Find the point(s) at which the function f(x)=8-6x equals its average value on the interval [0,6). The function equals its average value at x = (Use a comma to separate answers as needed.) re:

Answer:

Train A is travelling faster.

Step-by-step explanation:

Train A is going 55mph, and train B is going 45mph according to the table.

Answer:

Step-by-step explanation:

You want values of ∆y and dy for y = x² -6x and x = 5, ∆x = dx = 0.5.

The value of dy is found by differentiating the function.

  y = x² -6x

  dy = (2x -6)dx

For x=5, dx=0.5, this is ...

  dy = (2·5 -6)(0.5) = (4)(0.5)

  dy = 2

The value of ∆y is the function difference ...

  ∆y = f(x +∆x) -f(x) . . . . . . . where y = f(x) = x² -6x

  ∆y = (5.5² -6(5.5)) -(5² -6·5)

  ∆y = (30.25 -33) -(25 -30) = -2.75 +5

  ∆y = 2.25

__

Additional comment

On the attached graph, ∆y is the difference between function values:

  ∆y = -2.75 -(-5) = 2.25

and dy is the difference between the linearized function value and the function value:

  dy = -3 -(-5) = 2.00

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Light bulbs is normally distributed with a variance of 625 and a mean lifetime of 520 hours, we need to calculate the cumulative probability up to 549 hours. The answer will be rounded to four decimal places.

Given a normally distributed lifetime with a mean of 520 hours and a variance of 625, we can determine the standard deviation (σ) by taking the square root of the variance, which gives us σ = √625 = 25.

To find the probability of a bulb lasting for at most 549 hours, we need to calculate the area under the normal distribution curve up to 549 hours. This can be done by evaluating the cumulative distribution function (CDF) of the normal distribution at the value 549, using the mean (520) and standard deviation (25).

The CDF will give us the probability that a bulb lasts up to a certain point. Rounding the result to four decimal places will provide the desired precision.

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The problem involves using normal distribution to find the probability of a given outcome. Using the Z-score, we can determine that the probability of a light bulb lasting for at most 549 hours is approximately 0.8770 or 87.70%

Given the mean (µ) of the lifetime of a bulb is 520 hours. Also, the variance (σ²) is given as 625. Thus, the standard deviation (σ) is the square root of the variance, which is 25.

To find the probability of a bulb lasting for at most 549 hours, we first calculate the Z score. The Z-score formula is given as follows: Z = (X - µ) / σ, where X is the number of hours, which is 549. So substitute the given values into the formula. Z = (549 - 520) / 25, the Z value is 1.16.

We then look up the Z-table to find the probability associated with this Z-score (1.16), which is approximately 0.8770. Therefore, the probability of a bulb lasting for at most 549 hours is approximately 0.8770 or 87.70%.

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Answer:

Step-by-step explanation:

This is essentially a vocabulary question. You need to know the meanings of ...

and you need to know how angles are named.

__

Angles adjacent to MBP will share a side and a vertex. The shared side will be one of ray BM or ray BP. The shared vertex is B.

Adjacent angles to MBP are ...

  angle MBL and angle PBQ

__

Angle OBN is not a vertical angle with any shown, nor is it part of a linear pair with any angles shown. However, if we assume that LR is a straight line through B, then angle LBR is a "straight angle" and has a measure of 180°.

The angle addition postulate tells us ...

  ∠NBL +∠OBN +∠OBR = 180°

  30° +∠OBN +55° = 180°

  ∠OBN = 95° . . . . . . . . . . . . subtract 85° from both sides

__

No two of BM, BP, BR, BO form a straight line, so the given angles do not form a linear pair or vertical angles. (Neither)

Answer:

247cm^2

Step-by-step explanation:

Construct a formula to find the total area of the figure. To do that first figure out what shapes are in the given figure. In this case there are 2 triangles each with a height of 4cm and a base of 10cm, 1 sqaure with a width of 9cm and a length of 5cm, 1 square with a width of 9cm and a length of 8cm and one last square with a width of 9cm and length of 10cm.

The formula for the area of a triangle is A=(1/2)(b)(h) and the fromula for the area of a sqaure is A =  L*W.

The total area: A = (4)(10)+(9)(5)+(9)(8)+(10)(9) = 247cm^2

Answer:

D

Step-by-step explanation:

The 6 represents the initial value of 6000.  The cases are going down 5,000 a month.

The fire is 39.2 miles from tower A. This is calculated using the law of sines, which states that the ratio of the sine of an angle to the length of the opposite side is equal for all sides of a triangle. In this case, the angle is 40 degrees, the opposite side is 28 miles, and the unknown side is the distance from tower A to the fire. Solving for the unknown side, we get 39.2 miles.

The law of sines is a trigonometric equation that can be used to solve for the sides of a triangle when two angles and one side are known. In this case, we know two angles and one side (the angle opposite the unknown side is 40 degrees, the angle opposite the 28-mile side is 116 degrees, and the 28-mile side is known). Solving for the unknown side, we get 39.2 miles.

Tower height:

The tower is 312 ft tall. This is calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the height of the tower, and the other two sides are the 648-ft guy wire and the 295-ft distance from the tower to the point where the wire is attached to the ground. Solving for the height of the tower, we get 312 ft.

The Pythagorean theorem is a mathematical equation that can be used to solve for the length of the hypotenuse of a right triangle when the lengths of the other two sides are known. In this case, we know the lengths of the other two sides (the guy wire is 648 ft and the distance from the tower to the point where the wire is attached to the ground is 295 ft). Solving for the height of the tower, we get 312 ft.

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Answer:

2 terms

Explanation:

\(\dashrightarrow \ \ \sf 5(6 + 4x)\)

\(\dashrightarrow \ \ \sf 5(6) + 5(4x)\)

\(\dashrightarrow \ \ \sf 30 + 20x\)

→ There are total two terms in this factor.

Answer:

2 Terms

Step-by-step explanation:

There will be two terms ..

=> 5(6 + 4x)

=> 30 + 20x

Answer:

don't download thattttttttttttttt

Answer:

Max = 28

Step-by-step explanation:

The equation given is in the standard form of a qudaratic equation, which is:

\(y = ax^2+bx+c\)

The max value is the y-coordinate of the maximum and we can find it using the formula

\(x_{max}=-\frac{b}{2a}\\\\ y_{max}=a(-\frac{b}{2a})^2+b(-\frac{b}{2a})+c\)

As the formula shows, -b/2a yields the x-coordinate of the vertex (a maxiumum in this problem).  Then we allow this value to become the input of the quadratic function which yields the y-coordinate of the max and ultimately the maximum value:

Since 16 is b and -4 is a in our equation, we plug this in first to find the x-coordinate of the max:

\(x_{max}=-\frac{16}{2(-4)}\\ x_{max}=\frac{-16}{-8}\\ x_{max}=2\)

Since 2 is the x-coordinate of the maximum, we can now plug this in to yield the y-coordinate of the maximum (aka the max value):

\(y_{max}= f(2)=-4(2)^2+16(2)+12\\y_{max}=f(2)=28\)

The graph of the equation  r = 2 + 3 cos(3θ) with polar coordinates is illustrated below.

To begin, let's understand the relationship between polar and Cartesian coordinates. In the Cartesian coordinate system, a point is represented by its x and y coordinates, while in the polar coordinate system, a point is represented by its distance from the origin (r) and the angle it makes with the positive x-axis (θ).

The polar equation r = 2 + 3 cos(3θ) gives us the distance (r) from the origin for each value of the angle (θ). To convert this equation into Cartesian form, we'll use the relationships:

x = r cos(θ)

y = r sin(θ)

Substituting r = 2 + 3 cos(3θ) into these equations, we have:

x = (2 + 3 cos(3θ)) cos(θ)

y = (2 + 3 cos(3θ)) sin(θ)

Now, we can graph the Cartesian equation by plotting several points for various values of θ. Let's choose a range of θ values, such as θ = 0°, 30°, 60°, 90°, 120°, 150°, 180°, and so on. We'll calculate the corresponding x and y values using the equations above and plot the points on the graph.

Once we have a sufficient number of points, we can connect them to form a smooth curve. This curve represents the graph of the Cartesian equation derived from the given polar equation, r = 2 + 3 cos(3θ).

It's important to note that polar graphs often exhibit symmetry. In this case, the polar equation r = 2 + 3 cos(3θ) is symmetric about the x-axis due to the cosine function. Therefore, the Cartesian graph will also exhibit this symmetry.

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VNTR analysis involves examining and analyzing the variations in the number of repeated DNA sequences known as tandem repeats.

VARIABLE NUMBER TANDEM REPEAT (VNTR) analysis involves examining and analyzing the variations in the number of repeated DNA sequences known as tandem repeats.

These tandem repeats consist of short DNA sequences repeated in a head-to-tail fashion.

VNTR analysis primarily focuses on identifying and characterizing the variations in the number of repeats within specific genomic regions.

By studying VNTRs, scientists can gain insights into genetic diversity, individual identification, and genetic relationships among individuals or populations.

VNTR analysis typically involves techniques such as polymerase chain reaction (PCR) amplification of the target region, followed by fragment analysis to determine the number of repeats present.

The variations in VNTRs make them highly polymorphic, meaning they differ significantly between individuals.

This polymorphism allows VNTR analysis to be used in various applications, including forensic analysis, paternity testing, population genetics, and evolutionary studies.

In summary, VNTR analysis involves examining and analyzing the variations in the number of repeated DNA sequences known as tandem repeats, providing valuable information for genetic diversity and identification purposes.

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The option that is true about the parabola that opens up and has a vertex in the fourth quadrant, and for which the equation is y = a·x² + b·x + c is; a < 0, b > 0, c < 0

The general form of the equation of a parabola is; y = a·(x - h)² + k, where, (h, k) is the vertex of the parabola.

The effect of the coefficients on the graph of a parabola are as follows;

The equation of a parabola is f(x) = a·x² + b·x + c

When the value of a is positive, the parabola opens upwards and when a is negative, the parabola opens downwards.

When a is positive and the coefficient b is negative, or when a is negative and b is negative the axis of symmetry, and therefore, the graph shifts to the right.

The axis of symmetry shifts left when both a and b have the same sign

The constant c determines the y-intercept such as c increases, the y-intercept also increases.

A parabola that opens downward has a negative value of a (a < 0)

A parabola in the fourth quadrant is shifted right, therefore, b is positive (b > 0)

The ty-intercept in the fourth quadrant has a negative y-value, therefore, the constant, c < 0

The correct option is therefore; a < 0, b > 0, c < 0

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Answer:

13

Step-by-step explanation:

13 will go inside this box  

Answer:

13

Step-by-step explanation:

Finding Upper Quartile (Q₃)

Finding Lower Quartile (Q₁)

Interquartile Range = Q₃ - Q₁

Answer:

28°, 50°, 60°, 70°

Step-by-step explanation:

To calculate the total charge within the cylinder with dimensions r=1.5 and h=3, we use the potential function V = 5r + 4 cos Ø in cylindrical coordinates.

The total charge can be obtained by integrating the charge density over the volume of the cylinder.

The potential V within the cylinder is given by V = 5r + 4 cos Ø, where r represents the radial distance from the axis of the cylinder and Ø represents the angle in the cylindrical coordinate system. To calculate the total charge within the cylinder, we need to integrate the charge density over its volume.

The charge density ρ can be related to the potential by ρ = -∇²V, where ∇² is the Laplacian operator. In cylindrical coordinates, the Laplacian operator takes the form:

∇² = (1/r) ∂/∂r (r ∂/∂r) + (1/r²) ∂²/∂ز + ∂²/∂z²

Since the potential function V does not depend on the z coordinate, the Laplacian reduces to:

∇² = (1/r) ∂/∂r (r ∂/∂r) + (1/r²) ∂²/∂ز

Applying this operator to the potential function V, we find:

∇²V = (1/r) ∂/∂r (r ∂V/∂r) + (1/r²) ∂²V/∂ز

To find the charge density, we substitute this expression into ρ = -∇²V:

ρ = -(1/r) ∂/∂r (r ∂V/∂r) - (1/r²) ∂²V/∂ز

To calculate the total charge, we integrate the charge density ρ over the volume of the cylinder:

Q = ∫∫∫ ρ dV = ∫∫∫ -(1/r) ∂/∂r (r ∂V/∂r) - (1/r²) ∂²V/∂ز dV

The integration is performed over the cylindrical coordinates r, Ø, and z, with appropriate limits. Evaluating this integral will give us the total charge within the cylinder.

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Answer:

y = − 3 x + 9

Step-by-step explanation:

Answer:

x = 2, y = 7

Step-by-step explanation:

Express both ratios in fractional form, that is

\(\frac{x+1}{3y}\) = \(\frac{1}{7}\) ( cross- multiply )

7(x + 1) = 3y ← distribute left side

7x + 7 = 3y ( subtract 7x from both sides )

3y - 7x = 7 → (1)

and

\(\frac{2x}{y+3}\) = \(\frac{2}{5}\) ( cross- multiply )

2(y + 3) = 10x

2y + 6 = 10x ( subtract 10x from both sides )

2y - 10x + 6 = 0 ( subtract 6 from both sides )

2y - 10x = - 6 → (2)

Solve the 2 equations simultaneously\

Multiplying (1) by 2 and (2) by - 3 then adding will eliminate y

6y - 14x = 14 → (3)

- 6y + 30x = 18 → (4)

Add (3) and (4) term by term to eliminate y, that is

16x = 32 ( divide both sides by 16 )

x = 2

Substitute x = 2 into either of the 2 equations and solve for y

Substituting into (2)

2y - 10(2) = - 6

2y - 20 = - 6 ( add 20 to both sides )

2y = 14 ( divide both sides by 2 )

y = 7

Thus x = 2 and y = 7

Answer:13.All numbers are rational numbers because  they can be divided by 1.

14. All I can tell you is that what that thing is 19 is Not Rational.

15. I don’t know how to do this.........

and the rest I don’t know HOW to do those

Step-by-step explanation:

Answer:

77

Step-by-step explanation:

11- 6(x – 8)

f(-3)

11-6(-3-8)

11+18+48

=77

50 miles because of the miles

The result of combination of the exponential expressions to produce a single exponential expression is given by e²ˣ⁺¹.

We know that from the formulae of the exponent that,

aᵐ*aⁿ = aᵐ⁺ⁿ

aᵐ/aⁿ = aᵐ⁻ⁿ

(aᵐ)ⁿ = aᵐⁿ

where a, m, n are the any constants.

So here given that the expression is: eˣeˣ⁺¹

Here base is same which is 'e' (the exponential component) and exponentials are in multiplication so the powers of them will be added to each other.

eˣeˣ⁺¹ = eˣ⁺ˣ⁺¹ = e²ˣ⁺¹

Hence simplifying and converting the two exponentials into one exponential expression we get the result of e²ˣ⁺¹.

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The question is incomplete. The complete question will be -

"Combine the exponential expressions to produce a single exponential expression: eˣeˣ⁺¹"

To make a table of values for a linear relationship;

Choose a group of x values before creating the table. Add each x value from the left side column to the equation. Evaluate the equation (middle column) to arrive at the y value

Given,

Linear relationship;

A straight-line link between two variables is referred to statistically as a linear relationship (or linear association). Linear relationships can be represented graphically or mathematically as the equation y = mx + b.

Here,

We have to make a table of values for a linear relationship;

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Answer:

vertex(-3,27)

Step-by-step explanation:

f(x)= x^2+ 6x + 36 ( a=1,b=6,c=36)

V(h,k)

h=-b/2a=-6/2=-3

k=f(-3)=3²+6(-3)+36

f(-3)=9-18+36=27

vertex(-3,27)

Introduced in Florence in the early fifteenth century, the practice of creating the illusion of three-dimensional space on a two-dimensional surface using a mathematical formula is called linear perspective.

Linear perspective is a technique in art that involves using mathematical principles to create the illusion of depth and space on a flat surface. It relies on the concept that parallel lines appear to converge at a vanishing point on the horizon line. Artists use this knowledge to accurately depict spatial relationships and create realistic representations of three-dimensional objects in a two-dimensional artwork.

the practice of creating the illusion of three-dimensional space on a two-dimensional surface using a mathematical formula is known as linear perspective. It revolutionized the art world during the early fifteenth century and has since become a fundamental technique in creating realistic and lifelike artworks.

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Answer:

The solution to the question is g = 52

Step-by-step explanation:

Here, we want to find the solution to the equation ;

98 + g = 150

Apparently, we want to find the value of g.

To get the value of g, what we simply need is to bring 98 over the equal sign and this gives

g = 150-98

g = 52

Answer: B or how some people say it the second question. EDGE-MATHMATICS 2022

THE ANSWER IS B

step-by-step explanation: it is the second option  because when you find out what number g is (52) you can take 98-98= 0 + g/52 and get 52.

and then the second part of it says 150-98 which is 52! so  your answer is B hope this helps! have a wonderful day!

Based on the relationship of angles and sides of a triangle, the correct comparison is: B. m∠C < m∠S.

The relationship between the length of a triangle and its opposite length are relative in such a way that the largest angle will be opposite to the longest side while the smallest angle will be opposite to the shortest side of the triangle.

Given the image attached below that shows triangles ABC nd TRS, we are also given that:

Length of RT is greater than length of BA, invariably, it means the angle that is opposite to side RT will be greater than the angle that is opposite to side BA.

Therefore, in comparing angle C and S, the correct statement is:

B. m∠C < m∠S

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Answer:

22 times 4 1/2 divided by 2

Spherical coordinates are a system of coordinates that describe points in three-dimensional space using a distance from the origin, an angle of inclination from the positive z-axis, and an angle of rotation around the z-axis.

To calculate the triple integral of f(x, y, z)=x2 y2 over the region rho≤2 using spherical coordinates, we first need to express the function in terms of the spherical coordinates.

We know that in spherical coordinates,

x = ρ sin(φ) cos(θ)
y = ρ sin(φ) sin(θ)
z = ρ cos(φ)

where ρ is the radial distance, θ is the azimuthal angle, and φ is the polar angle.

So, f(x, y, z) = x2 y2 can be expressed as

f(ρ, φ, θ) = (ρ sin(φ) cos(θ))2 (ρ sin(φ) sin(θ))2

= ρ4 sin2(φ) cos2(θ) sin2(φ) sin2(θ)

= ρ4 sin4(φ) cos2(θ)

Now, we can set up the triple integral using spherical coordinates.

∫∫∫ f(ρ, φ, θ) ρ2 sin(φ) dρ dφ dθ

= ∫0^2π ∫0^π/2 ∫0^2 f(ρ, φ, θ) ρ2 sin(φ) dρ dφ dθ

= ∫0^2π ∫0^π/2 ∫0^2 ρ4 sin4(φ) cos2(θ) ρ2 sin(φ) dρ dφ dθ

= ∫0^2π ∫0^π/2 ∫0^2 ρ6 sin5(φ) cos2(θ) dρ dφ dθ

= ∫0^2π ∫0^π/2 [ρ7/7 sin5(φ) cos2(θ)]0^2 dφ dθ

= ∫0^2π ∫0^π/2 32/7 sin5(φ) cos2(θ) dφ dθ

= 32/7 ∫0^2π cos2(θ) dθ ∫0^π/2 sin5(φ) dφ

= 32/7 [π sin6(π/2)/6]

= 32π/21

Therefore, the triple integral of f(x, y, z) = x2 y2 over the region rho≤2 using spherical coordinates is 32π/21.

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