cone frustum the first-octant portion of the cone z = 2x2 y2>2 between the planes z = 0 and z = 3

Answers

Answer 1

The volume of the cone frustum is 4.19 cubic units.

How to find the volume of the cone frustum?

To find the volume of the cone frustum, we can use the formula:

[tex]V = (1/3)\pi h(R^2 + Rr + r^2)[/tex]

where h is the height of the frustum, R and r are the radii of the top and bottom bases, respectively.

In this case, the frustum is given by the inequality[tex]z = 2x^2 + y^2 < 2[/tex] and is bounded by the planes z = 0 and z = 3. This means that the height of the frustum is h = 3 - 0 = 3.

To find the radii R and r, we need to find the intersection of the cone [tex]z = 2x^2 + y^2[/tex] and the plane z = 2. Substituting z = 2 into the cone equation, we get:

[tex]2 = 2x^2 + y^2[/tex]

This is the equation of an ellipse in the xy-plane with major axis along the x-axis and minor axis along the y-axis.

To find the radii, we can use the standard form of the ellipse:

[tex](x/a)^2 + (y/b)^2 = 1[/tex]

where a and b are the semi-major and semi-minor axes, respectively. Comparing this with the equation of the ellipse above, we get:

[tex]a^2 = 1/2[/tex] and [tex]b^2 = 2[/tex]

Therefore, the radii are R = √(1/2) and r = √2.

Substituting these values into the formula for the volume, we get:

V = (1/3)π(3)(1/2 + √2/2 + 2)

Simplifying this expression, we get:

V = (π/3)(√2 + 5)

Therefore, the volume of the cone frustum is approximately 4.19 cubic units.

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Related Questions

Consider the equations y= |x-1 | and y = 3x + 2. The approxirate solution of this system of equations is

Answers

Answer:

Point Form: (- 1/4, 5/4)

Equation Form: x = - 1/4, y  = 5/4

Step-by-step explanation:

can someone please help me

Answers

Answer:

[tex]\frac{13\pi }{9}[/tex] radians

Step-by-step explanation:

to convert degrees to radians

degrees × [tex]\frac{\pi }{180}[/tex]

= 260 × [tex]\frac{\pi }{180}[/tex]

= 26 × [tex]\frac{\pi }{18}[/tex]

= 13 × [tex]\frac{\pi }{9}[/tex]

= [tex]\frac{13\pi }{9}[/tex]

Which fractions are equal to 2/3?


Check all that are true.

1
3

6
9

4
6

1
6

3
2

Answers

Answer:

It's the correct answer

PLEASE MARK AS BRAINLIEST

Step-by-step explanation:

Equivalent fractions of 2/3 : 4/6 , 6/9 , 8/12 , 

THX

Don't forget to mark me as brainliest

Please help me on this thanks, I got the right answer but I still don’t understand

Answers

His present age is 13 years.

How to solve words problems ?

The words problem can be solved as follows:

let

his present age = x

Therefore,

3(x + 5) = 54

Hence,

3(x + 5) = 54

3x + 15 = 54

subtract 15 from both sides

3x + 15 - 15 = 54 - 15

3x = 39

divide both sides by 3

3x / 3 = 39 / 3

x = 13

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What is the volume of the space filled with tissue paper in the packaging box? 81.84 cubic centimeters 105.84 cubic centimeters 198.264 cubic centimeters 222.264 cubic centimeters

Answers

The volume of the space filled with tissue paper in the packaging box is 198.264 cubic centimeters

Let l,b,h be the dimensions of small gift box V1 = Volume = l*b*h

= 24cm^3

Dimension of Large box are 2.1l , 2.1b,2.1h

Volume of large box = 2.1 l*2.1b*2.1h

= (2.1)^3*lbh

= (2.1)^3*24

V2 =222.264

Volume filled with tissue paper is V2-V1

222.264 - 24

= 198.264cm^3

Hence The volume of the space filled with tissue paper in the packaging box is 198.264 cubic centimeters

The complete question is shown below

Zoe is packaging a gift to send in the mail. A smaller gift box is placed inside a similar yet larger packaging box. The empty space inside the packaging box is filled with tissue paper to keep the gift box from moving. The dimensions of the larger box are each 2.1 times longer than the corresponding dimensions of the smaller box. The volume of the smaller box is 24 cubic centimeters.What is the volume of the tissue paper in the packaging box?

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Kady and Scott both invest £800.

Kady invests in an account that gives 15.2% compound interest per annum.

Scott invests in an account that gives 15.9% simple interest per annum.

After how many years is Kady's investment worth more than Scott's?

Answers

Answer:we smoking fredoooooooooo

NEED HELP ASAP

Which of the following correctly demonstrates how to factor x² - y²?
A.(x - y)²
B.(x-y)(x+y)
C.(x+y)(x+y)
D.2(x - y)

Answers

Answer:

B.(x-y)(x+y)

Step-by-step explanation:

The factor of x² - y² can be represented by,

A.(x - y)²

INCORRECT:

Translated to (x - y)(x - y) as the exponent says it multiplied by it self

(x - y)(x - y) = x²- 2xy + y² which doesn't match

B.(x-y)(x+y)

Correct!

x times x =  x²

-y times y = -y²

x² - y²

C.(x+y)(x+y)

INCORRECT

x times x =  x²

y times y = y²

x² + y² which doesn't match as y positive here

D.2(x - y)

INCORRECT

distribute 2 so 2x - 2y which isn't the original

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x =x=x, equals
^\circ

Answers

Answer:

x = 25°

Step-by-step explanation:

Hello!

25° and x° are vertical angles, therefore they are equal to each other.

Vertical angles are angles formed by two intersecting lines that are non-adjacent.

The angle to the right of 80° would be 55°, because the sum of angles on a line is 180°.

Angle x would be 25° because the other straight line contains angles 80°, 50° and x°.

A 14 oz bag of flour costs $2.95 and a 28 oz bag of flour costs $6.20. What is the price per ounce of the 14 oz bag of flour?

Answers

The price per ounce of the 14 Oz bag of flour is; ¢21.1.

What is the price per ounce of the 14 oz bag of flour?

Since it follows from the task content that the 14 Oz bag of flour sells for $2.95 which is equivalent to ¢295 since $1 = ¢100.

It follows that the price per ounce of the 14oz bag of flour is; = ¢295/14 = ¢21.1

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How much did Alexa make in 5.5 hours?

Answers

Using a proportional relationship, it is found that Alexa makes $146.45 in 5.5 hours.

What is a proportional relationship?

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

The constant in this problem is:

k = 213.6/8 = 427.2/16 = 827.7/31 = 26.7.

Hence her earnings for x hours of work is:

y = 26.7x.

For 5.5 hours of work, her earnings are:

y = 26.7(5.5) = $146.45.

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The following table shows each of Haruka's final exam scores last semester. Final exam Score on a 100100100-point scale Astronomy 727272 Biology 858585 Physics 929292 Chemistry \large

Answers

The mean calculated shows that the Chemistry score will be 87.

How to calculate the score?

From the information given, the total scores will be:

= 84 × 4

= 336

The addition of the scores given will be:

= 72 + 85 + 92

= 249

The Chemistry score will be:

= 336 - 249

= 87

Complete question:

If the mean of the data set is 84 points, find Harukas final exam score in Chemistry.

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Question 4 of 10
What can you say about the end behavior of the function f(x)--4x+6x²-52?
A. The leading coefficient is positive so the left end of the graph
goes down.
B. f(x) is an even function so both ends of the graph go in the same
direction.
C. The leading coefficient is positive so the left end of the graph
goes up.
D. f(x) is an even function so both ends of the graph go in opposite
directions.

Answers

The end behavior of the Polynomial f(x) = -4x⁶ + 6x² - 52 is;

B. f(x) is an even function so both ends of the graph go in the same

direction

What is the end behavior of the Polynomial?

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

Now, we are given the polynomial;

f(x) = -4x⁶ + 6x² - 52

Let us first test if the polynomial is even;

f(1) = -4(1)⁶ + 6(1)² - 52

f(1) = -50

Similarly;

f(-1) = -4(-1)⁶ + 6(-1)² - 52

f(-1) = -50

Since f(1) = f(-1), we can say that both ends of the graph go in opposite

directions.

Lastly, the leading coefficient is negative because it is -4 and as such it means that the left end goes down.

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Question down below about linear equations.

Answers

The system of equations is -x + y = 4 and -2x + y = 0

How to create the system of linear equations?

To do this, we make use of the following ordered pairs

(4, 8)

The above point represents April 2008.

Let the system of equations be

mx + ny = 4

2mx + ny = 0

Substitute (4, 8) for x and y in the above equations.

4m + 8n = 4

8m + 8n = 0

Subtract both equations

4m - 8m = 4

This gives

-4m = 4

Divide by 4

m = -1

Substitute m = -1 in 8m + 8n = 0

-8 + 8n = 0

This gives

8n = 8

Divide by 8

n = 1

So, the system of equations is -x + y = 4 and -2x + y = 0

The graph of the system of equations

The system of equations is -x + y = 4 and -2x + y = 0

See attachment for the graph of the system

Prove that the solution is (4, 8)

The above is represented in the (a) part of this solution

Verify that the solution is (4, 8)

We have:

-x + y = 4 and -2x + y = 0

Substitute (4, 8) for x and y in the above equations.

-4 + 8 = 4 --- true

-2*4 + 8 = 0 --- true

Both equations are true

Hence, the system of equations have been verified

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Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________

What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?

Answers

The final step in solving the inequality is to divide through by -2 and flip the sign

Solving Inequalities

From the question, we are to determine the final step in solving the inequality

The given inequality and the steps for solving are

Step 1: –10 + 8x < 6x – 4

Step 2: –10 < –2x – 4

Step 3: –6 < –2x

The final step will be to divide both sides of the inequalities by -2 and then flip the sign

That is,

–6 < –2x

Divide both sides by -2 and flip the sign

3 > x

OR

x < 3

Hence, the final step in solving the inequality is to divide through by -2 and flip the sign

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There were only 86 confirmed cases of Measles in the year 2000. In 2019, there was a reported 1,350 % increase in confirmed
cases of Measles. How many cases were there in 2019?

Answers

Answer:

1161 confirmed cases

Step-by-step explanation:

In 2000 the number of cases was 86

Percent means out of a hundred, so if we divide 1350 by 100 we get 13.5.

So, we must multiply 13.5 and 86 to get the amount of cases in 2019.

13.5*86 = 1161 confirmed cases in 2019

Tickets for a concert were \$5$5dollar sign, 5 for each child and \$8$8dollar sign, 8 for each adult.

Answers

Answer:

What exactly is the question

Step-by-step explanation:

There's no clear question.

The table below lists the tallest waterfalls in the world, in feet.
Name/Location Height (ft.) Mutarazi - Zimbabwe 24.99 x 102 Gocta Cataracts - Peru 2.532 x 103 Utigord - Norway 2,625 x 100 Angel - Venezuela .3212 x 104 Espelands - Norway 2.307 x 103 Yosemite - California (USA) 2,425 Monge - Norway 25.4 x 102 Tugela - South Africa 3.11 x 103 **Heights are approximations** [Part 1] List the waterfalls from tallest to shortest.. Show all of your work and/or explain your reasoning. [Part 2] What is the difference between the tallest and shortest heights? Show your work.

Answers

The difference between the tallest and shortest heights is 0.787 × 10

Statistics

Mutarazi - Zimbabwe 24.99 x 10²Gocta Cataracts - Peru 2.532 x 10³Utigord - Norway 2,625 x 10^0Angel - Venezuela .3212 x 10⁴Espelands - Norway 2.307 x 10⁴Yosemite - California (USA) 2,425Monge - Norway 25.4 x 10²ugela - South Africa 3.11 x 10³

From tallest to shortest:

Angel - Venezuela 3.212 x 10⁴Espelands - Norway 2.307 x 10⁴ugela - South Africa 3.11 x 10³Utigord - Norway 2,625 x 10^0Monge - Norway 25.4 x 10²Gocta Cataracts - Peru 2.532 x 10³Mutarazi - Zimbabwe 24.99 x 10²Yosemite - California (USA) 2,425

Difference between tallest and shortest heights =

3.212 x 10⁴ - 2,425

= 3.212 x 10⁴ - 2.425 × 10³

= (3.212 - 2.425) × 10^4 - 3

= 0.787 × 10

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Fill in the table using this function rule.

Answers

The complete table is

x     y

-1     -2

0     3

1     8

2    13

How to complete the table?

The function is given as:

y = 5x + 3

On the table, we have

x = -1, 0, 1 and 2

Using the above values, we have:

y = 5(-1) + 3 = -2

y = 5(0) + 3 = 3

y = 5(1) + 3 = 8

y = 5(2) + 3 = 13

So, the complete table is

x     y

-1     -2

0     3

1     8

2    13

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Find the volume of the composite figure. Round to the nearest tenth if necessary.

Answers

The volume of the given composite solid is 375 m³

Volume of composite solid

From the question, we are to determine the volume of the composite solid

The volume of the composite solid = Volume of the cuboid + Volume of the triangular prism

Thus,

Volume of the composite solid = (5 × 5 × 13) + 1/2(5 × 4 × 5)

Volume of the composite solid = 325 + 50

Volume of the composite solid = 375 m³

Hence, the volume of the given composite solid is 375 m³

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PLSSS HELP
Refer to your answers to the questions from Part 2 of Project 1.
A parabola goes through (negative 3, 3) & (1, negative 1). A point is below the parabola at (negative 3, 2). A line above the parabola goes through (negative 3, 4) & (0, 4). A point on the parabola is labeled (x, y).


What is the correct standard form of the equation of the parabola?

Enter your answer below. Be sure to show each step of your work.

Answers

The correct standard form of the equation of the parabola is:

[tex](x+3)^{2}[/tex]= 4(y - 3).

What is a parabola?

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively. It's also crucial to remember that the fixed point is not located on the fixed line. A parabola is a locus of any point that is equally distant from a given point (focus) and a certain line (directrix). An essential curve of the coordinate geometry's conic sections is the parabola.

For the given question,

Vertex of parabola is (-3,3)

Thus, the equation of the parabola is:

[tex](x-h)^{2}=4(y-k)[/tex]

[tex](x+3)^{2}[/tex]= 4(y-3)

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A group of Advanced Open Water Divers plans to make two dives. The first dive is on a reef in 22 metres of water for 20 minutes. The group then remains on the surface for 1 hour. The second dive is on a wreck in 16 metres of water, with a planned bottom time of 30 minutes. What will be the ending pressure group after the second dive

Answers

The ending pressure group after the second dive is R.

According to the statement

We have given that the

The first dive is on a reef in 22 metres of water for 20 minutes and The second dive is on a wreck in 16 metres of water, with a planned bottom time of 30 minutes.

And we have to find the pressure group after second dive.

So, For this purpose, we know that the

Recreational scuba diving (R) – this diving has prescribed limits, including a depth no greater than 130 fsw, using only compressed air, and never requiring a decompression stop.

From the above situation, we could note that there was a prescribed limit 18m/60ft of water with a bottom time of 30 minutes.

And due to its the ending pressure becomes R.

So, The ending pressure group after the second dive is R.

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What is the equation of the translated function, g(x), if f(x) = x2?


a.) g(x) = (x – 4)2 + 6


b.) g(x) = (x + 6)2 – 4


c.) g(x) = (x – 6)2 – 4


d.) g(x) = (x + 4)2 + 6

Answers

Answer: dfghj

Step-by-step explanation: xcfvghj

Answer: It's D

Step-by-step explanation:

Right on edge 2022

An object has a mass of 560 kg and a volume of 8 m3. find the density of the object in kg/m3.

Answers

The density is 70 kg/m3. Here’s how I found it:
1: the formula for density is mass divided by volume (560/8)
2: 560/8=70
3. The label is kg/m3

Find n if GCF(n, 40)= 10 and LCM (n, 40)= 280

Answers

Answer:

70

Step-by-step explanation:

GCF(x,y)*LCM(x,y)=xy

10*280=40n

2800=40n

70=n

n=70

b. Shawn has 42 points on his computer game. He loses the
next round though which takes away 50 points. How
many total points does Shawn now have?

Answers

Answer: -8 points

Step-by-step explanation: because he lost 50, and he originally had 42, a smaller number, the answer will go into the negatives.

42-50= -8, which is how you get the answer!

Answer:

-8

Step-by-step explanation:

42-50 is the same as 50-42, except the answer is negative

WILL MAKE BRAINLIEST!!
Find the correct angle measure for angle b in each figure.

_1. 52°

_2. 27°

_3. 32°

_4. 98°

Answers

Answer
a first one is 52 (90-38=52)
Second one is 32 (180-148=32
I can’t see the third or 4th one

Of india’s more than 1.2 billion population, about _____ percent are muslims.
a) 4
b) 15
c) 26
d) 62
e) 88

Answers

Fifteen percent of Muslims live in India

Select the correct answer.
Suppose the following function is graphed.
y = 8^5x +4
On the same grid, a new function is graphed. The new function is represented by the following equation.
y = -5^8x+8
Which of the following statements about these graphs is true?

Answers

The true statement about these graph is that: B. the graph of the original function (y = 8/5x + 4) is perpendicular to the graph of the new function (y =- 5/8x + 8).

What is a graph?

A graph can be defined as a type of chart that's commonly used to for the graphical representation of data on both the horizontal and vertical lines of a Cartesian coordinate, which are typically known as the x-axis and y-axis respectively.

How to interpret the graph?

Mathematically, the standard form of the equation of a straight line on a graph is given by;

y = mx + c

Where:

x and y are the points.m is the slope.c is the intercept.

The condition for perpendicularity.

In Mathematics, the condition for perpendicularity of two (2) lines is as follows:

m₁ × m₂ = -1

8/5 × (-5/8) = -1

Based on the graph (see attachment) of the original function and new function, we can infer and logically deduce that the true statement about their graph is that the graph of the original function (y = 8/5x + 4) is perpendicular to the graph of the new function (y =- 5/8x + 8).

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Complete Question:

Suppose the following function is graphed. y = 8/5x + 4 On the same grid, a new function is graphed. The new function is represented by the following equation. y =- 5/8x + 8. Which of the following statements about these graphs is true?

A. The graphs intersect at (0,8).

B. The graph of the original function is perpendicular to the graph of the new function.

C. The graph of the original function is parallel to the graph of the new function.

D. The graphs intersect at (0,4).

PLEASE HELP I GIVE 95 POINTS

Answers

D,
3^x is positive, and the y-in. is 1.
3^0 = 1
Process of elimination.

2. (01.01)
Evaluate 32+(5-2)-4-
O 19
O 16
O 46
24
3
. (1 point)

Answers

32+(5-2)-4
=32+3-4
=35-4
=31
Other Questions
just because there seems to be a linear relationship between an x and a y, does not mean that y is affected or influences by x. a. true b. false Given the following data on a hardware item stocked by AndreasWieland's paint store in Copenhagen, should the quantity discount be taken?D= 4,800 units: S=$25: H=$6: P=$2Discount Price = $1.50Quantity needed to qualify for discount = 4,800 unitsThe total cost without the discount is ?The total cost with the discount is ? As the price of good X rises from $12 to $14, the quantity demanded of good Y falls from 105 units to 75 units. The cross elasticity of demand is approximately . Therefore, X and Y are . sketch a (001) plane in a fcc material and an arbitrary vector within the plane making an angle t with the [100] direction The next dividend payment by Dizzle, inc will be $2.48 per share. The dividends are anticipated to maintain a growth rate of 4.5 percent forever. If the stock currently sells for $39.85 per share, what is the required return? What is the dividend yield? What is the expected capital gains yield? The ____ model suggests that people who put themselves in the shoes of a victim and imagine how they feel will help even if it involves a cost to them.A. empathy-altruismB. kin selectionC. dispositionismD. reciprocal altruism assuming a ratio of three atps per nadh and two atps per fadh2, the theoretical net atp production during prokaryotic aerobic respiration is A map is an abstract representation of the real world in a 2-D format. It must have/possess the following information to be considered as a map.Theme and date of the information shown on the mapDirection pointing the NorthA scale & legendprojection typeAll listed. Otherwise, it is not a map. 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The woman stood leaning on the shaft of a broken sweep, watching the man. With unhurried but almost superhuman strength he was working the other sweep from the rear, aiming for the opposite bank.The struggle seemed hopeless. Torrance read it at a glance, unaccustomed as he was to water. The tug of the rapids was drawing them swiftly downward in a course that was too slightly diagonal to its current to promise more than the faintest hope. The man seemed suddenly to grasp the extent of their peril, for his arms moved more quickly, the bow of the raft swinging about and pointing upstream; but still the current gripped them relentlessly.The woman lifted her head and looked down along the whirling eddies to the froth of broken water. For a moment she stood, rigid, then turned to the horses, and from among them sprang a huge dog. Into its mouth she pressed the end of a rope, and it leaped far into the water.(from The Return of Blue Pete by Luke Allan)How are the characters of the man and woman on the raft developed in the passage?1. by their actions as seen through the eyes of an observer2. by their own thoughts and streams of consciousness3. through the reactions of other characters to them 4. through a direct address to the reader that describes them Read the excerpt from America's First President: George Washington:(1) George Washington is often referred to as the founder of the United States. He was the first president of the country. Washington also played a pivotal role in the American wars and the drafting of the U.S. Constitution.Childhood(2) George Washington was born into a moderately wealthy family on February 22, 1732 in Westmoreland County, Virginia. The family owned a tobacco plantation. George was homeschooled and spent a lot of time learning hands-on skills. When George was sixteen, he became a land surveyor and helped to plot the land in Virginia's western territory. Through this experience, he learned skills such as farming and resourcefulness, and he developed an interest in western land holdings and purchases. It was this passion that brought about his belief that the future of the nation depended on the colonization of the West.The French and Indian War(3) In the early 1750s, border disputes began between Britain and France. Both countries were claiming rights to land in the Ohio River Valley. In December 1752, Washington was made commander of the Virginia militia even though he did not have any training or previous military experience.(4) In the summer of 1755, Washington joined Major General Edward Braddock and the British army in an attempt to overtake the French controlled Fort Duquesne. To reach the fort, the soldiers had to travel through the dense woods of the Allegheny Mountains. Washington knew the area well and helped lead the way, despite suffering from a terrible case of dysentery. When the soldiers reached the Monongahela River, ten miles from Fort Duquesne, they were ambushed by the French forces who were working with the native people. During the attack, most of the senior officers from the British Army were killed or severely wounded. Washington escaped injury with four bullet holes in his cloak and two horses shot out from under him.Select the statement that explains what made George Washington qualified to be commander of the Virginia militia. (2 points)His homeschool education gave him the skills and training in military activities.His family was wealthy, so they were able to provide him the training he needed to be successful.He attended prominent military training schools throughout his childhood.His land surveying skills gave him a strong knowledge of Virginia and his farming skills made him resourceful. Calculate the ionic strength of a 0.0020 m aqueous solution of MgCl2 at 298 k. law of sines calc: find beta, a=n/a, alpha=n/a, b=n/a ronaldo is an 80-year-old man who has noticed his walking abilities have declined in recent years. he used to walk 2 miles at least 4 days a week, but his joint pain and muscle fatigue have lessened that to less than 1 mile maybe twice a week. ronaldo has been feeling less positive and energetic lately, as he misses his longer walks. to feel better, what should ronaldo do to compensate for the weaknesses that occur as he ages? does american express have foreign transaction fees During the past five years, you owned two stocks that had the following annual rates of return:a. Compute the arithmetic mean annual rate of return for each stock. Which stock is most desirable by this measure?b. Compute the standard deviation of the annual rate of return for each stock. (Use Chapter 1 Appendix if necessary.) By this measure, which is the preferable stock?c. Compute the coefficient of variation for each stock. (Use the Chapter 1 Appendix ifnecessary.) By this relative measure of risk, which stock is preferable?d. Compute the geometric mean rate of return for each stock. Discuss the difference between the arithmetic mean return and the geometric mean return for each stock. Discuss the differences in the mean returns relative to the standard deviation of the return for each stock.