Write the fraction that would land on point A on the number line.

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Answer:

A) A = 200w - w²

B) w = 100 yards

C) Max Area = 10000 sq.yards

Step-by-step explanation:

We are told that Robert has available 400 yards of fencing.

A) we want to find the expression of the area in terms of the width "w".

Since width is "w", and perimeter is 400,if we assume that length is l, then we have;

2(l + w) = 400

Divide both sides by 2 gives;

l + w = 200

l = 200 - w

Thus, Area of rectangle can be written as;

A = w(200 - w)

A = 200w - w²

B) To find the value of w for which the area is largest, we will differentiate the expression for the area and equate to zero.

Thus;

dA/dw = 200 - 2w

Equating to zero;

200 - 2w = 0

2w = 200

w = 200/2

w = 100 yards

C) Maximum area will occur at w = 100.

Thus;

A_max = 200(100) - 100(100)

A_max = 10000 sq.yards

Stokes' theorem relates the surface integral of the curl of \(\vec F\) across \(S\) to the line integral of \(\vec F\) along the boundary of \(S\).

The boundary of \(S\) is a circle with radius 7 centered at the origin in the \(x,y\)-plane. Parameterize this path by

\(\vec r(t) = 7\cos(t)\,\vec\imath + 7\sin(t)\,\vec\jmath\)

with \(0\le t\le2\pi\). Observe that \(z=0\), so \(\cos(z) = 1\) and the \(\vec\jmath\)-component of \(\vec F\) contributes nothing. The double integral then reduces to

\(\displaystyle \iint_S (\nabla\times\vec F)\cdot d\vec S = \int_0^{2\pi} \vec F(\vec r(t)) \cdot \frac{d\vec r}{dt} \, dt \\\\ ~~~~~~~~ = \int_0^{2\pi} \left(e^{49\cos(t)\sin(t)}\,\vec\imath + 49\cos(t)\sin(t)\,\vec\jmath\right) \cdot \left(-7\sin(t)\,\vec\imath + 7\cos(t)\,\vec\jmath\right) \, dt \\\\ ~~~~~~~~ = -7 \int_0^{2\pi} e^{49\cos(t)\sin(t)} \sin(t) \, dt\)

Observe that by substituting \(t=u+\pi\), we have

\(\sin(t) = \sin(u+\pi) = \sin(u)\cos(\pi) + \cos(u)\sin(\pi) = -\sin(u)\)

so that the integral over \([\pi,2\pi]\) can be expressed in terms of the integral over \([0,\pi]\) as

\(\displaystyle \int_\pi^{2\pi} e^{49\cos(t)\sin(t)} \sin(t) \, dt = \int_0^\pi -e^{49\cos(t)\sin(t)} \sin(t) \, dt\)

Then the integrals over \([0,\pi]\) and \([\pi,2\pi]\) cancel each other and integral of the curl of \(\vec F\) is

\(\displaystyle -7 \int_0^{2\pi} e^{49\cos(t)\sin(t)} \sin(t) \, dt = -7 \int_0^\pi 0 \, dt = \boxed{0}\)

After answering the presented question, we may conclude that  the solution of the expressions are as follows.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

the solution of the expressions are as follows -

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Step-by-step explanation:

The limit of (sin(x)) / x as x approaches 0 is a well-known limit in calculus, known as the limit definition of the derivative of the sine function.

lim (x -> 0) (sin(x)) / x = 1

This limit can be proven using L'Hopital's rule or by considering the Taylor series expansion of the sine function about x = 0:

sin(x) = x - (x^3) / 6 + (x^5) / 120 + ...

As x approaches 0, the higher order terms in the Taylor series become arbitrarily small, and the expression (sin(x)) / x approaches 1. This shows that the limit of (sin(x)) / x as x approaches 0 is equal to 1.

A quotient will be halved if the divisor is doubled

information given in the question include

the divisor in a division problem is doubled

how does the quotient change = ?

Mathematics is fundamentally about patterns and structures. They enable to recognize when something intriguing is occurring and to broaden comprehension.

using division by two              

64 / 2 = 32

32 / 2 = 16

16 / 2 = 8

8 / 2 = 4

increasing the divisor by double

64 / 4 = 16

32 / 4 = 8

16 / 4 = 4

4 / 4 = 1

using division by 5

100 / 5 = 20

increasing the divisor by double

100 / 10 = 10

comparing the pattern we can see that doubling the  divisor by will half the quotient

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Answer:

16984

Step-by-step explanation:

Given

\(a = 16000\) ---- Initial

\(r = 1\%\) --- rate

Required

Determine the population after 6 years

To do this, we make use of the following exponential function

\(f(x) = a(r+1)^x\)

Substitute values for a and r

\(f(x) = 16000(1\%+1)^x\)

Express 1% and decimal

\(f(x) = 16000(0.01+1)^x\)

\(f(x) = 16000(1.01)^x\)

The population after 6 years is:

Substitute 6 for years

\(f(6) = 16000(1.01)^6\)

\(f(6) = 16984.3224096\)

\(f(6) = 16984\) -- approximated

The distance between point P and line L is 16/9√(13).

To find the distance between point P and line L, we can use the formula for the distance between a point and a line in two-dimensional space. The formula is as follows:

Let P = (x1, y1) be the point and L be the line ax + by + c = 0. Then the distance between P and L is:

|ax1 + by1 + c|/√(a² + b²)

To find a, b, and c for the given line, we need to put it in slope-intercept form y = mx + b by solving for y.

2x - 3y = 12=> 2x - 12 = 3y=> (2/3)x - 4 = y

The slope of the line, m, is the coefficient of x, which is 2/3. Therefore, the line is:

y = (2/3)x - 4The values of a, b, and c are: a = 2/3b = -1c = -4

Now we can substitute the coordinates of P and the values of a, b, and c into the formula for the distance between a point and a line.

Let P = (3, 5).|a(3) + b(5) + c|/√(a² + b²)= |(2/3)(3) - 1(5) - 4|/√[(2/3)² + (-1)²]= |-4/3 - 4|/√(4/9 + 1)= 16/9√(13).

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Answer:

Step-by-step explanation:

\(3x+ 2y=18\\\\Let \:x\:equal\:to\:0\\\\3(0)+2y=18\\\\0+2y=18\\\\2y=18\\\\Divide \:both\:sides\:of\:the\:equation\:by \:2\\\frac{2y}{2} =\frac{18}{2} \\\\y =9\\(0,9)\)

Answer:

y = 9

Step-by-step explanation:

3x + 2y = 18

required:

find the y-intercept

we have to eliminate x to get the y intercept value

3(0) + 2y = 18

2y = 18

y = 18/2

y = 9

so the x & y intercept would be (0, 9)

Answer: . x 10^5 miles from the earth. How long does it take light to from a source on earth to reach a reflector on the moon and then return to earth? The speed of light is 3.0 x 10^8 m/s. ... sec. to give us our final answer of 1.28 seconds (the time required for light to travel 2.4 x 105 miles). and the fastest spaceship goes 153,454 miles per hour

Step-by-step explanation:

The number of hours that should be taken to fly to the moon from Earth is 7 hours.

Given that

Now we know that

\(Time = \frac{Distance}{Speed} \\\\= \frac{2.4 \times 10^5 }{3.6 \times 10^4} \\\\= \frac{240}{36}\)

= 6.66 hours

= 7 hours

Therefore we can conclude that The number of hours that should be taken to fly to the moon from Earth is 7 hours.

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The graphing form of the function g(x) is: C) none of the answer choices.

The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.

Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:

a = 1 (coefficient of x^2)

b = 4 (coefficient of x)

c = -7 (constant term)

Therefore, the graphing form of the function g(x) is:

C) none of the answer choices

None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.

In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.

The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C

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Answer:

y = 5^(x+1)

Step-by-step explanation:

y = 5^(x+1)

x = 1 for the initial step

The difference between the depths in February and July is 31 feet.

The method of measuring depth depends on what we are trying to measure the depth of. Here are some general methods for measuring different types of depth:

Depth of water: The depth of water can be measured using a sounding device such as a sonar or a simple depth gauge. A sonar uses sound waves to determine the distance from the water's surface to the bottom. A depth gauge is a simple device that measures the distance from the surface of the water to the bottom using a weight and a line.

Depth of a hole: The depth of a hole can be measured using a tape measure or a ruler. Simply insert the measuring device into the hole and measure the distance from the top of the hole to the bottom.

Depth of a trench: The depth of a trench can be measured using a measuring tape or a surveyor's level. Place the measuring device at the edge of the trench and measure the distance from the top of the trench to the bottom.

Depth of a pool: The depth of a pool can be measured using a pool depth marker or by using a measuring tape. A depth marker is usually located on the side of the pool and indicates the depth at various points. Alternatively, you can use a measuring tape to measure the distance from the surface of the water to the bottom of the pool.

Depth of a well: The depth of a well can be measured using a well sounder or a tape measure. A well sounder is a device that sends a signal down the well and measures the time it takes for the signal to bounce back. The time it takes is then used to calculate the depth of the well. Alternatively, a tape measure can be used to measure the distance from the surface of the water to the bottom.

Given, In February, it measured 6 ft deep, or |−6| and in July, it was 25 ft deep, or |−25|.

The difference between the depths in February and July is:

|−6| − |−25| = 6 − (−25) = 6 + 25 = 31

Therefore, the correct choice is B) 31 feet.

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What is your question?

Answer:

yeah what's your question?

In ΔRST, s = 58 inches, ∠R=115° and ∠S=19°. the length of r, to the nearest 10th of an inch, is 365.9 Inches

Law of sines is a formula relating the length of the sides of a triangle to the angles of the triangle.

a/Sin A = b/Sin B = c/Sin C

Where a is the side facing angle A, b is the side facing angle B and c is the side facing angle C.

Hence,

58/Sin 19 = r/Sin 115

r = 58 Sin 115/ Sin 19

= 365.9 Inches

Therefore, In ΔRST, s = 58 inches, ∠R=115° and ∠S=19°. the length of r, to the nearest 10th of an inch, is 365.9 Inches.

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ANSWER:

The probability is 73.3%

STEP-BY-STEP EXPLANATION:

In this case, to calculate the probability, two values must be taken into account.

The number of students who do not play an instrument and the total number of students, the probability would be the quotient between these two values, like this:

Both the domain and range of the transformed function are the same as those of the parent function.

What are Range and Domain?

The collection of all potential output values that a function can generate given its domain is known as its range.

The set of all potential input values for which a function is specified is referred to as its domain.

The function that results from translating the left 5 units and reflecting the function f(x) = |x| across the y-axis is g(x) = |-x + 5|.

Since any real number's absolute value is always non-negative, the original function's domain is all real numbers, or f(x) = |x|.

A function's domain remains unaffected when it is reflected across the y-axis. Since all real numbers fall within the domain of the modified function g(x) = |-x + 5|, this is also true.

Since each real number's absolute value is always non-negative, the original function's range is also all non-negative real numbers, f(x) = |x|.

A function's sign is reversed when it is reflected across the y-axis. Since all non-negative real numbers fall within this range, the transformed function g(x) = |-x + 5| also has this range as well

So, the correct statement about the domain and range of each function is: Both the domain and range of the transformed function are the same as those of the parent function.

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Solution

We are required to graph the function f(x) = int(x - 1)

The graph of the function is shown below

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\( \frac{1}{2} x + 3 = \frac{2}{3} x + 1 \\ \)

Subtract sides 3

\( \frac{1}{2} x + 3 - 3 = \frac{2}{3} x + 1 - 3 \\ \)

\( \frac{1}{2} x = \frac{2}{3} x - 2 \\ \)

Multiply sides by 6

\(6 \times \frac{1}{2} x = 6 \times \frac{2}{3} x + 6 \times ( - 2) \\ \)

\(3x = 4x - 12\)

Subtract sides 4x

\( - 4x + 3x = - 4x + 4x - 12\)

\( - x = - 12\)

Negatives simplifies

\(x = 12\)

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CHECK :

\( \frac{1}{2} (12) + 3 = \frac{2}{3} (12) + 1 \\ \)

\(6 + 3 = 8 + 1\)

\(9 = 9\)

Thus the solution is correct .

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Answer:

\(\bf \sf \dfrac{1}{3}\)

Take points: (6, 2), (3, 1)

\(To \ find \ proportionality = \sf \dfrac{y_2-y_1}{x_2-x_1}\)

Insert values

\(\rightarrow \sf \dfrac{1-2}{3-6}\)

Simplify

\(\rightarrow \sf \dfrac{-1}{-3}\)

Cancel out the negatives

\(\rightarrow \sf \dfrac{1}{3}\)

Answer:

B) \(\frac{1}{3}\)

Step-by-step explanation:

When y varies directly with x, the relationship is \(y=kx\) where \(k\) is the constant of proportionality. Hence, \(k=\frac{y}{x}\).

So, your answer would not be correct because you did \(\frac{x}{y}\) instead of \(\frac{y}{x}\), so the correct option would be the reciprocal, or \(\frac{1}{3}\).

Answer:

The answer is "\(H_0:\mu \geq 50.1\ \ and \ \ H_0: \mu \geq 50.1\)"

Step-by-step explanation:

An initial random selection of mail-order physicians representing firm A worked an average of 50.1 hours per week. My goal is to reject the Null Hypothesis since it is employed to make no difference. In this case,\(H_0 =\mu \geq50.1\)

Medical insurance changes are attributed to reducing the average workweek. New medical coverage is claimed to be have reduced your average workday after the government change. \(H_1: \mu <50.1\)

Answer -

i think its \(8.5*10^{-5}\)

Answer:a car

Step-by-step explanation:

Using the law of sines, equation A). \(\frac{sin(51)}{2.6} = \frac{sin(76)}{z}\) is correct and can be used to solve for the value of z.

The law of sine or the sine law states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides. It is also known as the sine rule.

\(\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\)

Similarly, In triangle XYZ,

\(\frac{sin(51)}{2.6} = \frac{sin(76)}{z}=\frac{sin(53)}{x}\)

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Answer:

SA= 341.664

Step-by-step explanation:

2. replace letters by numbers:

SA= 2(3.10)(7.77) + 2(3.10)(13.50) + 2(13.50)(7.77)

3. simplify:

SA= 48.174 + 83.7 + 209.79

4. add:

SA= 341.664

Answer:

40x4x<60

x<5

Step-by-step explanation:

40x4x<60

4x<60-40

4x<20

x<20÷4

x<5

The 100th derivative of P(x) = (x+x⁵+x⁷)¹⁰(1+x²)¹¹(x³+x⁵+x⁷) will be zero.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given:

A polynomial,

P(x) = (x+x⁵+x⁷)¹⁰(1+x²)¹¹(x³+x⁵+x⁷).

To find the degree:

(x⁷)¹⁰(x²)¹¹(x⁷) = x⁹⁹.

The polynomial has a degree of 99.

If we think about it intuitively,

Therefore, if we were to multiply it all out,

the leading word would be x⁹⁹.

The term's first derivative is 99x⁹⁸,

followed by 99(98)x⁹⁷,

and 99(98)(97)x⁹⁶.

And finally,

the 99th derivative is 99×98×97×96×...4×3×3×2×1× (x⁰)

=99!

So, the 100th derivative will be zero.

Therefore, by the 100th derivative, all terms will cancel out.

100th derivative will be zero.

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Number of countries would west Virginia be expected to have is  18 countries

The number of campgrounds that North Dakota has = 465 campgrounds

The number of countries = 12 countries

The number of campgrounds that West Virginia has = 711 campgrounds

Given that the North Dakota was proportional to West Virginia in the number of campgrounds to counties.

The proportion will be

465 / 12 = 711 / x

Divide the terms

38.75 = 711 / x

x = 711 / 38.75

Divide the terms

x = 18.4

x ≈ 18 countries

Hence, number of countries would west Virginia be expected to have is  18 countries

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Answer:

0

It runs parallel to the z-axis and so has a zero slope

The cations and Anions for the given compounds are;

1) CuS: Cation; Cu²⁺ and Anion: Su²⁻

2) (NH₄)₂O; Cation; NH₄⁺ and Anion: O²⁻

3)Mn₃(PO₄)₂; Cation; Mn²⁺  and Anion: PO₄³⁻

4) VBr₅; Cation; V⁵⁺ and Anion: Br⁻

Cations are defined as Positively charged ions that are formed by loss of electrons by an atom. In a cation, number of electrons are less than number of protons.

Anions are defined as Negatively charged ions that are formed by gaining of electron by an atom. In anions, number of electrons are more than the number of protons.

Thus;

1) CuS

Cation; Cu²⁺

Anion: Su²⁻

2) (NH₄)₂O

Cation; NH₄⁺

Anion: O²⁻

3) Mn₃(PO₄)₂

Cation; Mn²⁺

Anion: PO₄³⁻

4) VBr₅

Cation; V⁵⁺

Anion: Br⁻

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