1.) A sphere with a radius of 3 cm has the same volume as a cone with a radius of 6 cm. What is the height of the cone? A.) 2cm B.) 3cm C.) 4cm D.) 5cm

2.) A cylinder with a radius of 1cm and a height of 21cm has the same volume as a cone with a height of 7cm. What is the radius of the cone? A.) 3cm B.) 5cm C.) 7cm D.) 9cm

Answers

Answer 1

Part A)
we know that
[volume sphere]=(4/3)*pi*r³------> (4/3)*pi*3³--------> 113.04 cm³
[volume cone]=113.04=pi*r²*h/3------> h=[V*3]/[pi*r²]
r=6 cm
h=[V*3]/[pi*r²]---------> [113.04*3]/[pi*6²]---------> 3
h=3 cm

the answer part A) is h=3 cm

Part B)
[volume cylinder]=pi*r² *h---------> pi*1²*21------> 65.94 cm³
[volume cone]=65.94 cm³=pi*r²*h/3
h=7 cm
r=√[(V*3)/(pi*h)]---------> √[(65.94*3)/(pi*7)]---------> 3 cm

the answer Part B) is r=3 cm

Related Questions

What is the value of h when the function is converted to vertex form?

Note: Vertex form is p(x)=a(x−h)^2+k .
p(x)=x^2−14x+29

H = ___

Answers

h=7.

To convert to vertex form, we complete the square. This means we move the constant, c, to the other side.

y=x²-14x+29
y-29 = x²-14x+29-29
y-29=x²-14x

To find the number that we then add to both sides, we look at the value of b (coefficient of x). We take half of that number; -14/2 = -7. Then we square it; (-7)²=49. This means we add 49 to both sides:

y-29+49=x²-14x+49

Now we combine like terms on the left:
y+20=x²-14x+49

Write the right hand side as a square:
y+20 = (x-7)²

Now move the 20 on the left back to the right by subtracting it from both sides:
y+20-20=(x-7)²-20
y=(x-7)²-20

The value of h is 7.

For which data representation is the median the better measure of center

Answers

we know that
The Median is the "middle" of a sorted list of numbers.
To find the Median, place the numbers in value order and find the middle

case a) the data is
3,8,4,8,3
place the numbers in value order-----> 3,3,4,8,8

the middle is 4
so
the median is 4

case b) the data is
2,2,3,5,5
place the numbers in value order-----> 2,2,3,5,5

the middle is 3
so
the median is 3

case c) the data is
6,2,6,2,6
place the numbers in value order-----> 2,2,6,6,6

the middle is 6
so
the median is 6

case d) the data is
1,3,4,3,1
place the numbers in value order----->1,1,3,3,4

the middle is 3
so
the median is 3

we know that
The Mean is most often chosen when the data is continuous and symmetrical (normal). ------> case a) case c) and case d) If the data has outliers or is skewed, then the mean would paint a skewed view of centrality

The Median is especially useful with skewed distributions as it draws the line right in the middle of your data set------> case b)

therefore

the answer is
case b)

Answer with explanation:

Mean is sum of all the observation divided by total number of observation, where as median is middlemost observation of the data set, while mode is most occurring variate or data value in the data set.

1. Variate or Data set which is represented in Histogram is

3,8,4,8,3

Arranging it in ascending order, we get

3,3,4,8,8

Data is skewed right.So, Mean >Median>Mode

Mean =5.2

Number of observation is 5. So,Median will be Middle term,that is third term equal to 4.

Mode =3 or ,8 which will be equal to 3,as data is skewed right.

→Mean gives better representation of data set,because, 5.2-3=2.2 and, 8-5.2=2.8

2. Variate or Data set which is represented through dots is

2, 2, 3,5,5

Arranging it in ascending order, we get

2,2,3,5,5

Data is skewed right.So, Mean >Median>Mode

Mean=3.4

Number of observation is 5. So,Median will be Middle term,that is third term equal to 3.

Mode =2 or 5 which will be equal to 2,as data is skewed right.

→Mean gives better representation of data set,because, 3.4-2=1.4 and, 5-3.4=1.6

3. Variate or Data set which is represented in Histogram is

6,2,6,2,6

Arranging it in ascending order, we get

2,2,6,6,6

Data is skewed left.So, Mean <Median<Mode

Mean=4.4

Number of observation is 5. So,Median will be Middle term,that is third term equal to 6.

Mode =6

→Mode gives better representation of data set.

4.Variate or Data set which is represented through dots is

1,3,4,3,1

Arranging it in ascending order, we get

1,1,3,3,4

Data is skewed left.So, Mean <Median<Mode

Mean=2.4

Number of observation is 5. So,Median will be Middle term,that is third term equal to 3.

Mode =1 or 3,data is skewed left,so mode =3

Here, in this data set, both mode and median are better measure of center than Mean,as there are two modes in the data set, so choosing median as measure of center,because data is skewed left,

For ,Option 4: Median is the better measure of center.

The segment image is drawn from F(2, 9) to H(10, 1) with point G on the segment. What coordinates for point G will divide image so that is imageis 3:5?

Answers

Answer: The point (5, 6) would divide the line segment so it is in the ratio of 3:5.

If the ratio of the line segment needs to be 3:5, that means the point will be at the 3/8 distance mark of the line segment. Because there are 8 total parts if the ratio is 3:5 (3 + 5 = 8).

The slope from (2, 9) to (10, 1) is -8/8. So our point would only move 3/8 of that distance. If we multiply -8 and 8 by 3/8, we have -3 and 3.

That means our point must fall 3 and move to the 3 spaces from our starting point of (2, 9). That will put us at (5, 6).

Sally buys a hand bag. there was a discount of 23%. If sally paid $20.02, what was the original price?

Answers

100-23 = 77%

20.02 / 0.77 = 26.00

original price was $26

Explain how to tell 100/105 is not in simplest form without finding all the factors

Answers

10 ends in 0 and 105 ends in 5 therefore it is divisible by 5.

(Incase you need simplified it is 20/21)

because you can divide it by 5 and when you do that you get an answer of...
20/21

PLEASE HELP NOWWWWWWWW 20 POINTS PLEASE HELP
Using the transformation T: (x, y) (x + 2, y + 1). Find the distance named.

Find the distance CA (the answer must be in the square root form)

Answers

Answer: The length of AC is: " 2√2 units " .
____________________________________________________
Explanation:
____________________________________________________
Note: (not to scale):
____________________________________________________

C
| \
| \
2 | \ "c"
|-- \
| \
|_|______\ A
• 2
(point
–at which
right angle forms)
_______________________________________________________
Use the "Pythagorean theorem" (since this is a right triangle) to solve for the length of AC — which is represented by "c" :

a² + b² = c² ;

↔ c² = a² + b² ; Solve for "c" ;

Given: "a = 2 ; b = 2 " ;

→ c² = 2² + 2²

→ c² = 4 + 4 ;

→ c² = 8 ;

Take the "positive square root" of each side of the equation;
to isolate "c" on one side of the equation; & to solve for "c" ;

→ √(c²) = √8 ;

→ c = √8 ;

→ √8 = √4 * √2 = 2√2 .
_____________________________________________________
Answer: The length of AC is: " 2√2 units " .
_____________________________________________________

The sum of 555 consecutive integers is 505505505. What is the third number in this sequence?

Answers

the correct question is
The sum of 5 consecutive integers is 505. What is the third number in this sequence?

Let
x-----------> first integer
x+1-----------> second integer
x+2-----------> third integer
x+3-----------> fourth integer
x+4-----------> fifth integer

we know that
x+(x+1)+(x+2)+(x+3)+(x+4)=505
then
5x+10=505----------> x=(505-10)/5---------> x=99

therefore
the third integer is (x+2)------> 99+2=101

the answer is 101

Answer: The answer is 101!

Step-by-step explanation:

Call the first number in the sequence x

The next integer in the sequence is x + 1

The sum of the 5 consecutive integers is:

x+ (x + 1)+ (x + 2)+ (x + 3)+ (x + 4) = 505

5x + 10= 505

5x = 495

x = 99

Since x is the first number, x + 2 is the third integer.

Thus, the third number in the sequence is 101

A small combination lock on a suitcase has 6 wheels, each labeled with the 10 digits 0 to 9.
How many digit combinations are possible if no digit is repeated? If digits can be repeated? If successive digits must be different?,

Answers

i have no clue but im going off a limb and say 56878

There will be, 590490 possible combinations.

What is combination?

The number of different groups which can be formed from the available things can be calculated using combinations.

Given that, A small combination lock on a suitcase has 6 wheels, each labelled with the 10 digits 0 to 9.

We have 10 for the first wheel, but second wheel only has 9 options because 2nd number can't be the same as first. The third and fourth wheels also has 9 options for the same reason.

10x9x9x9x9x9 = 590490 combinations

Hence, There will be, 590490 possible combinations.

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1)
What is the area of a sector with a central angle of 5π/7 radians and a diameter of 5.6 in.?

Use 3.14 for π and round your final answer to the nearest hundredth.

Enter your answer as a decimal in the box.

2)
What is the area of a sector with a central angle of 4π/5 radians and a radius of 11 cm?

Use 3.14 for π and round your final answer to the nearest hundredth.

Enter your answer as a decimal in the box.

Answers

The area of the given sectors of circles is required.

The area of the sector is [tex]8.79\ \text{in}^2[/tex]

The area of the sector is [tex]151.98\ \text{cm}^2[/tex]

Area of sector

[tex]\theta[/tex] = Central angle = [tex]\dfrac{5\pi}{7}\ \text{rad}[/tex]

d = Diameter = 5.6 in

r = Radius = 2.8 in

Area of a sector is given by

[tex]A=\dfrac{\theta}{2}r^2\\\Rightarrow A=\dfrac{\dfrac{5\times 3.14}{7}}{2}\times 2.8^2\\\Rightarrow A=8.79\ \text{in}^2[/tex]

[tex]\theta=\dfrac{4\pi}{5}\ \text{rad}[/tex]

r = 11 cm

[tex]A=\dfrac{\dfrac{4\times 3.14}{5}}{2}\times 11^2\\\Rightarrow A=151.98\ \text{cm}^2[/tex]

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Find the equatio of the line tht contains the point (5,6) and is perpendicualr to the line 4x+2y=2

Answers

--------------------------------------------------------------
Find Slope
--------------------------------------------------------------
4x + 2y = 2
2y= -4x + 2
y = -4/2 x + 2
y = -2x + 2

Slope = -2
Perpendicular slope = 1/2

--------------------------------------------------------------
Insert slope into the general equation y = mx + c
--------------------------------------------------------------
y = 1/2x + c

--------------------------------------------------------------
Find y-intercept
--------------------------------------------------------------
y = 1/2x + c
at (5,6)
6 = 1/2 (5) + c
6 = 5/2 + c
c = 6 - 5/2
c = 7/2

--------------------------------------------------------------
Insert y-intercept into y = 1/2 x + c
--------------------------------------------------------------
y = 1/2 x + 7/2
2y = x + 7

--------------------------------------------------------------
Answer: 2y = x + 7
--------------------------------------------------------------

Final answer:

The equation of the line that passes through the point (5,6) and is perpendicular to the line 4x+2y=2 is y = 1/2x + 7/2.

Explanation:

The question asks us to find the equation of a line that passes through a given point and is perpendicular to a given line. To solve this, we first need to determine the slope of the given line, then find the perpendicular slope, and finally, use the point-slope form of a line to write the equation for our new line.

Here are the steps:

Find the slope of the given line. For the equation 4x + 2y = 2, we rearrange it to slope-intercept form (y=mx+b), which gives us y = -2x + 1. The slope is -2.

Since we want a line that is perpendicular to the given line, we need the negative reciprocal of -2, which is 1/2.

Now we use the point-slope form of a line, y-y1 = m(x-x1), with point (5,6) and slope 1/2. This gives us y - 6 = 1/2(x - 5).

Solving for y to get the slope-intercept form, we multiply both sides by 2 to get rid of the fraction: 2y - 12 = x - 5, and then solve for y: y = 1/2x + 7/2.

The equation of the line that contains the point (5,6) and is perpendicular to the line 4x+2y=2 is y = 1/2x + 7/2.

The graph below shows a line segment MN: Which of the following equations best represents the line segment MN?
y = −3x + 2
y = −2x + 1
y = −3x − 2
y = −2x − 1

Answers

y= -2x-1 is the asnwer i think
hope this helped

Answer:

D. [tex]y=-2x-1[/tex]

Step-by-step explanation:

We have been given a line on coordinate plane. We are asked to find the equation of our given line.

First of all, we will find slope of our given line using points [tex](-2,3)[/tex] and [tex](0,-1)[/tex] in slope formula.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], where,

[tex]y_2-y_1[/tex] = Difference between two y-coordinates,

[tex]x_2-x_1[/tex] = Difference between two x-coordinates of same y-coordinates.

Upon substituting our given values in slope formula, we will get:

[tex]m=\frac{-1-3}{0--2}[/tex]

[tex]m=\frac{-4}{0+2}[/tex]

[tex]m=\frac{-4}{2}[/tex]

[tex]m=-2[/tex]

Now, we will use slope-intercept form of equation [tex]y=mx+b[/tex], where,

m = Slope of line,

b = The y-intercept.

Upon looking at our given graph, we can see that y-intercept is [tex]-1[/tex].

Therefore our required equation would be [tex]y=-2x-1[/tex] and option D is the correct choice.

What is the following quotient? 2- sqrt 8 / 4 + sqrt 12

Answers

C is the answer.

We multiply the top and bottom of this by the conjugate (switch the sign of the square root):

(2-sqrt8)(4-sqrt12)/(4+sqrt12)(4-sqrt12)

Multiying the top we have
8-2sqrt12-4sqrt8+sqrt(8×12)

Multiplying the bottom we have:
16-4sqrt12+4sqrt12-12

On top, we simplify the radicals and get
8-4sqrt3-8sqrt2+4sqrt6

On bottom, we have
16-12=4

Now we divide everything on top by 4 and get
2-sqrt3-2sqrt2+sqrt6

we have

[tex]\frac{2-\sqrt{8}}{4+\sqrt{12}}[/tex]

Multiply the numerator and denominator by the conjugate of the denominator

[tex]\frac{2-\sqrt{8}}{4+\sqrt{12}}*\frac{4-\sqrt{12}}{4-\sqrt{12}}=\frac{(2-\sqrt{8})(4-\sqrt{12)}}{4^{2}-(\sqrt{12})^{2}}\\ \\= \frac{2*4-2*\sqrt{12}-4*\sqrt{8}+\sqrt{12}*\sqrt{8}}{16-12}\\ \\=\frac{8-4\sqrt{3}-8\sqrt{2}+4\sqrt{6}}{4} \\ \\=2-\sqrt{3}-2\sqrt{2}+\sqrt{6}[/tex]

therefore

the answer is

[tex]2-\sqrt{3}-2\sqrt{2}+\sqrt{6}[/tex]

Next school year 4 out of every 9 students plan to take an elective computer course if there are 2664 students at the high school how many computer students should the school plan for

Answers

4 out of every 9 is represented by 4/9.
Your asked a fraction of a quantity and it is like finding a percentage of a quantity. So:
[tex]\dfrac{4}{9} \times2664= \dfrac{4\cdot2664}{9} =\dfrac{4\cdot296}{1}=1184[/tex]

Brainliest for best answer!

Answers

the answer to your question is A length =18 cm; width=5 cm

PLEASE HELP
Find the solution of this system of equations
-5x=-21+6y
-5x+y=-84

Answers

-5x - 6y = -21
5x - y =. 84

-7y = 63

y= -9

-5x = -21 - 54

-5x = -75

x = 15

A rectangular piece of sheet metal has a length that is 6 in. less than twice the width. a square piece 3 in. on a side is cut from each corner. the sides are then turned up to form an uncovered box of volume 1014 in. cubed find the length and width of the original piece of metal.

Answers

Final answer:

Determine the dimensions of the metal sheet by setting up and solving equations based on the given volume of the box and the relationship between its length and width.

Explanation:

This problem can be tackled by using a bit of algebra and understanding volume calculations. We can use the equation for the volume of a box which is V=length*width*height. The problem gave us the volume of 1014 cu in. When a 3 in. square is cut from each corner of the rectangular piece of metal, the sides fold up to form the box, the height of the box becomes 3 in. This means we're missing the length and width of the box to solve for volume.

Since the length equals to twice the width minus 6 in., we can express the length as 2W - 6. Substituting these into the volume equation we get: 1014 = (2W - 6)(W)(3) which when simplified gives W, the width of the metal piece. Then substitute W into the length formula 2W - 6 to solve for the length.

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What is the graph of y = x - 3 (shown below) translated up 2 units?

Answers

I don't see a "shown below," so I'm not sure if I could accurately answer your question. However, if your graph point is (x,-3), then it wants you to move your graphed point up two units. I believe that would be y = x -1? I'm not sure

Answer:

The graph is that one which corresponds to the equation y = x-1. The graph is shown in the image below.

Step-by-step explanation:

Translate a linear curve means to move the whole curve up or down, where the final line will be in parallel to the original curve.

For translate the graph up to 2 unit, it must to be summed 2 unit in the right member of the original equation:

[tex] y = (x-3) + 2 [/tex]

[tex] y = x-3 + 2 [/tex]

[tex] y = x-1 [/tex]

Which ordered pair (a, b) is a solution to the given system of linear equations?
A (1, 7)
B (3, 1)
C (11, –23)
D (23, –11)

Answers

11,-23 is the answer I plugged in the two number as a and b and I got 33+(-23)=10 and -44+ (46)= 2

Answer:

C. (11,-23)

Step-by-step explanation:

The given equations are

[tex]3a+b=10[/tex].....................equation 1

[tex]-4a-2b=2[/tex]...................equation 2

Multiply first equation by 2

[tex]6a+2b=20[/tex]

Now add this new equation to 2nd equation

[tex]6a-4a +2b-2b = 20+2[/tex]

[tex]2a = 22[/tex]

Divide both sides by 2

[tex]a=11[/tex]

We got a=11 , plug this value in anyone equation

3(11)+b=10[tex][/tex]

[tex]33+b=10[/tex]

Subtract 33 from both sides

[tex]b=-23[/tex]

So solution is (a,b) = ( 11,-23)

When calculating total savings, you must ____. (1 point)
A. calculate the total cost of the item when not on sale and subtract the sales cost.
B. calculate the total cost of the items at their sale price.
C. add all of the items together and divide by the total number of items.
D. calculate the total cost of the items at their sale price and subtract the original cost.

Answers

When calculating total savings, you must calculate the total cost of the item when not on sale and subtract the sales cost. The answer is A. This is the most effective way to calculate total savings on an item.

A= 48 degrees what is C

Answers

Hey there!

Angle C is 77 degrees.

Hope this helped, have a good night!

What is the slope of a line perpendicular to the line with equation y = 4x + 5?

Answers

Hello!

The thing to know what solving problems like these is that slopes of perpendicular lines are opposite reciprocals of each other.

For example, if you are given that the slope of a line is 6, and are told to find the slope of a line perpendicular to it, you would flip the 6/1 to 1/6 and negate it. The slope of a line perpendicular to a line with a slope of 6 is -1/6.

Here, you have an equation of a line in slope-intercept form. Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
In y = 4x + 5, 4 is m, thus 4 is the slope.

The opposite reciprocal of 4 is -1/4.

Answer:
-1/4

The slope of a line perpendicular to the line with equation y = 4x + 5 will be, [tex]-\frac{1}{4}[/tex].

What is a slope of a straight line?

A straight line is a combination of endless points joined on both sides of the point.

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The slope 'm' of any straight line is given by:

The given equation in the problem is;

y = 4x + 5

The slope of the given equation is found from the standard equation of the straight line as;

y=mx+c

On comparing, we get, m = 4.

The perpendicular line slopes are reciprocals with the negative sign of each other.

Hence, the slope of a line perpendicular to the line with equation y = 4x + 5 will be, [tex]-\frac{1}{4}[/tex]

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A rectangle basin is being filled with water. The basin is 7 feet long, 12 feet wide, and 4 feet high. How much water is going to be needed to fill the basin.

Answers

In this problem your going to need to find volume.

The formula for volume of a rectangular prism (Which is what we are trying to find)

Is Volume = Length x Height x Width

So in your problem we can create the equation:
7 x 4 x 12 = Your answer.

7 x 4 = 28
28 x 12 = 336.

Your going to need 336 feet^3 (D)

Hope this helps!
Brainliest is always appreciated if you feel its deserved.

John wants to buy a new bike that cost 337 and he already has saved 103. Estimate to find about how much more John needs to save to buy the bike

Answers

We can round numbers to estimate.

337 is approximately 340.
103 is approximately 100.

340 - 100 = 240

John needs to save around $240 more in order to be able to afford the bike.

Hope this helps!

The value of x must be greater than _____.

Answers

The answer is : The value of X must be greater then 5

The sum of any two sides of a triangle must be greater than the third. Therefore, x can be greater than or equal to 4.

1200 calories in 3 liters. Write a unite rate.

Answers

To do this we can do 1200 divided by 3

The answer to that is 400.

The unit rate is 400 calories in 1 liter.

1200 calories divided by 3 is 400 calories in one liter.

How to solve this question ? use appropriate metric prefix to write the following measurment without use exponents?
2.3x10^-10 L
4.7x10^-6 g
1.85x10^-12 m
16.7x10^6 s,

Answers

-12 = pico(p) So 10^-12 L = 1 pL Use following to find the count of 10^-12 L are there in 2.3×10^-10 L 2.3×10^-10 / (10^-12) = 2.3×10^2 = 230 pL -6 = micro (µ) 4.7×10^-6 g = 4.7 µg 1.85×10^-12 m = 1.85 pm 6 = Mega (M) 16.7×10^6 s = 16.7 Ms So the answer is 16.7 Ms

How Many Toys Will Remain?

Answers

FIND # OF INCREASED INVENTORY
=1600 + (1600 * 25%)
=1600 + 400
=2000 new inventory

FIND INVENTORY REMAINING
=2000 - (2000 * 75%)
=2000 - 1500
=500 toys remain

ANSWER: 2000 new inventory and 500 toys remain

Hope this helps! :)

What is the area of this figure?

Enter your answer in the box.

Answers

Answer:

[tex]\text {Area of figure is }44 units^2[/tex]

Step-by-step explanation:

Given the figure and we have to find the area of given figure.

Area of figure=ar(ABC)+ar(CDE)+ar(AEFH)+ar(GHF)

From the figure, dimensions according to square boxes can be written as

AE=HF=8 units, EF=3 units, BI=3 units, GH=2 units, AC=CE=4 units.

[tex]ar(ABC)=ar(CDE)=\frac{1}{2}\timesAC\times BI=\frac{1}{2}\times4\times3=6 units^2[/tex]

[tex]ar(AEFH)=HF\times EF=8\times 3=24 units^2[/tex]

[tex]ar(GHF)=\frac{1}{2}\timesHF\timesGH=\frac{1}{2}\times8\times 2=8units^2[/tex]

∴ [tex]\text {Area of figure is }44 units^2[/tex]

Help Plz!
1. The population of Linton is 12 times as great as the population of Ellmore. The combined population of both towns is 9,646 people. What us the population of Linton?
2. Jessie bought 3 T-shirts for $6 each and 4 T-shirts for $5 each. What expression can you use to describe what Jessie bought?

Answers

1. ratio is 12:1

13x = 9646
742

12x = 12 * 742
12(742) = 12 x 742

The population of Linton is 8,904.

2. (3 * 6) + (4 * 5)

easy math problem 5pts

Answers

The HL theorem applies.

NM and OP are the hypotenuses, given to be congruent.
Angles at H are right angles.
Sides HM and HP are congruent because MHP is isosceles. You have the hypotenuse and one leg of a right triangle congruent, which is the premise for the HL theorem.

Other Questions

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