Cone W has a radius of 8 cm and a height of 5 cm. Square pyramid X has the same base area and height as cone W. Paul and Manuel disagree on how the volumes of cone W and square pyramid X are related. Examine their arguments. Which statement explains whose argument is correct and why?
Answers
This question is incomplete because it lacks the appropriate attachment containing the argument of Paul and Manuel
Kindly find attached the appropriate attachment necessary to solve this question.
The attachment was sourced online
Answer:
a) Paul's argument is correct, Manuel used the wrong formula to find the volume of square pyramid X
Step-by-step explanation:
From the above question, we are given two shapes: Cone W and Square Pyramid
Cone W: Radius = 8cm, Height = 5cm
Volume of a Cone = 1/3 πr²h
Where π = 3.14
Volume of Cone X = 1/3 × 3.14 × 8² × 5
= 334.93cm³
For Square pyramid X
Volume = 1/3 × Base Area × Height
Base Area of Cone W = Base Area of square pyramid X = πr²
Where π = 3.14
Base area = 3.14 × 8² = 200.96cm²
Height of Square pyramid X = Height of Cone W = 5cm
Volume of Square pyramid = 1/3 ×200.96cm² × 5cm
= 334.93cm³
Therefore, from my above calculation and compared with the arguments of Paul and Manuel, Option a) "Paul's argument is correct, Manuel used the wrong formula to find the volume of square pyramid X" is the correct option.
The reason why is because the correct formula for the volume of a square pyramid = 1/3 × Base area × Height
This was the formula Paul used.
Manuel on the other hand used the formula: Base Area × Height to find the volume of cone W. This formula is wrong.
Option a, is the correct answer.
Answer: A. Paul's argument is correct; Manuel used the incorrect formula to find the volume of square pyramid X.
Proof of validity shown below along with the attached chart not included in initial question!
Related Questions
Students in an introductory statistics course were asked the following questions as part of a class survey:(1) What is your gender, male or female?(2) On average, how many hours of sleep do you get per night?(3) What is your bedtime: 8pm-10pm, 10pm-12am, 12am-2am, later than 2am?(4) How many countries have you visited?(5) On a scale of 1 (very little) - 5 (a lot), how much do you dread this semester? Identify the variables in the survey. Classify each variable as numerical or categorical. For each numerical variable, identify whether it is continuous or discrete. For each categorical variable, identify whether it is nominal or ordinal.
Answers
Answers:
Gender = categorical, nominal variable
Sleep length = numerical, continuous
Bedtime = categorical, ordinal
Number of countries visited = numerical, discrete
Scale of dreading semester = categorical, ordinal
=========================
Explanation:
Gender is categorical because there are two categories or labels, male or female. It is nominal because we simply attach names to each label and we can't sort them or order them from highest to lowest. There is no ranking for gender.
Sleep length is numerical as it deals with numbers. I put continuous because someone could write 2.5 hours or 3.75 hours. If whole numbers are only allowed, then the variable would be discrete.
The bedtime portion is categorical as each time slot is a category. Like with the first part, they are simply labels. We can order them however from earliest to later on, which is why this variable is ordinal.
The number of countries visited is numeric as expected, and it's also discrete because we can't visit 0.1 of a country. By "visit", I mean step foot in any part of the country for any length of time. It does not mean you have to explore every square inch of the territory.
The last part is categorical and ordinal. The scale ranking is ordered for us from 1 to 5. Despite the fact we have numbers here, the data is not numerical as the numbers 1 through 5 represent labels of "very little" through "a lot".
By which angle must AB turn about point A in the clockwise direction so that it coincides with AE?
Answers
Answer:b
Step-by-step explanation:
AB should be rotated by 180° or 360°.
What is rotation?Rotation can be defined as the motion of an object around an axis. It is a type of transformation that includes every point of a figure and rotates it by a specific number of degrees around a given point in a particular direction.
So, according to the given figure, if rotate the line AB, 180° clockwise or 360° clockwise, it will lie on AE.
Hence, AB should be rotated by 180° or 360°.
Learn more about rotations, click;
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Construct a perpendicular bisector to AB
Answers
Answer:
look below:
Step-by-step explanation:
Answer: See attachment - hopeful it helps -
I will update post once I get it back --
Step-by-step explanation: Kindly give me brainly :)
A security alarm requires a four-digit code. The code can use the digits 0–9 and the digits cannot be repeated. What is the approximate probability that the code only contains odd numbers? 0.0005 0.00099 0.012 0.02381
Answers
Answer:
0.02381
Step-by-step explanation:
As we know that
We have 10 digits i.e 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 out of these 5 are odd digits 1, 3, 5, 7, 9.
A security alarm needs a code of four digits that includes only odd values
In the first position of the code is 1 digit from 5 odd digits.
In the second position of the code is 1 digit from 4 digits left.
In the third place it is 1 from 3 digits left
And the last fourth position is 1 from 2 odd digits left
Now we can generate 5: 4: 3: 2 = 120 distinct four-digit code only with odd different numbers in total.
Likewise we can count how much of different codes you can generated from all digits
In the first position of the code it is 1 digit from 10 digits,
In the second position of the code it is 1 digit from 9 digits left,
In the third place it is 8 digits left
And the last fourth position it is 7 digits left.
Now overall you can generate 10:9:8:7 = 5040 that contains different four-digit code by considering different digits.
So, the probability is
[tex]Pr=\dfrac{120}{5040}[/tex]
[tex]=\dfrac{1}{42}[/tex]
[tex]\approx 0.02381 .[/tex]
ANSWER:
D = 0.02381
Step-by-step explanation:
Just took the exam :)
but basically, math. (edg 2020)
Mary wants to paint her bedroom. Each wall takes 1/3 of a liter of paint. If she buys 2 liters ? point
of paint, how many walls can she paint? *
Answers
2 liters of paint / 1/3 liter per wall = 2 x 3/1 = 6/1 = 6 walls
The height of a model rocket is 4% of the height of the actual rocket. The model is 2m high. How high is the actual rocket?
Answers
Answer:
50m
Step-by-step explanation:
The model rocket is 4% of the actual rocket and it is 2m high
That means that 4%=2m
4 fits into 100, 25 times so multiply both by 25:
100%=25*2m
100%=50m
100% being the actual rocket
hope this helped!
When a discount of 25% is allowed on the marked price then the selling price will be
Rs 1425. If the marked price is 18 above the cost price, what percent will be gained or lost
plz help me
Answers
Answer:
11.5% loss
Step-by-step explanation:
Discount = 25%
SP= 1425
MP= CP+18%
Profit or loss% - ?
---------
SP= MP- 25%= MP*0.75= 1425
MP= 1425/0.75= 1900
MP= CP+18%= CP*1.18
CP= MP/1.18= 1900/1.18 ≈ 1610.17
SP< CP, so there is loss
Loss%= (1610.17- 1425)/1610.17*100%= 11.5%
The diagram shows an empty tank in the shape of a horizontal prism of length 150 cm.
The cross section of the prisin is an isosceles trapezium ABCD.
AB= 50cm, CD- 70 cm and the vertical height of the trapezium is 40 cm.
(0) Calculate the volume of the tank. it is a math question
Answers
Answer:
2400
Step-by-step explanation:
Area of a trapezoid: (b₁ + b₂) / 2 * h
= (70 + 50) / 2 * 40
= 60 * 40 = 2400
2 Points
Two sides of an isosceles triangle have lengths of 2 and 12. What is the length of the third side?
Answers
Answer:
12
Step-by-step explanation:
An isosceles triangle are three sides of two sides being equal in lengths.
If that is the case, the two opposite slanting sides which are equal, must be longer. Invariably, the third side is 12.
The length of the third side of an isosceles triangle will be [tex]12[/tex] .
What is an isosceles triangle ?An isosceles triangle is the one which have two equal sides.
We have,
One side [tex]=2[/tex]
Second side [tex]=12[/tex]
So,
We know that,
In this condition,
Length of the third side should be [tex]12\ cm[/tex] Because if we take third side as [tex]2[/tex] cm then
The sum of two sides [tex]= 2+12= 14 cm[/tex]
So,
[tex]2 < 12 < 14[/tex]
Hence, we can say that the length of the third side of an isosceles triangle will be [tex]12[/tex] .
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What is the value of m in the figure below? In this diagram, ΔABD ~ ΔBCD.
Answers
Answer:
√126Option D is the right option.
solution,
[tex] \frac{ac}{bc} = \frac{bc}{dc} \\ or \: \frac{18}{ m} = \frac{m}{7} \\ or \: m \times \: m = 18 \times 7(cross \: multiplication) \\ or \: {m}^{2} = 126 \\ m = \sqrt{126} [/tex]
Hope this helps..
Good luck on your assignment.
Hope
Which equation represents a circle that contains the point (-5, -3) and has a center at (-2, 1)?
Distance formule: (x2 - x1)2 +(y2-y1)2
(x-1)2 + (y + 2)2= 25
(x + 2)2 + (y - 1)2=5
(x + 2)2+(y - 1)2 = 25
(X - 1)2 + (y + 2)2=5
Answers
Answer:
(x + 2)^2 + (y - 1)^2 = 25.
Step-by-step explanation:
The centre is at (-2, 1) so the equation is:
(x + 2)^2 + (y - 1)^2 = r^2 where r is the radius.
The radius is the distance from the centre to the point (-5, -3).
Using the distance formula:
r = √ [(-3- 1)^2 + (-5 - -2)^2]
and r^2 = (-3- 1)^2 + (-5 - -2)^2
= (-4)^2 + (-3)^2
= 16 + 9
= 25.
Decide if Y=3x-9 and Y=4x-9 have many solutions, one solution, or no solutions.
Answers
Answer:
(0,-9)
Step-by-step explanation:
Well first we need to solve the rowing eqation by combining like terms and separating x.
[tex]3x - 9 = 4x - 9[/tex]
So let’s do -3x
-9 = x -9
+9
x = 0.
So if x is 0 we can plug that in one of the equations.
y = 4(0) - 9
y = -9
So the solution where the 2 lines meet is at (0,-9)
For more proof look at the image below.
Take the numbers together and the variables together so you’ll get -9+9=0 and 4x-3x =1x or x so x is equals to zero then substitute the zero on both of the equations to get Y= -9
So the answer it has one solution which is -9 at Y and so it’s considered 1 cause (0,9) and 0 is not a solution.
Hope it helped:)
3.5 + 1.2(6.3 – 7x) = 9.38
Answers
Answer: 0.2
Step-by-step explanation:
subtract 9.38 - 3.5 = 5.88
distribute the 1.2.
7.56 - 8.4x = 5.88
subtract 5.88 - 7.56 = -1.68
-8.4x = -1.68
divide both sides by -8.4
answer = 0.2
In 1000 sq. meter of land a farmer cultivated 765 kg of rice with the wastage of 23.5%.I) Find the weight of the wastage. II) Find the weight and percentage of rice cultivated.
Answers
Answer:
i. weight of wastage(kg) = 179.775 kg
ii. weight of rice cultivated = 765 kg - 179. 775 kg = 585.225 kg
percentage of rice cultivated = 100 - 23.5 = 76.5%
Step-by-step explanation:
A land of 1000 sq. meter is used to cultivate 765 kg of rice with wastage of 23.5%.
i. The wastage in percentage is 23.5% but the weight of the wastage in weight is 23.5% of 765 kg
weight of wastage = 23.5/100 × 765
weight of wastage = 17977.5/100
weight of wastage(kg) = 179.775 kg
ii. weight and percentage of rice cultivated.
weight of rice cultivated = 765 kg - 179. 775 kg = 585.225 kg
percentage of rice cultivated = 100 - 23.5 = 76.5%
Write an equation in point-slope form for each line (If possible please show work)
Answers
Answer: y-2=1/4(x-1)
Step-by-step explanation:
The formula for point-slope is y-y₁=m(x-x₁). Since we are given the slope m, we can fill that in. We are also given the point (x₁,y₁). We can also fill that in.
y-2=1/4(x-1)
-28=7(x-7) What does x=
Answers
Answer:
so x=3
Step-by-step explanation:
-28=7(x-7)
opening the brackets by multiplying
-28=7x-49
adding 49 on both sides
-28+49=7x-49+49
21=7x
dividing 7 on both sides
21/7=7x/7
x=3
i hope this will help you :)
Answer:
-28=7(x-7)
First expand the terms on the right side
That is
-28 = 7x - 49
Group like terms
7x = -28 + 49
7x = 21
Divide both sides by 7
7x/7 = 21 /7
x = 3
Hope this helps
An empty container has a capacity of 60000 litres to 1 significant figure Tony pours in 5400 litres of water to 1 significant figure He says “I have filled more than 10% of the container” Is he correct
Answers
Answer:
The container's capacity could be anything from 55,000 to 65,000. Exactly 10% of that is anything from 5500 to 6500.
The amount of water poured in could be anything from 5350 or 5450. That is NOT in the range above, so the answer is NO.
No, Tony is not correct.
The following information should be considered:
The container capacity could be varied from 55,000 to 65,000. Now if do exactly 10% so it should be 5,500 to 6,000.But the amount of water poured could be 5,350 or 5,450.Based on the above information we can conclude that tony is not correct.
Learn more: brainly.com/question/3299455
AC=4, AE=7, AD=10, what is the length of AB?
A: 1 3/7
B: 2 1/2
C: 5 5/7
D: 17 1/2
Answers
Answer:
C. [tex] AB = 5\frac{5}{7} [/tex]
Step-by-step explanation:
When two polygons are considered similar, the ratio of their corresponding sides would also be equal.
Since ∆ABC and ∆ADE are similar, [tex] \frac{AE}{AC} = \frac{AD}{AB} [/tex]
[tex] \frac{7}{4} = \frac{10}{AB} [/tex]
Cross multiply
[tex] 7*AB = 10*4 [/tex]
[tex] 7*AB = 40 [/tex]
Divide both sides by 7 to find AB
[tex] \frac{7*AB}{7} = \frac{40}{7} [/tex]
[tex] AB = \frac{40}{7} [/tex]
[tex] AB = 5\frac{5}{7} [/tex]
Giovanna used the calculations below to determine the height of a stack of 7 books that are each 2 and StartFraction 5 over 8 EndFraction inches thick. What was her error? 7 (2 and StartFraction 5 over 8 EndFraction). 7 (2 + StartFraction 5 over 8 EndFraction). 14 + StartFraction 5 over 8 EndFraction. 14 and StartFraction 5 over 8 EndFraction The fraction was not simplified in the last step. Seven was not multiplied by StartFraction 5 over 8 EndFraction. There should be a subtraction step, not an addition step. Two should have been multiplied by StartFraction 5 over 8 EndFraction.
Answers
Answer:
She didn't do the multiplication of 7 times the fraction 5/8 by using distributive property.
so the correct answer is the one that looks like:
Seven was not multiplied by StartFraction 5 over 8 EndFraction.
in your list of options.
Step-by-step explanation:
If one has a stack of seven books each [tex]2\frac{5}{8} \,\,in[/tex] thick, one should first convert the mixed number to an addition of an integer plus a fraction
[tex]2\frac{5}{8} =(2+\frac{5}{8})[/tex]
as she did, and then multiply 7 by the addition, making sure to use distributive property and multiply both terms:
[tex]7\,\,(2+\frac{5}{8})=7\,*\,12+7\,*\,\frac{5}{8}=14+\frac{35}{8}[/tex]
and she didn't do the multiplication of 7 times the fraction 5/8
Using the distance formula, find the distance between two points. (6, 0) (-5, 4)
Answers
Answer:
11.7046999
Step-by-step explanation:
using the distance formula (d=√(x₂ -x₁)² + (y₂-y₁)²), we can plug in the two points to find the distance between them:
d=√(6-(-5)² + (0-4)²
d=√(11)²+ (-4)²
d=√121+16
d=√137
d approximately equal to (≈) 11.7046999 or 11.7 or 11
What is the length of AC?
Answers
Answer:
≈ 5.9
Step-by-step explanation:
AC/3= 5.5/2.8
AC= 5.5*3/2.8
AC ≈ 5.9
Please help if you think you can
Answers
Answer:
-32x-22y
Step-by-step explanation:
4x + 2y - 6(6x - 4y)
Use distributive property
4x + 2y - 6(6x - 4y)
4x + 2y - 36x -24y
-32x-22y
Step-by-step explanation:
4x + 2y - 6(6x - 4y)
To remove the parenthesis multiply 6 by the terms in the parenthesis
That is
4x + 2y - 36x + 24y
Group like terms
4x - 36x + 2y + 24y
Simplify the terms
- 32x + 26y
Divide all terms by 2
we get
- 16x + 13y
I hope this helps you
(10,16) and (-28, -16)
What is the midpoint of a segment
with the endpoints shown to the
left?
(-18, 0)
(-9, 2)
(19,16)
(-9,0)

Answers
Answer:
(-9, 0)
Step-by-step explanation:
To find the midpoint of the segment, we use the mathematical formula below;
(x,y) = {(x1+x2)/2 , (y1+y2)/2}
From the question;
(x1,y1) = (10,16)
(x2,y2) = (-28,-16)
Substituting these values into the equation we wrote above, we have;
(x,y) = (10-28)/2 , (16-16)/2
(x,y) = (-18/2, 0/2) = (-9,0)
Solve the equation 3/2(y-1) =y+5 and represent the solution on number line and on the cartesian plane...... pls solve it and spam answers will be reported and if it is truly the correct answer i will 100% sure mark it as brainleist
Answers
Answer:
y = 13
Step-by-step explanation:
Step 1: Distribute
3/2y - 3/2 = y + 5
Step 2: Subtract y on both sides
1/2y - 3/2 = 5
Step 3: add 3/2 on both sides
1/2y = 13/2
Step 4: Divide both sides by 1/2
y = 13
Answer:
y = 13.
Step-by-step explanation:
3/2(y-1) = y+5
3/2y - 3/2 = y + 5
3/2y - y = 5 + 3/2
1/2y = 6 and 1/2; 6.5; 13/2
y = 13.
To check out work...
3/2(13 - 1) = 13 + 5
3/2(12) = 18
3 * 6 = 18
18 = 18
On a number line, all you need to do is plot a point where it says 13. On a cartesian plane, you would have a horizontal line that expands infinitely in each direction, where y = 13.
Hope this helps!
determine o valor dos termos desconhecidos nos triângulos abaixo:
HELPP
Answers
Answer:
Option (B)
Step-by-step explanation:
By using the property of a triangle → " Sum of interior angles of a triangle is 180°"
Therefore, (4x - 40) + (x + 20) + x = 180°
(4x + x) + (-40 + 20) = 180°
5x - 20 = 180
5x = 180 + 20
5x = 200
x = 40
Therefore, value of x will be 40.
Option (B) will be the correct option.
If a vehicle travels 25x miles in 2 hours, what is the vehicle's average speed, in miles per hour.
Answers
Given that a vehicle travels 25 miles in 2 hours, determine the average speed of the vehicle in miles per hour.
Work:
In order to find the average mph of the vehicle, you have to divide the distance the vehicle travels in a certain period of time by that amount of time.
So, in this case, the vehicle traveled 25 miles in 2 hours, so you would divide 25 by 2.
25/2 = 12.5
That means, the vehicle is traveling at a speed of 12.5 mph.
Thus, the average speed of the vehicle is 12.5 miles per hour (mph).
Vicki and Tamra are working on their math homework together. Vicki has worked p problems, and Tamra has worked 4 times as many problems as Vicki. The expression shows how many problems they have worked altogether. p + 4p Which of the following is another expression that could be used to get the same result, and what does it represent? A. 5p2. This represents that Vicky and Tamra have worked on 5p2 problems altogether. B. p + 4. This represents that Vicky and Tamra have worked on p + 4 problems altogether. C. 5p. This represents that Vicky and Tamra have worked on 5p problems altogether. D. p + 5. This represents that Vicky and Tamra have worked on p + 5 problems altogether.
Answers
Answer:
c.5p
Step-by-step explanation:
we know that p + 4p can be simplified as 5 p.
Therefore when compared if theses 2 are equal or not , p+4p=5p
we can simply add p+4p(as p is 1p) which gives 5 p
Answer:
5p
Step-by-step explanation:
simplify (2 sqrt5 -4)(3 sqrt5 +2)
Answers
Answer:
work is shown and pictured
Plz help ASAP I WILL GIVE BRAINLIEST!!
Emily was going to sell all of her stamp collection to buy a video game. After selling half of them she changed her mind. She then bought seventeen more.IF SHE STARTED WITH 46 STAMPS, how many does she have now?
A. 75
B. 40
C. 29
D. 63
Answers
Answer:
B. 40
Step-by-step explanation:
She starts with 46 and sells half of them
That leaves her with 23 stamps left.
She then buys 17 more, 23 + 17 is 40
Answer is B
Answer:
B. 40 stamps
Step-by-step explanation:
We know that she sold half of her stamps. She started with 46 stamps.
First, find 1/2 of 46.
Multiply 1/2 and 46, or divide 46 by 2.
1/2 *46= 23
46/2=23
She sold 23 stamps, and was left with 23 stamps.
Then, she bought 17 more. If she bought more, she added to the amount she already had.
Therefore, we can add 23 and 17.
23+17=40
She has 40 stamps now.
30.10
A bag contains 4 red marbles, 3 a bag contains 4 red marbles, 3blue marbles, and 7 green marbles. If a marble is randomly selected from the bag,
find the probability that a blue marble will be drawn
Answers
Answer:
4/21
Step-by-step explanation:
It should be a porpotion