The elementary school in your town wants to replace its current playground. The space used for the new playground will be similar to that of the current playground. The current space is rectangular and has a length of 24 feet and a width of 26 feet. The length of the new space is 36 feet. Find the perimeter of the space used for the new playground.

The features of the sine function are given as follows:

The equation is given as follows:

y = 3sin(0.25πx) + 1.

The standard definition of a sine function is given as follows:

y = Asin(Bx) + C.

The parameters are given as follows:

The minimum value is of -2, while the maximum value is of 4, hence the midline is given as follows:

y = (-2 + 4)/2

y = 1.

The difference between the minimum and the maximum value is of 6 units, hence the amplitude is obtained as follows:

2A = 6

A = 3.

The function with no vertical shift would oscillate between -A = -3 and A = 3, while this function oscillates between -2 and 4, hence the vertical shift is given as follows:

C = 1.

The shortest distance between repetitions of the function is of 8 units, hence the period is of 8, the frequency is of 1/8, and the coefficient B is given as follows:

2π/B = 8

8B = 2π

B = π/4.

B = 0.25π.

Hence the function is defined as follows:

y = 3sin(0.25πx) + 1.

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The antiderivative of sin is -cos(x) + C.

The antiderivative of a function is the inverse operation of differentiation which is is also known as its indefinite integral.

So, the integral of sin

                 ∫sin(x) = -cos(x) + C

where C = constant of integration.

This can be verified by differentiating -cos(x) + C with respect to x, which gives sin(x).

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Work Shown:

5/32 divide 25/4

(5/32) * (4/25)

(5*4)/(32*25)

(5*4)/(8*4*5*5)

(1)/(8*5)

1/40

There are 6 employees who play musical instruments.

What is the ratio?

A ratio is a relationship between two quantities, indicating how many times the first quantity contains the second. Ratios are often expressed as a fraction or in the form "a:b", where "a" and "b" are the two quantities being compared.

The given ratio of employees who play musical instruments to employees who play sports is 3:20. This means for every 3 employees who play musical instruments, there are 20 employees who play sports.

We are given that there are 40 employees who play sports. We can use this information to find the number of employees who play musical instruments as follows:

Let's start with the ratio of employees who play sports to employees who play music, which is 20:3. This means that for every 20 employees who play sports, there are 3 employees who play music.

We know that there are 40 employees who play sports, so we can set up a proportion to find the number of employees who play music:

20/3 = 40/x

where x is the number of employees who play music.

To solve for x, we can cross-multiply:

20x = 3 * 40

20x = 120

Then, we can solve for x by dividing both sides by 20:

x = 6

Therefore, there are 6 employees who play musical instruments.

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In 1 billion, the probability of division being incorrect would be : {1/(11 x 10⁹)²}.

In science, the probability of an event is a number that indicates how likely the event is to occur.

Given is that the manufacturer initially claimed that the chance of any particular division being incorrect was only 1 in 11 billion.

The probability of division being incorrect would be -

P{incorrect} = (1/11 x 10⁹)

In 11 billion, the probability of division being incorrect is (1/11 x 10⁹).

Then, in 1 billion, the probability of division being incorrect would be -

{1/(11 x 10⁹)²}

Therefore, in 1 billion, the probability of division being incorrect would be : {1/(11 x 10⁹)²}.

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Answer:

Step-by-step explanation:

0.0869

Answer: look at the image for the answer and explanation

Step-by-step explanation:

Answer: 7 x 4 = 28

Step-by-step explanation: 7 + 7 + 7 + 7 = 28

The integral of sec(x) is ln |sec(x) + tan(x)| + C.

The integral of sec(x) is:

∫sec(x) dx = ln |sec(x) + tan(x)| + C

where C is the constant of integration.

To solve this integral, you can use the method of substitution. Let u = sec(x) + tan(x). Then [tex]du/dx = sec(x)tan(x) + sec^2(x)[/tex], which can be simplified to du/dx = u tan(x). Rearranging, we get du/u = tan(x)dx.

Substituting these expressions into the integral, we have:

∫sec(x) dx = ∫(sec(x) + tan(x))/(sec(x) + tan(x)) dx = ∫(1/u) du

Integrating this expression gives:

∫(1/u) du = ln |u| + C = ln |sec(x) + tan(x)| + C

Therefore, the integral of sec(x) is ln |sec(x) + tan(x)| + C.

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65  °F is equal to 18.3333 °C.

A temperature unit developed from the SI (International System of Units) is Celsius (symbol: °C).

Prior to the adoption of the metric system, Fahrenheit (symbol: °F) was a commonly used measurement of temperature.

To convert a temperature from Fahrenheit (°F) to Celsius (°C),

We can use the following formula:

°C = (°F - 32) x 5/9

Where °C is the temperature in Celsius

°F is the temperature in Fahrenheit.

Substituting 65 for °F,

We get:

°C = (65 - 32) x 5/9

Simplifying the expression:

°C = 33 x 5/9

°C = 18.3333333333

Therefore, 65 degrees Fahrenheit is equal to nearly 18.3333 degrees Celsius (rounded to four decimal places).

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The answer is 84 pairs of pants.

Explanation:
According to the problem, she donated half of her pants to charity, which means she donated (1/2)x pairs of pants.

After donating half of her pants, she kept her 7 favorite pairs of pants. So, the number of pairs of pants she kept is 7.

The problem states that she was left with 35 pairs of pants after donating half of her pants and keeping her 7 favorite pairs. This means that the remaining number of pairs of pants is (x/2) - 7 = 35.

Solving for x, we get:

(x/2) - 7 = 35

x/2 = 42

x = 84

Therefore, Kim had 84 pairs of pants in the beginning.

Answer:

my guess is 17 .,.

Step-by-step explanation:

The correct answer is:

greater than zero for all values of x.

Probability is a way of evaluating how likely something is to happen. Several things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.  One is the probability of every event in a sample space.

Now in the given question ,

A probability density function (PDF) of a continuous random variable x is a function that describes the relative likelihood of x taking on different values in a continuous range. The PDF is defined such that the area under the curve between any two values a and b represents the probability of x being in that range, i.e., P(a ≤ x ≤ b).

Since probabilities are non-negative, the PDF of a continuous random variable must also be non-negative. That is, f(x) > 0 for all values of x. This condition ensures that the area under the curve is non-negative, which is necessary for it to represent a valid probability distribution.

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Answer:

Step-by-step explanation:

No, the point is not (1,0)

Online calculator of variable cost is used to Total Variable Cost = Total Cost-Fixed Costs to calculate the Total Variable Cost.

A variable cost is an expense that changes as a company's production output rises and falls. Variable expenses vary according on the amount of output produced. Basic variable costs include, in large part:

Variable costs are frequently employed in business and are a crucial component of the analysis of the company's break-even point. The revenue or unit that must be sold to cover all costs is examined using the break-even approach.

The following calculation is the break-even point:

Break-even point in units = Fixed costs/(Sales price per unit – Variable cost per unit)

Variable costs are crucial for successful investors because they help them calculate the proportion of the set price and predict how the company will respond to various operational scenarios.

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At the end of 18 years, there will be a total of $5,890.37 in the account.  

Compound interest is a powerful financial tool that can help you grow your money over time.

In the case of the $1,800 deposited into an account earning 6% interest compounded weekly, the total amount in the account at the end of 18 years can be calculated as follows:

Let P be the principal balance, r be the interest rate, n be the number of times the interest is compounded per year, and x be the number of years. Using the compound interest formula, we can calculate the amount in the account at the end of 18 years:

A = P(1 + (r/n))ⁿˣ

A = 1800 * (1 + (0.06/52))⁵²ˣ¹⁸

A = 5,890.37

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The statement that "a surface generated by a closed plane curve rotated about a line that lies in the same plane as the curve but does not intersect" is true.

The surface generated by a closed plane curve rotated about a line that lies in the same plane as the curve but does not intersect it is called a torus. The torus is a three-dimensional surface that can be thought of as a doughnut shape. The curve that generates the torus is called the generator, and the line about which the curve is rotated is called the axis of rotation. The torus has the interesting property that it has a hole in the center, and the distance from any point on the surface to the center of the torus is constant.

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Answer:

21x + 7

Step-by-step explanation:

See picture below :)

Answer:

Penny had 13/20 of the pizza left.

Step-by-step explanation:

Let's start with the whole pizza, which we can represent as 1.

Pania ate a quarter of the pizza, leaving 3/4 (since 1/4 + 3/4 = 1) for Pita and Paula.

Pita then ate one sixth of what remained, which is one sixth of 3/4 or 3/24, leaving 21/24 (or simplifying to 7/8) for Paula.

Paula then ate two fifths of what remained after Pita had eaten, which is two fifths of 7/8 or 14/40, leaving 26/40 (or simplifying to 13/20) for Penny.

Therefore, Penny had 13/20 of the pizza left.

I hope this helps! And if you could label my answer brainliest that would be awesome.

- Dante

Answer:

3/8 of the pizza was left for Penny.

Step-by-step explanation:

Pania ate 1/4 and left 3/4.

Pita ate 1/6 (of the 3/4) and left 5/6.

Paula ate 2/5 (of the 5/6) and left 3/5.

What was left?

3/5 of 5/6 of 3/4

"of" means times

3/5•5/6•3/4

(cancel the 5s and a 3 with the 6, leaving a 2)

= 3/8

But see the illustrated story, it makes way more sense! See image

Answer:

67.872

Step-by-step explanation:

Answer:a

Step-by-step explanation:

70 degrees Fahrenheit is equal to approximately 21.1111 degrees Celsius (rounded to four decimal places).

The Celsius (symbol: °C) is an SI (International System of Units) derived unit of temperature.

The Fahrenheit (symbol: °F) is a unit of temperature that was widely used prior to metrication.

To convert a temperature from Fahrenheit (°F) to Celsius (°C),

We can use the following formula:

°C = (°F - 32) x 5/9

Where °C is the temperature in Celsius and °F is the temperature in Fahrenheit.

Substituting 70 for °F, we get:

°C = (70 - 32) x 5/9

Simplifying the expression:

°C = 38 x 5/9

°C = 21.1111111111

Therefore, 70 degrees Fahrenheit is equal to approximately 21.1111 degrees Celsius (rounded to four decimal places).

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The simplified answer is [tex]-16n^2 - 4n - 4.[/tex]

In mathematics, simplification refers to the process of simplifying an expression or equation without affecting its fundamental meaning or value. Using mathematical tools and rules to simplify an equation makes it simpler to manipulate or solve.

In algebra, simplification might take the form of factoring out common factors, grouping like concepts, or distributing multiplication across addition or subtraction. For instance, merging two like terms will simplify the formula 2x + 4x to 6x. The same strategy can be used to reduce the expression 3(x + 2) - 2(x - 1) to 3x + 4 by spreading out the multiplication and combining related terms.

Other types of mathematical simplification include determining the square root of a number, simplifying trigonometric functions, and reducing fractions to their simplest forms. In order to solve difficulties and comprehend mathematical concepts, simplification is a crucial step that removes superfluous complexity and facilitates understanding of the underlying structure of an equation or problem.

To find the product of 4 and the expression [tex](-4n^2 - n - 1),[/tex] we can distribute the 4 to each term inside the parentheses:

[tex]4(-4n^2 - n - 1) = -16n^2 - 4n - 4[/tex]

Therefore, the simplified answer is [tex]-16n^2 - 4n - 4.[/tex]

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In the given equation, the constant 6 represents the initial height of the football when it was thrown. This means that before the football was thrown, it was already at a height of 6 feet above the ground.

A mathematical equation proves the equality of two expressions by using symbols, numbers, and/or variables. Equations can be used to illustrate relationships between several numbers or to locate unknown values in order to solve problems.

An equation typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), which are separated by an equal sign (=). The LHS and RHS can contain constants, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

a. The constant 6 in equation f(t) = 6 + 30t - 16t represents the initial height of the football when it was thrown.

b. The term 30t in the equation represents the vertical distance covered by the football per second due to its initial velocity. This term is calculated by multiplying the initial velocity of the football by the time t.

c. The squared term -16t^2 in the equation represents the effect of gravity on the height of the football. This term is calculated by multiplying half the acceleration due to gravity (-16 feet per second squared) with the square of time t. The negative sign indicates that the height of the football is decreasing as time passes due to the influence of gravity.

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Answer:

Step-by-step explanation:

left a book at home. He turned around and walked home at the same speed.

The value of x is 2.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The point as far as she can tell are (3,5) and (x,10).

Slope is -5.

-5=10-5/x-3

-5=5/x-3

-5(x-3)=5

Apply distributive property

-5x+15=5

Substitute 15 from both sides

-5x=-10

Divide both sides by 5

x=2

Hence, the value of x is 2.

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Nominal, ordinal, interval, and ratio are measurement scales used in statistics to categorize and rank data.

Nominal, ordinal, interval, and ratio are four sorts of information estimation scales utilized in measurements.

Nominal scales are utilized to mark or classify information into particular gatherings, where each gathering is fundamentally unrelated and altogether comprehensive. Instances of ostensible information incorporate orientation, race, and occupation.

Ordinal scales include positioning information in a particular request, however the distinctions between values are not significant. Instances of ordinal information incorporate positioning motion pictures in view of their prominence or understudy execution on a test.

interval scales include positioning information in a particular request, however the distinctions between values are significant, and there is no obvious zero point. Instances of stretch information incorporate temperature, intelligence level scores, and time.

ratio scales are like span scales, however they have a genuine zero point, implying that values can be duplicated and partitioned. Instances of proportion information incorporate weight, level, and pay.

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The complete question is:

what is the nominal, ordinal, interval and ratio?

The correct answer is option B and it is equal to 30% of 81 because it shows 0.30 x 81.

We have to find that how much is equal to the 30% of 81.

We can use the percentage formula here and that is,

%age = Obtained value/total value x 100

Here in this case, we have to find the obtained value and the total value is 81 and the percentage that we are going to get  is equal to 30.

So, putting all the values, we get,

obtained value = 30 x 81/100

obtained value = 0.30 x 81

Hence, the value 0.30 x 81 is equal to 30 % of 81. hence option B is the correct answer.

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Complete question - Which of the following options have the same value as 30% of 81?

A. 0.03 x 81

B. 0.3 x 81

C. 0.03 x 81

D. 3 x 81

the shaded segment PQR will be 18.265m².

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The sum of all angle of triangle = 180

the diagram shows a sector OPQR of a circle, centre O and radius 8 cm.

Area of shaded part = Area of quadrant − Area of triangle

=πr²/ 4 - 1/2 bh

= π × 8²/ 4  - 1/ 2 × 8× 8

= 18.265m².

Hence the shaded segment PQR will be 18.265m².

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Answer:

Unit rate = 0.6

y = 0.6x

x= 24

Step-by-step explanation:

I cannot see the headings to the table, but on examining the questions, the first column contains the values for variable x and the second column the values for variable y

Unit Rate

Unit rate = increase in y for a unit increase in x
We see that the rate is constant for every unit increase in x and is = 0.6
Unit rate = 0.6

Equation
The equation therefore is y = 0.6x

Value of x when y = 14.4
When y = 14.4, plugging into the equation gives:
14.4 = 0.6x
or
0.6x = 14.4  by switching sides - no effect on equation

Divide both sides by 0.6
0.6x/0.6 = 14.4/0.6
x= 24

108ft is the length of the of the guy wire

Triangles are known to be similar if the ratio of the similar sides of the triangle are equal.

From the given diagram, we need to determine of the guy wire. Using the similarity theorem of a triangle;

8/2 = l/25+2
8/2 = l/27

2l = 8 * 27

l = 4 * 27

l = 108 ft

Hence the length of the of the guy wire, to the nearest foot is 108ft

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The number of $56 dollar tickets to center section was 200 and the number of tickets costing $38 to the left and right sections were 200.

Let us consider the number of tickets to the center section be x and right and left sections be y.

Here the total number of tickets sold are 540.

So,  x+ y = 540  ---------> i

The cost of tickets cost $56 will be 56x

The cost of tickets cost $38 will be 38y.

The total cost was given as $24120

So, 56x+ 38y = 24120 -----------> ii

Multiplying equation i with 56,

56x + 56y = 30240  ------------> iii

Subtracting equation ii from equation iii

   56x+ 56y = 30240

-   56x + 38y = 24120

So 18y = 6120

      y = 6120/18 = 340

Since x+ y = 540

          x+ 340 = 540

          x = 540- 340 = 200

So the number of $56 ticket sold is 200 and the number of $38 ticket sold is 340.

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