determine if the given expressions are equivalent

The total volume is 160.2cubic feet.

for the cone,

we can take π times the radius squared times the height.

volume = π x 9 x 4

volume = 113.0973

for the cone,

you would take π times the radius squared times the height and divide it all by 3

volume= (π x 9 x 5)/3

volume= 47.123

so, The total volume is 160.2cubic feet.

Cone

A cone is defined as a distinctive three-dimensional geometric figure with a flat and curved surface pointed towards the top.

Volume

Volume is a three-dimensional quantity that is used to measure the capacity of a solid shape. It means the amount of three-dimensional space a closed figure can occupy is measured by its volume.

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The complete question is :--

The figure is made up of a cylinder and a cone.

What is the exact volume of the figure?

Enter your answer in the box.

ft3

A shape made up of a cone on top of a cylinder. The cylinder has a height of four feet and a radius of three feet. The cone has a radius of three feet and a height of five feet.

When a > 0, the graph opens upward

When a < 0, the graph opens downward

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

The quadratic function y = mx²

The variable represents the leading coefficient

i.e. a = m

As a general rule:

Equations with negative leading coefficients open downwards, while other open upwards

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The given series in sigma notation is [tex]\sum_{k=1}^{88} 2.5(1.2)^{k-1}[/tex].

A geometric series is the summation of an infinite number of terms that have a constant ratio between consecutive terms.

This is an infinite geometric series with a first term of 2.5, a common ratio of 1.2, and 87 terms. It can be written as:

2.5 + 2.5(1.2) + 2.5(1.2)^2 + ... + 2.5(1.2)^87 = 2.5 × (1 + 1.2 + 1.2^2 + ... + 1.2^87)

If we look at the power, it is always one less the term, i.e., for the first term, the value of k = 0.

So, the series in the form of summation is as follows:

[tex]\sum_{k=1}^{88} 2.5(1.2)^{k-1}[/tex]

Hence, the correct answer is D.

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--The given question is incorrect; the correct question is

"what is this series written in sigma notation 2.5 + 2.5(1.2)+2.5(1.2)^2+...+2.5(1.2)^87"--

The measure of the angle of the triangular plot at which the surveyor stands is cos(0.125) = 83°

Since we have given that the lengths of the sides of triangle from figure :

a = 300 m

b = 250 m

c = 200 m

We need to find the measure of angle i.e. A

As we know the "Law of Cosine rules ":

Cos A = b^2 + c^2 - a^2 / 2bc

          = 250^2 + 200^2 - 300^2 / 2.250.200

          =  125 / 1000

          = 0.125

therefore , A = 82.81° approximate and close to 83°

Hence second option is correct.

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The intensity in watts per meter squared of 85.0-dB sound is 0.316 watts per meter squared.

To calculate the intensity in watts per meter squared of 85.0-dB sound, we first need to convert the dB sound level to a ratio.

This is done by calculating 10 raised to the power of the dB sound level divided by 10.

Therefore, 10^(85.0/10) = 316.

Next, we need to convert the ratio to intensity in watts per meter squared. This is done by dividing the ratio by 1,000,000.

Therefore, 316 / 1,000,000 = 0.000316.

Finally, we need to convert the intensity in watts per meter squared to a more readable number. This is done by multiplying the intensity by 1,000,000.

Therefore, 0.000316 * 1,000,000 = 0.316 watts per meter squared.

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The intensity in watts per meter squared of 85.0-dB sound is 0.316 watts per meter squared.

We must first translate the dB sound level into a ratio in order to determine the intensity of 85.0-dB sound in watts per square meter.

To do this, divide the decibel sound level by 10 and multiply the result by 10 raised to that power.

Consequently, 10 (10/85.0) = 316.

The ratio must then be changed to intensity in watts per square meter. To do this, double the ratio by 1,000,000.

316 divided by 1,000,000 equals 0.000316.

Finally, we must translate the intensity measured in watts per square meter into a more understandable value. The intensity is multiplied by 1,000,000 to achieve this.

Therefore, 0.316 watts per square meter are equal to 0.000316 * 1,000,000.

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Answer:

x = -3.84

y = -4.96

Step-by-step explanation:

-7x+3y=12

2x-8y=32

We multiply the first equation by 2 and the second equation by 7

-14x + 6y = 24

14x -56y = 224

-50y = 248

y = -4.96

Now put -4.96 in for y and solve for x

-7x+3(-4.96) = 12

-7x - 14.88 = 12

-7x = 26.88

x = -3.84

Let's check

-7(-3.84) + 3(-4.96) = 12

26.88 - 14.88 = 12

12 = 12

So, x = -3.84, and y = -4.96 is the correct answer.

The correct options regarding the domain of the functions are given as follows:

b 2x^2-4 domain all real numbers

c x^2-4 domain all real numbers

d 2x^2-2 domain all real numbers

The domain of a function is the set composed by all the input values that the function accepts.

Quadratic functions have no restrictions, hence the domain for all of them is of all real values, and thus options b, c and d are the correct options.

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The angle denoted by the letter x is an inscribed angle created by the intersection of the chords AC and BD, as can be seen.

Corner, whether it be a protruding element or a section of an enclosed space. the pattern created by two lines that diverge from the same point.

a measurement of an angle or the degree of rotation necessary to parallelize or align two angled lines or planes.

An angle in planar geometry is a form created by two rays or lines that have a common termination. The English word "angle" derives from the Latin word "angelus," which means "corner."

The vertex, which serves as the joint terminus of two rays, and the two rays are known to as the sides of an angle and an angle, respectively.

Our goal is to determine the size of the angle denoted by the x:

We may use the chord theorem formula because we can see that the angle denoted with x is an inscribed angle created by the intersection of the chords AC and BD.

x = BC + AD / 2

By replace BC with 39 and AD with 62, we get:

x = 39 + 62/2

x=50.5°

Therefore, measure of the angle marked x=50.5°

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Answer:

To convert inches to feet, we divide the number of inches by the number of inches per foot. One foot is equal to 12 inches.

So, to convert 5 inches to feet:

5 inches / 12 inches/foot = 5/12 feet

The answer can be simplified as a proper fraction.

5 inches = 5/12 feet

the answer would be 104

How you would get this answer if by dividing 156 ÷3 =52

then you would take the 52 and multiply it by 2 and get 104

I have also provided the work on how to write it out!

Hope this helps and have a good day!

Answer:

First find what f(-4) is, it is 2. Then substitute the 2 into x for e(x). Then is becomes e(2) which equals -4. The output is the same as the input because they are inverses. When putting the output of the original equation as the input of the inversed equation, the output of the inversed equation becomes the input of the original equation.

The function e(f(-4)) = -4. This happens because when two function machines are pushed together, the output of the first machine is used as the input for the second machine.

The inverse of a function f(x) is a function e(x) such that e(f(x)) = x for all x in the domain of f(x). To find the inverse of Amanda's favorite function, f(x) = 1 + sqrt(x + 5), we need to isolate x in the expression 1 + sqrt(x + 5) and call it y:

y = 1 + sqrt(x + 5)

Squaring both sides of the equation, we get:

y^2 = 1 + 2sqrt(x + 5) + (x + 5)

y^2 - 1 = 2sqrt(x + 5) + x + 5

Expanding the square on the left side, we get:

y^2 - y - 6 = x

So the inverse function, e(x), can be defined as:

e(x) = y^2 - y - 6

Finally, to evaluate e(f(-4)), we first need to find f(-4), then use the result as an input to the inverse function e(x):

f(-4) = 1 + sqrt(-4 + 5) = 1 + sqrt(1) = 1 + 1 = 2

e(f(-4)) = e(2) = 2^2 - 2 - 6 = 4 - 8 = -4

Therefore, e(f(-4)) = -4.

This happens because when two function machines are pushed together, the output of the first machine is used as the input for the second machine.

The inverse of Amanda's favourite function takes the output of the first machine and finds the original input that would have produced the same output. In this case, the original input was -4.

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Answer:

Step1

First look at the value for 4 and then rest numbers 1234

Step2

4 is Unit 3 is Tens 2 is Hundred and 1 is Thousand

Step3

So in the question 4 is Unit 8 is Tens 7 is Hundred and 4 is thousand

By lowest terms -4x + 20 / x² - x - 12 * x + 3 / x² - 25  this we get -4 / (x - 4) (x + 5).

A numerator and denominator's lowest value after being divided by their biggest common factor.

By multiplying the reciprocal of a fraction, divide it:

-4x + 20 / x² - x - 12 * x + 3 / x² - 25

The expression is multiplied:

4(-x + 5 ) / x² - x - 12 * x + 3 / x² - 25

The expression is multiplied:

4(-x+5) / (x-4)(x+3) * x+3 / x² - 25

Applying factoring to the phrase

a² - b² = (a+b) (4-b):

4(-x + 5 )/(x-4)(x+3) * x+3 / (x+5)(x-5)

Eliminate all but the lowest term from the expression:

-4 / (x - 4) * 1 / ( x + 5)

Put the following in one fraction:

-4 / (x - 4 ) (x + 5 )

Answer : -4 / (x - 4) (x + 5).

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Poisson's ratio v can get close to 1, but never reach it 1/2. G/B = 3(1-2v)/(2(1+v)) limits it.

The right hand side must be positive because the shear G and bulk B moduli must both be positive since else an elastic material would spontaneously deform. This results in -1 v 12.

Because of those  symbols, equality is not possible; consequently, G/B cannot be zero. The elasticity formulas are invalid because any substance with G = 0 is a fluid.

Keep in mind that v = 12 is the typical model for rubbers. Since the ratio G/B is greater than 6000 for gum rubbers, this estimate is only a rough guide. This presumption has the effect of ignoring any volumetric distortion.

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The direction and magnitude of the resultant vector are:

i. Magnitude = 6403

ii. Direction = 51.3^o

A resultant vector is just a single vector which represent two or more vectors acting at a point in both magnitude and direction.

To determine the magnitude of the resultant vector, we have;

let the resultant vector be represented by R, so that;

/Hyp/^2 = /Opp/^2 + /Adj/^2

R^2 = 5000^2 + 4000^2

      = 25000000 + 16000000

R^2 = 41000000

R = (41000000)^1/2

  = 6403.12

The resultant of the two vectors is 6403.

ii. To determine the direction (θ) of the vector,

Tan θ = y/ x

Tan θ = 5000/ 4000

θ = Tan^-1 1.25

  = 51.341

θ = 51.3^o

The direction of the resultant vector is 51.3^o.

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Gwen is correct. The expression 43 + 3 can be written as 43/1 + 3/1

In most cases, something is said to be equivalent if two of them are the same. Similar to this, analogous expressions in mathematics are those that, despite their differences in appearance, have the same meaning. The two expressions, however, produce the identical outcome when the values are inserted into them.

Gwen is correct. The expression 43 + 3 can be written as 43/1 + 3/1. To simplify, you can add the numerators (43 + 3) and keep the denominator the same (1). So the simplified expression is 46/1, which is equal to 46.

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1. The set of all points in a plane that are the same distance from a given point called Radius. So the option B is correct.

2. A straight line from the center to the circumference of a circle or sphere is Diameter. So the option A is correct.

The set of all points in the plane that are a fixed distance (the radius) away from a fixed point is referred to as a circle (the center).

Radius is the name for any distance that connects a point on a circle to its center. Any two radii have the same length when compared to the definition of a circle. Take note of the fact that the term "radius" is being used to describe both these intervals and their typical length.

The term "chord" refers to the space that connects two points on a circle.

The term "diameter" refers to a chord that runs through the center. Since a diameter is made up of two radii that are connected at their ends, each diameter has a length that is twice as long as its radius.

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The complete question is:

1. The set of all points in a plane that are the same distance from a given point called

1. Center

2. Radius

C. Surface area

D. Circumference

2. A straight line from the center to the circumference of a circle or sphere is

A. Diameter

B. Radius

C. Surface area

D. Circumference

The cost of producing an SSD that can store 4 TB of data can be represented by the function f(s), where s is measured in GB. Since there are 1024 GB in one TB, 4 TB is equal to 4 x 1024 = 4096 GB.

So, the cost of producing an SSD with 4 TB of storage can be represented by:
f(4096)

It is important to note that f(s) is the cost of producing an SSD with s GB of storage, not the cost of producing s SSD with 1 GB of storage.

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Answer:

There are 42 students in the musical.

Step-by-step explanation:

Let x be the number of students in both chorus and musical.

75 ⇒100%

x⇒56%

Find x,

x=56% divided by 100% times 75

Which equals 42 is your answer.

As per the given measurement, the scale drawing of the barn is attached below.

The term scale drawing is defined as a real object with accurate sizes reduced or enlarged by a certain amount.

Here we have given that a  barn is 40 feet wide by 100 feet long.

Here we have given in the question that if you draw a line that is 1/2 an inch on paper its proportional to 10 feet long on the house.

Which means that 1 inch would be 20, then 1.5 would be 30 feet, and then 2 inches would be 40.

Here we have given the proportion would be written as,

=> 2 in: 40 ft

As we know that if we make the ratios equal, then we have,

=> 1/20 = x/40

When we simplify this then we get the value of x as 2

Similarly, for the another one,

=> 1/20 = x/100

Now, we have to multiply both sides by 100:

=> 100/20 = x

Therefore, the value of x is 5.

Hence the scale drawing of the house would be 2 inches wide and 5 inches long.

And the drawing is attached below.

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This is an example of a decreasing sequence. In this case, each number is 13 numbers less than the previous.

A sequence is a term to refer to a group of numbers that have some characteristics in common. For example, in this case these numbers are more than 100 and the value of difference between them is 13.

To calculate the difference between these numbers we have to substract one of the number with the next number:

139 - 126 = 13

126 - 113 = 13

Accprding to the above, this sequence is characterized for a difference of 13 numbers between each value.

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Answer:

19.25 km

Step-by-step explanation:

7 days = 1 week

1 day = 2.75 km

7 days = ?

Then you cross multiply.

Therefore: 7×2.75/1

19.25/1

Answer: 19.25 km

The length of MN if ABC~LMN would be 11 unit.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Given that the side lengths of two similar triangles are always proportional.

Given that ∆ABC ~ ∆LMN, therefore:

AB = 10

LM = 5

MN = x + 4

BC= 3x + 1

Plug in the values

AB / LM = BC/ MN

Cross multiply

10/ 5 = (3x + 1)/(x + 4)

2 (x + 4) = (3x + 1)

2x + 8 = 3x + 1

x = 7

MN = x + 4 = 11

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The percentage decrease from the August price to the September price = 20%

Here, In July the price of a holiday is £500.

And in August the price increases by 25%.

Let 'p' represents the price of a holiday.

First we need to find the value of the 25 percent of £500.

25% of £500

= 500 × (25/100)

= £125

so, the value of p would be,

p = £500 + 25% of £500

p = £500 + £125

p = £625

In September the price drops to £500 again.

i.e., p = 500

So, the decrease in price is: 625 - 500 = 125

Now we find the percentage decrease from the August price to the September price.

(125/625) × 100 = 20%

the percentage decrease in price = 20%

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The inequality to compare it with the times others in the family skied without falling is 2f < 223.

In math the term inequality is defined as a relation which makes a non-equal comparison between two numbers or other mathematical expressions

Here we have given that Kelvin wants to know whether he skied without falling more than twice as long as anyone else in his family.

Here we have also given that his dad tells him that he can check by using the inequality.

Based on the given details we have identified that the inequality that compare it with the times others in the family skied without falling is written as

=> 2f < 223.

here the term f refers the time skied in seconds for each person.

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Kelvin wants to know whether he skied without falling more than twice as long as anyone else in his family. The total amount of time spent on skied without falling 223. Then write the inequality to compare it with the times others in the family skied without falling.

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The radical form for each expression is given as follows:

The general format of the exponential expression is given as follows:

[tex]a^{\frac{n}{m}}[/tex]

To obtain the radical form, we have that:

Hence the radical form of the exponential expression is given as follows:

[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]

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Answer: If your simplifying it's: 2x (power of 3) + x (power of 2) + 3x + 12x +2. Dividing would be 2x (power of 2) − 3x + 9 − 6/x+2. Have a nice day ;)

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{36^3}{12^5}}[/tex]

[tex]\mathsf{= \dfrac{36\times36\times36}{12\times12\times12\times12\times12}}[/tex]

[tex]\mathsf{= \dfrac{1,296\times36}{144\times144\times12}}[/tex]

[tex]\mathsf{= \dfrac{46,656}{20,736\times12}}[/tex]

[tex]\mathsf{= \dfrac{46,656}{248,832}}[/tex]

[tex]\mathsf{\mathsf{= \dfrac{46,656\div 15,552}{248,832 \div 15,552}}}[/tex]

[tex]\mathsf{= \dfrac{3}{16}}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\ \huge\boxed{\mathsf{\dfrac{46,656}{248,832}\ or\ \dfrac{3}{16}}}\huge\checkmark\\\\\ \huge\boxed{\uparrow}}\huge\text{ Either of those should work because they are}\\\huge\text{equivalent to each other :) }} \huge\boxed{\uparrow}}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer: 46656/248832

Step-by-step explanation:

Potentiation in fractions.

Power is made up of a base and an exponent. The exponent indicates how many times the base will be multiplied by itself.

[tex]\boldsymbol{\sf{\dfrac{36^3}{12^5}=\dfrac{36\times36\times36}{12\times12\times12\times12\times12 }=\dfrac{46656}{248832 } }}[/tex]

36³/12⁵ = 46656/248832