A scoop of ice cream has a 3-inch diameter. How tall should the ice cream cone of the same diameter be in order to contain all of the ice cream inside the cone?

Answers

Answer 1

Answer:

12 inches

Step-by-step explanation:

Suppose the ice cream scoop has the shape of a sphere of a radius (r) inches.

Thus, the top of the cone will also have a radius (r) inches.

Let consider h to be the height of the cone in inches.

So, the objective is to make the volume of the scoop of the ice cream to be the same as the volume of the cone.

To do that; we need to equate both volumes together and make h the subject of the formula:

The volume of a sphere = 4/3 πr³ and the volume of a cone = 1/3πr²h

4/3 πr³  = 1/3πr²h

Multiply both sides by 3

4πr³  = πr²h

4r = h

h = 4(3)

h = 12 inches

To contain all the ice cream inside the cone, the height of the ice cream cone needs to be 12 inches tall


Related Questions

¿Cual es la influencia de los movimientos sociales en la consolidación de la democracia en El Salvador sociales

Answers

Answer:

The influence is there is none

Step-by-step explanation:

what is the slope and equation of a line perpendicular to the y-axis passing through the point (-3,8)
a) slope is 0 and the equation is y= -3
b) slope is undefined and the equation is x=8
c) the slope is undefined the equation is x=-3
d) the slope is 0 the equation is y=8

Answers

Answer:

D

Step-by-step explanation:

I'm not entirely sure if I'm correct but from what I gathered I'm pretty sure it's D.

Answer to this please!

Answers

Answer:

the answer is 56

Step-by-step explanation:

Answer:

The measure to angle 2 is 44.

Step-by-step explanation:

The segment towards the bottom is a straight line meaning it should equal 180°. 180 - 68 = 112. A triangle should equal 180° as well... so you add 112 to 24, then subtract that value from 180: 180 - 136 = 44

The graph of g(x) is the result of translating the graph of f(x) = 3x six units to the right. What is the equation of g(x)?

g(x) = 3x – 6
g(x) = 3x + 6
g(x) = 3x – 6
g(x) = 3x + 6

Answers

Answer:

Its A

Step-by-step explanation:

Trust me

Answer:

a

Step-by-step explanation:

Evan told his mom that he could make 14/ 12 of a cake and 5/ 6 of another cake into 2 whole cakes his mom said no way prove it explain why or why not

Answers

Answer:

The mother is wrong

Step-by-step explanation:

What we do here will be to add the fractions of the cakes that we have

Mathematically, that will be;

14/12 + 5/6 = 24/12 = 2

This means that the mother is wrong and the cakes can actually be made into 2

Mr Johnson has 4 boxes of pencils with 7 pencils
in each box. If he gives each of his 26 students a
pencil, how many pencils will he have left?

Answers

Answer:

2 pencils leftover

Step-by-step explanation:

Given:

4 boxes with 7 pencils each

Number of students:

26

Total Pencils

4*7 = 28

He has 28 pencils in total.

Unknown:

Number of extra pencils

Unknown = total pencils - total students

= 28 - 26 = 2

Answer  = 2 pencils leftover

Hope this helped,

Kavitha Banarjee

Bob went out to dinner and paid a 15% tip on a $20 meal? How much is the total bill?

Answers

Answer:

23

Step-by-step explanation:

15% of 20 = 3  then add the 3 to the 20 to get 23

23Answer:

Step-by-step explanation:

15/100*20 = 3

20+3 = 23

the equation of a line is y-3x+10. the slope is changed to 3 and the y-intercept is changed to -4 what is the new equation of the line what is the effect to the line

Answers

y=3x-4
This affects the previous line because now the slope is a positive which completely turns it around. and the Y intercept is now on the opposite side of the X axis

Find the slope of the line passing through each of the following pairs of points.

(0, 7), (0, −8)

Answers

You need to show the graph they give you

Answer:

holy,  thats hard, I will try to do it for you

Step-by-step explanation:

pls help me yes you help

Answers

Answer:

C

Step-by-step explanation:

Answer:

C) A car can travel 80 miles on 2 gallons of gasoline.

Step-by-step explanation:

They gave us the unit rate which is 40 mile/1 gallon of gasoline. With the unit rate, we can then simplify each answer choice.

Simplified version of answer a: 1 mile/40 gallon of gasoline (we know it is wrong because it doesn't match with the unit rate.)

Simplified version of answer b: 41 mile/ 1 gallon of gasoline (we know it is wrong because it doesn't match with the unit rate.)

Simplified version of answer c: 40 miles/1 gallon of gasoline (this one is the correct answer since it matched the unit rate.

Simplified version of answer d: 40 miles/ 20 gallon of gasoline  (we know it is wrong because it doesn't match with the unit rate.)

Hope this helped you : )

what is 6(5g + 2) = 30g​

Answers

Answer:

g ∈ ∅

Step-by-step explanation:

Expand the expression

30 g + 12 = 30  

Cancel out the 30g on both sides

12 = 0

Decide whether the statement is true or false

g ∈ ∅

Solve for x.
4 + 2x = 10

Answers

Answer:

The answer is 3

Hope this helps!

Help me ASAP for this question.

Answers

The answers is 6 and 8

Answer:

<6 and <8

<1 and <7

Step-by-step explanation:

Supplementary are angles that add up to 180 degrees. (A straight line)

In a survey of 31,000 people who owned a certain type of​ car, 2,015 said they would buy that type of car again. What percent of the people surveyed were satisfied with the​ car?

Answers

Answer:

6.5%

Step-by-step explanation:

2,015/31,000 = .065

Heather sells cosmetics for a local company. During her first month of employment her sales were $60. During her second month her sales were $300. What was Heather’s percent of increase in sales? (Remember to move your decimal two places or multiply by 100 to make a decimal a percent!)

Answers

Answer:

80%

Step-by-step explanation:

300/3=100

60/3=20

100-20=80

HELPPP!! which of the following could be the ratio between the lengths of two legs of a 30,60,90 triangle
check all that apply:
whoever gives me the correct answer gets brianliest

Answers

Answer:

[tex]\sqrt{3}:3\\1:\sqrt{3}[/tex]

Step-by-step explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios. There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant, and cotangent.

The longest side of the triangle is called the hypotenuse and the other two sides are the legs.

Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.

The tangent ratio is defined as:

[tex]\displaystyle \tan\theta=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]

The cotangent ratio is defined as:

[tex]\displaystyle \cot\theta=\frac{\text{adjacent leg}}{\text{opposite leg}}[/tex]

As shown above, the tangent and the cotangent are the ratios of the two legs in any possible order.

If the triangle has angles of 30°, 60°, and 90°, then we can take one of the acute angles and find the tangent and cotangent to know the required ratios:

Let's take for example the 30° angle:

[tex]\displaystyle \text{ratio of legs: }\tan 30^\circ=\frac{\sqrt{3}}{3}[/tex]

[tex]\displaystyle \text{ratio of legs: }\cot 30^\circ=\sqrt{3}[/tex]

Thus the possible ratios from the list are:

[tex]\sqrt{3}:3\\1:\sqrt{3}[/tex]

The reciprocals of those ratios are also applicable

help me with this please

Answers

Answer:

C is correct

Step-by-step explanation:

3+6=9

2 sides on a triangle must be greater than the other side

In Triangle DEF, f = 160 cm, d = 670 cm and ZE=114°. Find the length of e, to the nearest
centimeter.

Answers

Answer:

This is an obtuse scalene triangle with the length of E measuring around 749 cm.

<D = 54.754° ≈ 55°

<E = 114°

<F = 11.246° ≈ 11°

Side D = 670 cm

Side E = 749.46937 cm ≈ 749 cm

Side F = 160 cm

Explanation:

When given two sides, and an angle, we can use trigonometry to find the missing angles, and sides.

Given the triangle ∆DEF with side D measuring 670 cm, side F measuring 160 cm, and angle E measuring 117°, we can apply the law of sines to identify the missing information. A & a chronologically refers to the first angle, and side. B & b chronologically refers to the second angle, and side. And C & c chronologically refers to the third angle, and side.

a / Sin (A) = b / Sin (B) = c / Sin (C)

[side 1]. [side 2]. [side 3].

↓ ↓ ↓

sideD/sin(<D) SideE/sin(<E) SideF/sin(<F)

______________________________

670cm / Sin(D) = E cm / Sin(114) = 160 / sin(F).

Since we are only given two sides with an angle measure, we can refer to the law of cosines to figure this one out.

It states that A = arccos(b²+c²-a²/2bc) → cos(A) = b²+c²-a²/2bc

B = arccos(a²+c²-b²/2ac) → cos(B) = a²+c²-b²/2ac

and C = arccos(a²+b²-c²/2ab) → cos(C) = a²+b²-c²/2ab

capital A, B, and C are angles A, B, and C.

lowercase a, b, and c are sides a, b, and c.

Therefore c² = a² + b² − 2ab cos(C),

b² = a² + c² - 2ac cos (B), and a² = b²+c² - 2bc.

SOH CAH TOA.

Since we know this, we can solve for pretty much everything as long as we are given at least 3 variables. Chronologically, because we are solving for side e, we must use b² = a² + c² - 2ac cos (B), because the rest are only variables we are given, making it easy to solve. So b² = 670² + 160² - 2(670 × 160) × cos(114°) = 561704.3362754.

Now take the square root of that to get b by itself, so √561704.3362754.... = 749.4693698046.... ≈ 749

Answer:749

Step-by-step explanation:

S.A.S law or Cosines

e=561704.33628= 749.469= 749

The relationship between the number of hours a plumber works and the total work fee
she charges is proportional. Her fee for 5 hours of work is $350.
Which of the following could be combinations of values for the plumber's work hours
and total work fee she charges?
Hours 3 - $270
Hours 3.5 - $245
Hours 6 - $440
Hours 7.25 - $530,50

Answers

Answer:

ANSWERS ARE B, C, AND D.

Step-by-step explanation:

I found the unit rate of 350 and 5, because we can use a calculator (as stated on top) I just punched in 350 divided by 5 and got 70. Now i know this may not sound that "professional", but nothing needs to always be professional as long as its efficient and most importantly gets you the right answer. I then took the time to multiply each number, (the ones on the left : 3, 3.5, 6, 7.25, and 8) by 70. If the answer you got on the calculator match up to the number on the right, (240, 420, 507.50, and 490) its correct, if it doesn't match up, you can tell that its most likely not the answer. You should end up with three answers that all end up having the unit rate of 70. Hope this helps anyone who needed it.

ANSWERS ARE B, C, AND D.

Answer:

The answer is B,C, And D

Step-by-step explanation:

I just saw it on Khan and got it right.

First answer the problem 3,216 divided by 8 and ur quotiont/answer u then will look at the answer and find the first diget and then answer what place is that didet in.

Answers

Answer:

Quotient/Answer = 402

Hence the first digit is 4 and it's place value = hundreds

Step-by-step explanation:

Quotient = Dividend ÷ Divisor

Dividend = 3216

Divisor = 8

Quotient = 3216 ÷ 8

= 402

We are asked to find the place value of the first digit

Hence the first digit is 4 and it's place value = hundreds

Jack earned $6.00 per hour before being given a 3% raise. What was Jack’s new wage after the raise?

Answers

Answer:

$6.18 per hour

Step-by-step explanation:

3% of 6 is 0.18

You can get this number by multiplying 0.03 by 6

Add 0.18 to 6 and that gives Jack $6.18

1. There are 10 people in a math club. Three people will be chosen for the Pi Day committee. How many different ways can club members structure the committee? a. 12 b. 120 c. 720 d. 604,800

Answers

Answer: 120

Step-by-step explanation:

From the question, we are informed that there are 10 people in a math club and that three people will be chosen for the Pi Day committee.

The number of different ways that the club members can structure the committee goes thus:

This can be solved by:

nCr = n! / r! (n - r)!

where n = 10

r = 3

= n! / r! (n - r)!

= 10! / 3! (10 - 3)!

= (10 × 9 × 8) / (3 × 2)

=120

interior and exterior of angles of triangles
please help !!

Answers

Answer:

x = 20

Step-by-step explanation:

Assuming you require the value of x

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

7x - 15 is an exterior angle of the triangle, thus

7x - 15 = x + 28 + 4x - 3 , that is

7x - 15 = 5x + 25 ( subtract 5x from both sides )

2x - 15 = 25 ( add 15 to both sides )

2x = 40 ( divide both sides by 2 )

x = 20

1 Which expression is equivalent to (7x – 5) – (3x - 2)?​

Answers

Answer:

The answer is D.

Step-by-step explanation:

A pair of shoes costs $30.99 and the state sales tax is 4%. Use the formula C = p + rp to
find the total cost of the shoes, where C is the total cost, pis the price, and r is the sales tax
rate.
$32.23
$39.19
$43.39
$34.99

Answers

Answer:

the answer is A. $32.23

Step-by-step explanation:

Answer:

$32.00

Step-by-step explanation:

To find the sales tax always multiply the sales tax to to the cost of you item.

Being your sales tax is 4%  you will Multiply 30.99 x .04 (not just 4)

30.99 x .04 = 1.2396  ( round to the nearest tenth) since the number after the 3 is 5 or above ,,,,round it off to 24...Making it $1.24 (tax)  Now add that to your cost of the shoes

$30.99 + $1.24 = $32,23

For future :  if the tax is 10, 20, 35%... You will multiply the cost of item by .10, .20, .35 (put the point in front of it .

A creek is rising at a rate of 2 inches per hour. If the creek raises more than 3 feet, it will exceed flood stage. How long can the river rise at this rate without exceeding flood stage? (Remember there are 12 inches in a foot.) *

Answers

Answer:

16 hours

because in 16 hours 2 inches per hour it will overflow

whats equivelent to 9a + 12

Answers

Answer:

Multiply both terms of the numbers

hense you would do: 2(9a + 12) = 18a + 24

It doesn't have to be 2 however. If can be any number you want it to be

Step-by-step explanation:

Answer:

12+9a is equivelent to 9a+12 :-)

Step-by-step explanation:

What is the value of a3 in the sequence?
5, 10, 20, 40, 80...

Answers

i can’t see a3 do you have a picture

The New England patriots scored 9 points in the first half. In the second half they scored 3 less than 2 times the points in the first half. What is the ratio of of the points and scored in the second half to the total number of points scored

Answers

Answer:

[tex]S : T = 5 : 8[/tex]

Step-by-step explanation:

Represent the first half with F and the second with S

We have that:

[tex]F = 9[/tex] --- From the first statement

[tex]S = 2F - 3[/tex] --- From the next statement

Required

Determine the ratio of S to the total point

First, we need to determine the value of S

Substitute 9 for F in [tex]S = 2F - 3[/tex]

[tex]S = 2 * 9 - 3[/tex]

[tex]S = 18 - 3[/tex]

[tex]S = 15[/tex]

Next, we determine the total points

[tex]Total = F + S[/tex]

[tex]Total = 9 + 15[/tex]

[tex]Total = 24[/tex]

The ratio of S to total is: (Represent total with T)

[tex]S : T = 15 : 24[/tex]

Divide both ration by 3

[tex]S : T = 15/3 : 24/3[/tex]

[tex]S : T = 5 : 8[/tex]

Hence, the ratio is 5 to 8

Choose the graph which represents the solution to the inequality.
3 - 2x 2-17

Answers

Answer:

X ≥ 12, (Or A)

Step-by-step explanation:

First, you would do two step equation.

3-2x     ≥   -17

+3        |     +3

----------|------------------

-2x      ≥       -14

Then you divide each side by -2

And you get, X≥12

Which, does not represent any of the graphs.

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