Find f-1(x) and it’s domain.

The answers both as whole numbers and fractions are given below:

In mathematics, the limit of a function is the value that the function approaches as its input (independent variable) gets arbitrarily close to a certain value, often denoted as a.

More precisely, given a function f(x), the limit of f(x) as x approaches a, written as "lim x → a f(x)", is the value that f(x) approaches as x gets arbitrarily close to a, but not necessarily equal to a.

If the limit exists and is equal to L, then we can write it as:

lim x → a f(x) = L

To solve this,

using the graph of y = f(x)

[tex]\lim_{x \to 4^+\} \frac{f(x) - 4}{f(x+3)}[/tex] = 3-4/6 = -1/6

[tex]\lim_{x \to 1^-\}{f(fx) +4) = f(4 +4) = f(8)[/tex] = 5

[tex]\lim_{h \to 0\} \frac{f(2+h) - f(2)}{h}[/tex] = f^1(2) = 1

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Answer:

Half the Area of MNPQ.

Step-by-step explanation:

The triangles outside of the square are all equilateral, which if connected makes a square. So, two squares multiplied together create one gigantic square, making the area of ABCD half of the area of MNPQ.

The equilibrium point for the market is (102.54, 351.81).

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

Given that, a group of retailers will buy 104 televisions from a wholesaler if the price is $350 and 144 if the price is $300.

Here, (104, 350) and (144, 300)

Now, slope (m)=(300-350)/(144-104)

= -50/40

= -1.25

Substitute m=-1.25 and (x, y)=(104, 350) in y=mx+c, we get

350=-1.25(104)+c

350=-130+c

c=480

Substitute m=-1.25 and c=480 in y=mx+c, we get

y= -1.25x+480

The wholesaler is willing to supply 68 if the price is $300 and 148 if the price is $390.

The coordinate points are (68, 300) and (148, 390)

Slope (m)= (390-300)/(148-68)

= 90/60

= 3/2

= 1.5

Substitute m=1.5 and (x, y)=(68, 300) in y=mx+c, we get

300=1.5×68+c

c=198

Substitute m=1.5 and c=198 in y=mx+c, we get

y=1.5x+198

So, the solution is (102.54, 351.81)

Therefore, the equilibrium point for the market is (102.54, 351.81).

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Step-by-step explanation:

a1) Through how many radians does Jamie turn in 99 minutes?

One revolution is equal to 2 * pi radians, so 1.08 revolutions is equal to 1.08 * 2 * pi radians.

In 99 minutes, the restaurant rotates for 99 / 60 = 1.65 hours.

Therefore, the angle Jamie turns through in 99 minutes is 1.65 * 1.08 * 2 * pi radians.

a2) Exact answer:

angle = 1.65 * 1.08 * 2 * pi radians

b1) Approximate answer (rounded to 3 decimal places):

angle = 11.045 radians

b2) How far does Jamie move in 99 minutes?

The distance Jamie moves can be calculated using the formula:

distance = angle * radius

where radius is Jamie's distance from the center of the restaurant, which is 22.2 meters.

b2) Exact answer:

distance = 11.045 * 22.2 meters

b2) Approximate answer (rounded to 1 decimal place):

distance = 245.3 meters

The slope-intercept form of the lines are given below.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

If a line passes through two points (x₁ ,y₁) and (x₂, y₂),

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Given:
A). Line 5 passes through (0, 5) and (10, 0),

then the equation of the line is,

y - 5 = -1/2(x)

y = -x/2 + 5

B). Line 6 passes through (0, 7) and (1, 7),

then the equation of the line is,

y = 7

C). Line 7 passes through (0, 0) and (9, 3),

then the equation of the line is,

y = 3x

D). Line 8 passes through (-1, 0) and (0, 1),

then the equation of the line is,

y = x + 1

E). Line 9 passes through (-1, 1) and (0, -1),

then the equation of the line is,

y = -2x - 3

F). Line 10 passes through (0, 2) and (-0.5, 8),

then the equation of the line is,

y = -12x + 24

G). Line 11 passes through (4, 0) and (4, 1),

then the equation of the line is,

x = 4

H). Line 12 passes through (0, 0) and (-3, 1),

then the equation of the line is,

y = (-1/3)x

Therefore, all the equations are given above.

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The given linear model and the correlation are true. The particular circumstance will, however, determine if there is a causal association between the two variables.

Yes, there is a correlation between the two variables in the supplied linear model, proving that there is a connection between them. This correlation, which is vital for assessing the strength of their link, is graphically displayed using the linear model. However, since this correlation is not always present, whether there is a causal association between the two variables depends on the particular circumstance. For instance, two variables could have a high correlation, but neither one of them necessarily causes the other. More investigation into the cause-and-effect relationship between the two variables is required to ascertain whether there is a causal correlation.

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The complete question is

for each situation, described given a linear model, is there a correlation. if so is there a causal between a linear model and a given situation?

The measure of the angle m∠BDE obtained using the exterior angles theorem is 86°. The correct option is therefore;

86°

The exterior angle theorem states that the angle formed by two secants, a secant and a tangent or two tangents of a circle is equivalent to the half of the difference of the arcs intercepted.

The specified interior angle of the triangle ΔOBJ, ∠J = 47°

The segments OJ and BO are radial lengths of the circle, therefore;

JO ≅ BO

JO = BO (definition of congruency)

The triangle ΔOBJ is an isosceles triangle (definition of isosceles triangles)

∠J ≅ ∠B (Base angles of an isosceles triangle)

∠B = ∠J = 47°

m∠BOJ = 180°- 47° - 47° = 86° (angle sum property of a triangle)

Whereby EJ is a diameter of the circle, with center at O, we get;

∠BOJ and ∠BOE are linear pair angles, therefore;

m∠BOJ + m∠BOE = 180° (Linear pair angles are supplementary)

m∠BOE = 180° - m∠BOJ

m∠BOE = 180° - 86° = 94°

The exterior angle theorem indicates that we get;

m∠BDE = Half the difference of the intercepted arcs BJE and BE, found as follows;

[tex]m\widehat{BE}[/tex] = m∠BOE = 94°

[tex]m\widehat{BJE}[/tex] = 360° - m∠BOE = 360° - 94° = 266°

[tex]m\widehat{BJE}[/tex] = 266°

m∠BDE = ([tex]m\widehat{BJE}[/tex] - [tex]m\widehat{BE}[/tex])/2

m∠BDE = (266° - 94°)/2 = 86°

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There is a total of 120 workers at the company

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

Using the above as a guide, we have the following:

Number of workers = 96/80%

Evaluate the quotient

Number of workers = 120

Hence, the workers are 120

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It took the 26 offshore oil workers an average of 94.85 seconds to complete the simulated escape exercise, with a variance of 828.19 and a standard deviation of 28.79 seconds.

The data set consists of 26 offshore oil workers who took part in a simulated escape exercise. The data set measures the time (in seconds) it took for each worker to complete the escape. To analyze the data, we can calculate the mean, variance, and standard deviation.

The mean is calculated by adding up the time for each worker and dividing the sum by the total number of workers (26). This results in a mean of 94.85 seconds.

The variance is calculated by subtracting the mean from each individual time, squaring the results, adding the squared results together, and dividing the sum by the total number of workers (26). This results in a variance of 828.19.

The standard deviation is calculated by taking the square root of the variance. This results in a standard deviation of 28.79 seconds.

In conclusion, it took the 26 offshore oil workers an average of 94.85 seconds to complete the simulated escape exercise, with a variance of 828.19 and a standard deviation of 28.79 seconds.

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Answer:

Step-by-step explanation:

The area of a rectangle can be calculated as the product of its length and width. In this case, the length of the rectangle is 11 inches and the width is 8.5 inches, so the area is:

Area = 11 inches * 8.5 inches = 93.5 square inches

So the units of the area of the rectangle defined by the flyer are square inches.

Step-by-step explanation:

Lance makes 8.5 an hour

He works for 40 hours

This means he earns 8.5 40 times

So 8.5 x 40

Which equals 340

This means lance earned $340.

16 percentage of seniors will score a 31 or higher on the ACT. This can be solved using the concept of standard deviation.

The Z-score provides information on how much a given value deviates from the standard deviation. The amount of standard deviations a given data point is above or below the mean is represented by the Z-score, also known as the standard score. Essentially, standard deviation is a measure of the degree of variability within a given data collection.

Given that,

SAT score is normally distributed with a mean score of μ = 1500 and the standard deviation of σ = 250,

The ACT score is also normally distributed with a mean score of μ = 21 and the standard deviation of σ = 5,

To calculate the percentage of scores above x = 21 is calculated by finding the Z score which is calculated as:

Z = (x - μ) / σ

Z = 31 - 21 / 5 = 2

now since 68% of scores is between 1 standard deviation and the shape is symmetric hence (100-68)/2 = 16% of values will be above 1 standard deviation.

Thus  16% of scores will be have score higher than 31.

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(a) The zero vector in the space of degree three polynomials is the polynomial with zero coefficients, i.e., p(x) = 0 for all x.

In mathematics, a vector is an ordered collection of numbers, typically referred to as scalars.

(b) The zero vector in the space of matrices is the matrix with all elments equal to zero, i.e., A = [0, 0, ..., 0] where A is an m x n matrix.

(c) The zero vector in the space of continuous functions is the constant function with value zero, i.e., f(x) = 0 for all x.

(d) The zero vector in the space of real-valued functions of one natural number variable is the function that maps every natural number to zero, i.e., f(n) = 0 for all natural numbers n.

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Answer:

1.  width = 35 m,  length = 5 m

2. 80 m

Step-by-step explanation:

From inspection of the given graph, when y = 175, x = 5.

Therefore, when the area of a rectangle is 175 m², its length is 5 m.

The equation for the area of a rectangle is:

[tex]\boxed{\sf Area=width \times length}[/tex]

Therefore, to find the width of the rectangle, input the area of 175 m² and length of 5 m into the equation and solve for width:

[tex]\begin{aligned}\sf Area&= \sf width \times length\\\implies 175&=\textsf{width} \times 5\\\sf width&=\dfrac{175}{5}\\\sf width&=35\; \sf m\end{aligned}[/tex]

Therefore, the dimensions of the rectangle with an area of 175 m² are:

The equation for the perimeter of a rectangle is:

[tex]\boxed{\sf Perimeter=2(width +length)}[/tex]

Given the width is 35 m and the length is 5 m:

[tex]\begin{aligned}\implies \sf Perimeter=&2(35+5)\\&=2(40)\\&=80\; \sf m\end{aligned}[/tex]

Therefore, the area of the square with coordinates at (–5, 3), (1, 1), (–5, –1), and (–1,3) is 40 square units.

A coordinate is indeed a geometry technique that uses one or more quantities or coordinates to better be able to watch points as well as other geometrical items on a continuum, such as Ellipsoid. A point or object's coordinates on the double plane are indeed a combination of integers. The y and x dimensions of a point on a plane surface are two numbers that identify its location. a collection of numbers that represent exact coordinates.

Here,

To find the area of a square with these coordinates, we need to find the length of one of its sides first. We can use the distance formula to find the length of the side between two adjacent vertices:

Side AB: √((1-(-5))² + (1-3)²) = √(36 + 4) = √(40) = 2√(10)

Side BC: √((-5-1)² + (-1-1)²) = √(36 + 4) = √(40) = 2√(10)

Since the opposite sides of a square are equal, we know that the other two sides also have a length of 2sqrt(10).

Now we can use the formula for the area of a square, which is side squared. In this case, the area is:

Area = (2√(10))² = 4 × 10 = 40

Therefore, the area of the square with coordinates at (–5, 3), (1, 1), (–5, –1), and (–1,3) is 40 square units.

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To print out all elements of a two-dimensional array you would normally use a(n) for loop.

A collection of elements with the same data type that are stored in sequential memory regions is known as an array. As a result, it is easier to determine each element's position by simply adding an offset to a base value, which is the address in memory where the array's first element is stored (generally denoted by the name of the array).

By defining iteration in a control flow statement, a for loop enables code to be run repeatedly.

A for loop's body, which is executed once for each iteration, and its header both specify the iteration.

Two for loops can be used to print the elements of a two-dimensional array.

Therefore, for loop is used for two dimensional array printing.

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The line tangent to the graphs are y = 77 and y = -74/49(x - 2) + [f(2)/g(2)].

Function (1)

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

y = 4x+ 3 and y = 6x - 5

At x = 2, we have

y = 4(2) + 3 and y = 6(2) - 5

So, we have

y = 11 and y = 7

So, we have:

Tangent line: y = 11 * 7

y = 77

Function 2

Here, we have

The derivative of the quotient of two functions:

(d/dx)(f(x)/g(x)) = (g(x) * df/dx - f(x) * dg/dx) / g(x)^2

Substituting the tangent lines for f and g, we get:

(d/dx)(f(x)/g(x)) = (6x - 5 * 4 - (4x + 3) * 6) / (6x - 5)^2

Evaluating at x = 2, we get:

(d/dx)(f(x)/g(x)) = (-16 - 18) / (-3)^2 = -74/49

Hence, the line tangent to the graph of y = f(x)/g(x) at x = 2 is y = -74/49(x - 2) + [f(2)/g(2)].

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Answer:

1723.9 mb

Step-by-step explanation:

Essentially, the question is asking "281 is 16.3% of what number.

Thus, we can find the percentage of a number using the formula

[tex]Px=y[/tex], where P is the percentage.  In context of the question, x is how many megabytes have already downloaded and y is 281.

We simply need to solve for x and round to the nearest:

[tex]\frac{16.3}{100}x=281\\ \\0.163x=281\\x=1723.92638=1723.9[/tex]

For the given function [tex]\displaystyle \lim_{x \to -\infty} \frac{5\sqrt[3]{x}-\sqrt[7]{x}}{8\sqrt[3]{x}+3\sqrt[7]{x}}[/tex] the value for limit is 5/8.

What is limit?

A limit in mathematics is a point at which a function approaches the outcome for the specified input values. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity.

The function is given as -

[tex]\displaystyle \lim_{x \to -\infty} \frac{5\sqrt[3]{x}-\sqrt[7]{x}}{8\sqrt[3]{x}+3\sqrt[7]{x}}[/tex]

Dividing the function by [tex]\sqrt[3]{x}[/tex] -

[tex]\displaystyle \lim_{x \to -\infty} \frac{5-\frac{1}{x^{\frac{4}{21} }} }{8+\frac{3}{x^{\frac{4}{21}}} }[/tex]

Use the formula [tex]\displaystyle \lim_{x \to a} \Bigg[\frac{f(x)}{g(x)}\Bigg]=\frac{\displaystyle \lim_{x \to a}f(x)}{\displaystyle \lim_{x \to a}g(x)} , \displaystyle \lim_{x \to a}g(x)\neq 0[/tex] -

With the exception of indeterminate form -

[tex]\frac{\displaystyle \lim_{x \to -\infty}\Bigg(5-\frac{1}{x^{\frac{4}{21}}} \Bigg)}{\displaystyle \lim_{x \to -\infty}\Bigg(8+\frac{3}{x^{\frac{4}{21}}} \Bigg)}[/tex]

Find the values individually -

[tex]{\displaystyle \lim_{x \to -\infty}\Bigg(5-\frac{1}{x^{\frac{4}{21}}} \Bigg)}=5[/tex]

[tex]{\displaystyle \lim_{x \to -\infty}\Bigg(8+\frac{3}{x^{\frac{4}{21}}} \Bigg)}=8[/tex]

So, the limit is 5/8.

Therefore, the limit is 5/8.

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Answer:

Below

Step-by-step explanation:

The two angles labeled are alternate angles of a pair of parallel lines crossed by a transversal ( the diagonal) ....so they are equal

x+ 18 = 4x+15    Solve for x

3 = 3x   ====>    x = 1    

Now....x+18  angle and angle ABD are complementary....the add to 90 °

   so   x+18    + ABD   = 90°        x = 1 from above....so

            1 + 18 + ABD = 90

               19  + ABD = 90

                        ABD = 71 °

Answer: a. The rate of change in this situation represents the average number of pages read per minute. From the table, it can be seen that the rate of change is constant, as the ratio of the change in y (pages) to the change in x (minutes) is always the same.

For example, when x increases from 0 to 5, y increases from 0 to 25, so the rate of change is 25/5 = 5 pages per minute.

b. To represent the total number of pages as it relates to the number of minutes read, a linear equation can be used. The slope of the line represents the rate of change, and the y-intercept represents the number of pages read when x is equal to 0 (minutes).

Using the rate of change from the above example (5 pages per minute), the equation can be written as y = 5x + 0, where x represents the number of minutes and y represents the total number of pages read.

Step-by-step explanation:

In summary, the statement states that the coordinate ring of an affine variety is a field if and only if the variety is reduced to a single point, making it a well-defined, irreducible, and non-redundant set.

Coordinates are a pair of integers that are used to locate a point or object in a two-dimensional plane. A point's location on a 2D plane is defined by two integers called the x-coordinate and the y-coordinate. The distance between two points is known as the x-coordinate, or abscissa, while the distance between two points is known as the y-coordinate, or ordinate. Point (3, 2), for example, is three units distant from the positive y-axis and two units away from the positive x-axis.

Here,

In algebraic geometry, the coordinate ring of an affine variety X, denoted by A(X), is a ring that encodes the algebraic information of the variety X. The ring A(X) is defined as the set of polynomial functions on X, with pointwise addition and pointwise multiplication.

The statement "The coordinate ring A(X) is a field if and only if X is a single point" says that the coordinate ring is a field only when the affine variety X is reduced to a single point.

This means that the only non-zero polynomial function on X is the constant function equal to one. In other words, if X is a single point, then any non-zero polynomial on X will have an inverse, making the coordinate ring a field.

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The point where the horizontal axis and the vertical axis intersect in a coordinate plane is called the ORIGIN.

Given the question below:

What is the intersection of the vertical and horizontal lines in a coordinate plane?

A coordinate plane is a plane formed by a horizontal number line (the x-axis) and a vertical number line (the y-axis) that intersect at a point called the origin.

The vertical intercept (y-intercept) is found by evaluating the function when the input variable, x, is 0 and is always the same as the constant b. It can be thought of as the original value of the function. The horizontal intercept (x-intercept) is the value of the variable x when the function value is 0.

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Answer:

354.933mmcube

Step-by-step explanation:

solution

Given,

Radius (r) = d/2

=11/2

5.5mm

Height (h) = 11.2

volume of cone (v) = ?

Now ,

volume of cone= 1/3 πrpower2×h

= 1/3×22/7×5.5×5.5×11.2

=1/3×22/7×338.8

= 1/3× 1064.8

= 354.933mmcube

Answer:

24

Step-by-step explanation:

The rate of change over a function f(x) is given by its first derivative
[tex]f'(x) = \dfrac{d}{dx} (f(x))[/tex]

[tex]\mathrm{Differentiating\; f(x) = 3x^2- 5 \;w.r.t \;x : }[/tex]

[tex]\dfrac{d}{dx}\left(3x^2-5\right) = \dfrac{d}{dx}\left(3x^2\right)-\dfrac{d}{dx}\left(5\right)\\\\= 6x - 0\\\\= 6x\\\\[/tex]

[tex]f'(x) = 6x\\\\[/tex]

Over the interval [2, 6] the average rate of change would be  [tex]f'(6) - f'(2)[/tex]
[tex]f'(6) = 6 \cdot 6 = 36\\\\f'(2) = 6\cdot 2 = 12\\\\f'(6) - f'(2) = 36 - 12 = 24\\\\[/tex]

Average rate of change of the function f(x)=3x²-5 over the interval [2,6]

= 24

Answer:

P = C(55,845, 40) / C(56,142, 40) = (55,845!) / (40! * (55,845 - 40)!) / (56,142!) / (40! * (56,142 - 40)!)

Step-by-step explanation:

To find the probability that none of the 40 subjects randomly selected left the treatment center against medical advice, we can use the formula for combinations. The number of ways to choose 40 subjects out of 55,845 that did not leave against medical advice is given by C(55,845, 40), which can be calculated as:

C(55,845, 40) = 55,845 choose 40 = (55,845!) / (40! * (55,845 - 40)!)

The probability that none of the 40 subjects randomly selected left the treatment center against medical advice is given by the number of ways to choose 40 subjects out of 55,845 that did not leave against medical advice, divided by the number of ways to choose 40 subjects out of 56,142 total subjects:

P = C(55,845, 40) / C(56,142, 40) = (55,845!) / (40! * (55,845 - 40)!) / (56,142!) / (40! * (56,142 - 40)!)

The value of f(-1) is 7

We have the equation of the polynomial as:

f(x) = - 2x² - 5x + 4 by x + 1

The question tells us that x = -1

We would have to put in the value of x into the polynomial

such that we would have

f (-1) = -2 (-1)² - 5 (-1) + 4

= -2 + 5 + 4

= 7

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Answer:

Time taken for both hikers to be at the same elevation = 14 minutes

At that time, they will both be at an elevation of 270 feet

Step-by-step explanation:

Let us represent Jenny's current elevation by x and Julian's current elevation by y

Let T be the time taken when the hikers reach the same elevation

For Jenny

For Julian

Check working
After 14 minutes, Jenny's elevation = 480 - 15 x 14 = 480 = 210 = 270 feet

After 14 minutes, Julian's elevation = 200 + 5 x 14 = 200 + 70 = 270 feet

So it checks out