set of all perfect squares in ℕ

PREIMAGES OF SET: The pre Given a function f:A→B , and  D⊆B , the preimage   D  of under   f  is defined as

f−1(D)={x∈A∣f(x)∈D}.(5.4.5)

Hence,  f−1(D)  is the set of elements in the domain whose images are in  C . The symbol  f−1(D)  is also pronounced as “ f  inverse of  D .”

The preimage of a value z by the function f are all the values for which the function f(x)=z.

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Answer:6 quizzes over 1  week

Step-by-step explanation: because if u add 6 + 6+ 6 that 18 so ya

It will take at least 39.5 minutes to raise the temperature of the magnesium sample to its melting point.

B. m ≥ 39.5

Formula:

[tex]m ≥ (650 - 255)/10[/tex]

We can use the formula [tex]m ≥ (650 - 255)/10[/tex] to solve for the number of minutes (m) needed to raise the temperature of the magnesium from 255 degrees to the melting point of 650 degrees.

First, we subtract the initial temperature of 255 degrees from the melting point of 650 degrees. This gives us 395.

Then, we divide 395 by 10, which is the number of degrees the temperature is increasing every minute. This gives us the result of 39.5 minutes.

Therefore, the answer is m ≥ 39.5, which means that it will take at least 39.5 minutes to raise the temperature of the magnesium to the melting point.

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Answer:

8 years old and Laura is 32

Step-by-step explanation:t

Let the daughter be equal to "x".

Laura would be "4x".

In 16 years Laura will be twice as old can be expressed as this:

4x+16=2(x+16)

Solve:

4x+16=2x+32

2x=16

x=8

Therefore at present time, the daughter is 8 years old and Laura is 32.

Answer:

24 6/7

Step-by-step explanation:

​5/14+24 1/2​

24 1/2 = 49/2

5/14 + 49/2

The common factor is 14

5/ 14 + 343 / 14 = 348 /14 = 174 / 7

174/ 7 = 24 6/7

Step-by-step explanation:

1. Convert the mixed number 24 1/2 to an improper fraction by multiplying the whole number (24) by the denominator of the fraction (2) and adding the numerator (1). This gives us an improper fraction of 49/2.

2. Find a common denominator for the fractions ​5/14​ and ​49/2​. The least common multiple of 14 and 2 is 14, so we can rewrite the fractions as ​7/7​ and ​49/14​, respectively.

3. Add the numerators and keep the denominator the same: ​7/7​ + ​49/14​ = ​(7+49)/7​ = ​56/7​

4. Simplify the fraction ​56/7​ by dividing both the numerator and the denominator by their greatest common factor, which is 7. This gives us a simplified fraction of ​8/1​, or 8.

5. The sum of ​5/14+24 1/2​ is equal to 8.

A function is a relationship between a set of possible inputs and outputs, where each input is associated with exactly one output.

A non-function is a relation between a set of inputs and a set of possible outputs where there is at least one input with more than one output.

The vertical line test can be used to ascertain whether a relation is a function. If you can draw a vertical line through the graph of the relationship and it intersects the graph at more than one point, then the relation is a non-function. If the vertical line intersects the graph at only one point, then the relation is a function.

Another way to determine if a relation is a function is to look at the equation defining the relation. If the equation does not contain any x's in the denominator, then the relation is a function. If the equation contains x's in the denominator, then the relation is a non-function.

For example, consider the relation defined by the equation y = x^2. This relation is a function because there are no x's in the denominator.

On the other hand, consider the relation defined by the equation y = 1/x. This relation is a non-function because the equation contains an x in the denominator.

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When a system has no solution it is called inconsistent equation

When a system has infinitely many solution it is called consistent and dependent equations

A system is considered to be inconsistent if there is no solution. There is no solution because the line graphs are parallel and not intersecting.

x + 5y = 4   and x + 5y = −2

subtracting gives

0 = -6 no solution  

this is an instance

A consistent system is dependent if there are an endless number of possible solutions. The two equations represent the same line when you graph them. An instance of the situation is

3x + y = 4

−6x − 2y = −8

subtracting gives

9x + 3y = 12 - none eliminates, meaning infinite many solutions

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2+2+2+4+4+2+4 = 20 and It's written in the addition form.

What is addition ?

One of the four fundamental mathematical operations, along with addition, subtraction, multiplication, and division, is addition. This operator is used to combine two or more objects or numbers.

Given,  2+2+2+4+4+2+4

The result can be found by applying addition,

So, 2+2+2+4+4+2+4  = 20

We can also find the sum of the above numbers by applying multiplication,

We've,  2+2+2+4+4+2+4

We will rearrange it in such a way that all the same numbers come together,

So, 2+2+2+2+4+4+4

Now, we can see that the number 2 is occurring 4 times and the number 4 is occurring 3 times,

So, It can be written as,

 (2 × 4) + (4 × 3)

= 8 + 12

= 20.

Hence, We get the same answer in both the cases.

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The equations allow us to compare the slopes of two lines to determine if they are parallel. The lines are parallel if the slopes are the same and the y-intercepts are different. The lines are not parallel if the slopes differ.

Perpendicular lines do meet, but parallel lines do not. They meet at a straight angle, or 90 degrees.Different perpendicular lines have different slopes. There is a distinct difference in the slopes of perpendicular lines.

One line's slope is equal to the other line's slope's negative reciprocal. A number's reciprocal and its product equal one. If m 1 and m 2 are negative reciprocals of one another, then multiplying them together will result in the number 1.

As with parallel lines, we can determine whether two lines are perpendicular by comparing their slopes. The slope of each line below is the negative reciprocal of the other so the lines are perpendicular.

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The slope of one line is equal to the negative reciprocal of the slope of the other line. The product and reciprocal of a number are both one. The outcome of multiplying m 1 and m 2 together if they are the negative reciprocals of one another is 1.

Similar to parallel lines, we can compare the slopes of two lines to determine if they are perpendicular. Each of the lines below has a slope that is the negative reciprocal of the other, making them perpendicular.

Answer:

x=4

Step-by-step explanation:

3x+2=5x-6

3x+2-2=5x-6-2

3x=5x-8

3x-5x=5x-8-5x

-2x=-8

divide by -8 by -2

x= 4

If the employee received maximum SSP in 28 weeks, then he or she is not qualified.

Here we have to identify the reason for the rejection of SSP for the employee.

In order to find the reason, we must know that is meant by SSP.

The term SSP refers a tool used to coordinate the supply and distribution of ad inventory to and from advertisers

Based on the definition, we have identified that if the employees does not qualify for SSP if they have received the maximum amount of SSP in last 28 weeks are getting Statutory Maternity Pay or Maternity Allowance then there are special rules for pregnant women and new mothers who do not get these payments.

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The Python range() method needs three arguments to work: start value, stop value, and step value. after increasing the values by the step value's stated amount.

For a specific data collection, the statistical range is the range of values between the highest and lowest values. The difference between the highest and lowest observation can also be used to illustrate the range. Subtracting the highest number from the lowest yields the sample interval. The sample range is a crucial indicator of variability for variables that are continuous.

here ,

The series of integers returned starts with this integer, startNumber (optional).

stopNumber: This number is the last in the series of integers returned by range().

the stepValue (optional): An integer value indicating how much each successive integer differs from the previous one.

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Answer:

An equation with a degree of 3 is called a cubic function.

Step-by-step explanation:

Functions are named by their degree.

Examples:

[tex]y = ax^2 + bx + c[/tex] is named a quadratic function because it has a degree of 2.

Similarly, [tex]y = ax^3 + bx^2 +cx + d[/tex] is named a cubic function because it has a degree of 3.

One-half squared is one-fourth. In other words , 1/ 4 is the square is 1/2 .

In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a superscript 2; for instance, the square of 3 may be written as 32, which is the number 9.

Squaring a number is simply multiplying the value by itself. When you take the square root of a number, you are figuring out what number had to be squared to get the original value.

The square of a number (let x) is given by the formula x².

According to the Question ,

Square of 1/2 is given by = (1/2)²

Since , the square of a number (let x) is given by the formula x².

  (1/2)²

= 1/(2)²

= 1/ 4

= 0.25

Hence, One-half squared is one-fourth. In other words , 1/ 4 is the square is 1/2 .

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The equation for the quadratic function in standard form is 4x² - 16x - 9

From the question, we are to write an equation for the quadratic function in standard form.

From the given quadratic graph,

The roots of the function are -0.5 and 4.5.

That is,

x = -0.5 and x = 4.5

That is,

x = -1/2 and x = 9/2

Therefore,

2x = -1 and 2x = 9

The factors of the quadratic function are (2x + 1) and (2x - 9)

Thus,

We can write that

(2x + 1)(2x - 9) = 0

4x² - 18x + 2x - 9 = 0

Simplify

4x² - 16x - 9 = 0

Hence, the equation is f(x) = 4x² - 16x - 9

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The calculated value of standard deviation for the given data set is 2.236.

Standard deviation is the measure of dispersion of the observed values relative to the mean value. It indicates how far each value is apart from mean value.

we have data list 2 4 6 8

 the list is denoted by X and X² is the square of the data set

    X        X²

   2          4

    4         16

     6        36

     8         64

we add all the data, and the result is ∑X = 20

similarly, we add all the squared value, and the result is ∑X² = 120

Standard deviation is calculated by using the formula below

SD = √[∑X²/N - (∑X/N)²]

here, N denotes the amount of data set

hence, N= 4

SD = √[120/4 - (20/4)²] = 2.236

hence, standard deviation is 2.236

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The relationship between the volume of the pyramid inscribed in a cube and the volume of the cube can be determined by comparing both. The volume of cube is three times the volume of the pyramid inscribed in the cube.

Let us say the cube is of side a. Then for a pyramid inscribed in the cube the base is the surface of the cube with dimensions a×a and is of height a.

Volume of a cube of side a is a³.

Vc = a³

Volume of a pyramid of base l×b and height h is given by

V = l×b×h/3

Therefore in this case volume of pyramid is

Vp = (a×a×a)/3

Vp = a³/3

Thus Vp = Vc/3, or we can say Vc = 3Vp.

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Rigid body motion is a change that preserves space's geometric characteristics. It is a distance-preserving map or isometric since Euclidean qualities may be described in terms of distance.

The separation between each pair of the geometric object's points is preserved during a rigorous change of the object. In other words, a rigid transformation maintains the object's size and shape. For instance, the rigid transformation of a triangle retains the angles and lengths of the triangle. Imagine a stiff shape distortion, similar to a cardboard shape. The form remains the same after being pushed left and right, rotated, and flipped. When the mold was created using putty, the opposite was true. The thing can then be twisted and stretched. These conversions, nevertheless, are not exact. Stretching a form alters the distances between each pair of its points.

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The elevation of point A is greater than 3350 feet.

The lines of equal elevation are known as contour lines. In relation to the mean sea level, it reflects the height of any specific site. The crucial elements on a topographic map are those that never cross each other.

Locations A and B are shown on the provided topographic map. By reading the contour and the contour interval, which is shown to be 50 feet, it is clear that Location A is higher up than Location B.

Location A is at a higher contour line, with respect to the contour 3250 feet, mentioned on the left side of location A.

Thus, the height of location A is slightly more than 3350 feet above the mean sea level.

(Refer to the image attached for the topographic map)

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Context lines are those lines that have the same elevation. It reflects the height of any particular site in relation to the average sea level. A topographic map's most important features are those that never cross one another.

The topographic map is displayed with the locations A and B. It is evident that Location A is higher up than Location B by reading the contour and the contour interval, which is indicated to be 50 feet.

In comparison to the contour line of 3250 feet listed on the left side of location A, position A is at a higher contour line.

As a result, position A is higher above the norm by about 3350 feet.

Answer: 3/10 cup of water

Step-by-step explanation:

Take 3 divided by 5 = 0.6

So, we know to get from 3 to 5 we need to times 0.6

So, we take 1/2 times 0.6

1/2 = 0.5

0.5 times 0.6 = 0.3 cup of water

0.3 = 3/10

So, the answer is 3/10 cup of water

Answer:

3.375 or 3 3/8

Step-by-step explanation:

divide 2 1/4 to get 1 1/8 or 1.125 then multiply by 3 to get 3.375 or 3 3/8

The expression y-3x-1 is not a direct variation as it does not satisfy the criteria.

It is a mathematical relationship between two variables shown by the form of an equation that says one variable is equal to the other variables that is multiplied by a factor.

Such as y =4x is an equation which express the direct variation between x and y as y is equal to four times of x

The formula for direct variation is given by the equation y = kx.

x and y are variables, k is the constant or factor.

Suppose we examine a number of linear equations and check the ratio of the variables such as x and y ratio. If we find a constant ratio, then it is termed as direct variation.

In the given expression, y-3x-1 that could not satisfy the criteria of direct variation because there is a constant -1 in the expression. And while writing in an equation form, we get y-3x-1 =0

 we never get constant ratio from x and y variables.

hence, this is not a direct variation.

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Let x=(i+1)^2. So the square of given expression will be x= 2i.

A square in mathematics is produced by multiplying a number by itself. To describe this operation, the term "to square" is employed. For example, the square of 3 may be expressed as 3^2, which is the number 9, since squaring is the same as raising to the power 2. Squaring is indicated by a superscript 2.

We'll examine the square of any number, which we'll refer to as "n." The square of the digit "n" is represented by the symbol "n^2," and it can be determined by multiplying n by n.

(i+1)^2= i^2+1+2i

         = -1+1 +2i

         =2i.

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The median for the next batch of observations is 2.

The median is the value in the middle of a data set, which indicates that 50% of the data points have a value less than or equal to the median, and 50% have a value greater than or equal to the median. The median is the number in the middle of a set of numbers. The median represents the 50th percentile of the set of numbers. In other words, the median is the value in the center of a set of numbers where half are less than the median and half are more than the median.

Here,

given set of observation,

=1,1,2,4,6,8

n=6

median=6/2

=3rd term

=2

The median for following set of observation is 2.

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The ordered pair found in inverse of g is  ( 1 , 4 ) .

Given :

Relation :

A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule .

Values for relation g are given in the table:

X  Y = g( X )

5  -3

4    1

3   -2

2    0

then the table for g inverse will be:

X      Y = g^-1 ( x )

-3       5

1       4

-2     3

0     2

Hence, the ordered pair found in inverse of g is ( 1 , 4 )

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Full question :

Values for relation g are given in the table. Which ordered pair would be found in the inverse of g?.

X  Y = g( X )

5  -3

4    1

3   -2

2    0

Answer:

EF = 7

Step-by-step explanation:

Take EG - FG = EF

19 - 12 = 7

So, the answer is EF = 7

Answer:

[tex]\frac{1}{a}[/tex]

Step-by-step explanation:

the product of a number and its multiplicative inverse = 1 , then

a × [tex]\frac{1}{a}[/tex] = 1

multiplicative inverse of a is then [tex]\frac{1}{a}[/tex]