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 %.
I NEED THE SLOPE INTERCEPT FORM!!! ITS DUE BY 12
Answer: y = 4x -1
Step-by-step explanation:
Given by the graph.
Y axis
and rise over run.
HELPPP PLZ :(( I WILL MARK BRAINLIEST PLZZZ
Answer:
y = -3/2x + 2
The line starts on (0,2) and then it run 3 spaces down and 2 spaces to the right. Hope this helps, thank you !!
HELP PLEASE!
A large pine tree was struck by lightning and fell as shown by the diagram below. Which equation could be used to find the length of the fallen part of the tree
Answer:
Option C should be the answer.
what is the y-value
y = 6x – 3
x+2y = 7
Answer:
i love algebra anyways
the ans is in the picture and the steps how got it
(hope it helps can i plz have brainlist it will make my day :D hehe)
Step-by-step explanation:
what's 4/6 in decimal form
is this exponential growth or decay y=6e^-x
Answer: It's always decreasing/decaying.
Step-by-step explanation: To find if it is increasing or decreasing, graph the exponential problem.
1. Start at the top.
2. Look at the exponent.
The exponent is -x. Since negative means opposite/down, it goes down.Therefore, it's always decaying.
Answer choices: 3,80,6,2,100.
Alan, Bobby and Chris are comparing their ages. The ratio of Alan's age to
Bobby's is 7: 8 and the ratio of Bobby's to Chris' is 5: 4. If Alan is 70, how
old is Chris?
Answer:
1638392772127273930337733930282823829393
Distribute and simplify the radicals below.
Help me please I really needed it
What is the value of x in the equation 2.5(6x - 4) = 10 + 4(1.5 +0.5 x)?
3
이를
02
0 13
Answer:
Step-by-step explanation:
15x - 10 = 10 + 6 + 2x
15x - 10 = 16 + 2x
Bringing like terms on one side
15x - 2x = 16 + 10
13x = 26
x = 26/13
x = 2
The value of x in the equation is 2.
Option C is the correct answer.
What is an equation?An equation is a mathematical statement that shows that two expressions are equal.
It consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. Equations are used to solve problems and find unknown values.
We have,
We are given the equation 2.5(6x - 4) = 10 + 4(1.5 + 0.5x) and we need to find the value of x that satisfies this equation.
First, we can simplify both sides of the equation by using the distributive property of multiplication.
This gives us:
15x - 10 = 10 + 6 + 2x
Next, we can combine like terms on both sides of the equation. Specifically, we can combine the constants on the right-hand side:
15x - 10 = 16 + 2x
Now, we want to isolate the term with x on one side of the equation.
We can do this by subtracting 2x from both sides of the equation:
13x - 10 = 16
Finally, we can solve for x by adding 10 to both sides of the equation and then dividing both sides by 13:
13x = 26
x = 2
Therefore,
The value of x in the equation is 2.
Learn more about equations here:
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Please do number 16 for me. (With work)
Answer:
m<5 = 75°
Step-by-step explanation:
16. Given:
m<1 = 75°; m<3 = 40°
Required:
m<5
Solution:
Since lines A and B are parallel, and m<1 corresponds to m<5, therefore,
m<1 = m<5 (corresponding angles are congruent)
m<1 = m<5 = 75°
m<5 = 75°
What is the equation for the line in slope -intercept form?
Answer:
I can't see it
Step-by-step explanation:
We need a bigger picture.
Show work pls for briskly
Answer:
She'll make 6 yard sticks
as,
1/2 yard = 1 pillow
1 yard = 1 * 2 / 1 = 2
so,
3 yard = 3 * 2
Hope this helped
Hope this helped ALL THE BEST !!
Answer:
6 pillows
Step-by-step explanation:
1/2*3=3
La suma de las edades de los hermanos Carlos y Felipe es igual a la edad de su tía María; Si María tiene 29 años y Carlos tiene 13 años, ¿Cuántos años tiene Felipe?
Answer:
16 años
Step-by-step explanation:
Si la suma de la edad de Carlos y Felipe es igual a la de Maria, y en la pregunta nos dan la edad de Maria (M) y Carlos (C), entonces tenemos que encontrar la edad de Felipe. Para calcular esto necesitamos restar la edad de Carlos de la edad de Maria. Esto nos dara la edad exacta de Felipe (f).
M - C = f
29 - 13 = f
16 = f
Finalmente, vemos que la edad de Felipe es de 16 años
What is the value of the 3 in 16.35 ?
Answer:
3 tenths
Step-by-step explanation:
The face and place value of 3 in the decimal number 16.35 is, 3 and 3×10⁻¹.
What is the standard decimal form of numbers?The standard decimal form of numbers is written in base 10 as there are 10 different numbers from 0 to 9.
Each digit has a face value and a place value.
We know, A number has two values face value and place value,
Given, A decimal number 16.35.
Now, The digit 3 is one digit after the decimal,
So, It has a face value of 3 and a place value of 3×10⁻¹.
learn more about face value and place value here :
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Jay mows 1 lawn everyday Monday through Saturday.He is paid $25 for each lawn.How much money does jay earn mowing lawns ?
Answer: $150
Step-by-step explanation: do 25x6 on a calculator
Sue decided to interview two of the six city council members. She labeled their names from 1 to 6, then rolled a six-sided die until she got two different numbers telling her which to interview. Is this sample of the city council members likely to be representative? yes no
Answer:
Step-by-step explanation:
This question seems a lot harder than it actually is since in the end of the day, she ends up interviewing 2 council members.
2 is 1/3 of 6 since 2/6 = 1/3
So there is a 33.3333... % or 1/3 chance that one of the 2 members she interviewed got chosen as representative.
Hope i could help you understand :D
If 6 is multiplied by the sum of a number and 5, the result is 30. Which equation could be used to find the value of the number?
Answer:
5x6
Step-by-step explanation:
5x6
5 groups of 6
=30
Can someone help please??
If 3x−y=12, what is the value of
8x/2y ?
A) 2 to the 12th power
B) 4 to the 4th power
C) 8 to the 2nd power
D) The value cannot be determined from the information given.
Answer:
A) 2 to the 12th power
Step-by-step explanation:
[tex] \frac{8x}{2y} = \: \frac{ {2}^{3x} }{2y} = {2}^{12} [/tex]
Let s represent the price of a meal in the local
coffee shop. Diana leaves a tip of 15%. Which
expression represents the total amount Diana
pays?
A- 1.15s
B- s
C- 15s
D- s+15
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
15% equals 0.15 so her total would be The price of one meal plus 0.15 or 1.15s.
Which shows the image of rectangle ABCD after the rotation (x, y) → (–y, x)?
Answer:
The answer is A
Step-by-step explanation:
I got it right
Answer:
Answer choice A is correct.
Step-by-step explanation:
I'm smort UwU
Simplify: (4 – 5) – (13 – 18 + 2).
Answer:
2
Step-by-step explanation:
(4 - 5) - (13 - 18 + 2)
According to PEMDAS, we should simplify the parentheses first.
= (-1) - (-3)
When you subtract a negative number, you are actually adding.
= -1 + 3
Now, add.
= 2
Hope this helps!
Can you do no7 doesn’t matter if u do just one part everything will help
The probability of a fair coin landing heads-up in one toss is 1/2.If a coin is
tossed 20 times, how many times would the coin be expected to land heads-
up?
20
1
10
2
Answer:
10/20 because then it's still a 50 50 chance so the answer it 10
-3x>18
(not in high school in middle school)
Answer:
x<-6
Step-by-step explanation:
-3x>18
Divide by -3, flip the sign since dividing by a negative.
x<-6
Answer:
x < -6
Step-by-step explanation:
Please answer!!
What is the perimeter of parallelogram WXYZ?
The perimeter is (Type an integer or a decimal.)
Answer:
196
Step-by-step explanation:
simplify the following 7+(-10)
Answer:
-3
Step-by-step explanation:
Seven plus negative ten is the same as seven minus 10. 7-10=-3
Answer:
-3
Step-by-step explanation:
all you have to do is switch the 10 and 7 and you get -10+7. then subtract the two and use the sign of the bigger number which is a negative sign
What is the equation, in point-slope form, of the line passing through the point (-5, 9) with a slope of -1/4?
Answer:
y = -1/4x + 7.75
Step-by-step explanation:
plug in the point
y = mx + b
9 = -1/4(-5) + b
9 = 5/4 + b
b = 31/4 (7.75)
plug b back into the equation
A cell phone retailer used a mark-up rate of 60% on a cellphone case that originally cost $5. To find the new price of the case in ONE STEP, my equation Part = %*whole will be...
Answer:
$8
Step-by-step explanation:
5 increase 60% =
5 × (1 + 60%) = 5 × (1 + 0.6) = 8
PLEASE HELP ASAP!!
Please could I have the answers or step by step I don’t mind just PLEASEE help asap!!