A movie theater is offering a special summer pass. Passholders pay $8 per movie for the first 5 movies and watch additional movies for free, up to a maximum of 15 movies. The function C gives the total cost, in dollars, for a passholder to watch n movies.
Is function C a piecewise function? Explain your reasoning.

Answer:

$7.09

Step-by-step explanation:

5% times 6.75 and add that is 7.09 dollars including tax

A linear equation can either be y = 5x + 2 or y = 3/x + b.

But the equation y= x² + b would not be a linear equation.

An equation is said to be a linear equation if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

The general equation of a linear equation is given below:

y = mx + b

Hence, the equation y = x (square root sign on it) + b would not be a linear equation because the power of the variable x is greater than 1.

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A. Using the given information, y expressed in terms of x is y = x + 50

B. The table that shows the relationship between y and x is

x               y

10             60

20            70

30             80

40             90

50             100

From the question, we are to express y in terms of x

From the given information,

There are x sparrows in a tree and 50 sparrows on the ground beneath the tree

If y represent the total number of sparrows in the tree and on the ground,

Then,

We can write that

y = x + 50

B.

We are to make a table to show the relationship between y and x

Using the equation above

y = x + 50

When x = 10

y = 10 + 50

y = 60

When x = 20

y = 20 + 50

y = 70

When x = 30

y = 30 + 50

y = 80

When x = 40

y = 40 + 50

y = 90

When x = 50

y = 50 + 50

y = 100

Thus,

The table is:

x               y

10             60

20            70

30             80

40             90

50             100

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The simplification of y=85,821.84 x (x-2) is y = 85,821.84x^2 - 171,643.68x

Mathematical simplification is the process of using basic mathematical operations (such as addition, subtraction, multiplication, and division) to reduce a complex equation or expression to its simplest form.

Also, a mathematical simplification is the process of making an expression or equation simpler and easier to understand or work with, without changing its value or meaning. This can involve combining like terms, factoring, canceling out common factors, and other techniques. For example, the expression 2(x+3) + 4(x+3) can be simplified to 6x + 18.

Therefore, the simplified expression is 85,821.84x^2 - 171,643.68x

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Slope = 1/4. Now let's put it into point slope form to find out the y-intercept. Then convert it into y=mx+ b form, the standard slope intercept form

How to calculate the linear equation?

Step1:

(-4,-2) and (4,0)

y=1/4x-1

Let's find the slope first, with the two given ordered pairs.

Slope = 1/4.

Now let's put it into point slope form to find out the y-intercept.

Then convert it into y=mx+ b form, the standard slope intercept form.

y + 2 = 1/4(x+4)

Then we convert it into y=mx+ b form (our final answer);

y=1/4x-1

Step 2:

(0,1)and(5,3)

y=2/5x+1

the equation of a line in slope-intercept form is.

y=mmx+ b

where m is the slope and b the y-intercept

to calculate the slope use the gradient formula

m=y2-y1/x2-x1

(x1,y1)=(0,1) and (x2,y2)=(5,3)

m=3-1/5-0=2/5

using m=2/5 and b=1

y=2/5x+1

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Isosceles, equilateral, scalene, obtuse, acute, and right triangles are the six different forms of triangles. Shapes with three sides are called triangles. The various triangle varieties go under various names.

Having three sides, three angles, and three vertices, a triangle is triangular. Every triangle's internal angles add up to 180 degrees. We refer to this as the triangle's angle sum attribute. Any two triangle sides can be added up to make any two sides longer than the third side.

Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one. The designation "triangle A B C" refers to a triangle with the vertices A, B, and C. When three points are non-collinear in Euclidean geometry, they each determine a distinct triangle and plane. 12 times the base plus the height, Triangle's side lengths added together to form the perimeter. 3, vertices total. 3 edges total Inside angle: 60 degrees (for equilateral) 180  degrees is the sum of interior angles. Consists of convex, cyclic, equilateral, isogonal, and isotoxal properties.

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Answer:

[tex]x=35^o\\y=85^o[/tex]

Step-by-step explanation:

[tex](2x + 25)^o = (3x - 10)^o\\2x + 25 = 3x - 10 \\2x - 3x = -10 - 25\\-x = -35\\x = 35[/tex]

[tex](2x+25)^o+y^o=180^o\\ 2(35) + 25 + y = 180\\70 + 25 + y = 180\\95 + y = 180\\y = 180 - 95\\y = 85[/tex]

The basis for the principle of substitution is the fact that algebraic equations and expressions remain unchanged when the same quantity is substituted into them. This principle allows us to solve equations and simplify expressions by substituting one expression for another.

The principle of substitution is a powerful tool used in algebra and calculus to solve equations and simplify expressions. This principle works by allowing us to substitute one expression for another, and the resulting equation or expression remains unchanged.

For example, when solving equations, we can substitute one value for the unknown variable to obtain a simpler equation which can then be solved. Similarly, when simplifying an expression, we can substitute one expression for another to reduce the complexity of the expression.

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The number and percentages of the parameters in the question are;

A percentage is a representation of a part of a whole as a fraction with a hundred (100) as the denominator.

T

From the attached table in the question, we get;

The number of people that make more than $60,000 = 388 + 198 + 66 = 652

The number of police officers in the survey  = 224 + 703 + 198 = 1125

The number of police officers that make less than $40,000 = 224

The percentage of police officers that make less than $40,000 is therefore;

Other information obtainable from the table are as follows;

The number of police officers that make more than $40,000 = 703 + 198 = 901

The percentage of all police officers that make more than $40,000 is therefore;

(901 ÷ 1125) × 100 ≈ 80.09%

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Answer:

3.50 × 12 = 42

Therefore, she spent 42 dollars.

3 seconds.

The problem states that the ball was kicked from a height of 12 ft, this would be the initial height of the ball. Hence:

h₀= 12 ft

Also, initial velocity is 44ft/s. Hence:

v₀= 44ft/s

[tex]h(x)=-16x^{2} +v_{0} x+h_{0} \\ \\h(x)=-16x^{2} +(44ft/s) x+(12ft)[/tex]

[tex]h(x)=-16x^{2} +44 x+12[/tex]

Since the height when the ball hits the ground is 0, we need to substitute the height value (h(x)) by 0, and then solve the equation for "x".

Using the quadratic formula (check the attached image) we can get the value of time.

Taking the coefficients:

A= -16

B= 44

C= 12

[tex]x_{1} =\frac{-(44)+\sqrt{(44)^{2}-4(-16)(12) } }{2(-16)}= -0.25s\\ \\x_{2} =\frac{-(44)-\sqrt{(44)^{2}-4(-16)(12) } }{2(-16)} =3s[/tex]

Since "x" is being used to represent time, and time is a variable that can only be positive, we're only taking the positive value.

Hence, we can conclude that after 3 seconds after being kicked, the ball wil hit the ground.

Answer:

1,230 square miles

Step-by-step explanation:

100 times bigger than 12.3 square miles is

100 × 12.3 square miles

= 1,230 square miles

The formulae that specify how much 8% solution in equation and how much 24% solution were utilized are x+ y=200 and x+3y=450.

A mathematical equation is a formula that uses the equals symbol (=) to link two expressions and represent their equivalence. A mathematical statement that demonstrates the equality of two mathematical expressions is an equation in algebra, in its most basic form. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Let x and y be the volume of the 8% and 24% solutions, respectively, that were utilized.

The entire solution volume, as stated in the question, will be 200ml. The resulting equation is: x +y=200

Now that it has been stated that 8%, 18%, and 24% saline mixes would be employed as the solution, the following equation will be:

[tex]0.08x+ 0.24y=0.18*200\\8x/100+24/100=18/100*200\\8x+24y=3600\\\\8(x+3y)=3600\\ x+3y=450\\[/tex]

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On solving the provided question, we can say that For the specified percentage, the 95% confidence interval is (0.864, 0.3580).

A confidence interval in statistics expresses the probability that a population parameter would fall between a set of values for a specific percentage of the time. Analysts commonly utilize 95% or 99% confidence intervals for their predictions.

If total samples = E = 36, then

8 results were obtained.

Chance = p = 8/36 = 0.2222

Z value at 95% confidence level = 1.96

p = [tex]0.2222 + 1.96 ( \sqrt{ 0.2222() 1 - 0.2222) / 36 } ) = 0.3580[/tex]

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The graph of the equations are added as attachment

Choose two linear equations

In this case, we make use of the following linear equations

y = 2x + 4 and y = -3x + 5

The slope and y-intercept of each equation

A linear equation is represented as

y = mx + c

Where

Slope = m and y-intercept = c

This means that the slope and y-intercept of each equation are

y = 2x + 4

Slope = 2

y-intercept = 4

y = -3x + 5

Slope = -3

y-intercept = 5

See attachment for the graph of the functions

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Applying the equation of free fall the time it will take for the ball dropped from a TV tower 2120 feet high to reach the ground is 11.51 seconds

The equation relating time and distance travelled which is  s = -16t² + 2120, as used in the problem is a quadratic equation

The equation is already modelled for the height of the tower which is 2120 feet high. because of this calculating the time the ball will reach the ground is done when the s = 0

Time when the ball will reach the ground

s = -16t²  + 2120

0 = -16t²  + 2120

16t² = 2120

divide both sides by 16

t² = 132.5

t = √132.5

t = 11.51 seconds

The time is 11.51 seconds

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Because the ten distances are not evenly distributed, Raul's overall performance should be determined by the median. Although nine distances are clustered together, the homerun is an outlier in the data set. The median is the best measure of centre for a data set with outliers.

The median is defined as the middle value in a given set of numbers or data. In mathematics, there are three different measures for determining the average value of a given set of numbers.

They are as follows: mean, median, and mode. These three measures are referred to as central tendency measures. Mean calculates the average value of the given data. A median defines the data's middle value.

The median is defined as the middle value of a sorted list of numbers in mathematics. By ordering the numbers, the middle number is discovered. The numbers are sorted ascending. After the numbers are ordered, the middle number is referred to as the data set's median.

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Full question:

Of the 10 swings, Raul hit 1ball over the outfield fence for a home run, but the other 9 hits were ground balls that stayed in the infield. Which measure of center will best summarize Raul’s overall performance? Why?

The correct option is A) √0.036 as it is the only irrational number.

Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, like p/q where p and q are integers.

Considering option A) √0.036, there is no number among integers and fractions that equals

√0.036

option B) is a terminating decimal and can be expressed as a fraction.

option C) will result to the whole number 1 just like the option D) 10 which is also a whole number.

In conclusion, only option A) √0.036 is an irrational number as it cannot be expressed as the quotient of two integers.

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In this case, the highest power on any variable is 23. As a result, the degree of polynomial is 23.

The degree of a polynomial in mathematics is the highest of the degrees of the polynomial's monomials with non-zero coefficients. A term's degree is the sum of the exponents of the variables in it, and it is thus a non-negative integer. The degree of a polynomial is the greatest or maximum power of a variable in a polynomial equation. A degree represents the polynomial with the greatest exponential power. Finding the degree of a polynomial. 2 x 2 + 2 x - 364 = 0. The maximum degree of the polynomial in the preceding equation.

Here,

Given : 2x^2 + 5x^23 + 7

Degree of polynomial = Highest power of a variable.

Here, 23 is the highest power on any variable. So, degree of polynomial is 23.

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Best saker out of 5 participants is Contestant D because his speed of skating is the highest. He has a speed 30 m/min.

Skating is a kind of sports as well as exercise. It is such a sport in where a participant needs to move on skates.

Best skater is determined by the performance of each participant.

The performance can be detected by observing the speed of skater.

speed = distance travelled by skater / time

we notice from the above question that contestant A covered a distance 1100m within 40 minutes.

so, speed of A = 1100 m/ 40 min = 27.5 m/min

Contestant B covered a distance 1800m within 1 hour and 10 minutes.

speed of B contestant = 1800m/ 70 min= 25.71 m/min

Contestant C covered a distance 1000m within 60 minutes.

speed of contestant C = 1000m/ 60 min = 16.67 m/min

Contestant D covered a distance 900m within half an hour.

speed of D = 900m /30 min = 30 m/min

Contestant E covered a distance 1500m within 55 minutes.

speed of contestant E = 1500m/ 55 min = 27.27 m/min

from the above discussion, we find that contestant D has the highest speed among all other skaters.

speed of contestant D = 30 m/min

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The first time that she will have tutoring and cooking class at the same time is given as follows:

6 weeks.

Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.

The periods for each event in this problem are given as follows:

The least common factor of 3 and 2 is given as follows:

3 x 2 = 6.

(prime numbers, hence we just multiply them to obtain the least common factor).

The least common factor of six means that the period is of six weeks.

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The net of the cube is attached to this answer, and;

a. The surface area of the cube = 6X^2 squared centimeters

b. The volume of the cube = x^3 cubic centimeters

The net of a shape or figure is the shape gotten when it is opened through its edges and spread out on a flat surface. If this shape is folded with respect to its edges, the original shape would be reproduced.

The net of the given cube is attached to this answer.

a. To determine surface area of the cube, we have;

surface area of a cube = 6*length*length

                                      = 6l^2

Given that the length of the sides of the cube is x centimeters,

area of the cube = l^2

                            = x^2

surface area of the cube = 6x^2

b. The volume of a cube = length^3

                                         = l^3 ;l

The volume of the cube = x^3

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The set of ordered pairs (x, y) that could represent a linear function include the following:

A. A = {(0, 3), (3, 0), (6, -3), (9, -6)}

C. C = {(−6,4),(−3,3),(1,2),(7,0)}.

In order to determine the ordered pairs that could represent a linear function, we would have to determine the slope of each ordered pair. In Mathematics, the slope of a linear function can be calculated by using this this mathematical expression;

Slope = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (0 - 3)/(3 - 0) = (-6 + 3)/(9 - 6)

Slope = -1 = -1 (it represents a linear function).

For ordered pair B, we have:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (7 - 9)/(2 + 1) = (3 - 5)/(7 - 4)

Slope = -2 ≠ -1 (it does not represents a linear function).

For ordered pair C, we have:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (3 - 4)/(-3 + 6) = (0 - 2)/(7 - 1)

Slope = -1/3 = -1/6 (it represents a linear function).

For ordered pair C, we have:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (-1 + 2)/(0 + 3) = (3 - 0)/(8 - 2)

Slope = 1/3 ≠ 1/2 (it does not represents a linear function).

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The value of x is x = 5, and the value of y is y = 6.

What is Pythagorean theorem?

The Pythagorean theorem, also 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 area of the square whose side is the hypotenuse.

We have to find the values of x and y.

First to find the value of x.

Since, by Pythagorean theorem,

3^2 + 4^2 = x^2

     9 + 16 = x^2

          25 = x^2

            5 = x

            x = 5

Now to find the value of y.

Again by using the Pythagorean theorem,

[tex](3 + 5)^2 + 6^2 = (y+4)^2\\64 + 36 = y^2 + 8y + 16\\100 = y^2 + 8y + 16\\y^2 + 8y - 84 = 0\\y^2 + 14y - 6y - 84 = 0\\y(y+14) - 6(y + 14) = 0\\(y -6)(y+14)=0[/tex]

(y - 6) = 0,   (y + 14) = 0

y = 6,  y = -14

Length is not negative.

⇒ y = 6

Hence, the value of x is x = 5, and the value of y is y = 6.

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The set of real numbers is a subset of the set of complex numbers because any real number, a, can be written as a + 0i

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The graph of the linear relationship is represented by the equation y = 3x - 5

An equation is an expression relating two or more numbers and variables.

The standard form of a linear equation is:

Ax + By = C

where A, B and C are constants

The slope - intercept form of a linear equation is:

y = mx + b

Where m is the rate of change(slope) and b is the y intercept.

The graph of the linear relationship was plotted using the points from the table. The graph is attached

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Two centimeters of dilation is considered early labor. At this stage, the cervix is considered "soft" or "favorable" for labor to begin. The cervix has become thinner and softer, allowing the baby to move into the birth canal.

However, the cervix is still long and closed, and the baby is not yet ready to come out.  During this stage, contractions may become more frequent and intense, but they are usually not regular and will often stop and start. Women in early labor may feel cramping, backache, and increased pressure in the pelvis and vagina as the cervix begins to open. If a woman is not having regular contractions, she may be instructed to rest until labor progresses to the active phase.  

Women in early labor may also begin to experience increased vaginal discharge, the "bloody show," as the cervix further softens and thins. At this stage, it is common for the amniotic sac to begin to bulge out of the cervix. This is a sign that the cervix is continuing to dilate, and it may rupture when contractions become more powerful.

At two centimeters of dilation, labor is just beginning, but the cervix is showing signs that it is opening and preparing for delivery. Women should be aware of the signs of early labor and discuss any changes they experience with their healthcare provider.

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There can be an infinite number of integer values of x possible.

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side for it to be a valid triangle. So, for a triangle with side lengths 15, 47 and  [tex]$\dfrac{x}{2}$[/tex] the condition for the triangle to be valid is:

15 + 47 >[tex]$\dfrac{x}{2}$[/tex]

30 > [tex]$\dfrac{x}{2}$[/tex]

2\times30 > x

x > 60

Since xmust be an integer, the possible values of x are any integer greater than 60. Thus, there can be an infinite number of integer values of x possible.

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The factorization of the given expression is 16x² + 8x + 1- 9y² = (4x +3y +1)(4x -3y +1).

What is the meaning of  Factorize?

Factorization or factoring is defined in mathematics as the breaking or breakdown of one entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together provide the original number or matrix, etc.

Given expression is 16x² + 8x + 1- 9y²

Now make two groups of the expression:

(16x² + 8x + 1)- (9y²)

= (16x² + 8x + 1)- (3y)²

Now applying Algerical identity (a + b)² = a² + 2ab + b².

= ((4x)² + 2×4x×1 + 1²)- (3y)²

= (4x + 1)² - (3y)²

Now applying Algerical identity (a² - b²) = (a+ b)(a - b)

= (4x + 1 + 3y)(4x + 1 - 3y)

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Define the problem , Gather information, Generate possible solutions, Evaluate ideas and then choose one, Evaluate are the 5 types of problem-solving.

What are fundamental techniques for fixing issues?

Identifying the issue, considering potential solutions, and selecting the best course of action are the three primary components of problem-solving.

               Different problem-solving techniques include elucidating, ideating, developing, and implementing.

What advantages does problem-solving have?

Making decisions is necessary to solve issues. People who are "happier, more confident, and more autonomous" are typically those who have good problem-solving abilities.

                     Children develop resilience when they take on challenges individually or in groups. They pick up the ability to approach problems from a different angle.

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