Twenty wooden spheres, each with a radius of 2 inches, are packed snugly into a square box that is 18 inches on each side. The remaining space is filled with packing beads. What is the volume occupied by the spheres?

Vsphere=[tex]\frac{4}{3}\pi r^3[/tex]

Answers

Answer 1

Answer:

670.21 inches^3

Step-by-step explanation:

To find the volume of the spheres, all you need to know is the formula for the volume of a sphere, which you've included in your problem. From the problem, you also know that r = 2. From here, you calculate the volume of 1 of the spheres, which turns out to be:

V = 33.51032

Since there are 20 spheres in this box, you multiple the volume of a single sphere by 20 to get the total volume occupied by the spheres.

V = 20 * 33.51032

V = 670.2064

If you round to 2 decimal places, this becomes 670.21.


Related Questions

Help Please!!!!!!!
I give Brainlist

Your grandmother gives you $1500 to invest in a savings account on your 15th birthday. The only condition is that you may NOT use it until you have graduated high school at 18. After researching savings accounts, you come up with two options.



1) A high interest savings account, with 2.5% simple interest annually or

2) A High Yield Savings account with 2% interest compounded annually.



Which account will you chose and why?

Answers

Answer:

Step-by-step explanation:

This is a logical question that can be d=solved thus;

To decide which decision to make,one has to calculate the amount for both methods to detrmine which is higher.

1. Using simple interest formula of ( P X R X T)/ 100

Since p  = 1500, r  = 2.5%,  T = 3

1500 x 2.5% x 3  / 100  =  1500 x 0.025 x 3 / 100

112.5 / 100 = 1.125

to find amount  = 1.125 + 1500 = 1501.25 for the three 3years.

2. Using compound interest formula of ( P ( 1 + r/n)∧nt

1 + (2%/3) ∧3(3)

1500( 0.02/3) ∧ 9

1500  x 0.006 ∧9

1500 x 2.60 = 3900

A = 3900 + 1500 = 5400

SO FROM THE ABOVE I WILL G FOR THE HIGH YIELD SAVINGS AS IT IS HIGHER THAN THE INTEREST SAVINGS

Given the data from the question, the best account to use is:

A high interest savings account, with 2.5% simple interest annually (Option 1)

Simply interest formula

I = PRT / 100

A = I + P

Where

I is the interest P is the principal R is the rate T is the time A is the amount after time t

Compound interest formula

A = P(1 + r/n)ⁿᵗ

Where

A is the amount after time tP is the principal r is the rate t is the time n is number of times compounded per annual

Case 1 (simple interest) Principal (P) = $ 1500Rate (R) = 2.5%Time (T) = 3 years Interest (I) =? Amount (A) =?

I = PRT / 100

I = (1500 × 2.5 × 3) / 100

I = $ 112.5

Thus

A = I + P

A = 112.5 + 1500

A = $ 1612.5

Case 2 (compound interest) Principal (P) = $ 1500Rate (R) = 2% = 0.02Time (T) = 3 years Number of time compounded annually (n) = 1Amount (A) =?

A = P(1 + r/n)ⁿᵗ

Since n = 1,

A = P(1 + r)ᵗ

A = 1500(1 + 0.02)³

A = $ 1591.8

SUMMARY

The amount at the end of 3 years using:

A High interest savings account, with 2.5% simple interest annually is $ 1612.5A High Yield Savings account with 2% interest compounded annually is $ 1591.8

Thus, the best account to use is a high interest savings account, with 2.5% simple interest annually (option 2)

Learn more about simple interest:

https://brainly.com/question/15528344

Describe these points with a double inequality

Answers

Answer:

-3 < x ≤ 13

Step-by-step explanation:

the filled circle is the less/greater than or equal to sign and the open circle is a less/greater than sign.

If you are asked to factorize only, can you also expand the brackets ? Or you can’t u less you are asked to? Please answer..

Answers

If you could give a sample question I think it would be easier to explain

Find the value of x.

Answers

Answer:

38

Step-by-step explanation: subtraction:

Input interpretation: x: 105-67=

Ratio in lowest terms: 38

Division:

105/67= 1.56...=1 38/67---1R 38= 1 with the remainder of 38. So just 38.

The value of the variable 'x' using the exterior angle theorem will be 38°. Then the correct option is A.

What is the triangle?

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The exterior angle of a triangle is almost always equal to the addition of the interior and opposing interior angles. The term "external angle property" refers to this feature.

By the above theorem, the equation is written as,

x + 67 = 107

Simplify the equation, then we have

x + 67 = 105

x = 105 - 67

x = 38°

The value of the variable 'x' using the exterior angle theorem will be 38°. Then the correct option is A.

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ7

NEED HELP! I JUST NEED HELP ON 31 PLEASSEE HELP

Answers

Answer:

A

Step-by-step explanation:

the quartiles are illustrated as 55 and 59. The average is 57.5 so 58? These are the key points on this type of graph.

8. The sum of the ages of Sarpong and Quartey is 50 years. In five years time, the age of Quartey will be four times the age of Sarpong now. How old is each boy?​

Answers

Answer:

Sarpong is 11.

Quartey is 39.

Step-by-step explanation:

Let Sarpong's age now = s.

Let Quartey's age now = q.

Now:

q + s = 50

In five years, their ages will be

Sarpong: s + 5

Quartey: q + 5

q + 5 = 4s

We have a system of two equations in two variables.

q + s = 50

q + 5 = 4s

We will use the substitution method.

Solve the second equation for q.

q = 4s - 5

Substitute 4s - 5 for q in the first original equation and solve for s.

4s - 5 + s = 50

5s = 55

s = 11

q + s = 50

q + 11 = 50

q = 39

Answer:

Sarpong is 11.

Quartey is 39.

Find the geometric mean of 24 and 32

Answers

Answer:27.712812921102

Step-by-step explanation:

24*32=x*x

√768=√x²

27.712812921102=x

Geometric mean formula

GM=√ab

a=24

b=32

Find GM

√(24)(32)√76827.7128

On rounding

GM=27.7

The diameter of a circle is 6 millimeters. What is the circle's circumference?
Use 3.14 for ​.

Answers

Answer:

18.84

Step-by-step explanation:

Answer:

18.8495559215

Step-by-step explanation:

In order to find circuference we use the formula

C= 2π(r)

c= circumference

r= radius

since they gave you the diameter, you first have to find the radius so you would divide the diameter by two since radius is half of a circle so 6 divided by 2 is 3. From here we would plug in 3 for "r" in the formula I wrote above. So C= 2π(3). then type this into a calculator to get the answer I wrote above. Then round as directed

Helpp me with my sister's math​

Answers

Answer:

pq - 12r

step by step explanation:


ABC and AED are straight lines.
BE and CD are parallel.
A
B
AD = 10.5 cm
AE = 4.2 cm
BE = 2.9 cm
a) Work out length CD.
AC = 8.75 cm
b) Work out length BC.

Answers

Answer:

  a) CD = 7.25

  b) BC = 5.25

Step-by-step explanation:

a)

The parallel lines mean the triangles are similar. ΔADC ~ ΔAEB. Corresponding sides are proportional, so ...

  AD/AE = DC/EB

  10.5/4.2 = CD/2.9

  CD = 2.9(5/2) = 7.25

__

b)

Corresponding sides are proportional, so ...

  BC/AC = ED/AD

  BC = AC(ED/AD) = 8.75(10.5 -4.2)/10.5 = 8.75(3/5) = 5.25

Hi! Please help. (Geometry Btw)

Answers

Answer:

It is C

Step-by-step explanation:

Reflection in X axis

Reflecting over the x axis, the x values remain the same and the y values become opposite.


answer: c. (X,y) becomes (x,-y)

MN is a diameter of a circle with centre ' O ' . If BD = CD , prove that ∠OAD = ∠OCD
~Please help!! Thanks in advance:)​

Answers

Answer:

[tex] \sf \: Proved \: \angle \: OAD \: = \angle \: OCD[/tex]

Step-by-step explanation:

Given:

Mn is diameter of circle having centre O

and BD = OD,

To prove that:

[tex]\angle \: OAD \: = \angle \: OCD[/tex]

Solution:

Join the points O and B and draw OB,

On joining the line,

in ∆OCD and ∆OBD,

OC =OB → (Radius of same circle)

BD =CD → (from given)

OD =OD → (Common side in both the triangles)

Hence ∆OCD and ∆OBD are congruent from SSS property.

so we can say that,

[tex]\angle \: OBD \: = \angle \: OCD[/tex]

Consider above prove as statement A

Corresponding angles of congruent traingle.

in ∆ OAB,

OA = OB (radius of same circle)

hence ∆OAB is an isosceles traingle.

We know that opposite angle of isosceles traingle are always equal. hence,

[tex]\angle \: OBD \: = \angle \: OAB \\ \angle \: OAB \: = \angle \: OAD (same \: angles) \\ \angle \: OBD \: = \angle \: OAD[/tex]

Consider above prove as statement B

From Statement A & B we can say that

[tex]\angle \: OAD \: = \angle \: OCD[/tex]

Thanks for joining brainly community!

In circle L with m KLM = 82°, find the angle measure of minor arc KM.
K
M
L
O
Answer: m KM=
Submit Answer
attempt 1 out of 2

Answers

The angle measure of minor arc KM is 41 degrees

Circle geometry

From the given diagram, we have the following parameters

mKLM = 82 degrees

Required

arcKM

Since the angle at the vertex is twice that of the intercepted arc, then:

<KLM = 2(arcKM)
arcKM = <KLM/2

arcKM = 82/2

arcKM = 41 degrees

Hence the angle measure of minor arc KM is 41 degrees

Learn more on circle geometry here:  

https://brainly.com/question/26594685

A contractor has two choices for billing a completed job. · $500 flat rate, regardless of the number of hours worked · $20 per hour worked the graph shows the relationship between pay per hour and number of hours worked for both scenarios.

Answers

Answer:

C. (25,20)

Step-by-step explanation:

Edge2022 <3

Good luck and remember (yall that take edge) , you can get through the day no matter how hard it may seem. I have faith In you guys :).

If number of hours worked is less than 20, 500 flat rate is preferable

and, If number of hours is more than 20, hourly rate i.e. 20 per hour is better.

What is Inequality?

An inequality is a mathematical statement that compares two values or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

In the first scenario, where there is a $500 flat rate regardless of the number of hours worked, the pay per hour remains constant at $500 divided by the number of hours worked.

So, the graph for this scenario would be a horizontal line at a height of $500.

In the second scenario, where the contractor is paid $20 per hour worked, the pay per hour is fixed at $20.

let the number of hours be worked be x.

Then, 20x < 500

x< 25

So, if number of hours worked is less than 20, 500 flat rate is preferable

and, If number of hours is more than 20, hourly rate i.e. 20 per hour is better.

Learn more about Inequality here:

https://brainly.com/question/11854205

#SPJ7

Solve:
(m+2) (m+1) - (3m - 5) (9-5m)

Answers

Step-by-step explanation:

please mark me as brainlest

help help help help help

Answers

Answer: 10

Step-by-step explanation:

We can get this is a right triangle with a hypotenuse of c and legs equal to the height and radius.

So, the hypotenuse is c and the legs are 6 and 8.

This means that c=10

HELP WITH EXPLANATION, NO LINKS

Answers

Answer:

  3x³ and 6x³, y and 7y

Step-by-step explanation:

Like terms have variables with the same exponents. This fact eliminates choices A, C, D.

The like terms are ...

  3x³ and 6x³, 7y and y . . . . . . choice B

The answer is b, because you have to have the same variable and exponent to the coefficient of the number.

robert gets a loan from his bank.
he agrees to borrow £6000 at a fixed annual simple interest rate of 7%
he also agrees to pay the loan back over a 10-year-period.
how much money in total will ha have paid back at the end of the 10 years?

Answers

Answer:

£10200

Step-by-step explanation:

Amount borrowed (P) = £6000

Rate of interest (R) = 7%

Time (T) = 10 years

First, let us calculate the simple interest (SI) for 10 years.

Formula for simple interest is given as:

[tex]S.I.=\frac{PRT}{100}[/tex]

Plugging the values of P, R and T in the above formula, we find:

[tex]S.I.=\frac{6000(7)(10)}{100}[/tex]

S.I.= £4200

Total money paid back at the end of the 10 years

= £6000 + £4200

= £10200

ASAP ANSWER PLEASE! 20 POINTSS!

A cylindrical shaped silo has a diameter of 18 feet and a height of 4 feet. How much water can the silo hold, in terms of π?

Refer to your STAAR 8th Grade Math Reference sheet for the appropriate formula.

Question 3 options:

162π ft3


324π ft3


648π ft3


12962π ft3

Answers

Answer:

th answer is 324

Step-by-step explanation:

i took the test

HELP PLEASE URGENT, ASAP. THIS IS GRADE 11 TRIGONOMETRY ILL GIVE THE BRAINLIEST!!!!!!!!!!!!

Answers

Answer:

1. [tex] \theta = 61.9^\circ [/tex]

2. [tex] x = 23.7~cm [/tex]

Step-by-step explanation:

Problem 1.

Use the Law of Sines.

This is SSA.

[tex]\dfrac{a}{\sin A} = \dfrac{c}{\sin C}[/tex]

[tex] \dfrac{31.2~cm}{\sin 51^\circ} = \dfrac{35.4~cm}{\sin \theta} [/tex]

[tex] \sin \theta = \dfrac{35.4~cm \times \sin 51^\circ}{31.2~cm} [/tex]

[tex] \sin \theta = 0.88176 [/tex]

[tex] \theta = \sin^{-1} 0.88176 [/tex]

[tex] \theta = 61.9^\circ [/tex]

Problem 2.

m<A + m<B + m<C = 180°

m<A + 67° + 58° = 180°

m<A = 55°

Use the Law of Sines.

[tex]\dfrac{a}{\sin A} = \dfrac{c}{\sin C}[/tex]

[tex]\dfrac{x}{\sin 55^\circ} = \dfrac{24.5}{\sin 58^\circ}[/tex]

[tex]x = \dfrac{\sin 55^\circ \times 24.5}{\sin 58^\circ}[/tex]

[tex] x = 23.7~cm [/tex]

State a mathematical phase to for each English phase
1.) three or more than a number
2.) the sum of a number and ten
3.) seven less than a number
4.) cube of a number increase by nine
5.) square of the sum of a number

Thanks for your answer :)

Answers

Answer:

the sum of a number

Step-by-step explanation:

0.017

Consider a sequence whose first five terms are: 4, 8, 16, 32, 64.
Which function (with domain all integers n 2 1) could be used to define and continue this sequence?
A f(n) = 4(n-1)
® f(n) = 4(2)"-1
f(n) = 4n2
f(n) = 4n

Answers

Answer:

Considere una secuencia cuyos primeros cinco términos son: 4, 8, 16, 32, 64.

¿Qué función (con dominio todos los enteros n 2 1) podría usarse para definir y continuar esta secuencia?

A f(n) = 4(n-1)

® f(n) = 4(2)"-1

f(n) = 4n2

f(n) = 4n

Step-by-step explanation:

A box of sunflower seeds contains p packets. Each packet of sunflower seeds contains s seeds. Which equation can be used to find the number of sunflower seeds in a box, b? *
5 points
p = sb
s = pb
b = sp
b + s = p

Answers

Answer:

b = sp

Step-by-step explanation:

box = seeds per packet

The given relation can be used to find the total number of seeds in box b, using the equation b = sp. Hence, 3rd option is the right choice.

What are equations?

Equations are relations shown between two equal algebraic expressions.

How do we solve the given question?

We are given a box of sunflower seeds, containing p packets of seeds, each of which contains s number of seeds.

We are asked to write an equation that can be used to find the total number of seeds in the box, b.

We know that the box contains p packets of seeds.

In 1 packet we have s number of seeds.

∴ In p packets, we will have an s*p number of seeds or sp seeds.

Since the box contains p packets and the total number of seeds in the box is b, then we can say that

b = the number of seeds in p packets

or, b = sp, which is the required equation.

∴ The given relation can be used to find the total number of seeds in box b, using the equation b = sp. Hence, 3rd option is the right choice.

Learn more about equations at

https://brainly.com/question/2972832

#SPJ2

Help Please!!!!!!!!!!!!!

Answers

Answer:

A. 2086 yd²

Step-by-step explanation:

SA = 2lw + 2wh + 2lh
SA = 2*17*20 + 2*20*19 + 2*17*19
SA = 680 + 760 + 646
SA = 2086
Hope this helps :)

determine the equation of the circle with center (0,6) containing the point (74,2)

Answers

The circle with center (0,6) containing the point (74,2) has an equation of x² + (y - 6)² = 74.1²

How to calculate the equation of a circle

The equation of a circle is:

(x - h)² + (y - k)² = r²

Where (h, k) is the center and r is the radius.

The circle with center (0,6) containing the point (74,2). Hence:

[tex]Radius=\sqrt{(2-6)^2+(74 -0)^2}=74.1\ unit[/tex]

The equation is:

x² + (y - 6)² = 74.1²

Find out more on circle at: https://brainly.com/question/24375372

If the slope of a line is zero the line must be a
line.

Answers

Answer:

Straight along the horizontal axis

Step-by-step explanation:

Hope this helped :)

-5x-21 find value of x

Answers

Answer:

The value of x = -21/5

Step-by-step explanation:

=> -5x-21 =0

=> -21 = 5x

=> -21/5 = x

Answer:

Step-by-step explanation:

you want to set the equation equal to 0

-5x - 21 = 0

add 21 to both sides to get the variable by itself

-5x = 21

divide both sides by -5

x = - 21/5

How to create a quadrilateral with vertices at the following points PLEASE ASAP

Answers

Answer:

The points are in the form (x,y) this means you count x (right) if positive and left if negitive, for y up is positive and down negitive. for example the point (3,-2) would be three to the right two down

Step-by-step explanation:

The points are in the form (x,y) this means you count x (right) if positive and left if negitive, for y up is positive and down negitive. for example the point (3,-2) would be three to the right two down

Lines j and k are intersected by line m. At the intersection of lines j and m, the uppercase left angle is 93 degrees. At the intersection of lines k and m, the bottom right angle is 93 degrees.
Given the information in the diagram, which theorem best justifies why lines j and k must be parallel?

alternate interior angles theorem
alternate exterior angles theorem
converse alternate interior angles theorem
converse alternate exterior angles theorem

Answers

Answer: converse alternate exterior angles theorem

Step-by-step explanation:

The angles are alternate exterior angles.


a=340
rounded to the nearest 10
b=49.8
rounded to 1 DP
Find the minimum of
a x b

Answers

Answer:

  16666.25

Step-by-step explanation:

For rounded values, the minimum value they could have been rounded from is the given value less half its least-significant digit.

That means the minimums are ...

  a: 340 ⇒ 340 -5 = 335

  b: 49.8 ⇒ 49.8 -0.05 = 49.75

Then the minimum product would be ...

  (335) × (49.75) = 16666.25

Other Questions
If a scale reads 1/1000, one foot on the map equals how many feet in the real world?. Giving Brainliest if answered correctly What was a purpose of the Wilmot Proviso?to allow for popular sovereignty in the states of Kansas and Nebraskato decide which states would be free and which states would allow enslavement as the United States expanded westto require citizens to help return formerly enslaved people who had fledto ban enslavement in the territory that had been acquired from Mexico Which ion combines with ba2 to form a compound that is most soluble in water How many potassium ions are needed to bond with a phosphate ion?. A condition or event in the environment is called astimulusO homeostasisO reproductionO species Which statement could be categorized in the overlapping section of the Venn diagram? A bottle is launched from a bottle launcher. The height of the bottle is modeled by the equation h(t) = 16t2 + 78t + 10. How long does it take the bottle to reach the ground? A. 10 seconds B. 5 seconds C. 4.7 seconds D. 1.1 seconds Multicultural Studies!HELP PLEASEGisela didn't say anything when her friend made a joke about the texture ofBlack people's hair. What is Gisela showing?O A. Assertive behavior toward racismB. Institutional racismC. Passive acceptance of racismD. Intolerance toward racism A cube has a side length of 5 centimeters. What is its surface area of the cube? kit is going to build a 3 feet walk around a pool that measures 20 feet by 15 feet find the area of the walk in square feet Does the budgeted amount cover the actual amount for expenses, savings, and emergencies?A)No, it's short $207.00,No, it's short $227,00,oYes, there's a surplus of $207.000D)Yes, there's a surplus of $227.00, The panting responses observed in overheated birds and mammals dissipate heat loss by what process? ASAPPPPPPPPPPPP!!!!!! Which scenarios can be represented by a ratio of 4 : 5 ? Assume you borrow money to buy a new car at 10 percent interest, and you think that the economy-wide rate of inflation over the life of the loan will be 8 percent. If you are correct in your assumption, your real rate of interest on the car loan will be One mole of copper atoms is 6.02 x 1023 copper atoms.True or false? Julian has a points card for a movie theater. He receives 85 rewards points just for signing up. He earns 3.5 points for each visit to the movie theater. He needs 120 points for a free movie ticket. Which equation or tape diagram could be used to represent the context if xx represents the number of visits Julian must make to earn a free movie ticket? What is the slope-intercept equation for this line?y = [?]x +[?] The school cafeteria sells two kinds of wraps: vegetarian and chicken. The vegetarian wrap costs $1.00 and the chicken wrap costs $1.90. Today they made $78.60 from the 57 wraps sold. How many of the wraps so ld were vegetarian?