1. a. A cube’s volume is 512 cubic units. What is the length of its edge?
b. If a sphere fits snugly inside this cube, what is its volume?
c. What fraction of the cube is taken up by the sphere? What percentage is
this? Explain or show your reasoning.
Answer:
a) The length of its edge is 8 units.
b) The volume of the sphere is approximately 268.083 cubic units.
c) The fraction of the cube that is taken up by the sphere is 0.524, whose equivalent in percentage form is 52.4 %.
Step-by-step explanation:
a) The volume of a cube ([tex]V_{c}[/tex]), measured in cubic units, is defined by the following expression:
[tex]V_{c} = L^{3}[/tex] (1)
Where [tex]L[/tex] is the side length of the cube, measured in units.
If we know that [tex]V_{c} = 512\,u^{3}[/tex], then the length of its edge is:
[tex]L = \sqrt[3]{V_{c}}[/tex]
[tex]L = 8\,u[/tex]
The length of its edge is 8 units.
b) The volume of a sphere ([tex]V_{s}[/tex]), measured in cubic units, that fits snugly inside this cube is defined by:
[tex]V_{s} = \frac{\pi}{6}\cdot L^{3}[/tex] (2)
If we know that [tex]L = 8\,u[/tex], then the volume of the sphere is:
[tex]V_{s} \approx 268.083\,u^{3}[/tex]
The volume of the sphere is approximately 268.083 cubic units.
c) The fraction of the cube taken by the sphere is the ratio of the volume of the sphere to the volume of the cube. That is to say:
[tex]r = \frac{V_{s}}{V_{c}}[/tex]
If we know that [tex]V_{c} = 512\,u^{3}[/tex] and [tex]V_{s} \approx 268.083\,u^{3}[/tex], then the fraction of the cube that is taken up by the sphere is:
[tex]r = 0.524[/tex]
The result in percentage form is calculated by multiplying the result above by 100.
[tex]\% r = 52.4\,\%[/tex]
The fraction of the cube that is taken up by the sphere is 0.524, whose equivalent in percentage form is 52.4 %.
5. Triangle ADE is enlarged to form triangle
Answer: the scale factor would be 2
Step-by-step explanation:
If you add all lengths for triangle ABC you can see that triangle ADE x 2 will give you the lengths for ABC
How many grams are in a kilogram
Answer:
1000
Step-by-step explanation:
the prefix kilo means 1000
please help me with this
Answer: 5
Step-by-step explanation:
please help me !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
#1 i know for a fact ur not going to pay us
#2 theres no picture
#3 Sorry :(
plz help me
The container below contains 2 gray. 1 white, and 4 black marbles. Without looking, if Eric chooses a marble from the container will the probability be closer to O or to 1 that Eric will select a white marble? A gray marble? A black marble? Justify each of your predictions.
Step-by-step explanation:
Probability of Grey ball = 2/7 or 0.285. It is closer to 0
Probability of White marble = 1/7 or 0.142. It is closer to 0
Probability of Black marble = 4/7 or 0.571. It is closer to 1
What is fifty seven over one hundred
Answer:
57/100
Step-by-step explanation:
57/100
Fifty-seven(57) over one-hundred(100), or 57 more than 100 would be 157!
Hope this helps, if not, comment below please!!!
:L
Kevin led 150 adults, plus 6 student groups. Monica led 134 adults, plus 8 student groups. If each student group had the same number of students, write and solve an equation to show the amount of students in the student groups
Answer:
Number of students in a student group = 8
Step-by-step explanation:
Let number of student in a student group = x
∴ Kevin lead 150 adults and 6x students
⇒Kevin lead = 150 + 6x
And,
Monica lead 134 adults and 8x students
⇒Monica lead = 134 + 8x
So, the number of students are equal
⇒150 + 6x = 134 + 8x
⇒150 - 134 = 8x - 6x
⇒16 = 2x
⇒x = [tex]\frac{16}{2}[/tex] = 8
∴ we get
Number of students in a student group = 8
PLEASE HELP!!!!!! IM HORRIBLE AT MATH
Im bad at math too! we can be horrible at math together
Find the missing side
Answer:
72
Step-by-step explanation:
The pythagorean theorem states that in a right triangle A^2 + B^2 = C^2 where A and B are the two smaller sides and C is the hypotenuse.
Because of this, in this triangle 30^2 + B^2 = 78^2
Which means B^2 = 5184
And B = 72
The Lee family buys a new car that has a sales price of $35,000. If the car dealer requires a minimum down payment of 15%, what is the minimum down payment in dollars the Lees must pay for their car?
Choose the correct value.
$525
$5,250
$3,500
$15,000
Answer:
Si un electrón no consume, ni libera energía el átomo se encuentra en
Step-by-step explanationSi un electrón no consume, ni libera energía el átomo se encuentra en:
Please help will give Brain!!
Answer:
x=3
Step-by-step explanation:
Jonathan drives 845 miles in 5 hours. What is his average rate of speed in miles per hour?
Answer:
ok so it is 169
Step-by-step explanation:
ok i hope this is correct i used a calculator so sorry if its wrong all i did was divide some stuff
if its correct can u give me the crown
if u dont want to thats alright
i divided 845 and 5 and got 169
Order the decimals from least to greatest.
0.7, 0.71, 0.07
Answer:
0,07, 0.7, 0.71
Step-by-step explanation:
0.07, 0.7, 0.71
that's it
the set of all numbers greater than or equal to 5 and less than or equal to 7
The notation according to the set will be "[tex][5, + \infty) \cup (- \infty , 7][/tex]".
Let,
"x" belongs to a set of (Real numbers) R.∴ [tex]x \ \epsilon \ R[/tex]
Now,
[tex]x \geq 5[/tex][tex]x \leq 7[/tex]hence,
→ [tex]x \leq 7 \rightarrow (- \infty, 7][/tex]
→ [tex]x \geq 5 \rightarrow [5, + \infty)[/tex]
then,
The notation will be:
→ [tex][5, + \infty) \cup (- \infty , 7][/tex]
Thus the above solution is appropriate.
Learn more:
https://brainly.com/question/11375885
Paula has 2 bananas. She wants to divide each of them into sections. How many 's are there in 2 bananas?
Answer:
Answer is 1
2 divided by 2
Step-by-step explanation:
John plans to practice piano at least 2 1/2 hours this weekend. if he practices 1 1/6 hours on Saturday and 1 1/4 hours on Sunday, will he meet his goal?
Answer:
No, it does not meet the goal. 2 hours and 10/24
The balance on Matthew’s gift card is $228. His card was debited by $178 from purchasing several items. What is the remaining balance on his card?
Answer:
50 dollars
Step-by-step explanation:
228-178=50
HELP DUE IN 20 MINUTES
Answer:
A = 30 cents or $0.30
B = $2.70
Step-by-step explanation:
i hope it helps
Answer: per lemon : $0.30, 9 lemons: $2.70
Step-by-step explanation: Ok so first if you wanna find the cost per lemon then you need to either divide or multiply for the longer way so what i did is divide and after i divided then i got $0.30 because if you multiply that by 5 it'll get you $1.50. So now for 9 lemons I just multiplied 0.30 by 4 so then after I got that answer i added it to the amount of dollars for 5 so it could be 9 lemons givin you the answer of $2.70 dollars.
ASAP! Which side lengths form a right triangle?
Choose all answers that apply:
Answer:
c
Step-by-step explanation:
4^2+7.5^2=8.5^2
Based on the diagram below, which of the following expressions is equal to π?
Answer: 3.14
Step-by-step explanation:
Answer:
none is equal to π
Step-by-step explanation:
no graph shown.
Can someone answer this please with an explanation.
Answer:
x=92
Step-by-step explanation:
those to angles are supplementary meaning that they add up to equal 180
so you set up the equation 180=x+x-4
180=2x-4
step 1 add 4 to each side
184=2x
step 2 divide each side by 2
x=92
so the angles equal 92 and 88
Answer:
92°
Step-by-step explanation:
180 degrees on a straight line.
2x - 4 = 180
2x = 184
X = 92°
geometry help, it’s easy!!!!!
Answer:
b
Step-by-step explanation:
all you do is divide 10.2 by tan (67) and you get 4.33
Answer: 4.33 I did the work.
find the area of the shape
Answer:
787.5
Step-by-step explanation:
23×14=322
A=a+b /2h=15+34 /2·19=465.5
322+465.5=787.5
Find the value of x AND the value of each angle.
Answer:
x=63
x+15=78
Step-by-step explanation:
180-102=78
78-15=63
x=63
x+15=78
What is the formula to find the area of a polygon?
To find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem.
you can watch this!!
https://youtu.be/n1YKOggLjUQ
what property is ( 3y + 7 ) + 6 = 6 + ( 3y + 7 ) .
Associative Property
Commutative Property
Distributive Property
Answer:
Commutive Property
Step-by-step explanation:
The numbers switched that's all
Answer:
Commutative property
Step-by-step explanation:
Change
Order
m
m
u
t
a
t
i
v
e
so basically you’re not changing the group ( associative ) and you’re not multiplying into the groups ( Distribuative ) so the only other option would be Commutative, and you’re changing the order of the numbers so it would be commutative.
Write the prime factorization of each number
5). 48
6). 20
7). 66
8). 34
Answer:
5). 4×4×3
6). 5×2×2
7). 11×3×2
8). 17×2
Step-by-step explanation:
These are the prime factorizations.
Jim makes $5 an hour at the surf shop. His boss gives him a one-time bonus of $50. Sarah makes $8 an hour at the clothes store. Her boss givers her a one-time bonus of $14. If they both work 15 hours, who will have a bigger paycheck?
Answer:
Sarah had the bigger paycheck of $134
Step-by-step explanation:
First we would need to find the total amount of money each one of them made in those 15 hours. We do this by multiplying their hourly rate by the hours worked and then adding the bonus
Jim: (5*15) + 50 = x
75 + 50 = x
125 = x
Sarah: (8 * 15) + 14 = x
120 + 14 = x
134 = x
Finally, we can say that Sarah had the bigger paycheck of $134 which is $9 more than Jim's
I have $1000 invested in a coin worth $43000. If the coin reaches $100000 how much will I have invested?
Answer:
$2326
Step-by-step explanation:
I have $1000 invested in a coin worth $43000. If the coin reaches $100000 how much will I have invested?
To solve the above question, we have:
$43,000 = $1000
$100,000 = x
Cross Multiply
43000 × x = 100,000 × 1000
x = 100000 × 1000/43000
x = $2325.5813953
Approximately = $2326
Therefore, If the coin reaches $100000 you would have invested $2326