Answers
Answer:
D. 288π
Step-by-step explanation:
Volume = [tex]\frac{4}{3}[/tex]π[tex]r^3[/tex]
A = π [tex]\frac{4}{3} (6)^3[/tex]
A = π [tex]\frac{4}{3} (216)[/tex]
A = 288π
I hope this helps!
Related Questions
A rectangle has a width that is 5 feet less than the length. The area of the rectangle is 126 square feet. Find the dimensions of the rectangle
Answers
Given:
A rectangle has a width that is 5 feet less than the length. The area of the rectangle is 126 square feet[tex]\\[/tex]
❍Let's assume, Length of rectangle x feet and width of the rectangle x - 5 feet respectively.
[tex]\\[/tex]
To calculate the dimensions of the rectangle we will use the formula of Area of rectangle:
[tex]\\[/tex]
[tex] \: \: \: \: \: \: \: { \underline{ \boxed{ \pmb{ \frak{ Area_{(rectangle)} = Length \times width }}}}} \\ \\ [/tex]
[tex]\\[/tex]
[tex] \underline {\sf{Substituting \: the \: values~ in~ above~formula: }} \\ [/tex]
[tex]\\[/tex]
[tex] : \implies \sf \:x \times (x - 5) = 126 \\ \\ \\ : \implies \sf \:x^2 - 5x = 126 \\ \\ \\ : \implies \sf \:x^2 - 5x - 126 = 0 \\ \\ \\ : \implies \sf \:x^2 - 14x - 9x - 126 = 0 \\ \\ \\ : \implies \sf \:x (x - 14) - 9 (x + 14) = 0 \\ \\ \\ : \implies \sf \:(x - 14)(x - 9) = 0 \\ \\ \\ : \implies { \boxed { \purple{\pmb { \: x = 14 \: \: or \: \: x = -9}}} } \\ \\ \\ [/tex]
We know that side can't be negative. So, x = 14 feetHence,
Width of rectangle = x - 5 = 9 feetLength of rectangle = x = 14 feet[tex]\\[/tex]
[tex] \\ { \underline{ \pmb{ \frak{\therefore Dimensions \: of \: rectangle \: are \: 9~ feet \: and \: 14 ~feet \: }}}}[/tex]
Given that, width of the rectangle is 5 feet less than the length and area of the rectangle is 126 sq. feet, and we are told to find the dimensions i.e the length and width of the rectangle.
As we know that the area of a rectangle is length times it's width, so if we assume our length to be x, so our width is just going to be (x - 5) , and putting it in the area formule we can thus obtain;
[tex]{:\implies \quad \sf x(x-5)=126}[/tex]
[tex]{:\implies \quad \sf x^{2}-5x-126=0}[/tex]
[tex]{:\implies \quad \sf x^{2}-14x+9x-126=0}[/tex]
[tex]{:\implies \quad \sf x(x-14)+9(x-14)=0}[/tex]
[tex]{:\implies \quad \sf (x-14)(x+9)=0}[/tex]
So, here either (x - 14) = 0 or (x + 9) = 0, when you equate both, you will get x = 14 or -9 but as x ≠ -9, so x = 14, and then x - 5 = 14 - 5 = 9
Hence, the required length and width are 14 feet and 9 feet respectively
which fraction is between 2/3 and 6/7
Answers
Answer:
For example, 16/21
Step-by-step explanation:
Are there choices?
There is an infinite number of numbers between any two numbers.
2/3 = 14/21
6/7 = 18/21
One example of a fraction between 2/3 and 6/7 is 16/21
16/21 is between 2/3 and 6/7.
Which problem solving strategy would be best to solve this problem?
Your friend's house is 12 miles from your home. Your school is one-third the way from your friend's house and your home. The park is one-fourth the way from the school to your friend's house. How far is the park from your home?
A. guess, check and revise
B. write an equation
C. make a table, chart or list
D. make a model or diagram
Answers
The speed of the jet Alyssa flew on from Boston to London was 480 mph. on her return flight, the speed of the jet was 600mph with a tail wind. What was Alyssa's average speed on the round trip?
Answers
Based on the speed Alyssa used to get to London and the speed back to Boston, the average speed was 540 mph.
What is the average speed?The average speed that Alyssa was going can be found by the formula:
= (Initial speed + Final speed) / 2
Solving gives:
= (480 + 600) / 2
= 1,080 / 2
= 540 mph
In conclusion, Alyssa's average speed was 540 mph.
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find the x-intercept of the following linear equation -2x + 3y = 12
Answers
Answer:
X = 6
Step-by-step explanation:
Hope this helped!!
maybe mark brainiest
solve for the x in the triangle .
Answers
In all triangles the angles must add up to 180 so 68 + 90 =158 + 22 =180
The scale factor of a figure and its enlargement is 4. what is the new length of the enlarged figure if the original length is 4.5 cm? 4.0 cm 8.5 cm 16 cm 18 cm
Answers
The new length of the enlarged figure will 18 cm.
What is scale factor?A scale factor is a number which scales, or multiplies, the original figure by some quantity.
We have the equation for the scale factor.
Y=Cx
C is a scale factor for x. It is called the constant of proportionality or scale factor of y to x.
As the given length is 4.5 cm, so with a scale factor of 4, the length of the enlarged figure will be
[tex]Y=4.5\times4=18\ cm[/tex]
Therefore, the new length of the enlarged figure will 18 cm.
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Line n goes through points A and B. What is the slope of line n?
Point A;(4,7)
Point B:(18,17)
Answers
Answer:
The slope is 5/7.
Step-by-step explanation:
Use a slope formula.
Slope:
[tex]\sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]
y₂ = (17)
y₁ = (7)
x₂ = (18)
x₁ = (4)
Rewrite the problem down.
[tex]\sf{\dfrac{17-7}{18-4}=\dfrac{10}{14}={\dfrac{10\div2}{14\div2}=\boxed{\sf{\dfrac{5}{7}}}[/tex]
Therefore, the slope is 5/7.
I hope this helps! Let me know if my answer is wrong or not.
Answer:
5/7
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(17-7)/(18-4)
m=10/14
simplify
m=5/7
consider the equation 21= m +14 1/6 which which step will help to solve this equation
Answers
Answer:
m = 41/6
Step-by-step explanation:
21 = m + 14 1/6Convert everything into improper fractions with a denominator of 6.
21 = m + 14 1/6126/6 = 6m/6 + 85/6126 = 6m + 856m = 126 - 856m = 41m = 41/6what's another way to say a+a
A. a^2
B. a+2
C. a-a
D. 2a
Answers
Answer:
[tex]\boxed{\sf{2a}}[/tex]Step-by-step explanation:
In order to solve this problem, you need to add their similar elements together.
First, add similar to elements.
[tex]\sf{a+a=\boxed{\sf{2a}}[/tex]
So, the correct answer is D. 2a.I hope this helps you! Let me know if my answer is wrong or not.
Margaret is building storage boxes. each box will have a length of 8 feet, a width of 512 feet, and a height of 412 feet. a pint of paint covers 50 square feet. how many pints of paint does margaret need to buy in order to paint 3 boxes? 7 pints 10 pints 12 pints 13 pints
Answers
The surface area of a cuboid is the area of all the six faces of a cuboid. The Paint that is required to paint 3 boxes is 13 pints.
What is the surface area of a cuboid?The surface area of a cuboid is the area of all the six faces of a cuboid. It is given by the formula,
[tex]\rm \text{Surface area of the box}= 2[(Length \times width)+(Width \times Height)+(Length \times height)][/tex]
As it is given the dimensions of the storage box are a length of 8 feet, a width of 5 1/2 feet(5.5 feet), and a height of 4 1/2 feet(4.5 feet). Therefore, the surface area of the box can be written as,
[tex]\rm \text{Surface area of the box}= 2[(Length \times width)+(Width \times Height)+(Length \times height)][/tex]
[tex]\rm \text{Surface area of the box}= 2[(8\times 5.5)+(5.5\times 4.5)+(8 \times 4.5)] = 209.5\ ft^2[/tex]
As it is given that the surface area that can be covered with a pint of paint is 50 square feet, therefore, the paint that will be required to paint 209 square feet is,
[tex]\text{Paint Required} = \dfrac{\text{Total area that is needed to be paint}}{\text{Area covered in a pint of paint}}[/tex]
[tex]\rm \text{Paint Required} = \dfrac{209.5}{50} = 4.19\ pints[/tex]
Now, we know that the surface area of the box is 209 square feet, while the paint required to paint a complete box is 4.19, therefore, the paint that will be required to paint 3 boxes will be,
[tex]\text{Paint required to paint 3 boxes} = 3 \times 4.19 = 12.57 \approx 13[/tex]
Hence, the Paint that is required to paint 3 boxes is 13 pints.
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What is the area and circumference of the circle? diameter = 12 cm
Answers
Answer:
Circumference = 7.68 cm
Area = 113.04 cm²
Step-by-step explanation:
First, let us find the radius of the given circle.
d = 2r
r = d / 2
r = 12 / 2
r = 6 cm
And now, let us find the circumference of the circle using the below formula.
C = 2 π r
C = 2 × 3.14 × 6
C = 37.68 cm
And now let us find the area of the circle using the below formula.
A = π r²
A = 3.14 × 6 × 6
A = 113.04 cm²
Please help math in the sreenshot
Answers
Answer:
yeh
Step-by-step explanation:
1 gallons = 4 quarts
4,8,20,28
quarts= 2 pints
1,3,6,16
1 pint= 2 cups
2,6,5,18
Consider the system and find the eigenvalues and the eigenvectors
Answers
Eigenvalues are the special set of scalar values which is associated with the set of linear equations in matrix equations.
What are Eigenvalues?
Your information is incomplete. Therefore, an overview will be given. An eigenvector of a linear transformation is a nonzero vector that changes by a scalar factor when the linear transformation is applied to it.
The eigenvectors of matrix A are those vectors X for which multiplication by A will result in a vector in thesame direction or opposite direction to X.
Since the zero vector 0 has no direction, 0 is never allowed to be an eigenvector.
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An eigenvector of a linear transformation and eigenvectors of a system
Ax = Bx can be determined where B is an eigenvalue of A.
What are Eigenvalues?An eigenvector of a linear transformation is a nonzero vector that changes by a scalar factor when the linear transformation is applied to it.
The eigenvectors of matrix A are those vectors X for which multiplication by A will result in a vector in the same direction or opposite direction to X.
The basic equation is
Ax = Bx
here B is an eigenvalue of A.
Since the zero vector has no direction, zero is never allowed to be an eigenvector.
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A bedroom door in the house has the same
dimensions as the front door, but the length is
30 inches rather than 36 inches. How much greater is
the volume of the front door than the bedroom door?
Answers
The difference in the volume of bedroom door in the house taken the length and width into consideration will be 120 inches³.
How to calculate the bedroom door?It should be noted that the volume of a door is simply gotten by multiplying the length by width.
Let's assume that the width is 20 inches. Therefore, the difference will be:
= (36 × 20) - (30 × 20)
= 720 - 600
= 120 inches³
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Express in the form n : 1. Give n as a fully simplified fraction. 10 : 12
Answers
Answer:
[tex]\frac{5}{6}:1[/tex]
Step-by-step explanation:
[tex]10:12[/tex] divide both sides of this ratio by 12 to give a ratio in the form [tex]n:1[/tex]
[tex]\frac{10}{12}:1[/tex] which simplifies to [tex]\frac{5}{6}:1[/tex]
Help anyone?Can u be specific and tell how u got it
Answers
Answer:
6 1/4
Step-by-step explanation:
3+2=5
2+3
1/2+3/4= ----------------------------------------------------
4
=5/4
=1 1/4
5+ 1 1/4
=6 1/4
Use a diagram to show that (3x+1)(x+2) is equivalent to 3x2+7x+2.
Answers
3x*2 = 6x
x*1 = x
1*2 = 2
that's basically the FOIL method, multiply first terms, the x terms
then the outside terms, the the inside terms, then the constant (last) terms
F=first, O=outside, I = Inside, L = last
add them up to get 3x^2 +6x +x + 2 = 3x^2 +7x +2
(3x+1)(x+2) = 3x^2 +7x+2
draw a rectangle with one side as 3x+1, the other side as x+2. The area of the rectangle is their product
divide the rectangle into 4 smaller rectangles. with sides 3x by x, 3x by 2, x by 1 and 2 by 1
calculate the areas of each rectangle the sum them.
standard form is
y=ax^2 +bx + c or
f(x) = x^2 +7x +2 where a=1, b=7, c=2
another standard form is to put the quadratic equation in vertex form
by completing the square
f(x) or y = x^2 +7x + 49/4 = -2 + 49/4
y = (x+3/2)^2 = 41/4
where the vertex = (3/2,41/4)
standard equation in vertex form is
y= a(x-h)^2 + k where (h,k) = vertex = (3/2,41/4) with a=1
It's an upward opening parabola with y intercept = 41/4 = 10 1/4, axis of symmetry x=3/2
Find the area of the shaded sector of the circle. Give the exact answer in terms of straight pi.
A circle has a central angle that measures 120 degrees and a radius of 8.
fraction numerator 48 straight pi over denominator 9 end fraction units squared
fraction numerator 64 straight pi over denominator 3 end fraction units squared
fraction numerator 32 straight pi over denominator 3 end fraction units squared
fraction numerator 16 straight pi over denominator 9 end fraction units squared
Answers
The area of the sector that has a central angle of 120 degrees and radius of 8 units is 64π / 3 units²
Area of a sectorThe area of a sector is defined as follows:
area = ∅ / 360 × πr²
where
r = radius∅ = central angleTherefore,
r = 8
∅ = 120°
Hence,
area of the sector = 120 / 360 × π × 8²
area of the sector = 1 / 3 × π × 64
area of the sector = 64π / 3 units²
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There are a total of 21 marbles in the box. And 5 of the marbles
are black and 6 of them are blue. A single marble is chosen at
random from the box. What is the probability of choosing a
black ball or a blue ball?
Answers
Step-by-step explanation:
there are in total 21 marbles.
5 black, 6 blue = 11 black or blue marbles.
so, the probability of pulling a black or blue marbles is as always desired possible outcomes / total possible outcomes = 11/21
Use the information given to answer the question.
which two inequalities represent the constraints for the art studio classes
per week?
an art studio offers classes for painting and pottery. each painting class is 1
2+ y = 40
hour long. each pottery class is 1.5 hours long. the art studio is only open
0 2 +1.5y = 40
for classes a maximum of 40 hours per week, and only one class is offered at
o +1.5y > 40
35(2 + y) < 1,000
a time. each class costs $35,and the art studio earns a minimum of $1,000
35(x + y) > 1,000
per week from all classes. let be the number of painting classes offered per
calculator
week, and let y be the number of pottery classes offered per week.
Answers
The two inequalities that represents the constraints for the art studio classes per week are:
x + 1.5y = 40
35(x + y) > 1,000
What two inequalities represent the constraints?Here are inequalities signs and what they mean:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
= means equal to
The inequality that represents the total hoursthe art studio is open would be an equal to sign. This is because the store is open for a maximum of 40 hours.
The inequality that represents the total earnings would be represented with a greater than sign because the studio earns more than $1000 weekly.
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Someone help me with this pls
Answers
Answer:
MAYBE
Step-by-step explanation:
Answer:
SORRY
Step-by-step explanation:
ANSWERAnswer:
SORRY
Step-by-step explanation:
ANSWERAnswer:
SORRY
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ANSWERAnswer:
SORRY
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ANSWERAnswer:
SORRY
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ANSWERAnswer:
SORRY
Step-by-step explanation:
ANSWERAnswer:
SORRY
Step-by-step explanation:
ANSWERAnswer:
SORRY
Step-by-step explanation:
ANSWERAnswer:
SORRY
Step-by-step explanation:
ANSWERAnswer:
SORRY
Step-by-step explanation:
ANSWERAnswer:
SORRY
Step-by-step explanation:
ANSWERAnswer:
SORRY
Step-by-step explanation:
ANSWERAnswer:
SORRY
Step-by-step explanation:
ANSWER
SOORY
I would just like to know what this means and how to do it consistently. Thanks (:
Answers
Answer:
This question is asking for you to determine if the tables represent linear functions, functions in y=mx+b form, and to find the equation for the line.
If something is a linear function, each of the input values will have it's own corresponding y value, therefore c cannot be linear, as -1 and 1 both have 10 as the output.
I hope this helps, but if you need more clarification, please tell me in the comments!
There was a bottle of milk at home. After the brother drank 1.94L of it, there were 0.56L left. How many litres of milk was there at the beginning?
Answers
Answer:
add the 1.94+0.56 to get 2.5 liter
Step-by-step explanation:
wow, he drank almost 2 liters of milk more or less in one turn ? he might spend quite some time in the bathroom ...
anyway, x = original amount of milk.
x - 1.94 = 0.56 now we add 1.94 to both sides
x = 2.5 L
The table shows the sales receipt for your purchase.
a) the items with a "t" next to the price are subject to sales tax. what percent sales tax did you pay?
b) calculate the price of the top.
c) the price you paid for the top was 60% of the original price. what was the original price of the top?
Answers
The sales receipt for the purchase includes the sales tax
The sales tax is 6%The price at the top is $7.50The original price at the top is $12.50How to determine the percent of sales tax?The sales tax is calculated as:
Percentage sales tax * (Sum of Items subjected to tax) = Sales tax.
So, we have:
T * (3 + 0.5) = 0.21
Evaluate the sum
T * (3.5) = 0.21
Divide both sides by 3.5
T = 6%
Hence, the sales tax is 6%
The price at the topThe price (p) at the top is calculated using:
p = 13 - 3 - 2 - 0.5
Evaluate the difference
p = 7.5
Hence, the price at the top is $7.50
The original price at the top60% of the original price (P) is p.
So, we have:
60% * P = p
Substitute 7.5 for p
60% * P = 7.5
Divide both sides by 60%
P = 12.5
Hence, the original price at the top is $12.50
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Liam buys three identical plastic
containers that are right rectangular
prisms. one face of each container
measures 4 and 1/2 in. by 2 in. the total
volume of the three containers is
135 in.. how many of these containers
can liam set on a shelf that is 24 in. long
with the 4and 1/2in-by-2 in. faces touching?
Answers
The number of rectangular prism container that would be set on the shelf is: 4.
What is the Volume of a Rectangular Prism?Volume of rectangular prism = length × width ×height
Given the following:
Volume of three containers = 135 in.³Volume of each rectangular prism container = 135/3 = 45 in.³One face = width × height = 4.5 × 2 = 9 in.Find the length of one rectangular prism using the volume formula since volume for one prism = 45 in.³
45 = length × 9
length = 5 in.
Each rectangular prism container is 5 in. long, therefore, the number of the containers that can be set on the shelf that is 24 in. long, if the 4.5 in by 2 in. face touches each other = 24/5 = 4.8.
The fifth container won't fit in. Therefore, the number of rectangular prism container that would be set on the shelf is: 4.
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-4=7t/5 +4t/5 solve for t
Answers
Answer:
t=-\frac{20}{11}
Step-by-step explanation:
15. If y varies directly as x and y = 540 when x = 10, find x when y = 1080
Answers
[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\stackrel{\textit{"y" varies directly as "x"}}{y = kx}\qquad \textit{we also know that} \begin{cases} y = 540\\ x = 10 \end{cases}\implies 540=k(10) \\\\\\ \cfrac{540}{10}=k\implies 54=k~\hfill \boxed{y=54x} \\\\\\ \textit{when y = 1080, what is "x"?}\qquad 1080=540x\implies \cfrac{1080}{540}=x\implies 2=x[/tex]
The value of x when y = 1080 for the condition when its given that y varies directly as x and that y = 540 when x = 10, is found to be x = 20
Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
[tex]p = kq[/tex]
where k is some constant number called constant of proportionality.
This directly proportional relationship between p and q is written as
[tex]p \propto q[/tex] where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n are two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
For this case, it is specified that y varies directly as x.
That means
[tex]y \propto x\\or\\y = kx[/tex]
At x = 10, y is 540. Putting these values in the equation y = kx as they're related, we get:
[tex]540 = k \times 10\\\\\text{Dividing both the sides by 10}\\\\\dfrac{540}{10} = k\\\\k = 54[/tex]
Thus, the relationship between x and y is: y = 54x
Now, when y = 1080, we get:
[tex]1080 = 54x\\\\\text{Dividing both the sides by 54}\\\\\dfrac{1080}{54} = x\\\\x = 20[/tex]
Thus, the value of x when y = 1080 for this condition is when x = 20.
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help on this please.
Answers
i need help cause is due at 11:59 est
Answers
Answer:
Matt used diameter of the ball instead of Radius
Step-by-step explanation:
The volume of a sphere is given as:
4/3πr³Radius, r = diameter / 2Given that, the diameter = 15 cm ; The Radius = 15 / 2 = 7.5 cm
⇒ Matt made an error in his calculation by failing to covert the value of the diameter given to Radius.
⇒ By dividing the diameter by 2 = 15 / 2 = 7.5, we obtain the Radius, which is what Billy did in her own calculation.