Answer:
243.92cm³
Step-by-step explanation:
We have two shapes given in this question. A spherical ornament and a cubic box
Step 1
Find the volume of the Sphere
Volume of the sphere is given as
4/3 πr³
In the question, the radius of the sphere is given as = 4 centimeters.
Therefore,
Volume of the sphere = 4/3 × π × 4³
Volume of the sphere = 268.08cm³
Step 2
We have to find the length of the side or the edge of the cube.
It is important note that: because the spherical ornament is insides the cubic box,
Hence, the diameter of the spherical ornament = length of the side (edge) of the cube.
In the question we are given the radius of the sphere = 4 cm
Diameter = 2 × radius = 2× 4 cm = 8cm
Since,the diameter of the spherical ornament = length of the side (edge) of the cube,
The length of the side of the edge of the cube = 8cm
Step 3
We find the Volume of the cube
Volume of the cube = Length × Width × Height
Where the Length = Width = Height
Therefore, Voulme of the cube = 8cm × 8cm × 8cm
= 512cm³
Step 4
The fourth and final step is to find the space is left in the box to be filled with packing material.
The space left to be filled with packing material = Volume of the cube - Volume of the Spherical ornament
Volume of the cube= 512cm³ Volume of the Spherical ornament =
268.08cm³
Therefore, amount or Volume of space left for the packing material = 512cm³ - 268.08cm³
= 243.92cm³
Therefore, amount of space that is left in the box to be filled with packing material is 243.92cm³
The area of the remaining space for packing the material is 243.9 square cm.
What is a sphere?It is defined as three-dimensional geometry when half-circle two-dimensional geometry is revolved around the diameter of the sphere that will form.
[tex]\rm V = \dfrac{4}{3} \pi r^3[/tex]
The radius of the sphere = 4 cm
Side of the cube = 8 cm
The volume of the cube = 8×8×8 = 512 square cm
The volume of sphere = (4/3)π(4)³ = 268.082 square cm
Remaining space = 512 - 268.082 = 243.9 square cm
Thus, the area of the remaining space for packing the material is 243.9 square cm.
Learn more about the sphere here:
brainly.com/question/11374994
#SPJ5
Find the greatest common factor of 24, 40 and 60
Please answer asap ty!!
Answer:
4
Step-by-step explanation:
Answer:
GCF=4
Step-by-step explanation:
It's 4
24/4=6
40/4=10
60/4=15
You can't go any higher because there is no GCF of 6, 10, and 15.
Marsha has two cubes with one number on each side,each cube is numbered from 1 to 6 marsha rolls both number cubes at the same time. What is the probability that the total of numbers facing up will equal 12
Answer:
1/36
Step-by-step explanation:
If the cubes are numbered from 1 to 6 there is just one way that the sum of both of them equals 12 and this is when Marsha gets 6 in the first cube and 6 in the other.
Thus, to know what the probability that the total of numbers facing up will equal 12 we would have to calculate the probability that the first cube is 6 AND the second one is also 6.
The probability that the first cube has the number 6 is: 1/6
The probability that the second cube has the number 6 is: 1/6
We need to multiply this numbers because they both have to be 6 (rule of multiplication),
so: [tex]\frac{1}{6}(\frac{1}{6} )= \frac{1}{36}[/tex]
Thus, the probability that the sum of them equals 12 is 1/36
What is the distance between the points (4, 5) and (10, 13) on a coordinate plane?
A. 10 units
B. 14 units
C. 12 units
D. 8 units
Answer:
10
Step-by-step explanation:
Distance = √(x2-x1)² + (y2-y1)²
d = √(10-4)² + (13-5)²
d = √6² + 8²
d = √36+364
d = √100
d = 10
What is the end behavior of the polynomial function?
Answer:
D) as x approaches neg. infinity, y approaches neg. infinity
Step-by-step explanation:
This is because you get to negative x infinity which is towards the right, you see that the y value is going down sharply as well towards the direction of negative infinity in y direction (x direction is right to left and y direction is up and down)
Answer:
D one Edge 2021 ;))
Step-by-step explanation:
solve for x using the master product.
2x^2 + 7x – 9 = 0
Answer:
x = - 4.5, and x = 1
Step-by-step explanation:
~ Let us solve for x through factorization, but first change the equation to an expression for the simplicity ~
1. First break this expression into groups ⇒ ( 2x^2 - 2x ) + ( 9x - 9 )
2. Now factor 2x from 2x^2 - 2x ⇒ 2x ( x - 1 )
3. Now factor 9 from 9x - 9 ⇒ 9 ( x - 1 )
3. Combine these factored expressions ⇒ 2x ( x - 1 ) + 9 ( x - 1 )
4. Factor out common term x - 1 ⇒ ( 2x + 9 )( x - 1 )
5. Now add 0 to this expression as provided in the start: ( 2x + 9 )( x - 1 ) = 0
6. And now we recieve two answers, calculated through zero product property ⇒ 2x + 9 = 0 and x - 1 = 0, ⇒ 2x = - 9 and x = 1 ⇒
x = - 4.5, and x = 1
The solution of the given expression would be as x = - 4.5, and x = 1.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
First we have to break this expression into groups
[tex]( 2x^2 - 2x ) + ( 9x - 9 )[/tex]
Now factor 2x
2x ( x - 1 )
Now factor 9 from 9x
9 ( x - 1 )
Combine these factored expressions as;
2x ( x - 1 ) + 9 ( x - 1 )
Then Factor out common term;
( 2x + 9 )( x - 1 )
Then add 0 to this expression as provided in the start;
( 2x + 9 )( x - 1 ) = 0
By zero product property
2x + 9 = 0 and x - 1 = 0,
⇒ 2x = - 9 and x = 1
x = - 4.5, and x = 1
The solution of the given expression would be as x = - 4.5, and x = 1.
To know more about an expression follow;
brainly.com/question/19876186
#SPJ2
Someone help me please
Step-by-step explanation:
Step 1: Convert degrees into radians
[tex]\frac{degrees}{1}*\frac{\pi }{180}[/tex]
[tex]\frac{52}{1}*\frac{\pi}{180}[/tex]
[tex]\frac{52\pi}{180}[/tex]
[tex]\frac{13\pi}{45}[/tex]
Step 2: Find the arc length
[tex]S = r\theta[/tex]
[tex]S=(3)(\frac{13\pi}{45})[/tex]
[tex]S = \frac{39\pi}{45}[/tex]
[tex]S=\frac{13\pi}{15}[/tex]
Answer: Option B
What is the volume of a rectangular prism with a length of 12 feet, a width of 7 feet, and a height of 8 feet?
Answer:
672
Step-by-step explanation:
V=LWH
V=12*7*8
V=672
Answer:
672 ft cubed
Step-by-step explanation:
L x W x H = Area of a Rectangular Prism
12 x 7 x 8 = 672 ft cubed
A submarine at a depth of 675 feet below the surface rose to 1/3 this depth. Which of the following represents the new depth of the submarine below the surface?
Answer:
225
Step-by-step explanation:
Take 675/3 to find one third of its current depth. That gives you your answer. Does that make sense?
Graph f(x) = x and g(x) =
and g(x) =-1/3x+2
x on the same coordinate plane.
Hey there!
Let's think of both of these functions as two different slope-intercept equations (y=mx+b). Don't let all of the fs and gs confuse you; those are just showing that they are two different functions!
Our function f has an equation of y=x, which is a diagonal line that passes through the origin and goes across each small grid on the graph diagonally.
Our function g has an equation of y=-1/3x+2, which means that it will intersect with the y-axis at two units above the origin and for every three whole steps it goes to the right, it will have gradually gone down one whole step as well.
Attached to my answer is what a graph of it would kind of look like. Sorry if the lines don't look too much like a line it's a bit difficult to draw with a mouse haha!
I hope that this helps! Have a wonderful day!
At 8:00 am, it is 10 degrees outside. 12 hours later at 8:00 pm, it is -20 degrees outside. What is the difference in temperatures?
Answer:
-30
Step-by-step explanation:
Find the circumference of a circle whose area is 24 ft2
Answer: [tex]17.33ft[/tex]
Step-by-step explanation:
We need to go from area to radius to circumference.
Formula for the area:
[tex]A=\pi r^2[/tex]
Solve for r;
Divide by pi
[tex]r^2=\frac{A}{\pi}[/tex]
Extract the square root.
[tex]r=\sqrt{\frac{A}{\pi} }[/tex]
Plug in the value of the area.
[tex]r=\sqrt{\frac{24ft^2}{3.14} } \\r=2.76ft[/tex]
Now that you've found the radius, use the circumference formula to calculate it.
[tex]C=2\pi r\\C=2(3.14)(2.76ft)\\C=17.33ft[/tex]
Two random samples were taken to determine how often people in a community listen to the local radio station each month.
The first sample surveyed 15 people as they exited the bank on Main Street. The first sample found that the mean number of hours they listened to the radio each month was 20.
The second sample surveyed every sixth person as they exited the only local grocery store until 100 people were surveyed. The second sample found that the mean number of hours they listened to the radio each month was 12.
Which statements are true? Check all that apply.
A. The second sample is random.
B. The second sample is likely to be more representative of the population.
C. The first sample is likely to be more representative of the population.
D. The second sample will give a better representation because is it larger.
E. The first sample will give a better representation because it is smaller.
F. Community members are more likely to listen to the radio station an average of 12 hours a month than 20 hours a month.
Answer:
1 2 4 6. Tell me if im wrong.
Step-by-step explanation:
Answer:
yes the answer is 1 2 4 6
Step-by-step explanation:
What is the y-intercept of the quadratic function f(x) = (x-8)(x+3)
Answer:
-24
Step-by-step explanation:
To find the y intercept, plug x in as 0.
Answer:
-24
Step-by-step explanation:
Y intercept is where graph cuts the y axis and it satisfies x=0
So put x=0 in your equation
F(0)= -8 x 3
F(0)= -24
Therefore y-intercept= -24
Find the greatest common factor.
бах2 + бах + ба
Answer:
6a
Step-by-step explanation:
The GCF (Greatest Common Factor) is a number/variable that you can take out of all of the terms in the expression.
In this case, each term in this expression has a 6, and an a, but not all have an x, so we only take out:
6a
By taking 6a, you get:
6a([tex]x^2[/tex] + x + 1)
what's the change in Dana's profit from Saturday to sunday? simplify the expression
Answer:
14 did this lesson rn
Step-by-step explanation:
The required change in Dana's profit is given as $12, as of the given condition.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
On Saturday Dana's profit = -$2
On Sunday Dans;s profit = $12
Change in Dana's profit = 12 - 2 = $12
Thus, the required change in Dana's profit is given as $12.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ2
These two I don’t know
Answer:
In this subtraction, PR5T and 47Y6 represent 4-digit numbers. What number does PR5T represent?
PR5T - 47Y6 = 1998
Step-by-step explanation:
3. Find x, y, and z.
zº
xº
y
18°
64°
Answer:
[tex]y = 18 \: \: degrees[/tex]( vertically opposite angles)
[tex]x = 64 \: \: degrees[/tex]
[tex]y + z + x = 180 \\ 18 + z + 64 = 180 \\ 82 + z = 180 \\ z = 180 - 82 \\ z = 98 \: \: degrees[/tex]
i really need help guys can some one plz help me it's for 10 points
Answer:
[tex]\sqrt{8}----- 2units,2units[/tex]
[tex]\sqrt{7} ------\sqrt{5}units,\sqrt{2}units[/tex]
[tex]\sqrt{5}-------1unit,2units[/tex]
[tex]3------2units, \sqrt{5}units[/tex]
Step-by-step explanation:
Use pythagorean's theorem to solve each pair individually.
The instructions say that you have the two sides (a and b) and you have to match it with their hypothenuse.
[tex]Formula: c^2=a^2+b^2[/tex]
1. [tex]a=\sqrt{5}, b=\sqrt{2}[/tex]
Plug this into the formula.
[tex]c=\sqrt{(\sqrt{5} )^2+(\sqrt{2})^2 }[/tex]
The square here eliminates the roots.
[tex]c=\sqrt{5+2}\\ c=\sqrt{7}[/tex]
2. [tex]a=\sqrt{3}, b=4[/tex]
[tex]c=\sqrt{(\sqrt{3} )^2+(4)^2}\\ c=\sqrt{3+16}\\ c=\sqrt{19}[/tex]
3. [tex]a=2, b=\sqrt{5}[/tex]
[tex]c=\sqrt{(2)^2+(\sqrt{5})^2 }\\ c=\sqrt{4+5}\\ c=\sqrt{9}\\ c=3[/tex]
4. [tex]a=2, b=2[/tex]
[tex]c=\sqrt{(2)^2+(2)^2}\\ c=\sqrt{4+4}\\ c=\sqrt{8}[/tex]
5. [tex]a=1, b=2[/tex]
[tex]c=\sqrt{(1)^2+(2)^2}\\ c=\sqrt{1+4}\\ c=\sqrt{5}[/tex]
Reid has a bag that contains fruit. The bag contains 16 pineapple 17 pomegranates and 12 melons. what is the probability pulling pomegranate out of the bag?
Answer:
17/45
Step-by-step explanation:
Answer:
is your brainly working?
Step-by-step explanation:
81-4x^2
please explain how you got your answer
Answer:
b = 2 x .
(9+2x) (9-2x)
Step-by-step explanation:
Since both terms are perfect squares, factor using the difference of squares formula, a 2 − b 2 = ( a + b ) ( a − b )
Answer:
Step-by-step explanation:
81 - 4[tex]x^{2}[/tex]
notice how this is difference of squares, meaning you can simplify
(9-2x) (9+2x)
if the question is asking to find roots, then you just set this equal to 0, and that means that either 9-2x or 9+2x must be equal to 0.
9-2x = 0 9+2x = 0
9 = 2x 9 = -2x
x = 4.5 x = -4.5
Therefore the two roots of this equation are ±4.5
4
Select the correct answer from each drop-down menu.
A line parallel to the
has no defined slope, and a line parallel to the
has a slope of zero.
X-axis
Reset
Next
y-axis
020 Edmentum. All rights reserved.
Com
Answer:
Step-by-step explanation:
A line parallel to y-axis has no defined slope and line parallel to x-axis has a slope of zero.
A house is valued at 213,000.After several years,the value increased by 8%.How much did the house value increase in dollars?.What is the current value of the house?
Answer:
The house value increase by $17,040 in dollar terms
The current value of the house $ 230,040
Step-by-step explanation:
The increase in value of the house can be determined as the difference between the value of the house now after 8% increase in value and the earlier value of $213,000
new value=earlier value *(1+% increase in value)
% increase in value is 8%
new value=$213,000*(1+8%)
=$213,000*1.08=$230,040.00
increase in value= $230,040-$213,000=$17,040
The increase in value of the house of 8% translated into a dollar value of $17,040
What if the slope of the line ?
Answer:
The slope of the line is 1
Step-by-step explanation:
To figure out the slope, you just have to do rise over one, if the line is going up from left to right then the slope is positive, which is the case shown
When a cycle is sold allowing 10% discount on its marked
price a seller gains 5% and allowing 5% discount the profit is
Rs 351. Find the cost price of the cycle. (Ans: Rs. 3240)
The cost price of the cycle is Rs.3240
Represent the cost price of the cycle with x and the selling price with y
A gain of 5% when the marked price is at a discount of 10% implies that:
[tex]5\%=\frac{(1 - 10\%)y-x}{x}[/tex]
Express 10% as decimal
[tex]5\%=\frac{(1 - 0.10)y-x}{x}[/tex]
[tex]5\%=\frac{0.90y-x}{x}[/tex]
Express 5% as decimal
[tex]0.05=\frac{0.90y-x}{x}[/tex]
Cross multiply
[tex]0.05x=0.90y-x[/tex]
Collect like terms
[tex]x + 0.05x=0.90y\\[/tex]
This gives
[tex]1.05x=0.90y[/tex]
Make y the subject of the formula
[tex]y = \frac{1.05x}{0.90}[/tex]
Also, when the discount is 5% and the profit is 351, we have:
[tex]351=(1 - 5\%)y -x[/tex]
Express 5% as decimal
[tex]351=(1 - 0.05)y -x[/tex]
This gives
[tex]351=0.95y -x[/tex]
Make y the subject
[tex]0.95y = 351 + x[/tex]
Substitute [tex]y = \frac{1.05x}{0.90}[/tex]
[tex]0.95 \times \frac{1.05x}{0.90} = 351 + x[/tex]
[tex]\frac{0.9975x}{0.90} = 351 + x[/tex]
Subtract x from both sides
[tex]\frac{0.9975x}{0.90} -x= 351[/tex]
Take LCM
[tex]\frac{0.9975x - 0.9x}{0.90}= 351[/tex]
[tex]\frac{0.0975x}{0.90}= 351[/tex]
Multiply both sides by 0.90
[tex]0.0975x= 315.9[/tex]
Divide both sides by 0.0975
[tex]x= 3240[/tex]
Hence, the cost price of the cycle is Rs.3240
Read more about discounts and price at:
https://brainly.com/question/13651341
what is the solution of this equqtion? 1w= -17
Answer:
-17
Step-by-step explanation:
1w= -17
(1)(-17)=
-17
Answer:
-17
Step-by-step explanation:
in this situations, we normally divide both sides by the number next to the unknown.
1w is the same as saying w
so,
w = -17
Will give brainliest! I only need e f and g done!!!!
Answer:
E) the new price is going to be $3.92
Work: 3.50 × 12 / 100 = 0.42
3.50 + 0.42 = 3.92
F) Dont understand what this one is asking
G) You would save 1.03$ with the 10% off.
Work: 10.3 x 10 / 100
103 / 100
$1.03
hope this helps
help me plzzzzzzz!!!!
[tex] {y}^{2} + 14 = 3 {y}^{2} \times 5[/tex]
Answer:
[tex]y=1,\:y=-1[/tex]
Step-by-step explanation:
[tex]y^2+14=3y^2\cdot \:5\\\y^2+14-14=3y^2\cdot \:5-14\\y^2=15y^2-14\\y^2-15y^2=15y^2-14-15y^2\\-14y^2=-14\\\frac{-14y^2}{-14}=\frac{-14}{-14}\\y^2=1\\\\y=\sqrt{1},\:y=-\sqrt{1}\\y=1,\:y=-1[/tex]
Answer:
y = ± 1
Step-by-step explanation:
Given
y² + 14 = 3y² × 5, that is
y² + 14 = 15y² ( subtract y² from both sides )
14 = 14y² ( divide both sides by 14 )
1 = y² ( take the square root of both sides )
± [tex]\sqrt{1}[/tex] = y , that is
y = ± 1
Thus y = - 1 or y = 1
find the variable: n/14=3
Answer:
n=42
Step-by-step explanation:
3. Which of the following represents a function?
O (5, 1), (5,2), (5, 3), (5, 4)
O (-1,2), (-2, 1), (-1, -2), (-2,-1)
O (3, 4), (-3, 2), (3, 8), (5,5)
O (2, 3), (4, 3), (-2, -3), (-4,-3)
Answer: D is a function.
Step-by-step explanation:
A function need to have exactly one output to each input.
Answer: D. (2, 3), (4, 3), (-2, -3), (-4,-3)
Step-by-step explanation: This represents a function because they're the opposing of each other. Hope this helps happy holidays! :)
find the area of the following trapezoid
Answer:
12
Step-by-step explanation:
Answer:
82 cm is the area of trapezoid
