A certain cylinder and square prism have equal lateral surface area. Given the height of the cylinder is equal to the height of the prism, what is the ratio of the volume of the cylinder to the volume of the prism?

(a) The expressions (x + x + x + x) and (4x) are equivalent.

(b) The expressions (5x) and (x + 5) are not equivalent.

Equivalent expressions are expressions that perform the same function notwithstanding their appearance. If two algebraic expressions are equivalent, they have the same value when the variable is set to the same value.

a) True

The expressions (x + x + x + x) and (4x) are equivalent.

Both expressions represent the same mathematical operation, which is adding x four times.

b) False

The expressions (5x) and (x + 5) are not equivalent. They represent different mathematical operations.

The expression (5x) is multiplying x by 5, while the expression (x + 5) is adding x and 5.

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The sketch field of given differential  equation is attached in image .

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

The equation  y′=f(x,y) gives you a slope at each point in the  (x,y)-plane. And this is the slope a solution y(x) would have at x  if its value was y. In other words,  f(x,y) is the slope of a solution whose graph runs through the point  (x,y). At a point  (x,y), we plot a short line with the slope f(x,y).

We have y'=y2

we can write it,

[tex]\frac{dy}{dx}=y^2[/tex]

[tex]\int y^{-2}dy=dx\\\\\frac{-1}{y}=x+c\\[/tex]

The sketch field of the given differential equation is attached in image.

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The mutually exclusive events are:

A = {Chevrolet, Pontiac, Buick}

B = {Ford, Mercedes}

C = {Lincoln, Chrysler}

Explanation:

We will identify the given three events that are mutually exclusive.

From example 2.10

A = {Chevrolet, Pontiac, Buick }

B = {Ford, Mercedes }

C = {Lincoln, Chrysler }

Step 1 of 1

If A∩B=∅ where A and B

are two events then we can say that they are mutually exclusive.

And if there are three or more events then they are mutually exclusive if no two events have an element in common.

Now, events from example 2.10

are:

A = {Chevrolet, Pontiac, Buick}

B = {Ford, Mercedes}

C = {Lincoln, Chrysler}

We can see that all the name card are car brand and their intersection is empty.

Hence, they are mutually exclusive.

Then,

A∩B=∅ and A∩C =∅ and B∩C=∅

Final answer

The mutually exclusive events are:

A = {Chevrolet, Pontiac, Buick}

B = {Ford, Mercedes}

C = {Lincoln, Chrysler}

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The mutually exclusive events are:

A = {Chevrolet, Pontiac, Buick}

B = {Ford, Mercedes}

C = {Lincoln, Chrysler}



We will identify the given three events that are mutually exclusive.

From example 2.10

A = {Chevrolet, Pontiac, Buick }

B = {Ford, Mercedes }

C = {Lincoln, Chrysler }

Step 1 of 1

If A∩B=∅ where A and B

are two events then we can say that they are mutually exclusive.

And if there are three or more events then they are mutually exclusive if no two events have an element in common.

Now, events from example 2.10

are:

A = {Chevrolet, Pontiac, Buick}

B = {Ford, Mercedes}

C = {Lincoln, Chrysler}

We can see that all the name cards are car brands and their intersection is empty.

Hence, they are mutually exclusive.

Then,

A∩B=∅ and A∩C =∅ and B∩C=∅

Final answer

The mutually exclusive events are:

A = {Chevrolet, Pontiac, Buick}

B = {Ford, Mercedes}

C = {Lincoln, Chrysler}

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The sum of a rectangle's length (a) and breadth (b) equals the area of the rectangle (A). So, the area of a rectangle is equal to (a b) square units. l × b.

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The equation representing the total amount Emma earns at the event is y = $10x.

If the total amount Emma earns, y, is proportional to the number of bracelets, x, she sells and she earns $10 for each sold bracelet, then we can write the equation as follows:

y = kx

where k is the constant of proportionality. To find k, we can use the information that Emma earns $10 for each sold bracelet:

y = $10 * x

Therefore, the equation representing the total amount Emma earns at the event is y = $10x.

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The equation representing the total amount Emma earns at the event is y = $10x.

If the total amount Emma earns, y, is proportional to the number of bracelets, x, she sells and she earns $10 for each sold bracelet, then we can write the equation as follows:

y = kx

where k is the constant of proportionality. To find k, we can use the information that Emma earns $10 for each sold bracelet:

y = $10 * x

Therefore, the equation representing the total amount Emma earns at the event is y = $10x.

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The equation formed will be - cost × number of hiking boots + cost × number of canteens and the cost of canteens will be 15.

The equation that will be formed is -

Total cost of purchase = cost of hiking boots × number of hiking boots + cost of canteens × number of canteens

Keep the values in formula to find number of canteens, as it is the only value not provided in the question.

98 = 2×34 + 2× cost of canteens

Performing multiplication on Right Hand Side of the equation

98 = 68 + 2×cost of canteens

Rewriting the formula -

2× cost of canteens = 98 - 68

Performing subtraction on Right Hand Side of the equation

2× cost of canteens = 30

Cost of canteens = 30/2

Performing division on Right Hand Side of the equation

Cost of canteens = 15 each

Thus, the cost of canteens is 15 each.

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The standard deviation of the data set will increase by a factor of 10. This is because standard deviation measures how much variation or dispersion exists from the mean of a data set. Adding 10 to every value of the data set will increase the overall spread of the data and thus increase the standard deviation.  

To prove this mathematically, let's consider a data set A with mean M and standard deviation SD. Let's add 10 to every value of the data set to get a new data set B. The mean of set B is M+10 and the standard deviation of set B is SD'.   The formula for SD' is:  

SD':[tex]\sqrt{(x_{1} -(M+10))^{2} +(x_{2} -(M+10))^2+ (x_{3}-(M+10))^2 +...+ (x_{n}-(M+10))^2)/n }[/tex] We can simplify this by substituting the values for the xi:

 SD' =[tex]\sqrt{(((x_{1}-M-10)^2 + (x_{2}-M-10)^2 + (x_{3}-M-10)^2 +...+ (x_{n}-M-10)^2)/n) }[/tex]  Now let's consider the original data set A and its standard deviation SD:

 SD =[tex]\sqrt{(((x_{1}-M)^2 + (x_{2}-M)^2 + (x_{3}-M)^2 +...+ (x_{n}-M)^2)/n) }[/tex] ,We can substitute the values for xi in this formula as well:  

SD= [tex]\sqrt{ (((x_{1}-M-10)^2 + (x_{2}-M-10)^2 + (x_{3}-M-10)^2 +...+ (x_{n}-M-10)^2)/n)}[/tex]  If we compare SD and SD', we can see that they are identical, except that the value of M has been replaced with M+10. This means that when we add 10 to every value of the data set, the standard deviation increases by a factor of 10.

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Kilograms Pounds, kilograms and ounces, 64 kilos 141.1 lbs 141 lbs, 2 ounces.

Remember that 1 kg is equal to 2.2046 lbs when converting between the two units.

One pound generally weighs 0.45359237 kilos. One can convert a pound to kilogrammes by multiplying the stated number of pounds by an average of 0.45359237.

One kilogramme is equivalent to 2.2 pounds (kg). The kg to pounds conversion results in 2.2 pounds for 1 kilogramme. One of the keys to remembering this conversion is the capacity to compute your own weight in pounds and kilogrammes.

The kilogramme will probably be used going forward because it is a smaller figure and is easier for you to memorise.

The kilograms to pounds conversion table

Kilograms Pounds

kilograms and ounces

64 kilos 141.1 lbs 141 lbs, 2 ounces.              

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The correct statement regarding the sign of the absolute value function is given as follows:

B. The function is never negative.

A function is classified as positive in the intervals that it's graph is positioned above the x-axis.

A function is classified as negative in the intervals that it's graph is positioned below the x-axis.

When the graph of the function is exactly at the x-axis, it is said that the function assumes a value of zero.

For this problem, the lowest value assumed by the function is at the x-axis, hence it is of zero and the function is never negative, meaning that option B is correct.

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Answer: 1/30 is the probability.

Answer:

z = -3

Step-by-step explanation:

-7(z - 3) = 42

Distribute -7 to both numbers inside the parenthesis:

(-7(z) - -7(3)) = 42

-7z + 21 = 42

Subtract 21 from both sides:

-7z = 21

Divide both sides by -7:

[z = -3]

Gauss-Jordan Elimination is a technique for solving systems of linear equations and for determining the inverse of any invertible matrix.

Gauss-Jordan Elimination is a method for finding the inverse of any invertible matrix and for solving systems of linear equations. It is based on the three simplest row operations one may do on a matrix: Place two of the rows in opposite positions. A nonzero scalar multiplied by one of the rows

Since a similar version was described by Wilhelm Jordan in 1888 in his book "Handbuch der Vermessungskunde" independently of B. I. Clasen, who published something similar in the same year, the procedure known as Gauss-Jordan elimination for converting a matrix into reduced echelon form also includes the name Jordan.

This method, which is also known as row reduction, has two steps: forward elimination and back substitution. These two Gaussian elimination method steps differ from one another not by the operations that can be performed through them but rather by the outcome that is obtained.

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The cost of a bus in 1984 is =$ 7360 and in 1992 is $28140.and CPI in 1950 is 20.5.

The consumer price index (CPI) is the index that shows how much prices have changed over time. This index mainly focuses on the retailer prices for market players. Usually, this index increases due to inflation.

Part(1)

% change in CPI (1984-70)

[tex]=\frac{36.8-100}{100} \\=-63.2 \ percentage \\=-0.632[/tex]

Cost of bus = 20000(1-0.632)=$ 7360

Part II

% change in CPI (1984-92)

[tex]=\frac{140.7-199}{100}[/tex]

=40.7%

= 0.407

cost of a bus in 1992 = 20,000(1+0.407)

= $28140

part (3)

% change in CPI (1950-84)=% change in price

[tex]\frac{100-x}{x}*100=[[20000-4100]/4100]*100\\100-x=3.878x\\=x=20.5\\the\ cpi\ in\ 1950\ was \ 20.5.[/tex]

The complete question is -

In 1984, a school bus cost $20,000. To answer each of the parts below, assume that the consumer price index (CPI) was 36.8 in 1970, 100 in 1984, and 140.7 in 1992.

Part I: If the price of a school bus increased at the same rate as the CPI from 1970 to 1984, how much did a school bus cost in 1970? By how much did the price of a school bus increase from 1970 to 1984?

Part II: If the price of a school bus increased at the same rate as the CPI from 1984 to 1992, how much did a school bus cost in 1992? By how much did the price of a school bus increase from 1984 to 1992?

Part III: If a school bus cost $4100 in 1950, and if the price of a school bus increased at the same rate as the CPI from 1950 to 1984, what was the CPI to the nearest tenth in 1950?

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Chuck and Wendy's investment assets is to use their gross assets as a base and then add in any net assets.

For example, if Chuck and Wendy have $100,000 in gross assets and $50,000 in net assets, their investment assets would be $120,000.

Chuck and Wendy's fixed assets and total wealth depend on many factors, including the level of risk they are willing to take, expected return, and overall financial stability.

For example, Chuck and Wendy's may have higher risk if they have a higher return on investment but still have $100,000 in total assets if their expected return is 5%.

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The maximum value of the function f(x) = (x − x²)/(1 + 8x²) is 1/4, and it occurs when x = 1/2.

A function is a mathematical relationship between input and output values.

In this problem, we have a specific function defined as

=> f(x) = (x − x²)/(1 + 8x²).

Let's start by analyzing the expression of the function.

The function is composed of two parts:

=> (x − x²) and (1 + 8x²).

The first part is a simple polynomial expression with degree 2. It represents a parabolic shape with a vertex located at (1/2, 1/4).

The second part, (1 + 8x²), is always positive, so it does not affect the shape of the function.

The maximum value of the function will occur when the first part, (x − x²), is at its maximum. Since this part is a parabolic shape with a vertex at (1/2, 1/4), the maximum value is 1/4.

So, the maximum value of the function

=>  f(x) = (x − x2)/(1 + 8x²) is 1/4.

To find the value of x at which this occurs, we will have to find the x-coordinate of the vertex of the parabolic shape.

This can be done using the formula for the x-coordinate of the vertex of a parabolic equation, which is -b/2a.

Plugging in the values of a and b from the equation (x − x²) gives us

x = 1/2.

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dW/dt represents rate of change of mouse weight with respect to time, or derivative of weight with respect to time.

What is weight ?

Weight is a measure of the force exerted on an object due to gravity. It is commonly defined as the mass of an object multiplied by the acceleration due to gravity. In physics, weight is often expressed in units of Newtons or pounds.

The expression dW/dt represents the rate of change of the weight of the mouse (W) with respect to its age (t) in weeks. The symbol dW/dt is known as the derivative of the weight with respect to time and represents the rate of growth or decline of the mouse's weight.

dW/dt represents rate of change of mouse weight with respect to time, or derivative of weight with respect to time.

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dW/dt represents rate of change of mouse weight with respect to time, or derivative of weight with respect to time.

Weight is a measure of the force exerted on an object due to gravity. It is commonly defined as the mass of an object multiplied by the acceleration due to gravity. In physics, weight is often expressed in units of Newtons or pounds.

The expression dW/dt represents the rate of change of the weight of the mouse (W) with respect to its age (t) in weeks. The symbol dW/dt is known as the derivative of the weight with respect to time and represents the rate of growth or decline of the mouse's weight.

dW/dt represents rate of change of mouse weight with respect to time, or derivative of weight with respect to time.

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The equation representing the given situation is 40 + 5x = 62.50 and the price of a small bag of popcorn will be $ 4.5. Option C is correct.

What is the equation?

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, five buddies each pay $8 for a ticket to the matinee. Additionally, they each buy a little bag of popcorn. The pals spend $62.50 altogether.

Suppose x represent the price of a small bag of popcorn.

(cost of ticket + cost of popcorn) × number of friends = total cost

⇒ (8 + x) 5 = 62.5

Simplify the equation to obtain the value of x as,

⇒  (8 + x) = 62.5/5

⇒ 8 + x = 12.5

⇒ x = 12.5 - 8

⇒ x = 4.5

Thus, the equation representing the given situation is 40 + 5x = 62.50 and the price of a small bag of popcorn will be $ 4.5. Option C is correct. Option C is correct.

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The equation representing the given situation is 40 + 5x = 62.50 and the price of a small bag of popcorn will be $ 4.5. Option C is correct.

What is the equation?

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, five buddies each pay $8 for a ticket to the matinee. Additionally, they each buy a little bag of popcorn. The pals spend $62.50 altogether.

Suppose x represent the price of a small bag of popcorn.

(cost of ticket + cost of popcorn) × number of friends = total cost

⇒ (8 + x) 5 = 62.5

Simplify the equation to obtain the value of x as,

⇒  (8 + x) = 62.5/5

⇒ 8 + x = 12.5

⇒ x = 12.5 - 8

⇒ x = 4.5

Thus, the equation representing the given situation is 40 + 5x = 62.50 and the price of a small bag of popcorn will be $ 4.5. Option C is correct. Option C is correct.

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a) On solving the linear equations y = - 6x - 11  and y = 4x + 19, the solutions are x = -3 and  y = 7.

b) The system of equations has one solution.

c) The solution is obtained as x = -3 and y = 7.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The two linear equations given are -

y = - 6x - 11 .... (1)

y = 4x + 19 .... (2)

Substitute equation (1) in (2) -

- 6x - 11 = 4x + 19

Collect all the like terms -

- 6x - 4x = 19 + 11

-10x = 30

x = 30 / -10

x = -3

Substitute the value of x in equation (1) -

y = - 6(-3) - 11

y = 18 - 11

y = 7

The two equations form a linear graph and intersect at point (-3,7).

So, there is only one solution to the system of equations.

Therefore, the solutions are x = -3 and y = 7.

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Answer:

c

Step-by-step explanation:

Answer:

Let x be Jenny's hourly rate. Then Mary's hourly rate is x + 0.2x = 1.2x.

The total amount of money they earned for the hours they worked is the same, so we can set up the equation:

30x + 25(1.2x) = 610

Expanding the second term and solving for x:

30x + 30x = 610

60x = 610

x = 10.17

So Jenny's hourly rate is $10.17 and Mary's hourly rate is $12.20.

Answer:Write the slope-intercept form of the line with the given slope and point.

m=−2; (5, 1)

Step-by-step explanation:

"The customer yields $780 per year in profits for this retailer."

Customer lifetime value (CLV) is a prediction of the total value a customer will bring to a business over their entire relationship with the company. Retailer profits refer to the financial gain a retailer makes after subtracting all costs, including the cost of goods sold, operating expenses, and taxes, from the revenue generated by their retail sales.

The customer spends $250 a week, so the retailer profits:

If the shopper visits the store every week for a year, the retailer profits:

If this shopper remains loyal for a 10-year lifespan, the retailer profits:

This is the CLV  without considering inflation or any other factors. To consider inflation, we can apply the 8% annual interest rate to calculate the present value of the future profits. The present value of $7,800 over 10 years with an 8% interest rate is approximately $5,100 (the exact value will depend on the method used to calculate the present value).

This question should be provided as:

Assume that a customer shops at a local grocery store spending an average of ​$250 a​ week, resulting in a retailer profit of ​$15 each week from this customer. Assuming the shopper visits the store all 52 weeks of the​ year, calculate the customer lifetime value if this shopper remains loyal over a​ 10-year life span. Also assume a 8 percent annual interest rate and no initial cost to acquire the customer.

The customer yields ​$_____ per year in profits for this retailer.

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The probability of rolling an even number and then an odd number when rolling two number cubes is 1/4 or 0.25.

The sample space is the set of all possible outcomes, which in this case is 36. The number of desired outcomes is 9, as the question specifies.

The probability of rolling an even number and then an odd number when rolling two number cubes is 1/4 or 0.25. You calculate this by taking the number of desired outcomes (9) and dividing it by the total number of possible outcomes (36).

The probability of rolling an even number and then an odd number when rolling two number cubes is 1/4 or 0.25. This is calculated by taking the number of desired outcomes (9) and dividing it by the total number of possible outcomes (36).

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When rolling two number cubes, the likelihood of first getting an even number and then an unusual one is 1/4, or 0.25. You can determine this by dividing the total number of possible outcomes by the number of intended outcomes (9). (36).

When rolling two number cubes, the likelihood of first getting an even number and then an unusual one is 1/4, or 0.25. This is calculated by dividing the total number of possible outcomes (which is 36) by the number of intended outcomes (9). (36).

The coterminal angle with -210° is -570°. This is because subtracting 360° from -210° gives us -570° which is between -720° and -360°.

To find an angle coterminal with -210° that is between -720° and -360°, we need to subtract 360° from -210°. By doing this, we end up with -570° which is the coterminal angle with -210° that lies between -720° and -360°. This is because angles on the circle can 'wrap around' infinitely, and when we subtract 360° from -210°, we end up with an angle that is still equivalent to -210°, but between the two values we are looking for. Therefore, the angle we were looking for is -570°.

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If DE = 4x + 5 and GJ = 3x + 25, and the value of both the expressions is same, then value of DE is, 85

An expression is a sentence with at least two numbers or variables having mathematical operation. Maths operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

Two expressions,

DE = 4x + 5 and GJ = 3x + 25,

If DE = 4x + 5 and GJ = 3x + 25, and they have the same value, then we can set the two expressions equal to each other:

4x + 5 = 3x + 25

Solving for x, we get:

x = 20

So, when x = 10,

DE = 4 x20 + 5

      = 85

and GJ = 3 x 20 + 25

            = 85

Therefore, the value of DE is 85.

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If  company packages puzzles in boxes that are 6 Inches by 4 Inches by 2 inches and the shipping e is a cube with 12-inch sides. The greatest number of puzzle boxes that can be packed into a shipping crate is: 36 puzzle boxes.

Volume of the puzzle box = 6 * 4 * 2

Volume of the puzzle box = 48 cubic inches

Volume of the shipping crate = 12 * 12 * 12

Volume of the shipping crate = 1728 cubic inches

Greatest number of puzzle boxes that can be packed into a shipping crate is:

Greatest number of puzzle boxes = 1728 / 48

Greatest number of puzzle boxes = 36 puzzle boxes

Therefore the Greatest number of puzzle boxes is 36 puzzle boxes.

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The solution to the system is:

(x, y) = (2.236, 1), (-2.236, 1), (2.236, -1), or (-2.236, -1).

This represents two equations hyperbola and ellipse which intersect at exactly 4 points.

The system of equations, as follows:

3x² + y² = 16

x² - y² = 4

We can solve this system of equations by substitution.

Starting with the first equation, we can isolate y²:

y² = 16 - 3x²

Substituting that into the second equation, we get:

x² - (16 - 3x²) = 4

Expanding the right side:

x² - 16 + 3x² = 4

4x² = 4 + 16

4x² = 20

Dividing both sides by 4:

x² = 5

Taking the square root of both sides:

x = ±√5 = ± 2.236

With x found, we can substitute it back into the expression for y²:

y² = 16 - 3x²

y² = 16 - 3(√5)²

y² = 16 - 3(5)

y² = 16 - 15

y² = 1

Taking the square root of both sides:

y = ±1

So the solution to the system is:

(x, y) = (2.236, 1), (-2.236, 1), (2.236, -1), or (-2.236, -1)

This means the two equations are hyperbola and ellipse which intersect at exactly 4 points.

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Answer:c

Step-by-step explanation:

Answer:

To calculate the geometric mean of two numbers, you would multiply the numbers together and take the square root of the answer.

3 * 17 = 51

The square root of 51 is: 7.141

7.141 is the geometric mean of 3 and 17.

Step-by-step explanation:

Hope it helps! =D