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The volume is 3315 cubic feet.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given polynomial function is V(x)=x³-4x.

Here, W(x)=V(3x)

Replace x by 3x in the function V(x)=x³-4x, we get

V(3x)=(3x)³-4(3x)

V(3x)=27x³-12x

W(x)=27x³-12x

Replace x by 5 in the function W(x)=27x³-12x, we get

Now, W(5)=27(5)³-12(5)

= 27×125-60

= 3375-60

= 3315 cubic feet

Hence, the volume is 3315 cubic feet.

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"Your question is incomplete, probably the complete question/missing part is:"

A polynomial function V(x)=x³-4x that represents the volume of the right triangle pyramid when measured in cubic feet.

The function (x) =(3x) gives the volume (in cubic feet) of the pyramid when x is measured in yards.

Find a function W(x) that gives us the volume when measured in yards also to find W(5).

The circumference of a circle is equal to 2π multiplied by its radius. Therefore, the circumference of a circle with a radius of 15 cm is equal to 2π multiplied by 15 cm, or 30π cm.

To show that the wave function y=e^(b(x-vt)) is a solution of the linear wave equation (eq. 16.27), we need to plug the wave function into the equation and see if it satisfies the equation.

The linear wave equation (eq. 16.27) is given by:

∂^2y/∂x^2 = (1/v^2) ∂^2y/∂t^2

Plugging in the wave function y=e^(b(x-vt)) into the equation, we get:

∂^2(e^(b(x-vt)))/∂x^2 = (1/v^2) ∂^2(e^(b(x-vt)))/∂t^2

Taking the second derivative with respect to x, we get:

b^2 e^(b(x-vt)) = (1/v^2) ∂^2(e^(b(x-vt)))/∂t^2

Taking the second derivative with respect to t, we get:

b^2 e^(b(x-vt)) = (1/v^2) b^2 v^2 e^(b(x-vt))

Simplifying, we get:

b^2 e^(b(x-vt)) = b^2 e^(b(x-vt))

This shows that the wave function y=e^(b(x-vt)) satisfies the linear wave equation (eq. 16.27) and is therefore a solution of the equation.

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The equation to represent the given scenario is 642=239+64x.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Ed is on a road trip. He has already traveled 239 miles and is driving at a rate of 64 miles per hour.

Let x be the number of hours.

We know that, Distance =Speed×Time

Now, total distance = 239+64×x

642=239+64x

Therefore, the equation to represent the given scenario is 642=239+64x.

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The equation is y = (-0.5)x + 34 and it will take 16 days for the water level to be 26 feet.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

Let the number of days = x, and the water level = y.

Given that,

Water level of river = 34 ft (initial value/y-intercept)

Rate of change = -0.5 ft per day (slope)

The equation of the line is given as:

y = mx + c

where, m is the slope

c is the y-intercept.

Substituting the values we have:

y = (-0.5)x + 34

The number of days in which the water level will reduce to 26 ft is:

26 = (-0.5)x + 34

26 - 34 = -0.5x

x = 16 days.

Hence, it will take 16 days for the water level to be 26 feet.

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Answer:

Step-by-step explanation:

you first take A15 and square it. Then you take B20 and square it also. Then you add them together and that is your answer. the hypotenuse of a triangle.

Answer: Side length C will be 25

Step-by-step explanation:

C^2 = A^2+B^2

15^2+20^2=C^2
225+400=625

Take square root of 625 to get side C

The length of major arc CBD is given as follows:

C = 40.39 m.

The circumference of a circle of radius r is given by the multiplication of 2 by the number π = 3.14 and the radius r, as follows, hence the equation is given as follows:

C = 6.28r.

For this problem, the parameters are given as follows:

Hence the arc length is given as follows:

C = 5/7 x 6.28 x 9

C = 40.39 m.

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Answer:

Reflection across the x-axis followed by dilation by a scale factor of with the center of dilation at the origin

Step-by-step explanation:

Rectangle EFGD has vertices at points E(-6,8), F(0,8), G(0,1) and D(-6,1).

1 transformation - reflection across the x-axis with the rule

So, the image rectangle E''F''G''D'' has vertices with coordinates

2 transformation - dilation by a scale factor of with the center of dilation at the origin. This transformation has the rule

Thus,

These are exactly vertices of rectangle E'F'G'D'.

The rate of change for Modis building stairwell is 0.68 feet per step.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Part A: In the Modis building, he climbs 22 steps for every 15 ft of horizontal travel.

Now, rate = 15/22

= 0.68 feet per step

In Sears Tower, he climbs 17 steps for every 7 ft of horizontal travel

Here, rate 7/17

= 0.41 feet per step

Part B: Sears Tower steps are easy to climb, because rate is lesser than Modis building steps.

Therefore, the rate of change for Modis building stairwell is 0.68 feet per step.

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The number of wires that cut from of 200 meters is 66 meters 66 centimeters.

What are the nearest two places?

The second place to the right of the decimal point, or the hundredth place, is used to round a decimal number to two decimal places. For instance, you can round 2.83620364 to two decimal places as 2.84 and 0.7035 to two decimal places as 0.70.

Given the length of the wire is 200 meters.

Assume that he cuts n pieces of length 3 meters.

The length of n pieces is 3n.

Therefore the equation is

3n = 200

n = 200/3

n= 66.66

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A line of reflection in a triangle can be any line that acts as a mirror image, such that the reflected image of the triangle is congruent to the original triangle.

This line is perpendicular to the plane of the triangle and bisects the angle between the two sides that are being reflected.

To be sure that each point was reflected across this line, we apply the reflection rule.

The reflection rule states that the distance from a point to the line of reflection is equal to the distance from its reflection to the line of reflection. This ensures that the reflected image of the triangle is congruent to the original triangle.

In an isosceles right triangle, two of its sides are congruent. This means that it satisfies the Angle-Side-Angle (ASA) congruence theorem. The ASA theorem states that if two triangles have two congruent angles and a congruent side between them, then the two triangles are congruent.

In addition to satisfying the ASA congruence theorem, an isosceles right triangle also satisfies the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Finally, the reflection of a triangle is considered a rigid motion, as it preserves the size and shape of the triangle.

Rigid motions do not change the lengths of the sides or the angles between them. They only change the position of the triangle in space. In the case of reflection, the triangle is flipped over the line of reflection, but its size and shape remain unchanged

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Isosceles Right Triangle Reflection to prove ASA Congruence

Answer the following questions:

What line of reflection did you choose for your transformation?

How are you sure that each point was reflected across this line?

What reflection rule did you apply to your triangle?

What other properties exist in your triangle? Discuss at least two theorems you learned about in this module that apply to your triangle. Make sure to show evidence by discussing your triangle's measurements.

Did your triangle undergo rigid motion? Explain why.

The complete table is

Sulfur atoms         6     9     12   27

Oxygen atoms     12    18    24   54    

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other.

A ratio can be compared by the division of two numbers. For example, the ratio of a and b can be represented as a: b and read as a is to b. Here a: b can be written as a/b

Here we have  

The ratio of oxygen atoms to sulfur atoms in sulfur dioxide is always the same. The table shows the number of atoms in different quantities of sulfur dioxide.  

The given table is

Sulfur atoms         6     9     12   ___

Oxygen atoms     12    __   ___   54      

Let x, y, and z be the missing values in the table

Given that ratio of oxygen atoms to sulfur atoms in sulfur dioxide is always the same.  

=> 12/6 = x/9 = y/12 = 54/z    

Now the x, y, and z values can be calculated as follows

Take 12/6 = x/9  

=> 2 = x/9    

=> x = 18  

Take 12/6 = y/12  

=> 2 = y/12

=> y = 24

Take 12/6 = 54/z  

=> 2 = 54/z

=> z = 54/2

=> z = 27    

Therefore,

The complete table is

Sulfur atoms         6     9     12   27

Oxygen atoms     12    18    24   54      

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The complete Question is given in the picture

Answer:2\1

Step-by-step explanation:24\12 then simplify and get 2\1

Function g(x) is function f(x) translated 3 units to the left and 2 units down.

Here we know that the function f(x) = (x − 2)³ is transformed to g(x) = (x + 1)³ − 2.

Remember that:

A vertical translation of N units is written as:

g(x) =f(x) + N

if N > 0, the translation is up.

If N < 0, the translation is down.

A horizontal translation of N units is written as:

g(x) =f(x) + N

if N > 0, the translation is left.

If N < 0, the translation is right.

Here we can see that:

g(x) = f(x + 3) - 2

Then we have a translation of 3 units to the right and 2 units downñ.

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Answer:

25 minutes

Explanation:

Subtract the two times to find the duration.

The probability that all four of the selected bolts are torqued to the proper limit is approximately 0.28.

To calculate the probability that all four of the selected bolts are torqued to the proper limit, we need to find the number of combinations of 4 bolts out of 20 that have been torqued to the proper limit.

Let's call the number of proper bolts n = 20 - 5 = 15.

The number of combinations of 4 proper bolts out of 15 is given by the binomial coefficient nCk, where n is the number of bolts and k is the number of bolts selected.

nCk = n! / (k! (n - k)!).

So, the number of combinations of 4 proper bolts out of 15 is:

15C4 = 15! / (4! (15 - 4)!) = 15! / (4! 11!) = 1365.

Therefore, the probability of selecting all 4 proper bolts out of 20 is:

P = number of combinations of 4 proper bolts / number of combinations of 4 bolts = 1365 / 20C4 = 1365 / 4845 = 0.28

So, the probability that all four of the selected bolts are torqued to the proper limit is approximately 0.28.

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The y-intercept is 5, and the slope is -4. As a result, the line's equation is y = -4x + 5, where -4 is the slope and 5 is the y-intercept.

A linear equation is an algebraic equation of the form y = mx + b, where the slope is m and the y-intercept is b, and only a constant and a first-order (linear) term are included.

The slope and y-intercept of the linear equation 4x + y = 5,

we need to solve for y and put the equation in slope-intercept form, y = mx + b,

where the slope is m and the y-intercept is b

4x + y = 5

Subtract 4x from both sides:

y = -4x + 5

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Answer:Part A: To determine the average test score in your math class after completing test 2, substitute 2 for x in the linear function f(x) = 0.5x + 80.

f(2) = 0.5 * 2 + 80 = 81

So, the average test score in your math class after completing test 2 is 81.

Part B: To determine the test average for your science class after completing test 2, we can use the table of values for g(x) given in the problem. When x = 2, g(2) = 83. So, the average test score in your science class after completing test 2 is 83.

Part C: To determine which class had a higher average after completing test 4, we need to calculate the average test scores for both classes after test 4.

For the math class, we can use the linear function f(x) = 0.5x + 80 to find the average test score.

f(4) = 0.5 * 4 + 80 = 82

For the science class, we can use the table of values for g(x) given in the problem. When x = 4, g(4) = 85.

So, the average test score in your science class after test 4 is higher, 85 compared to 82 in your math class.

Step-by-step explanation:

Answer:96

Step-by-step explanation:

uwu yay

The required equation represents the inverse function b(a), which takes the trapezoid's area is B(a) = a/6 - 9.

A trapezoid is a quadrilateral having two parallel bases and one set of other sides called as legs.

We have been given that the trapezoid's base is nine and its height is twelve.

As an outcome, 'b' is the base's parallel side.

The function that represents the trapezoid's area is given by:

A(b) = [12(b + 9)]/2

Let's consider A(b) = a

Then, a =  [12(b + 9)]/2

Now solving for b, we get

2a = 12(b + 9)

a = 6(b + 9)/2

a = 6b + 54

6b = a - 54

b = (a - 54)/6

b = a/6 - 9

Assuming that the length of the side parallel to the base 'b' = B(a), the equation will be:

B(a) = a/6 - 9

Thus, the correct answer would be option A. B(a) = a/6 - 9.

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Answer: 4

Step-by-step explanation:

A solution to this system of linear equations is (1, -2).

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

4x - 2y = 8     ......equation 1.

y = -2     ......equation 2.

Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant IV and it is given by the ordered pair (1, -2).

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The number of children and adults that swam at the public pool are 247 and 208 respectively

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.

Represent the number of children by x and the number of adult by y

this means;

x+y = 455 equation 1

1.75x + 2.5y = 952.25 equation 2

using substitution method,

x = 455-y

substitute 455-y for x in equation 2

1.75(455-y) + 2.5y = 952.25

796.25-1.75y+2.5y = 952.25

0.75y = 952.25-796.25

0.75y = 156

divide both sides by 0.75

y = 156/0.75

y = 208

substitute 208 for y in equation 1

x = 455-208

x = 247

therefore the number of children and adults in the pool are 247 and 208 respectively.

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The spot on the shoreline is moving at a rate of about 1.764 feet per minute when it is 13 feet from the point on the shoreline closest to the lighthouse.

What is differentiation?

Differentiation is a mathematical operation that is used to find the rate at which a function changes. More specifically, it is the process of finding the derivative of a function.

The derivative of a function at a given point is a measure of how quickly the function is changing at that point. It gives the slope of the tangent line to the graph of the function at that point. The derivative can be thought of as the instantaneous rate of change of the function at that point.

Let's call the point on the shoreline closest to the lighthouse "P". We know that the distance from the spotlight to P is 130 feet, and we want to find the rate at which the distance from the spotlight to P changes when the spotlight is 13 feet from P.

To do this, we can use the chain rule to differentiate the distance formula with respect to time. Let's call the distance between the spotlight and P "d". Then:

                           d²= 130² + x²

Taking the derivative of both sides with respect to time gives:

                   2d * dd/dt = 0 + 2x * dx/dt

We can solve for dd/dt by plugging in the values we know:

130² + 13² = d²

d = [tex]\sqrt{(130^2 + 13^2)}[/tex] = 130.325 ft

2(130.325) * dd/dt = 2(13) * dx/dt

dd/dt = (13/130.325) * dx/dt

We know that the spotlight revolves at a rate of 281 rad/min, or 281/2π ≈ 44.7 revolutions per minute. Each revolution of the spotlight covers a distance of 2π * 130 feet, so its speed is:

(2π * 130 ft/rev) * (44.7 rev/min) = 18410.8 ft/min

To find dx/dt when x = 13, we need to find the angular velocity of the spotlight at that point. The spotlight makes one full revolution every 60/14 ≈ 4.29 seconds, so its angular velocity is:

2π radians/rev ÷ 4.29 s/rev = 1.47 radians/s

At any given moment, the angle between the spotlight and the line connecting the lighthouse and P is equal to the arctangent of x/130. When x = 13, this angle is:

arctan(13/130) ≈ 5.71°

The rate at which the angle is changing is equal to the angular velocity of the spotlight, so we can use the formula for the derivative of the arctangent to find dx/dt:

dx/dt = 130 * tan(5.71°) * (1.47 radians/s)

dx/dt ≈ 17.602 ft/min

Finally, we can substitute this value into the expression we found for dd/dt:

dd/dt = (13/130.325) * 17.602

dd/dt ≈ 1.764 ft/min

So the spot on the shoreline is moving at a rate of about 1.764 feet per minute when it is 13 feet from the point on the shoreline closest to the

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The set X ∪ Y is the union of sets X and Y, which is the set of all elements that are in either X or Y. In this case, X ∪ Y = X = {1, 2, 4, 8, 16, 32}.

The most appropriate chart to see the correlation between car mileage and year the car was built for various car models would be a scatterplot chart.

In a scatterplot chart, each point represents a pair of values: one value on the x-axis (in this case, year the car was built) and another value on the y-axis (in this case, mileage). By plotting these pairs of values for each car model in the sample, we can visually examine the relationship between mileage and year built for each car model and determine if there is a correlation between the two variables.

A line chart is used to display data that changes over time, typically for a single variable. A heatmap chart is used to show the magnitude of values for different categories using different colors. Therefore, neither of these chart types would be appropriate to show the correlation between mileage and year built for various car models.

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The answer would be D. 35x² + 29x +6.

What is the Solution of an Equation?

The value of a variable in an equation is the answer that, when inserted into the equation, makes the equation true. It is discovered by relegating the variable to one side of the equation, with the value on the other side being the solution.

To multiply two polynomials, we use the distributive property.

Starting with the first term, we multiply 5x and 7x, then add 2 and 7x, and then add 2 and 3. The result is:

= (5x + 2)(7x + 3)

= 35x² + 33x + 14x + 6

= 35x² + 29x + 6

Therefore, The answer would be D. 35x² + 29x +6.

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