Tim is an elementary school art teacher. His students are sculpting a replica of a shark out of clay. Tim has given them one block of clay to make 20 conical shark teeth for the sculpture. The block contains 81 cm3 of clay. If each tooth is solid and has a 2. 5 cm base diameter, what is the maximum height each tooth can be? Assume that the students use all the clay. A. 1. 25 cm B. 2. 27 cm C. 2. 47 cm D. 3. 57 cm E. 4. 50 cm.

Answers

Answer 1

The maximum height each tooth is 2.47cm.

The first step is to determine the maximum volume of a tooth.

Maximum volume of a tooth = volume of the block / number of teeth

81 cm³ / 20 = 4.05cm³

The formula to determine the height of a cone is:

Height = volume ÷ [tex]\frac{1}{3}[/tex]πr²

Where:

π = pi = 22/7 r = radius = 2.5 / 2 = 1.25cm

Height = 4.05  ÷ [tex]\frac{1}{3}[/tex] x [tex]\frac{22}{7}[/tex] x 1.25² = 2.47 cm

To learn more about the volume of a cone, please check: https://brainly.com/question/1315822


Related Questions

Solve for p if L = 2 1/2 ft and W = 3 2/5 ft. P = 2L + 2W​

Answers

Answer:

[tex]\frac{59}{5}[/tex] or 11 [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

hope this helps :)

A school staff meeting had 30 teachers in attendance, 60% of whom were first-year teachers. How many first-year teachers were in the meeting?

Answers

Answer:

I personally think the answer is because if the 60% of the teachers among 30 teachers were first-year teachers,then it would mean the other 40 % of the teachers were recent/ this year teachers.

The diameter of the circle is 34cm and a chord is at a distance of 15cm from the centre. Find the length of the chord of the circle

Answers

Answer:  16 cm

===================================================

Explanation:

The drawing is shown below.

Point A = center of circlePoints B,C,E = points on the circle's edgePoint D = midpoint of chord CE

The goal is to find the length of CE based on these facts

BC = 34 = diameterAD = 15 = distance from center to chordx = length of segment CD = length of segment DE

Notice how AB = AC = AE = 17 because they are all radii of the same circle. We cut the diameter in half to get the radius.

Focus on triangle CAD. We'll use the pythagorean theorem to find x.

a^2 + b^2 = c^2

(AD)^2 + (DC)^2 = (AC)^2

15^2 + x^2 = 17^2

225 + x^2 = 289

x^2 = 289 - 225

x^2 = 64

x = sqrt(64)

x = 8

Segment CD is 8 cm long, and so is segment DE.

To wrap things up, we then say:

CE = CD + DE

CE = 8 + 8

CE = 16

Chord CE is 16 cm long.

Consider the relation {(1,3), (2,5), (-6,-3), (0,0)}. What is the range of the relation?

Answers

Answer:

the domain is:

{

3

,

0

,

1

,

6

}

the range is:

{

2

,

3

,

4

,

6

,

4

}

the relation is not a function since it has TWO distinct y values '4' and '-6' for the same x value of '1' .

Step-by-step explanation:

In the relation:

{

(

3

,

2

)

,

(

0

,

3

)

,

(

1

,

4

)

,

(

1

,

6

)

,

(

6

,

4

)

}

:

The domain:

Is the set of all the first numbers of the ordered pairs.

In other words, the domain is all of the x-values.

So in this case the domain is:

{

3

,

0

,

1

,

6

}

The range:

Is the set of the second numbers in each pair, or the y-values.

So in this case the range is:

{

2

,

3

,

4

,

6

,

4

}

A relation is a function if it has only One y-value for each x-value.

So in this case the relation is not a function since it has TWO distinct y values '4' and '-6' for the same x value of '1' .

Answer:

the domain is:  { − 3 , 0 , 1 , 6 }

the range is: { 2 , 3 , 4 , − 6, 4 }

the relation is not a function since it has TWO distinct y values '4' and '-6' for the same x value of '1' .

Step-by-step explanation:

In the relation: { ( − 3, 2) , ( 0 , 3 ) , ( 1 , 4 ) , ( 1 , −6 ) , ( 6 , 4 ) } :

The domain:

Is the set of all the first numbers of the ordered pairs.

In other words, the domain is all of the x-values.

So in this case the domain is: {− 3 , 0 , 1 , 6 }

The range:

Is the set of the second numbers in each pair, or the y-values.

So in this case the range is: { 2 , 3 , 4 , − 6, 4 }

A relation is a function if it has only One y-value for each x-value.

So in this case the relation is not a function since it has TWO distinct y values '4' and '-6' for the same x value of '1' .

Have a good day/night!

solve the equation on the interval [0, 2π).
3(sec x)^2 -4=0

Answers

[tex] \: \: \: \: \: [/tex]

[tex]x = \frac{\pi}{6} , \frac{(k)\pi}{6} , \frac{(5)\pi}{6} , \frac{(k)\pi}{6} [/tex]

refer to the attachmenthope it helps

Find the answer:
2(-5-3)

Answers

Answer:

-16

Step-by-step explanation:

start with brackets

-5-3 = -8

2(-8)

= -16

What is the answer to 3(y - 1 + 2y)

Answers

Answer:

Collect like terms.

3((y+2y)-1)

3((y+2y)−1)

2 Simplify (y+2y)-1(y+2y)−1 to 3y-13y−1.

3(3y-1)

3(3y−1)

estimate the area please.​

Answers

Answer: You need to count how many squares are shaded (at least half of it), therefore the area is 32 square units.

It is 32 have a great day

What is the reciprocal of 3 1/3

Answers

Answer:

3/10

Step-by-step explanation:

make 3 and 1/3 to an improper fraction (3 multiplied by 3 plus 1) which is 10/3. the reciprocal is 3/10

Answer:

0.3

Step-by-step explanation:

Have a great day!

What is the range of the graph

Answers

On the other hand When the tangent to the graph is not unique that is more than one tangents can be drawn to the graph then that graph must represents a curve.

In other words when the slope is constant then it represents straight line and when the slope is variable then it represents a curve

NO LINKS!
Part A: Find the LCM of 5 and 12. Show your work. (3 points)

Part B: Find the GCF of 72 and 81. Show your work. (3 points)

Part C: Using the GCF you found in Part B, rewrite 72 + 81 as two factors. One factor is the GCF and the other is the sum of two numbers that do not have a common factor. Show your work. (4 points)

Answers

Answer:

Part A: 60

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60.

12, 24, 36, 48, 60.

---------------------------------

Part B: 9

81 / 72 = 9

----------------------------------

Part C: 9 (8 + 9)

GCF of 72 and 81 is 9...

Divide 72 by 9 and get 8.

Divide 81 by 9 and get 9.

To check multiply 9 with 8, and multiply 9 by 9.

----------------------------------

Easy! :D (if you don't mind, may I get brainliest please?)

Please help!!

Select the correct answer.
Consider functions f and g.

f(x)= square root 2x+2
g(x) = x^2-2/2

Which statement is true about these functions?

See in photo

Answers

Since g(h(x))=h(g(x))= x, hence functions h and g are inverses of each other

Given the functions expressed as:

[tex]h(x) =\sqrt{2x+2}\\g(x)\frac{x^2-2}{2} \\[/tex]

In order to check whether they are inverses of each other, we need to show that h(g(x)) = g(h(x))

Get the composite function h(g(x))

[tex]h(g(x))=h(\frac{x^2-2}{2} )\\h(g(x))=\sqrt{2(\frac{x^2-2}{2} )+2}\\h(g(x))=\sqrt{x^2-2+2} \\h(g(x))=\sqrt{x^2}\\h(g(x))=x[/tex]

Get the composite function g(h(x))

[tex]g(h(x))=\frac{(\sqrt{2x+2} )^2-2}{2} \\g(h(x))=\frac{2x+2-2}{2}\\g(h(x))=\frac{2x}{2}\\g(h(x))=x[/tex]

Since g(h(x))=h(g(x))= x, hence functions h and g are inverses of each other

Learn more on inverse functions here; https://brainly.com/question/14391067

CAN SOMEONE HELP ME PLEASE ASAP!?

Answers

Answer: 20 ft.

Step-by-step explanation:

Simply multiply 5 x 4.

Answer:

20 ft`

Step by step explanation:

N/A

Evaluate the function for = and =.
()=−

Answers

Answer:Example: evaluate the function f(x) = 2x+4 for x=5

Just replace the variable "x" with "5":

f(5) = 2×5 + 4 = 14

Answer: f(5) = 14

Step-by-step explanation:

Studying a group of children from first grade through high school to see the effect of pre-schooling on educational success would be which
type of study?
a
longitudinal
cross-sectional
Ос
natural observation
Od
experimental

Answers

Answer:

Longitudinal study

Step-by-step explanation:

Information is collected over extended periods of time in a longitudinal study, but in cross-sectional, natural observation, and experimental studies, information is collected over short periods of time or in one time only. Based on the choices given, this type of study would be a longitudinal study.

If a = - 4 and b = 5x + 2i , then find the value of a ^ 3 b in fully simplified form.

Answers

Answer:

  -320x -128i

Step-by-step explanation:

Put the values where the variables are and do the arithmetic.

  a³b = (-4)³(5x +2i) = -64(5x +2i) = -320x -128i

Drag the numbers below to put them in order from least to greatest:

-9 -12 -4
–4 20 -1 -6

Answers

Answer:

-12, -6, -4, -1, 9, 20

Step-by-step explanation:

9, -12, -4, 20 -1, -6

putting them in order from least to greatest means that negatives should go to the left (1st), largest should go to the right (last).

The number -9, -12, -4, 20, -6, -1 in the order from least to greatest is -12, -9, -6, -4, -4, -1, 20.

Given data: -9, -12, -4, 20, -6, -1

Starting from the smallest number:

-12 is the smallest number.

Next is -9, which is larger than -12 but smaller than -6.

Then comes -6, larger than -9 but smaller than -4.

After that, we have two occurrences of -4.

Following that is -1, greater than -4.

Finally, the largest number is 20.

So, the numbers in ascending order are: -12, -9, -6, -4, -4, -1, 20.

Learn more about ascending order here:

https://brainly.com/question/31946606

#SPJ12

Enter <, > or = to make the statement true. 17.001 [?] 17.0001​

Answers

Answer:

17.001>17.0001

Answer:

17.001>17.0001

Step-by-step explanation:

17.001 is greater than 17.0001

An item is regularly priced at $97. It is now priced at a discount of 40% off the regular price.

Answers

Answer:

38.8

Step-by-step explanation: 40% of a discount from the regular price of 97 dollars is 38.8

A man has a collection of 19 coins worth $2.55. There are twice as many nickels as dimes. If the rest are quarters, how many quarters are there?

Answers

Answer:

4

Step-by-step explanation:

Split 19 into two numbers, 9 and 10. If there are 10 nickels, there are 5 dimes. That means there rest are quarters and there are 4.

edit : im not american and have little knowledge of how much each are worth

lines y = -x+2 and y=x+1. The point of intersection of the linear equations is *

(0,2)
(0.5, 1.5)
(-1,0)
(2,0)

Answers

We can solve it by seeing the graph but let's solve the equations.

[tex]\\ \sf\Rrightarrow y=-x+2[/tex]

[tex]\\ \sf\Rrightarrow y=x+1[/tex]

Now

[tex]\\ \sf\Rrightarrow -x+2=x+1[/tex]

[tex]\\ \sf\Rrightarrow -2x=-1[/tex]

[tex]\\ \sf\Rrightarrow x=0.5[/tex]

Put in eq(2)

[tex]\\ \sf\Rrightarrow y=0.5+1[/tex]

[tex]\\ \sf\Rrightarrow y=1.5[/tex]

Done

what does 2y-x=-14 equal?

Answers

Answer:

x=2(y+7)

Step-by-step explanation:

2y−x=−14

Subtract 2y from both sides.

−x=−14−2y

The equation is in standard form.

−x=−2y−14

Divide both sides by −1.

x=2y+14

Then use the inverse property of distrubtion.

x=2(y+7)

or if you want to you can leave it as x=2y+14

Answer:

y=x/2-7

Step-by-step explanation:

Move x to the side with the constant and then divide.

1. -x from both sides

2. the divide by 2

it can also be written like

y=1/2x-7

If N = 6 x 2 x 3, what is the value of N?

Answers

Answer:N= 36

Step-by-step explanation:

one of 50 states is chosen at random. What is the probability of not choosing a state that begins with the letter n?

Answers

Answer:

8 states start with the letter N. Because you’re looking for the amount of states not starting with the letter N, we’ll subtract 8 from 50. Then you’ll put that over the total amount of states. So you should end up with 42/50 which will simplify to 21/25. Hope this helped!

Step-by-step explanation:

8% of 60 is half of what number

Answers

Answer:

9.6

Step-by-step explanation:

8% of 60 is 4.8

4.8 is half of 9.6

hope this helps! :D

have a miraculous day!! <3

Answer:

9.6

Step-by-step explanation:

8% of 60 is equal to 4.8

To find what 4.8 is half of, multiply 4.8 by 2

4.8 times 2 equals 9.6


Look at picture this is so hard pls help

Answers

Answer:

D) 8

Step-by-step explanation:

What the problem is asking you to do is multiply the two expressions and substitute x=3 into the product.

[tex]f(x)=2^x[/tex]

[tex]g(x)=2x-5[/tex]

[tex](f*g)(x)=f(x)g(x)=(2^x)(2x-5)[/tex]

[tex](f*g)(3)=f(3)g(3)=(2^3)(2(3)-5)=(8)(6-5)=(8)(1)=8[/tex]

Therefore, the correct answer is D

Zoom if you have to see more clearly ! Answer #4 , #5 , & #6 for me !! Show proof for all please ! I'll be giving brainliest and report wrong answers or answers that are correct but no proof !​

Answers

Answer:

N/A; 32; -8

Step-by-step explanation:

4) You have to graph this equation... basically pick two points on the line and connect them. I'd do (0,4) and (4,1) because they're the easiest

5) Just plug -2 into the equation! -3x³+2x², so when you substitute x for -2, you get -3*(-2)³+2*(-2)²=-3*(-8)+2*4=24+8=32

6) -6m+6+6=4-7m, so m=-8

if 3a-b=3 and a+2b=15, then a+b ?

Answers

Step-by-step explanation:

please mark me as brainlest

what set does -15/2 belong to

Answers

Answer:

Rational numbers

Step-by-step explanation:

any number that can be written as the ratio of two integers and that is terminating or repeating in decimal form



hoped that helped

Answer:

Rational numbers

Step-by-step explanation:

These numbers are numbers that can be expressed as a ratio of two integers and includes decimals that terminate (they end like 5.1 or 6.349) or repeat (such as 5.33333333333...)

What sentence represents this equation? 4 1/3=11−x

Answers

Answer:

4 1/3 is the same as 11 decreased by a number.

Step-by-step explanation:

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