Answer:
The baseball's volume will be less than the number of cubic inches in the display case. The cube's edge will be 8.
2. If a sphere fits snugly inside this cube, what is its volume?
the volume of a cube is the side^3, 512^(1/3)=8. 3. 4/3pi(r^3)/512,
3. What fraction of the cube is taken up by the sphere? What percentage is this? Explain or show your reasoning.= the radius will be 4 since the edge of the cube is 8. 4/3pi(4^3)/512, so pi/6 when simplified or 52.3598%.
Step-by-step explanation:
a) The side length of the cube with volume V = 512 units³ is a = 8 units
b) The volume of the sphere is V₁ = ( 4/3 )π ( 4 )³
c) The faction of the cube taken up by the sphere is A = 52.35 %
What is the Volume of a Cube?The formula of volume of the cube is given by:
Volume of Cube = a x a x a
Volume of Cube = a³
where a is the length of its sides or edges
Given data ,
a)
Let the volume of the cube be represented as V
Now , the value of V is V = 512 unis³
And , Volume of Cube = a³
On simplifying , we get
512 = a³
Taking cube roots on both sides , we get
a = ∛512
a = 8 units
Therefore , the side length of the cube is 8 units
b)
The volume of the sphere is V₁ = ( 4/3 )πr³
Now , the radius of the sphere is r = a/2 = 4 units
And , volume of the sphere is V₁ = ( 4/3 )π ( 4 )³
c)
Let the fraction of the cube is taken up by the sphere be A
And , A = volume of sphere / volume of cube
On simplifying , we get
A = ( 4/3 )π ( 4 )³ / 512
On further simplification , we get
A = ( 4 )⁴ / 1536 ( π )
A = 0.5235
So , the value of A is 52.35 %
Therefore , the fraction of the cube is taken up by the sphere is 52.35 %
Hence , the volume of cube is 512 units³ and the side length is 8 units
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Point P is located at (–4, –7). P is reflected across the x-axis to create P'. In which quadrant is P' located? Quadrant I Quadrant II Quadrant III Quadrant IV
Answer:
The answer is: B) Quadrant IIStep-by-step explanation:
The point P' lies in II Quadrant.
What is Transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
We have,
Point P is located at (–4, –7) and P is reflected across the x-axis to create P'.
Here we can see P (-4, -7) lies in third quadrant.
So, if we reflect it across x -axis to create P' then it would be in Second quadrant.
Then, the point P' lies in II quadrant and P (-4, -7) would be P'( -4 , 7).
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2) Write
algorithm to find
to find the value of
the expression (a+b)2 = (a +b) x (a+b)
Answer:
(a+b)2 = a² + b² + 2×a×b
Step-by-step explanation:
What is the first step in solving the following system of equations?
3 x + y = 23. 8 x + 2 y = 23.
Substitute the value of y from one equation into the other equation.
Solve the first equation for y.
Subtract the second equation from the first equation.
Substitute the value of x from one equation into the other equation
Answer:
B
Step-by-step explanation:
its b solve the first equation for y \
hope this helps
brainliest would be appreciated
Answer:
B. Solve the first equation for y
Step-by-step explanation:
If x – 9 is a factor of x2 – 5x – 36, what is the other factor?
Answer: (x+4)(x−9)
Step-by-step explanation:
Answer:
(X - 9) is one factor
(X + 4) is the other factor
Step-by-step explanation:
You can factor polynomials with guess work or with polynomial division
To factor using guess work search for a number that will multiply with -9 to equal -36 and add with -9 to equal -5.
In order for -9 to add with another number and equal -5 you need to add 4 to it. And because -9 will multiply with 4 to equal -36 as well, 4 is confirmed to be the other factor. You can write out the factor as (x + 4)
On a coordinate plane, 2 polygons are shown. Polygon A B D C has points (negative 5, 2), (negative 3, negative 1), (negative 3, 1), and (negative 1, 2). Polygon A prime B prime D prime C prime has points (negative 3, 3), (1, negative 3), (1, 1), and (5, 3).
Which composition of similarity transformations would map polygon ABDC to polygon A'B'D'C'?
a dilation with a scale factor greater than 1 and then a translation
a dilation with a scale factor greater than 1 and then a rotation
a dilation with a scale factor less than 1 and then a reflection
a dilation with a scale factor less than 1 and then a translation
Answer: A.) a dilation with a scale factor greater than 1 and then a translation
Step-by-step explanation: i hope this helps :)
Determine whether the system of equation has one solution, no solution, or infinitely many solutions. PLS ANSWER
Mathematics Fractions please help quickly
Answer:
= 1/5, 5/8, 2/3
Step-by-step explanation:
Arrange from least to greatest (small to large)
2. 1/5, 2/3, 5/8
change the fraction into decimal for easy ranking
0.2, 0.67, 0.63
= 1/5, 5/8, 2/3
3. 1/2, 2/5, 6/10
0.5, 0.4, 0.6
= 2/5, 1/2, 6/10
4.
4/5 inch, 3/12 inch, 5/6 inch
From least to largest
0.80, 0.25, 0.83
= 3/12 inch , 4/5 inch, 5/6 inch
Please help it's Geometry!
Answer:
B
Step-by-step explanation:
15^2= 225
23^2 = 529
225+529= 754
28^2= 784
They aren't equal
What do the symbol mean
Answer:
≤ and ≥ means bigger / smaller or even.
x≤23 means that x is either smaller than 23 or it is 23
x≥23 means that x is either bigger than 23 or it is 23
< and > means bigger / smaller
x<23 means that x is smaller than 23
x>23 means that x is bigger than 23
hope it helps (:
Write the mRNA strand for the given DNA strand.
GAAGCGATCAGTTACG
ATGTCGCTGATACTGT
AATGAATAGCTAGCTT
Answer:
CUUCGCUAGUAAUGC
UACAGCGACUAUGACA
UUACUUACGAUCGAA
Step-by-step explanation:
guanine goes with cytosine
thymine turns into adenine
adenine turn into uracil
NOTE uracil is not found in dna
g(x)=x-1
f(x)=x² +3 + x
Find g(x) - f(x)
Answer:
-(x^2 + 4)
Step-by-step explanation:
x - 1 - ( x^2 + x + 3 )
x - 1 - x^2 - x - 3
-x ^2 - 4
-(x^2 + 4)
solving systems of equations by graphing
Answer:
Hi! The correct answer is x = -1 y = -1 and the ordered pair is (-1,-1)
Step-by-step explanation:
~Solve the first variable in one of the equations, then substitute the result into the other equation~
Corresponding angles are
Answer:
Angles that are congruent and have the same value
Step-by-step explanation:
Answer: angles on the same side of the transversal and also have the same degree of measurement
Step-by-step explanation:
Round 3.023 to the nearest meter
Answer:
if it is nearest whole number it is 3
Step-by-step explanation:
Please please please help
Answer:
All in fractional form is irrational and all those not in fractional form is rational.
Step-by-step explanation:
can someone answer this please
Answer:
Range: (-∞, 0]
General Formulas and Concepts:
Algebra I
Range is the set of y-values that are outputted by function f(x)Step-by-step explanation:
When we graph the equation, we should see that our y-values span from -∞ to 0. Since 0 is a closed dot, it is inclusive in the range:
(-∞, 0] or y ≤ 0
I need help fast.. pls help me
The length of the base of an isosceles triangle is x. The length of a leg is 4x-6. The perimeter of the triangle is 96. Find x.
Answer:
12 units
Step-by-step explanation:
base is x
one of the legs measure 4x-6
therefore, perimeter is equal to
2 (4x - 6) + x = 96
8x - 12 + x = 96
9x = 96 + 12
9x = 108
x = 108/9 = 12 units
Help please due today
WILL GIVE BRAINLISY IF SOMEONE Answers
Answer: 1
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
A movie theater sells popcorn and fountain drinks. Brett buys 1 popcorn bucket and 3 fountain drinks for his family, which costs him a total of $12.50. Sarah buys 3 popcorn buckets and 4 fountain drinks for her family, which costs her a total of $23.75. If p represents the number of popcorn buckets and d represents the number of drinks, then the system of equations
Answer: the systems of equations to solve the unit price of popcorn and rinks are
1 p + 3 d= 12.50---- equation 1
3 p + 4 d= 23.75 ---- equation 2
The price of A popcorn bucket = $4.25 and price of 1 fountain drink = $2.75
Step-by-step explanation:
Step 1
If p represents the number of popcorn buckets
and d represents the number of drinks,
The expression that Brett buys 1 popcorn bucket and 3 fountain drinks for his family, which costs him a total of $12.50 becomes
1 p + 3 d= $12.50
and The expression that Sarah buys 3 popcorn buckets and 4 fountain drinks for her family, which costs her a total of $23.75 becomes
3 p + 4 d= $23.75
such that the systems of equations to solve the unit prices of popcorn and drinks are
1 p + 3 d= $12.50---- eqn 1
3 p + 4 d= $23.75 ---- eqn 2
Step 2
1 p + 3 d= $12.50---- eqn 1
3 p + 4 d= $23.75 ---- eqn 2
Multiplying equation 1 by( 3 )
1 p + 3 d= $12.50---- eqn 1 x 3
3p+ 9d= 37.5----- equation 3
and subtracting equation 2 from equation 3 becomes
3p+ 9d= 37.5----- equation 3
- 3 p + 4 d= $23.75
5d= 13.75
d= 13.75/5
d= 2.75
to find p, sinceaa d = 2.75,
1 p + 3 d= 12.50
1 p + 3 x 2.75= 12.50
p= 12.50-8.25
p=4.25
THerefore the price of popcorn = $4.25 and price of drinks = $2.75
2/4 plus 1/3 as a fraction
Answer: 5/2
Step-by-step explanation:
5/6 is the answer for 2/4 plus 1/3. A fraction represents a part of whole.
We need to find value of 2/4+1/3
What is fraction?A fraction represents a part of whole
We need to add two fractions i.e 2/4 plus 1/3
We need to find LCM of 4 and 3.
12 is the LCM of 4 and 3.
=(6+4)/12
=10/12
=5/6
Therefore 2/4+1/3 is 5/6
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The ____states that in a right triangle the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
Answer:
pythagorean theorem
Step-by-step explanation:
can u help me pls it’s urgent
Answer:
The equation is y=x+3 !
Step-by-step explanation:
The y-intercept is 3, and the slope is 1/1, so you can just put x!
IF UR SMART PLEASE HELP ME OUT, I CANT FAIL MAN
PLEASEEEE
Just a quick question:
I'm doing a math problem regarding exponential decay, where the number of acres in a rainforest starts at 800 square miles, and decreases by 20%. Because it's decreasing, would that mean that the equation would be [tex]800(0.2)^x[/tex]?
You need to subtract the rate of decay from 1.
The equation would be 800(1-0.2)^x = 800(0.80)^x
what is prime factorization and how do I solve this question???
Answer:
rime factorization or integer factorization of a number is breaking a number down into the set of prime numbers which multiply together to result in the original number Step-by-step explanation:
so for that you do 3 x 7 which is 21 x 2= which is 42 and on the the other right side you write 2 and the bottom you just write 2 please mark brainliest
Given that 1 inch = 2.54 cm, how many centimeters are there in 5 feet? Answers may be written using decimal form and should be rounded to the nearest hundredth when necessary.
Answer:
152.4
Step-by-step explanation:
60 * 2 then 60 * 0.5 then 60 * 0.04
120 + 30 + 2.4
!!NEED URGENT MATH HELP!! Please help me this is due in like 30 min and I have no idea how to do it. I will name u brainliest and like ur answer and give a 6 stars and try to answer any question you have asked. Please help and ty! :) <3
Answer:
Step-by-step explanation:
Maybe try asking yourself what problem you need more then keep working tell me if you need anything else:)
Answer:
Here u are
Step-by-step explanation:
Yes i does represent a linear equation because all the numbers are according to there point. Ur welcome
factor the polynomial 5x^4+10x^3+15x^2
Answer:
5x²(x² + 2x + 3)
Step-by-step explanation:
