What are the four values that would complete the function table?

The equivalent expression will be;

B) -2 +4 (x+3) and 4x + 10

C) 3x+5(x - 1) and 8x - 5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There are some expressions.

Now,

From option (A),

⇒  2 (x+3) + 2x and 4x + 3

Solve as;

⇒ 2 (x + 3) + 2x = 2x + 6 + 2x

                         = 4x + 6

Which is not equal to 4x + 3.

From option (B),

⇒ -2 +4 (x+3) and 4x + 10

Solve as;

⇒ - 2 + 4 (x + 3) = - 2 + 4x + 12

                        = 4x + 10

Hence, This is equivalent expression.

From option (C),

⇒ 3x+5(x - 1) and 8x - 5

Solve as;

⇒ 3x + 5 (x - 1) = 3x + 5x - 5

                      = 8x - 5

Thus, This is equivalent expression.

From option (D),

⇒ 5x² (x + 4) and 3x + 8

Solve as;

⇒ 5x³ + 20x²

Thus, This is not correct.

From option (E),

⇒ 4-5 (x+2) and 5x - 6

Solve as;

⇒ 4 - 5 (x + 2) = 4 - 5x - 10

                      = - 5x - 6

Thus, This is not correct.

Therefore, The value of equivalent expression is;

⇒ -2 +4 (x+3) and 4x + 10

⇒ 3x+5(x - 1) and 8x - 5

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The maximum volume of the box in terms of A will be √3A/4 -3√3/4 cu cm.

It is given that the box has an open top and a square base.

This implies length = breadth.

Let them be x cm

Now, the area of the box is A sq cm

This means

lb + 2bh + 2lh = A

or, x² + 2xh + 2xh = A

or, 4xh + x² = A

or, h = A/4x - x/4

Now volume (V) = lbh

= x²(A/4x - x/4)

= Ax/4 - x³/4

Now to maximize volume we will first differentiate with respect to x and equate it to zero. Hence we get

V' =0

or, A/4 - 3x²/4 = 0

or 3x²/4 = A/4

or, x² = 3

or, x = √3

Now t check whether this gives us the maximum volume we will calculate V"(√3)

V" = -3x/2

V"(√3) = -3√3/2

Since V"(√3) is negative we will get maximum value for x = √3

Now the volume is

A√3/4 - (√3)³/4

= √3A/4 -3√3/4 cu cm

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The probability when the value of W = 1 is 0.1 , probability when the value of W = 10 is 0.2 and probability when the value of W = 25 is 0.7  .

In the question ,

the marked price slips are $1, $1, $1, $10 and $25 .

If the winner selects two slips of paper, then the possible outcomes would be ,

total number of slips is = 5 ,

Total number of cases possible = ⁵C₂ = 10

There would be only 1 case in which the winner will win $1

that means when both the slips selected has $1.

So, P(Winning $1) = 1/10 = 0.1

the number of cases to win $10 is {(1,10) , (10,1)}

So , P(Winning $10) is

= 2/10 = 0.2

So , P(Winning $25) is

= 1 - (0.1 [tex]+[/tex] 0.2)

= 0.7

Therefore , the required probability P(Winning $1) = 0.1 , P(Winning $10) = 0.2 and P(Winning $25) = 0.7

The given question is incomplete , the complete question is

A box contains five slips of paper, marked $1, $1, $10, $25, and $25. The winner of a contest selects two slips of paper at random and then gets the larger of the dollar amounts on the two slips. Define a random variable w by w = amount awarded. Determine the probability distribution of w. (Hint: Think of the slips as numbered 1, 2, 3, 4, and 5, so that an outcome of the experiment consists of two of these numbers.)

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The number of gallons the citizens waste this year is 5229

information from the problem

The citizens of Washington wasted 7,470 gallons of water last year

This year, they wasted 30% less

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

30%

= 30 / 100

= 0.3

The factor 0.3 less

= 1 - 0.3 = 0.7

The number of gallons wasted this year

= 0.7 * 7470

= 5229

The number of gallons wasted is 5229 gallons

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Answer: y = -1/2x - 3

Step-by-step explanation:

The group of all possible dependent values that a function can produce from its domain values is known as its range.

In the given question we have to explain what is range of a function.

The range refers to all the entities (output) that result from a relation or function. The Range set is made up of all used output values (dependent values).

The group of all possible dependent values that a function can produce from its domain values is known as its range. It consists of every potential output.

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The value of x is 10°.

What is triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Given:

In ΔRST, m ∠R = (5x+15), m ∠S = (6x+8), m ∠T = (4x+7)

Since the addition of three angles of triangle is 180 degrees.

So,

          m ∠R + m ∠S + m ∠T = 180°

(5x + 15) + (6x + 8) + (4x + 7) = 180°

                               15x + 30 = 180°

                                       15x = 180° - 30°

                                       15x = 150°

                                           x = 10°

Hence, the value of x is 10°.

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Answer:

It is not possible to determine the amount of ingredients needed to make 1 quart of cereal without knowing the specific recipe being used. Different types of cereal require different ingredients and proportions of those ingredients, so the amount needed to make 1 quart of cereal will vary depending on the recipe being followed.

In general, most cereals are made from a mixture of grains, such as wheat, corn, oats, or rice, which are ground into flour or meal and mixed with other ingredients such as sweeteners, flavorings, and preservatives. The exact proportions of these ingredients will depend on the type of cereal being made and the specific recipe being used. To determine the amount of ingredients needed to make 1 quart of cereal, you would need to consult a specific recipe and follow its instructions.

Step-by-step explanation:

Answer:

The most appropriate method for solving the first system of equations would be elimination. This can be done by adding the two equations together, which will eliminate one of the variables and leave us with an equation in terms of the remaining variable. We can then solve for the value of this variable and substitute it back into one of the original equations to find the value of the other variable.

For the second system of equations, substitution would be the most appropriate method. This is because one of the equations can be rearranged to solve for the value of one of the variables, which can then be substituted into the other equation. This will eliminate one of the variables and allow us to solve for the value of the remaining variable.

For the third system of equations, graphing would be the most appropriate method. This is because both equations are in the form "y = mx + b," which is the standard form of a linear equation. We can graph both equations on the same coordinate plane and find the point of intersection, which will give us the values of both variables.

Answer:

7x + 1 Remainder -6x - 1

or

7x + 1 - (6x + 1)/(x² + 1)        

Step-by-step explanation:

(7x³ + x² + x) ÷ (x² + 1)

                                        7x + 1

                                     ---------------------

                         x² + 1   |  7x³ + x² + x

                                        7x³ + 0  + 7x

                                       ------------------------

                                                 x² - 6x

                                                 x² + 0x  + 1

                                            --------------------

                                                       -6x - 1

(7x³ + x² + x) ÷ (x² + 1) = 7x + 1 Remainder -6x - 1

or

(7x³ + x² + x) ÷ (x² + 1) = 7x + 1 - (6x + 1)/(x² + 1)                                            

Jelly beans are $1.5/lb and trail mix is $2.063/lb, according to the data.

A heterogeneous mixture would be a trail mix. When the components of a combination are dispersed unevenly across the mixture, the mixture is said to be heterogeneous. As a mixture of nuts, raisins, and other seeds, trail mix cannot have an evenly distributed dispersion of its ingredients.

t = trail mix, j = jelly beans

3t + 8j = 21

5t + 2j = 18

Solving the first for t

2t = 6j - 3

t = (6j - 3)/2

Substituting

5(6j - 3)/2 + 2j = 18

j = 51/34

j = 1.5, Jelly beans cost $1.5/lb

now,

8t + 3(1.5) = 21

8t = 16.5

t = 2.0625, trailmix costs $2.063 dollars/lb

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Based on the graph, a solution for the system of equations is 2 and 4.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of games Kaylee played and number of rides Kaylee went on, and then translate the word problem into algebraic equation as follows:

Since each game costs $1.25 and each ride costs $2.50, and Kaylee spent $12.50 altogether, we have;

1.25x + 2.50y = 12.50.      ..........equation 1.

Additionally, the number of rides she went on is twice the number of

games she played;

y = 2x                      ..........equation 2.

Next, we would use an online graphing calculator to graphically solve the system of linear equations. Therefore, the required solution for the given system of linear equations is the point of intersection of the two (2) lines on the graph, which is given by this coordinate (2, 4).

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Therefore, the length of the c from the given figure comes out to be c= 10.63cm.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Here,

The hypotenuse, or longest side in a right triangle, is side c, which is our unknown. With the use of Pythagorean's Theorem, we have

[tex]7^{2} +8^{2} =c^{2}[/tex]

which simplifies to

[tex]7^{2} +8^{2} =c^{2}[/tex]

and

49 + 64 = [tex]c^{2}[/tex]

and

  [tex]c^{2}[/tex] = 113

c = 10.63 cm

Therefore, the length of the c from the given figure comes out to be c= 10.63cm.

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The distance covered by a car in one hour is 36.15 miles, and the distance covered by a car using 1 gallon of fuel is 12.05 miles.

A thing that moves quickly and with high speed, covering a lot of ground in a short time. On the other hand, a slow-moving object traveling at a low speed covers a comparatively small distance in the same amount of time. An object with zero speed does not move at all.

Given:

A car traveled at a constant speed for 4 hours and covered 144.6 miles,

The fuel used = 12 gallons,

Calculate the distance covered in 1 hour as shown below,

The distance covered in 1 hour = 144.6 / 4

The distance covered in 1 hour = 36.15 miles

Calculate the distance traveled using 1 gallon of fuel,

The distance traveled using 1 gallon of fuel = 144.6 / 12

The distance traveled using 1 gallon of fuel = 12.05 miles.

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Rotation is the rigid type of transformation which is equivalent to the two reflections across intersecting lines.

Therefore, the rigid type transformation which is equivalent to two reflection across the intersecting lines is called rotation.

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By ay applying logical reasoning, we can conclude that (C) Kaylon is incorrect because the provided image indicates that the shaded temperature is -°.

Induction and abduction are two additional categories of logical reasoning that are typically distinguished in addition to the formal deduction.

If one has a premise or precondition, a conclusion or logical consequence, and a rule or material conditional that signals the conclusion given the premise, one can explain the following.

Philosophical logic and mathematical logic are often used to support the assertion that "Objects outside get wet when it rains.

Since the grass is outside, it gets wet when it rains."

Inductive reasoning is used to support a finding of the rule.

Based on the information provided, it is clear that Kaylon is mistaken because the temperature in the shade is -°.

Therefore, by applying logical reasoning, we can conclude that (C) Kaylon is incorrect because the provided image indicates that the shaded temperature is -°.

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The graph in this problem shows a proportional relationship, because the line passes through the origin, and the rate of change is of 40.

A proportional relationship is a special case of a linear function, with an intercept of zero.

The slope is the constant of proportionality, hence the proportional relationship has the equation defined as follows:

y = kx.

Hence the constant is given as follows:

k = y/x.

Two points from the graph are given as follows:

(1,40) and (2,80).

The constants for each point are given as follows:

The constants are the same for each point, hence the graph represents a proportional relationship.

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The probability is the odds thus the probability it will rain today will be 5/9.

Probability is the concept that describes the likelihood of an event occurring.

Probability is also known as chance because, if you flip a coin, the possibilities that it will land on its head or tail are just chances that either a head will show up or not.

The odds of rain today are 5:9

Odds will be the same as probability because the probability is the same as chance.

Probability = 5/9

Hence "Since probability equals odds, the likelihood that it will rain today is 5/9.".

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Answer:

option a) since the arcs r drawn on both the sides of the line

and also as the arcs intersect each other at the center of the line AB

The element b₂₄ is the number in the second row and fourth column of the matrix, and we can see that it is equal to 10.

For a matrix M, the element Mₐₙ is the element in the a-th row and in the n-th column.

In this case we want to find b₂₄, so you need to look at the element that is in the second row (counting from the top) and in the fourth column (counting from the right) that element is a 10, then we can conclude:

b₂₄ = 10

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If 16 ounce bottle of orange juice contain 200 milligram was 250% from total of daily recommended amount , then 100% or recommended vitamin C to daily consume is 80 milligram.

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the table:4 represents  a linear function.

What is system of linear equations?

The intersections or meetings of the lines or planes that represent the linear equations are known as the solutions of linear equations. The set of values for the variables in every feasible solution is a solution set for a system of linear equations.

Not a Solution

If there is no intersection of any lines, or if the graphs of the linear equations are parallel, then the system of linear equations cannot be solved.

An Endless Number of Options

A set of infinite points exists for which the L.H.S. and R.H.S. of an equation become equal, indicating that a system of linear equations has an infinite number of solutions.

Unique fixing a series of linear equations

For table 4: The slope will be (8-6)/(3-5) = 2/-2 = -1

and (10-8)/(1-3) = 2/-2 = -1

Hence, the table:4 represents a linear function.

For a function to be linear the slope of all the segments should be same.

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Answer:

62.3

Step-by-step explanation:

To find how much a percentage is worth you take the initial number then multiply it by the percentage over a hundred. So in this situation it would be

566.37 times 11/100

Since it's 11 over a hundred you can turn that into 0.11 making it

566.37 times 0.11 or 566.37(0.11)

Coming out to 62.3007

rounded to nearest cent

$62.3

Answer:

first option

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 8 ) and (x₂, y₂ ) = (6, 4 )

m = [tex]\frac{4-8}{6-0}[/tex] = [tex]\frac{-4}{6}[/tex] = - [tex]\frac{2}{3}[/tex]

the line crosses the y- axis at (0, 8 ) ⇒ c = 8 , then

y = - [tex]\frac{2}{3}[/tex] x + 8 ← option 1

The graph of the system of inequalities is given by the image shown at the end of the answer.

The system of inequalities in this problem is defined as follows:

Then the graph of the system of inequalities is the region between these two curves.

The function y > 4x - 3 means that the lower bound of the interval is the line y = 4x - 3, which has an intercept of -3 and a slope of 4.

In standard format, the second line is defined as follows:

3y - x ≤ 9.

In slope-intercept format, it is defined as follows:

3y ≤ 9 + x

y ≤ x/3 + 3.

Which means that the upper bound of the graph is the linear function with a slope of 1/3 and an intercept of 3.

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For the function k(x) = 80, must have an x- value of 5 < x ≤ 6 in the given graph.

The greatest integer function takes the greatest integer that is less than or equal to a specified value.

Mathematically, the greatest integer function ⌊x⌋ can be defined as follows:

⌊x⌋ = n, where n ≤ x < n + 1 and 'n' is an integer.

According to the given question,

The function is below as

⇒ k (x)

We have to determine the value of k (x) = 80

As per the given graph, the required solution would be as: [x] + 5

Here ⌊x⌋ = 5, where 5 < x ≤ 5 + 1 and '5' is an integer.

5 < x ≤ 6

Thus, the required value of x would be 5 < x ≤ 6 for the given function k(x) = 80.

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The predicted value and residual for y is 9.4 and -0.4 respectively.

In statistics, a regression equation is used to determine whether or not there is a relationship between two sets of data. If you measure a child's height every year, you might discover that they grow about 3 inches per year. A regression equation can be used to model that trend (growing three inches per year). In fact, most things in the real world (from gas prices to hurricanes) can be modelled mathematically, allowing us to forecast future events.

Regression equations can assist you in determining whether your data can be fit to an equation. This is extremely useful if you want to make predictions based on your data, whether they are future predictions or indications of past behaviour.

Given,

Regression equation is y=11-038x

Observed value of y = 9

predicted value of y can be determined by substituting x=2 in the equation

y=11-0.8(2)=11-1.6=9.4

The residual can be calculated by formula,

residual = observed value - predicted value

residual = 9 - 9.4

residual = -0.4

Thus, the predicted value is 9.4 and residual is -0.4.

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Your question is incomplete, here is the complete question.

suppose the estimated regression equation is given by y=11-0.8x . what are the predicted value of y and the residual when x is 2 and y is observed to be 9?

the actual area of the bedroom is 324 square feet

What is square?

Having four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. Each square form may be recognised by its equal sides and 90° inner angles. A square is a closed form with four equal sides and interior angles that are both 90 degrees. Numerous different qualities can be found in a square.

Given the square bedroom have 3 feet side

The area of the bedroom is = 3² = 9 sq inch

1/2 inch = 3 feet

1 inch = 6 feet

1 square inch = 36 square feet

9 square inch = 36*9 = 324square feet

Hence the actual area of the bedroom is 324 square feet

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the built-in math function is square root or cube root.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

The correct options are:

A solution to the equation x2=81 is x=9.

A solution to the equation x3=125 is x=5.

A solution to the equation x3=216 is x=6.

Hence the built-in math function is square root or cube root.

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By using probability, it can be calculated that-

the optimal number of cookies to make is 2400 dozens

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Here

Each dozen of cookies is sold for $1.99 and cost $0.99

Shortage = $(1.99 - 0.99) = $1

Cookies that are not sold at the end of the day are reduced to $0.49

Overage = $(0.99 - 0.49) = $0.5

Service = [tex]\frac{1}{1 + 0.5}\\[/tex]

              [tex]=\frac{1}{1.5}\\\\=\frac{2}{3}\\\\=0.67[/tex]

Now the table is

Demand               Probability of demand             Cumulative probability  

(Dozen)

1800                          0.05                                             0.05

2000                         0.15                                              0.2

2200                         0.2                                               0.4

2400                         0.3                                                0.7

2600                         0.2                                               0.9

2800                         0.1                                                 1

Here the closest to service is 0.7

So the optimal number of cookies to make is 2400 dozens

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Complete Question

Famous Albert prides himself on being the Cookie King of the West. Small, freshly baked cookies are specialty of his shop. Each dozen sells for $1.99 and costs $0.99, which includes handling and transportation. Cookies that are not sold at the end of the day are reduced to $0.49 and sold the following day as day-old merchandise. Famous Albert has asked for help to determine the number of cookies he should make each day. From an analysis of past demand he estimates demand for cookies as

Demand                Probability of demand            Cumulative probability    

(Dozen)

1800                          0.05                                          

2000                         0.15                                            

2200                         0.2                                              

2400                         0.3                                              

2600                         0.2                                            

2800                         0.1                                                

Using the information in q8, what is the optimal number of cookies to make? 2,600 dozen 2,400 dozen 2,200 dozen 2,000 dozen 2,800 dozen

2,600 dozen 2,400 dozen 2,200 dozen 2,000 dozen 2,800 dozen