A theater can be rented for exactly 2,3, or 4 hours. The cost is a $100 deposit plus $200 per hour. Write a function to describe the situation. Find the reasonable domain and range for the function

The regular price of a ticket to the game is: $24.25

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

According to the data problem,

Calculating the cost per tickets we get:

Cost per tickets = 296/16 = $18.5

Calculating the regular price we have:

regular price = $18.5 + $5.75 = $24.25

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Correctly written question:

Mason bought 16 tickets to a baseball game. The group rate saved him $5.75 per ticket He paid a total of $296.00 for the tickets. What was the regular price of a ticket to the game?

The number of different rectangles with an area of 5 sq cm is 2

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

Area = 5 sq cm

The length of each square box is given as

Length = 1 cm

Assume the box cannot be divided

Then the number of rectangles to draw is 2

This is so because the height of the grid is 5 cm and it cannot take more than 5 cm

Also, because the square boxes cannot represent fractions

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The length of each of piece of board is 40 cm or 0.4 m.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Gillian has a board that is 2 meters long.

She cuts the board into 5 equal pieces.

Now, the length of each piece is

= 200 cm /5

= 40 cm

Hence, the length is 40cm or 0.4 m.

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The region included by a hexagon's sides is known as the area of the hexagon.

What is a hexagon?

A hexagon is a two-dimensional shape with six sides, six angles, nine diagonals, and a total of 720 degrees in its inner angles.

The space included within the polygon's sides is referred to as the hexagon's area.

The area of a regular hexagon is calculated using the formula

(3√3s^2)/2, where 's' is the length of a hexagonal side.

The fact that all the sides are the same length should be noted since we are discussing a regular hexagon.

Hence, area of hexagon is the region included by a hexagon's sides.

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The area of the rhombus would be [tex]$\mathbf{5 0} \sqrt{3}$[/tex].

A parallelogram has a unique variation known as a rhombus. A rhombus has opposing sides that are parallel and opposing angles that are equal. A rhombus also has equal-length sides and diagonals that are at right angles to one another. The term "rhombus" can also refer to a diamond or rhombus.

Given:

Each side length in a rhombus is $10, and one of the angles is equal to $120 circumference.

If the angle is 120 degrees, its half, 60 degrees, creates a right-angled triangle.

[tex]& \sin 60=\text { Height } / 10 \\[/tex]

[tex]& \sqrt{3} / 2 * 10=\text { height } \\[/tex]

[tex]& \text { height }=5 \sqrt{3} \text {. } \\[/tex]

Let the equation be

[tex]& \text { Area of rhombus = base }* \text { height } \\[/tex]

simplifying the above equation, we get

[tex]& =10 * 5 \sqrt{3} \\[/tex]

[tex]& =50 \sqrt{3}[/tex]

Therefore the area of the rhombus is [tex]$\mathbf{5 0} \sqrt{3}$[/tex].

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Choosing h and k in the given system of linear equations such that they they have no solution, a unique solution, and  many solutions is determined by the augmented matrix.

The augmented matrix is

  [1     h      2

  4     8      k].

Reduce matrix to row echelon form

a)We need to determine the values of h and k such that the system has no solution

8 - k =/ 0 and h -2 = 0

Hence, The System has No solution only when h=2, and k not equal to 18.

b)We need to determine the values of h and k such that the system has unique solution when

h - 2 =/ 0

The System has a Unique Solution only when h not equal to 2 and k is any Real number

c)We need to determine the values of h and k such that the system many solution when

8 - k = 0 and h -2 = 0

The system has many solutions only when h=2 and k= 8

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The complete question is :

choose h and k such that the system has (a) no solution, (b) a unique solution, and (c) many solutions. h & k

      x1 + hx2 = 2

     4x1 + 8x2 = k

The sample space when 3 coins are tossed is given as follows:

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.

The outcomes in which the first coin is tails is given as follows:

THH, THT, TTH, TTT.

A sample space is a set that contains all possible outcomes in the context of an experiment.

In this problem, we have three trials, each with two possible outcomes, hence the cardinality of the sample space is obtained as follows:

2³ = 8.

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The conclusion can be made using the data in option A the negative linear correlation means that as the preparation time increases, the final score decreases in a linear pattern.

The conclusion that can be made from the data in the scatter diagram is that the more time that was used to prepare, the lower the score (answer A). The negative linear correlation means that as the preparation time increases, the final score decreases in a linear pattern. This suggests that there may be a relationship between the amount of preparation time and the final score, but further investigation and statistical analysis is needed to confirm this relationship.

Linear correlation refers to the relationship between two variables that can be represented by a straight line on a scatter plot. The relationship between the two variables can be positive, negative, or neutral. Positive linear correlation means that as one variable increases, the other variable also increases in a linear pattern. Negative linear correlation means that as one variable increases, the other variable decreases in a linear pattern. A neutral linear correlation means that there is no relationship between the two variables.

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The conclusion can be made using the data in option A the negative linear correlation means that as the preparation time increases, the final score decreases in a linear pattern.

The conclusion that can be made from the data in the scatter diagram is that the more time that was used to prepare, the lower the score (answer A). The negative linear correlation means that as the preparation time increases, the final score decreases in a linear pattern. This suggests that there may be a relationship between the amount of preparation time and the final score, but further investigation and statistical analysis is needed to confirm this relationship.

Linear correlation refers to the relationship between two variables that can be represented by a straight line on a scatter plot. The relationship between the two variables can be positive, negative, or neutral. Positive linear correlation means that as one variable increases, the other variable also increases in a linear pattern. Negative linear correlation means that as one variable increases, the other variable decreases in a linear pattern. A neutral linear correlation means that there is no relationship between the two variables.

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Answer:

Step-by-step explanation:

.

For positive acute angles A and B, it is known that sin A= 4/5 and tan B= 45/28 . Find the value of IIT A+B in simplest form. Question. user avatar image ...

the solution of sin(A + B) in simplest form is 27/35.

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

Now, We use the trigonometric identity as;

sin(A + B) = sin A cos B + cos A sin B

Hence, we need to find cos A and cos B.

Here, We know that;

⇒ sin A = 4/5,

By use the Pythagorean identity;

sin²A + cos² A = 1

sin² A + cos² A = 1

(4/5)² + cos² A = 1

16/25 + cos² A = 1

cos² A = 9/25

cos A = 3/5

And, we can use the identity;

tan B = sin B / cos B

to find sin B:

tan B = sin B / cos B

45/28 = sin B / √(1 - sin² B)

(45/28)² = sin² B / (1 - sin² B)

sin² B + (45/28)² sin² B = (45/28)²

sin² B (1 + (45/28)²) = (45/28)²

⇒ sin B = 3/7

Now that we have sin A, cos A, sin B, and cos B,

We can put them into the formula for sin(A + B):

sin(A + B) = sin A cos B + cos A sin B

sin(A + B) = (4/5)(45/28) + (3/5)(3/7)

sin(A + B) = 27/35

Therefore, the solution of sin(A + B) in simplest form is 27/35.

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A conclusion which the diagram support include the following: A. UV/VW = ZY/YX.

The value of x is equal to: D. 15.

The value of x is equal to 4.

In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

Since side TU is parallel to side QR, side TU will divide both sides QS and RS proportionally in accordance with the triangle proportionality theorem as follows;

Since line segment UW is parallel to line segment ZX, side UW will divide both sides ZY and YX proportionally in accordance with the basic proportionality theorem as follows;

UV/VW = ZY/YX

For triangle JKL, we would apply the basic proportionality theorem as follows:

(x - 6)/3 = x/5

5x - 30 = 3x

5x - 3x = 30

2x = 30

x = 30/2

x = 15.

For triangle ABD, we would apply the basic proportionality theorem as follows:

12/x = 27/(x + 5)

12x + 60 = 27x

27x - 12x = 60

15x = 60

x = 60/15

x = 4.

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a) The alternative that provides Clay Whybark the greatest expected monetary value (EMV) is an alternative to Large Stock.

b) The expected value of perfect information (EVPI) is $13,800.

a) The alternative large stock's expected monetary value (EMV) = 22000 × 0.3 + 12000 × 0.5 - 2000 × 0.2

The alternative large stock's expected monetary value (EMV) = $12,200.

Expected Financial Value of Alternative Average Stock = 14,000 × 0.3 × 1000 × 0.5 × 6000 × 0.2

Expected Financial Value of Alternative Average Stock = $ 10,400

Expected Financial Value of an Alternative Small Stock = 9,000 × 0.3 + 8,000 × 0.5 + 4,000 × 0.2

Expected Financial Value of an Alternative Small Stock = $7,500

b) The expected value with perfect information (EVPI) = 22000 × 0.3 + 12000 × 0.5 + 6000 × 0.2

The expected value with perfect information (EVPI) = $13,800

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The equation that can be used to find d is 0.25d - 3.50 = $55.

The first step is to determine the total cost when the distance travelled is d.

Total cost when the first rental company drives d miles = $55

Total cost when the second rental company drives d miles = cost per day + [cost per mile x (d - 150)

= $34 + [$0.25 x (d - 150)]

$34 + 0.25d - 37.50

0.25d - 3.50

When the total charges are the same, the two equations would be equal

0.25d - 3.50 = $55

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Answer: x+42

Step-by-step explanation:

If red tomatoes was 42 more than yellow, it would be x=yellow tomatoes, x+42 because we do not know how many yellow tomatoes there are.

To solve an initial value problem, you need to find a function that satisfies the given differential equation and initial condition(s).

What is the initial value problem?

In multivariable calculus, an initial value problem (IVP) is an ordinary differential equation together with an initial condition that specifies the value of the unknown function at a given point in the domain. Modeling a system in physics or other sciences frequently amounts to solving an initial value problem.

This can be done using various numerical and analytical methods, such as:

Separation of variables

Euler's method

Runge-Kutta methods

Laplace transforms

Series solutions

Qualitative analysis

The method used depends on the form of the differential equation, the required accuracy, and the computational resources available.

Hence, To solve an initial value problem, you need to find a function that satisfies the given differential equation and initial condition(s).

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Answer: 8 ounces

Step-by-step explanation:

the puppy will weigh 8 ounces at three weeks old if the weight gain continues in the same pattern (33 ounces - 5 ounces + 6 ounces).

The least number of hours from now when the clock will again show the correct time is 720 minutes

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

According to the data problem,

The clock will show the correct time again when it lost 12 hours

As every hour it loses 1 minute,  the clock have to lose 12 hours in minutes, so we get:

12 hour * (60 minutes / 1 hour) = 720 minutes

Therefore, the least number of hours from now when the clock will again show the correct time is 720 minutes.

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4.5 cups of lemonade is required to fill 6 containers.

Multiplication is a mathematical operation that embodies the fundamental concept of repeated addition of the same integer.

The multiplied numbers are known as the factors, and the outcome of the multiplication of two or more numbers is known as the product of those numbers.

Multiplication is used to make repetitive adding of the same number easier.

As per the data given in the questions,

We have,

To fill one container, Tyreick needs 3/4 of a cup of lemonade.

So, to fill 6 containers, he will need 6 * 3/4 = 4.5 cups of lemonade.

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The turtle’s distance from the starting point is increasing for 18 seconds, and the distance between 10 and 12 seconds, the turtle, is -10cm, and the distance between 12 and 14 seconds, the turtle, is 0 cm.

The turtle’s distance from the starting point is 16+(20-16)*1/2=16+2=18sec.

To calculate the distance between 10 and 12 seconds, the turtle is as per the graph shown below we can consider the turtle is in 12:30 cm and 10:30 cm so 30-40=-10cm

To calculate the distance between 12 and 14 seconds, the turtle is as per the graph shown below we can consider the turtle is in 14:30 cm and 12:30 cm so 30-30=0cm

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Answer:The turtle’s distance from the starting point is increasing for

✔ 10

seconds.

Between 10 and 12 seconds, the turtle’s distance is

✔ decreasing

.

Between 12 and 14 seconds, the turtle is

✔ standing still

.

Step-by-step explanation:

Since 0.0493 < 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.

The P-value for a z-score of 1.58 can be found using a standard normal table or a calculator with a cumulative distribution function. The P-value is the area to the right of the z-score, or in this case, 1 - the area to the left of 1.58.

Using a standard normal table or calculator, we find that the P-value is approximately 0.0493.

If the level of significance is 0.05, we compare the P-value to the significance level. If the P-value is less than the significance level, we reject the null hypothesis (H0), and if it's greater than or equal to the significance level, we fail to reject the null hypothesis.

Since 0.0493 < 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.

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The width of the fountain will be 3 feet and the fraction of the area of the courtyard will be occupied by the fountain is 3/44

Is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft^2, m^2

The formula and procedure to solve this geometry exercise is:

A(rectangle) = length * width

Information about the problem:

A(stone) = 246 ft^2

A(fountain) = ?

Width = ?

Calculating the area of the fountain we get:

Area of fountain = area of the rectangle - 246

Area of fountain = (12 x 22) - 246

Area of fountain = 264 - 246

Area of fountain = 18 ft^2

Calculating the width of the fountain we have:

A(rectangle) = length * width

18 = W x 6

W = 18/6

W = 3 feet

Calculating the fraction of the area of the courtyard will be occupied by the fountain we get:

Fraction = Area of fountain / area of the rectangle

Fraction = 18 ft^2 /264 ft^2

Fraction = 18/264

Simplifying we have:

Fraction = 3/44

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The point Q = (-12, 1, 24) is a point at which the vector field F and the line l are perpendicular, and the equation for the set of all points at which f and l are perpendicular is 6x₁ + 3y₁ + 4z₁ = 0.

To find a point at which the vector field F and the line l are perpendicular, we need to find the point at which the dot product of the vector F and the direction vector of the line l is zero.

The direction vector of the line l is given by:

d = (1, 1, 4)

The vector F at the point (x₁, y₁, z₁) is given by:

F(x₁, y₁, z₁) = x₁ i + (x₁ + y₁) j + (x₁ - y₁ + z₁) k

The dot product of F and d is:

F(x₁, y₁, z₁) ⋅ d = x₁ + (x₁ + y₁) + 4(x₁ - y₁ + z₁)

Setting this equal to zero, we have:

x₁ + (x₁ + y₁) + 4(x₁ - y₁ + z₁) = 0

Expanding, we get:

6x₁ + 3y₁ + 4z₁ = 0

We can substitute x₁ = 3 - 5t, y₁ = t - 4, and z₁ = 4 + 4t into this equation to find t:

6(3 - 5t) + 3(t - 4) + 4(4 + 4t) = 0

Expanding, we get:

72 - 30t + 3t - 12 + 16 + 16t = 0

Simplifying, we get:

100 = 20t

So, t = 5.

Substituting t = 5 back into x₁ = 3 - 5t, y₁ = t - 4, and z₁ = 4 + 4t, we get:

x₁ = 3 - 5 * 5 = -12

y₁ = 5 - 4 = 1

z₁ = 4 + 4 * 5 = 24

The point Q = (-12, 1, 24) is a point at which the vector field F and the line l are perpendicular.

The set of all points at which F and l are perpendicular is given by the equation:

6x₁ + 3y₁ + 4z₁ = 0

This represents a plane in 3-dimensional space, perpendicular to the vector F at all points.

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--The given question is incomplete; the complete question is

"Let F = (x)i + (x+y)j + (x-y+z)k. Let the line l be x = 3 - 5t, y = t - 4, z = 4 + 4t.                                 Find a point Q= (x₁, y₁, z₁) at which F and l are perpendicular. Give an equation for the set of all points at which F and I are perpendicular."--

The axis of symmetry of the graph of the quadratic function represented by the equation is x=-b/2a

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

The standard formula for a quadratic equation is expressed as

y=ax^2+bx+c

All quadratic functions have an axis of symmetry and they are expressed according to the equation  x=-b/2a

Hence the axis of symmetry of the graph of the quadratic function represented by the equation is  x=-b/2a

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Answer:

x = 24

Step-by-step explanation:

Now we have to,

→ find the required value of x.

The equation is,

→ x/12 = 2

Then the value of x will be,

→ x/12 = 2

→ x = 2 × 12

→ [ x = 24 ]

Hence, the value of x is 24.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{x}{12} = 2}[/tex]

[tex]\mathsf{\dfrac{1}{12}x = 2}[/tex]

[tex]\large\text{MULTIPLY 12 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{1}{12}x\times 12 = 2 \times 12}[/tex]

[tex]\large\text{Simplify it}[/tex]

[tex]\mathsf{x = 12\times 2}[/tex]

[tex]\mathsf{x = 24}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = 24}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

x=64 degrees

Step-by-step explanation:

because triangle IHG is isosceles, angle HIG is 58 degrees. the sum of angles in a triangle is 180 degrees, and 180-58-58=64

Answer:

x= 64

Step-by-step explanation:

180-58-58=64

By organizing the data into intervals and counting the frequency of observations, we can identify the range of values in which the most data points are located.

In statistics, an interval is a range of values within which we expect to find a certain amount of observations.

The number of observations within an interval is known as the frequency, and it can be used to determine where the majority of values lie in a data set.

When we are looking for the interval with the largest number of observations, we are trying to find the range of values in which the most data points are located.

In order to do this, we need to first organize the data into intervals, often called bins, and then count the frequency of observations within each bin.

For example, if we have a data set of 100 heights of people, we could create 10 bins with a range of 10 cm each. The first bin would cover the range of heights from 0-10 cm, the second bin from 10-20 cm, and so on. After counting the number of people in each bin, we can easily see which bin has the largest frequency, and therefore the interval with the largest number of observations.

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The first column of matrix B is -3, -1 and the second column of matrix B is 4, 128.

First Column of B (b1): -3, -1

Second Column of B (b2): 4, 128

A1-3 is the first row of matrix A, so b1 = -3.

A2-4 is the second row of matrix A, so b2 = 4.

AB-1 is the first row of matrix B, so b1 = -1.

A2B-128 is the second row of matrix B, so b2 = 128.

The first column of matrix B (b1) is determined by the first row of matrix A (A1-3) and the first row of matrix B (AB-1). The first value of b1 is -3, which comes from the first row of matrix A, and the second value of b1 is -1, which comes from the first row of matrix B. The second column of matrix B (b2) is determined by the second row of matrix A (A2-4) and the second row of matrix B (A2B-128). The first value of b2 is 4, which comes from the second row of matrix A, and the second value of b2 is 128, which comes from the second row of matrix B. To summarize, the first column of matrix B is -3, -1 and the second column of matrix B is 4, 128.

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Answer:

i think it is the second one?

Step-by-step explanation:

i hope it helped!

For congruent segments, the following are required:

Perpendicular Bisector of a Segment:

Congruent Angles:

Angle Bisector:

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Note that the value of a for which 9 is equal to the equation (1/27)ᵃ⁺³ is a = -11/3.

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol "=".

Note that the given equation is:

9 = (1/27)ᵃ⁺³

In order to find the value of a for which both sides of the equation become equal, we can revise the equation as:

9 = 27⁻¹⁽ᵃ⁺³⁾

that is:

3³ = 3⁻³⁽ᵃ⁺³⁾

Because the bases are equal, we can cancel out to derive:

2  =  -3(a  +  3)

2  =  -3a  -  9

2+9  =  -3a

-3a  =  11

a  =  -11/3

Thus it is correct to state that the value of a for which 9 = (1/27)ᵃ⁺³ is:
a = -11/3.

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The missing value in the table is 12.

We assume that there is a proportional relation between the two variables, which can be written as:

y = k*x

Where k is a constant.

The first pair is:

x = 2

y =3

Replacing that we get:

3 = k*2

3/2 = k

(you will get the same value of k if you use any one of the pairs on the table).

Now to complete the table we need to evaluate in x = 8.

y = (3/2)*8

y = 3*4

y = 12

That is the missing value.

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The missing value in the table of values is 12.

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

The table of values

From the table of values, we can see that

The relationship between x and y is:

The product of 1.5 and x gives y

Mathematically, this can be represented as

y = 1.5x

When the value of x is 8, we have

y = 1/5 * 8

Evaluate the product

y = 12

Hence, the missing value is 12

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