Extra Credit:
8 congruent spheres are packed into a cube with
edge length x so that each sphere is tangent to 3
faces of the cube and 3 other spheres as shown.
what is the ratio of the total volume of the
spheres of the volume of the cube?
Answers
Answer:
Ratio of the volumes of the spheres and cube = 0.523
Step-by-step explanation:
From the figure attached,
Diameter of one sphere = Half of the measure of one side of the cube
= [tex]\frac{x}{2}[/tex]
Radius of the sphere = [tex]\frac{\frac{x}{2}}{2}[/tex]
= [tex]\frac{x}{4}[/tex]
Volume of a cube is given by the formula,
V = [tex]\frac{4}{3}\pi r^{3}[/tex]
Therefore, volume of one sphere = [tex]\frac{4}{3}\pi (\frac{x}{4})^{3}[/tex]
= [tex]\frac{x^3\pi}{48}[/tex]
Volume of 8 spheres = [tex]8\times \frac{x^3\pi}{48}[/tex]
= [tex]\frac{x^3\pi}{6}[/tex]
Volume of a cube = (side)³
= [tex]x^3[/tex]
Ratio of the volumes of the sphere and cube = [tex]\frac{\frac{\pi x^3}{6} }{x^3}[/tex]
= [tex]\frac{\pi}{6}[/tex]
≈ 0.523
Related Questions
help with these all no links- I MEAN IT! and no oh i just came for the points cr_ap brainlyest if correct
Answers
Answer:
#1
Least value = 5#2
Median = 56, option C#3
Median = 113, option C#4
A = 10, the minimum point#5
Q1 = 99.5, the median of the lower half of data, option C
14 In a book, 98% of the pages contain text, diagrams on both. If 88% of the pages
contain text and 32% contain diagrams, what percentage contain
a.neither text nor diagrams
b. only diagrams
c.only text
d.both text and diagrams?
Answers
Answer:
2%
10%
66%
22%
Step-by-step explanation:
For the first one we just need to find the compliment of the union (.98) which is .02
Union formula:
A∪B=A+B-A∩B
We will let T= text and D= diagram
we know that
.98=.88+.32-T∩D
Solve and find that T∩D= .22
Only diagram: .32-.22= .1
Only text: .88-.22= .66
Text and diagrams is the intersection we found earlier or .22
charlies goal is to sell an average of 18 cars each month this year. this table shows how many cars he sold each month from january to november. how many cars does charlie need to sell in december in order to meet his goal of a mean of 18 cars per month?
A. 17
B. 19
C. 26
D. 28
Answers
Answer: C-26
Step-by-step explanation: First you need to figure out how many total cars he needs to sell through the year by multiplying 12 by 18. This should get you 216. Now, we need to add all of his actual stats that we have so far to get a total of 190 cars sold. We know he needs 216 total by the end of the year, so we just have to subtract 190 from 216 to get our answer, 26.
Which statement is true?
Answers
Answer:
B is the correct answer
Step-by-step explanation:
Find the solution of the system of equations.
-2x-6y=8
-6x-6y=0
Answers
y=7
First solve for x in -2x-6y=8, and you will get -7. Then plug -7 into x for -6x-6y=0 and you will get 7.
links will get banned
Answers
Answer:
22 cm long
eeeeeeeeeeeeeeeeeeeeeeeeeeee
36x+27y in factored form
Answers
What is the area of the figure below?
Answers
The polygons in each pair are similar. Find the scale factor of the smaller figure to the larger figure
Answers
Answer:
1:2
Step-by-step explanation:
Find the value of x.
A.18
B.15
C.16
D.19
PLEASE HELP!!!!!
Answers
Answer:
x = 19
Step-by-step explanation:
123°+3x = 180°
3x = 180°-123°
3x = 57
x = 57/3
x = 19
The reason why we use 123° + 3x = 180° because both are adjacent angles. Adjacent angles add up to 180°
BRAINIEST TO WHOEVER RIGHT
Answers
Answer:
answer is C the means and the standard deviation because the data sets are normally disturbed
Answer: d
Step-by-step explanation:
May i get some help please
Answers
Answer:
[tex]\huge\boxed{\sf 995.4 in.\²}[/tex]
Step-by-step explanation:
Area of the circle:
= πr²
Where r = 21 in.
= (3.14)(21)²
= (3.14)(441)
= 1385.4 in.²
Area of triangle:
= [tex]\sf \frac{1}{2} (Base)(Height)[/tex]
Where Base = 20 in. , Height = 39 in.
= [tex]\sf \frac{1}{2} (20)(39)[/tex]
= (10)(39)
= 390 in.²
Area of the shaded region:
= Area of the circle - Area of the triangle
= 1385.4 - 390
= 995.4 in.²
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807how do we say the expression in words?
can somebody help me pls rn
Answers
Answer:
Step-by-step explanation:
1 Escritura unida
Según la NGLE se unen las palabras que se interpretan como una unidad y en las que, por tanto, la marca de plural solo afecta al último elemento:[1]
el bajorrelieve, los bajorrelieves
la mediapunta, las mediapuntas
En un buen número de casos, el primer elemento puede seguir teniendo individualidad para parte de los hablantes y admitir la marca del plural. La Gramática admite algunos de esos casos, de modo que las dos formas son posibles, que se escribirán unidas o separadas según se dé ese plural o no:
el puercoespín, los puercoespines; el puerco espín, los puercos espines
el arcoíris, los arcoíris; el arco iris, los arcos iris
el medioambiente, los medioambientes; el medio ambiente, los medios ambientes.
el pavorreal, los pavorreales; el pavo real, los pavos reales
La Gramática prefiere, como norma general, la forma en una palabra.
beau completed 2/5 of his science project on Friday and 1/3of the project on Saturday what fractional part of his project did she complete during these two days
Answers
Answer:
beau completed 2/5 of his science project on Friday
beau completed 1/3 of his science project on Friday
Now
he completed during these two days=1/3+2/5=11/15 part of his project
Find the area of the regular nonagon
Answers
Answer:
267.3
Step-by-step explanation:
area of a regular polygon =
(perimeter * apothem)/2
perimeter: 9 * 6.6 = 59.4
area: 59.4 * 9 = 534.6
534.6/2 = 267.3
area = 267.3
Solve the system using
the elimination method.
(3x + 4y = 6
<
(2x + 3y = 3
Answers
Answer:
[tex]3x + 4y = 6 - - - (a) \\ 2x + 3y = 3 - - - (b) \\ 2 \times (a) - 3 \times (b) : \\ = > 0x - y = 3 \\ y = - 3 \\ 2x - 9 = 3 \\ 2x = 12 \\ x = 6 \\ { \boxed{x = 6}} \\ { \boxed{y = - 3}}[/tex]
Mr.Q's class is having a giveaway where his students can receive 100 classroom credits. He will pull names out of a hat and select two winners. Once a student wins, they are not eligible to win a second time. If there are 40 total people in the class, including you and your best friend.
What is the probability that both you and your best friend get the 100 classroom credits?
PLEASE SHOW WORK!!
Answers
Answer:
1/1560
Step-by-step explanation:
The chance of you winning is 1/40, since there are 40 students and you are one of those students. Since, you cannot win again once you win once, you are eliminated. This leaves us with 39 people left. The chances of your friend being chosen out of the 39 people left is 1/39. Now you must multiply 1/40 and 1/39. After multiplying, you get 1/1560.
Name two pairs of adjacent angles and two pairs of vertical angles in
the figure.
Answers
Answer:
choice 2
Step-by-step explanation:
The perimeter of a rectangle is 48cm. its length is 4 cm. what is its width?
Answers
Answer:
P = 48
4 + 4(two given lengths) = 8
48(perimeter) - 8(length of two given lengths) = 40(length of two unknown sides)
40(length of two unknown lengths) divided by 2(two missing sides) = 20 cm
Please help
Thanks I really need help and appreciate it
Answers
Answer:
umm can you tell us the options then I can say what the answer is and I'll edit or put it in the comments
Step-by-step explanation:
have a good rest of your day tho :) ❤
A sphere with a radius of 6 pi.What is the surface area of the sphere 36Pi3 square units 114Pi2 square units 144Pi3 square units 576Pi4 square units
Answers
Answer:
6×36=216.I hope the answer is correct. I will be happy when I get 5 pointsAnswer:
Step-by-step explanation:
Which equation is equal to 4a + 2b = 10?
options:
b = -2a + 10
b = 2a + 10
b = -2a + 5
b = 2a + 5
Answers
good luck :)))
14
4(x + 6)
+
2(3x – 5) =
A) 4x + 14
B) 10x + 34
C) 10x + 14
D) 10x – 24
E) NOTA
Answers
Answer:
D) 10x - 24
Step-by-step explanation:
Bc I know maths a lot
A cube has side length of 1 meter. Determine the volume of the cube. Include all of your calculations in your final answer.
Answers
Answer:
look at the picture i sent......
choose 3 values that would make this inequality true 28 + x > 42
100
0
13
15
5
14
24
Answers
Answer:
100, 15, 24 I think that is it
Step-by-step explanation:
Answer: 100, 24, 15
Step-by-step explanation:
28+100= 128, 128>42
28+24=52, 52>42
28+15=43, 43>42
for the bud to see... and one person to get poi.nts XD
so addison got banned yesterday but got her account back today and then drake got banned today
Answers
Answer:
WHAT!? THEY BOTH GOT BANNED?! HOW
Question 4: *
What are the solutions to the equation 4x2 – 52x + 169 = 121?
Answers
Answer:
1.0769
Step-by-step explanation:
multiply 4x2 to get 8
move -52x over the equal sign to make it 52x
so we get something like this: 8 + 169 = 121 + 52x
also move 121 over the equal sign to make it -121
Like this: 8 + 169 - 121 = 52x
Now when you simply, you will get 56 = 52x
Divide both sides by 52
Final answer is 1.0769
57 divided by 592,346
Answers
Answer:
9.62 x 10⁻⁵
Step-by-step explanation:
57 / 592346 = 0.0000962275
Scientific notation: We moved the decimal 5 times to the right, and in order to put the number back in standard form, we have to move the decimal 5 times to the left. So the scientific way of saying this is 9.62 x 10⁻⁵
9.62 x 10⁻⁵ or 57 / 592346 = 0.0000962275
How to: Divide the first expression by the second expression.
Have a great day and stay safe ! srry if im wrong
Can someone help me with this
Answers
Answer:
C
Step-by-step explanation:
1. Absolute values are in the shape of a V, so the answer is automatically C.
2. If you did not know that, you can see that the graph is a function because it passes the vertical line test. This rules out option A. By looking at the graph, you can see it passes the x-axis twice, meaning that it has 2 x-intercepts. This rules out option B. X-intercepts always have a y-coordinate of 0, so we can rule out option D. The only option left after this is C.
slove the system of substitution
y=x-8
y=2x-4
Answers
Answer:
x + y = 4 , x − y = 2
x + 2 y = 4 , x − y = − 3
x 2 − y = 2 , 2 x − y = − 1
Step-by-step explanation:
Answer:
x=-4
Step-by-step explanation:
x-8=2x-4
+8 +8
---------------
x=2x+4
-2 -2
-----------
-x=4
-1 -1
----------
x=-4