25 ft 8 yd 11 in.
Which is greater?

The Fourier series of one period a(x) on [tex]-\pi[/tex] to [tex]\pi[/tex] is 23.096.

What is Fourier series ?

A fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier Series makes use of the orthogonality relationships of the sine and cosine functions. Expand the function f(x) = ex in the interval [ – π , π ] using Fourier series formula.

Have given,

a(x) on domain ([tex]-\pi ,\pi[/tex])

Let ,

I = ∫[tex]\pi[/tex] [tex]e^{x}[/tex] dx

on integration

I = [tex][e^{x}]^{\pi }_{-\pi }[/tex]

I = [tex]e^{\pi } - e^{-\pi }[/tex]

I = 23.14 - 0.043

Thus, I = 23.096

The Fourier series of one period a(x) on [tex]-\pi[/tex] to [tex]\pi[/tex] is 23.096.

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The number 119.43 when approximated to 1 significant figure is 100

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

Number = 119.43

The number is to be approximated to 1 significant figure

This means that we approximate all number leaving only the first digit

When this is done, we have

Approximation = 100

Hence, the number in 1 significant figure is 100

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0.707 is obtained by multiplying one by root 2 . Commonly used to represent the square root is the symbol '√'. Using this symbol, the number "x" can be represented as the square root of "x" by writing '√x'.

A mathematical term for a factor that, when multiplied by itself, equals the original value of the original integer is the square root. Early in the second millennium BC, the Babylonians devised effective methods for approximating square roots.

here

=√2 / 2

= 1 / √2

=√2 / √2=1

=1√2 / √2√2

=√2 / 2

= 0.707

so , 0.707 is obtained by multiplying one by root 2.

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Answer:

5.22 is the answer required

The correct statement regarding the comparison of the linear functions is given as follows:

D. The function shown on the graph has a lower slope and a lower starting point.

The slope of a linear function represents the rate of change of the output variable y relative to the input variable x, that is, the change in y when x is increased by one.

Function y in this problem in this problem is given as follows:

y = 6x + 1.

Considering the slope-intercept definition, we have that:

From the graphed function, we have that:

Thus option D is correct.

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

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Answer:

4 nautical miles per hour

Step-by-step explanation:

Speed = Distance / Time

Distance = Speed x time

D1 = D2

S1 = 16 nautical miles per hour

t1  =10 hours

We know S2 is unknown and the t2 = 8 hours

So, we take

S1 x T1 = S2 x T2

16 x 10 = S2 x 8

S2 = 16 x 10 / 8

S2 = 20 nautical miles per hour

20 - 16 = 4 nautical miles per hour

So, it has to increase its speed by 4 nautical miles per hour

Answer: 4 nautical miles per hour

It is given that in the first case, the ship takes 10 hours to travel at the speed of 16 nautical miles per hour. distance=speed × time=16×10=160 nautical miles. Therefore, the answer to the above question is 4 nautical miles per hour.

Step-by-step explanation:

The value of 0 1 is 1.

This is because any number to the power of 0 is equal to 1. This is part of the fundamental rules of exponents in mathematics. For example, if we take 2 to the power of 0, that would be equal to 2^0=1.

Similarly, 5^0=1, and so on. This is because any number to the power of 0 is equal to 1, regardless of the number. This is because any number multiplied by 1 is equal to itself. This holds true for 0 as well, and so 0^1=1. This is why the value of 0 1 is 1.

This is a basic mathematical equation in which the answer is 1. This equation can be used to illustrate the concept of addition, which is the process of combining two numbers to get a total.

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To determine if a graph has a positive or negative leading coefficient, look at the sign of the coefficient of the first term of the equation for the graph. If the coefficient is positive, the graph has a positive leading coefficient. If the coefficient is negative, the graph has a negative leading coefficient.

To determine the sign of the leading coefficient of a graph, first look at the equation for the graph. The leading coefficient of a graph is the coefficient of the first term in the equation, so find the coefficient of the first term. If the coefficient of the first term is positive, then the leading coefficient is positive. If the coefficient of the first term is negative, then the leading coefficient is negative. For example, if the equation is y = 4x2 + 3x + 5, the coefficient of the first term is 4, and so the leading coefficient is positive. Conversely, if the equation is y = -2x2 + 3x + 5, the coefficient of the first term is -2, and so the leading coefficient is negative.

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To graph a linear equation which is in the form of a straight line one easy method is by identifying two points on that line and drawing a straight line passing through the two points.

A linear equation of the form y = mx + c having slope m and y-intercept c is a straight line.

To find the two points, we can substitute a value for one variable and find the corresponding value of the other variable. In this case

For x = 0

y = -5×0 + 3

y = 3

So (0, 3) is a point on the line y = -5x + 3.

Similarly for y = 0

0 = -5x + 3

5x = 3

x = 3/5 = 0.6

So (0.6, 0) is a point on the line y = -5x + 3.

Now we can graph y = -5x + 3 by joining (0, 3) and (0.6, 0). Refer the attached figure for the graph.

--The question is incomplete, answering to the question below--

"How do you graph y = -5x + 3?"

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The coefficients in a balanced equation compare quantities of two substances by the ratio of the substances' coefficients equals the ratio of their number of moles.

A mole is defined as 6.02214076 × 10²³ of some chemical unit, be it atoms, molecules, ions, or others. The mole is a convenient unit to use because of the great number of atoms, molecules, or others in any substance.

In many chemical situations, mole ratios are employed as conversion factors between products and reactants.

In a balanced chemical equation, the coefficients in front of the formulae can be used to determine the mole ratio.

Complete question:

How do the coefficients in a balanced equation compare quantities of two substances?

A. The ratio of the coefficients equals the ratio of the masses of the

substances

B. The sum of the coefficients of the reactants equals the sum of the

products

C. The ratio of the substances' coefficients equals the ratio of their

number of moles.

D. The coefficient of the reactant tells how many product molecules

will form.

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A mole is defined as 6.02214076 × 10²³ of some chemical unit, be it atoms, molecules, ions, or others. The mole is a convenient unit to use because of the great number of atoms, molecules, or others in any substance.

In many chemical situations, mole ratios are employed as conversion factors between products and reactants.

Complete question:

How do the coefficients in a balanced equation compare quantities of two substances?

A. The ratio of the coefficients equals the ratio of the masses of the

substances

B. The sum of the coefficients of the reactants equals the sum of the

products

C. The ratio of the substances' coefficients equals the ratio of their

number of moles.

D. The coefficient of the reactant tells how many product molecules

will form.

An example of a complex equation is the Navier–Stokes equations, which are used to describe the motion of fluids and are one of the most important equations in fluid mechanics.

A complex equation is a mathematical expression that contains multiple variables, operations, and powers. This can include exponents, logarithms, trigonometric functions, and other variables. Complex equations can be used to solve problems or to make predictions, and can be used in a wide range of fields, including economics, engineering, and physics.

These equations consist of a set of partial differential equations that describe the motion of a fluid, such as air or water, and the forces acting on it. The Navier–Stokes equations are used to predict the behavior of liquids and gases in a wide range of applications, from aeronautics, to weather prediction, to oceanography.
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The legs of a right isosceles triangle are the height and the base of the right isosceles triangle.

It is known that an isosceles triangle is a triangle which has two equal sides.

It is a right isosceles triangle when one side of the triangle is a perpendicular dropped from the vertex and forms a right angle with the base.

As the two sides are equal, the base also turns out to be perpendicular to the height forming a hypotenuse of the third side.

Hence, the two perpendiculars base and height are considered to be the legs of the right isosceles triangle.

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The graph that grows the fastest is green i.e., the graph of exponential function.

In this question we need to determine which  graph grows the fastest.

Given graph contains graph of quadratic function (blue colored graph), exponential function (green colored graph), cubic function (pink colored graph) and linear function (black straight  line)

We know that the exponential function grows faster because it grows by a factor that is multiplied by the previous y-value instead of being added

like the linear function.

In given graph the green function is an exponential function and it grows the fastest.

Therefore, the green graph grows the fastest.

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Consider following image.

To solve for x in an angle, you first need to identify what type of angle you are dealing with. Depending on the type of angle, you will use different formulas to solve for x. For example, if you are dealing with a right angle, you can use the Pythagorean Theorem to solve for x.

1. Identify the given information:-

First, identify the type of triangle and the angles that are given.

2. Use the appropriate formula:-

If it is a right triangle, use the Pythagorean Theorem to solve for the missing side. If it is an isosceles triangle, use the law of sines to solve for the missing angle.

3. Substitute the given values into the appropriate formula:-

Substitute the given values into the appropriate formula and simplify.

4. Solve for the unknown:-

Solve the equation for the unknown value (x).

5. Check your answer:-

Check your answer by plugging it back into the original equation to make sure it is correct.

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The change of score of the test score from 8 to 80, would have the greatest effect on A. Mean.

Numbers in a data collection that are significantly greater or smaller than the rest are known as outliers. The metrics of central tendency are mean, median, and mode. The only index of central tendency that is consistently impacted by an outlier is the mean.

The value of 8 was an outlier from the rest of the test scores and so it would have had a great effect on mean. If the score was taken back to 80, then the mean would be adjusted correctly and change the greatest.

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Perimeter of the NCAA court is 288288 ft

Perimeter of the new court is 259.2ft

Perimeter of NCAA court

=2(length +width)

=2(94ft+50ft)

=2⋅144ft

=288ft

The perimeter of the new court in the school:

=2(length +width)

=2(84.6ft+45ft)

=2⋅129.6ft

=259.2ft

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​

First make the graph of the functions, then  if the two graphs are symmetric with respect to the line y = x (mirror images over y = x ), then they are inverse functions.

Symmetric

A figure or shape that can be divided into two equal parts by a line is called symmetric figures.

Inverse Functions

The inverse function of a function f  is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by F^-1.

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Answer: (read the explanation)

Step-by-step explanation:

To graph the solution set to the given system of inequalities, we can begin by graphing the two inequalities separately. For the first inequality, y > x^2 – 2, we can graph the function y = x^2 – 2 on the coordinate plane and shade the region above the graph. This will represent the values of x and y that satisfy the inequality.

For the second inequality, y ≥ –x^2 + 5, we can graph the function y = –x^2 + 5 on the coordinate plane and shade the region below the graph. This will represent the values of x and y that satisfy the inequality.

Next, we can combine the two graphs by intersecting the shaded regions. The resulting graph will show the solution set to the system of inequalities. The solution set can be identified as the points on the coordinate plane that are contained within the shaded region on the combined graph.

Overall, to modify the graphs of f(x) and g(x) to graph the solution set to the given system of inequalities, we can graph the functions y = x^2 – 2 and y = –x^2 + 5 on the coordinate plane and shade the regions that satisfy the inequalities. The solution set can then be identified as the points within the shaded region on the resulting combined graph.

Answer:

Step-by-step explanation:

3000000000000000000000000000000000000

In total, 15 to 16 gallons or 55 to 60 liters of paint were used to paint the interior of your 2000 square foot home.

It might be challenging to calculate or estimate the precise amount of paint that you will need when painting your home. Every paint has a varied coverage, which determines how many square feet may be painted with each gallon of paint.

According to a rule of thumb and general recommendations, you will need about 15 to 16 gallons, or 55 to 60 liters, of interior paint for a G+1/2 storey house with a 2000 square foot area, as well as 3 gallons of paint for interior trim for two to three coats, which includes painting the interior surface/wall area, overhangs, and soffits. In total, 15 to 16 gallons or 55 to 60 litres of paint were used to paint the interior of your 2000 square foot home.

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Can you explain the rest of the problem please?

The value of the sine of angle D to the nearest hundredth will be 0.25.

The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.

The sine law in the triangle ΔCDE is given as,

CD / sin E = DE / sin C = EC / sin D

In triangle ΔCED, the measure of angle ∠E = 90°, ED = 63, DC = 65, and CE = 16. Then we have

65 / sin 90° = 63 / sin C = 16 / sinD

Compare the first and the last term, then we have

65 / sin 90° = 16 / sin D

65 = 16 / sin D

sin D = 16 / 65

D = 14.25°

The worth of the sine of point D to the closest 100th will be 0.25.

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Answer:

slope of line w = - [tex]\frac{8}{4}[/tex]

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 )

y = [tex]\frac{5}{8}[/tex] x + [tex]\frac{9}{4}[/tex] ← is in slope- intercept form

with slope m = [tex]\frac{5}{8}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{5}{8} }[/tex] = - [tex]\frac{8}{5}[/tex]

The domain and scope of the identity function are the same. Equation for the identity function is  f(x) = x, or y = x.

An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.

identity function are the same.

Equation for the identity function is

f(x) = x, or y = x.

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The 4 types of algebra are  Elementary Algebra,  Linear Algebra, Abstract Algebra, Boolean Algebra.

1. Elementary Algebra - This type of algebra deals with basic operations such as addition, subtraction, multiplication, and division. An example of elementary algebra is solving for x in the equation 2x + 3 = 7. In this equation, the variable x has a value of 4.

2. Linear Algebra - This type of algebra deals with linear equations and linear transformation. An example of linear algebra is solving for the vector x in the equation Ax = b, where A is a matrix and b is a vector.

3. Abstract Algebra - This type of algebra deals with abstract concepts such as groups, rings, and fields. An example of abstract algebra is finding the inverse of a matrix A. The inverse of A can be found by solving the equation A x A-1 = I, where I is the identity matrix.

4. Boolean Algebra - This type of algebra deals with logical operations such as OR, AND, NOT, and XOR. An example of Boolean algebra is finding the logical complement of a statement P. The logical complement of P can be found by solving the equation P OR NOT P = TRUE.

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As the correlation coefficient moves from 0 to 1 or -1 to 0, the points would be closer to the line. Option A

The term correlation coefficient is used to show the level of the relationship between the variables. If the correlation coefficient is very close to 1 then it means that there is greater association between the variables. If it is far from one then it means that the variables are not associated at all.

We know that the regression lines show how variables can be associated and they can be used to show us the relationship between variables.

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