Answers
Answer:
a. height: 36 units
b. radius: 4 units
Step-by-step explanation:
The volume of a cone is given by the formula ...
V = 1/3πr²h . . . . . for radius r and height h
This tells you the volume is jointly proportional to the height and the square of the radius. This means that for a given volume, the height is inversely proportional to the square of the radius. We can use this proportionality to answer the questions here.
__
a.The radius of Cone B is 2 units. Compared to Cone A, the radius of Cone B is 2/6 = 1/3 of the radius of cone A. The square of this ratio is (1/3)² = 1/9, and the inverse of that square is 9/1. This means the height of Cone B is 9 times the height of Cone A, so is ...
Cone B height = 9 × 4 units = 36 units
__
b.The height of this Cone B is 9 units, whereas the height of Cone A is 4 units. This means the height of Cone B is 9/4 times the height of Cone A. This is the inverse of the square of the ratio of radii of Cone B to Cone A. Inverting the height ratio, we get 4/9. Taking the square root of that, we get √(4/9) = 2/3. This means the radius of Cone B is 2/3 the radius of Cone A:
Cone B radius = 2/3 × 6 units = 4 units
_____
Additional comment
We can check the above dimensions using the volume formula.
a. V = 1/3π(2 units)²(36 units) = 48π units³
b. V = 1/3π(4 units)²(9 units) = 48π units³
These are the expected volume, so the answers check OK.
Related Questions
what is the value of n in the equation -1/2(2n+4)+6= -9+4(2n+1)
Answers
Answer:
n=1
Step-by-step explanation:
Still stuck? Get 1-on-1 help from an expert tutor now.
The side of the clip on a clip board appears to be a right triangle. The
leg lengths are 2 millimeters and 2.1 millimeters and the hypotenuse
is 2.9 millimeters. Is the side of the clip a right triangle?
Answers
Answer:
Yes, it is a right triangle.
Step-by-step explanation:
Answer:
Yes, this is a right triangle.
Step-by-step explanation:
For this, you would use the Pythagorean theorem a^2 + b^2=c^2
Here we have 2^2+2.1^2=2.9^2
So we must check to see if that checks out. What we find is that both sides are equal to 8.41 which means we have a right triangle.
I need help quick please
Answers
B=53
The reason I am saying this is because you can see the 90 degree angle in A
Angle A = 137
Angle B = 93
what is a quadrialateral?
A quadrilateral is four sided polygon. squares and rectangles are more common examples of a quadrilateral. Each quadrilateral has it's unique features however generally the sum of angles of a quadrilteral is 360
Introducing angle C such that
A + C = 180 (angle on a straight line)
C + 47 + 90 = 180 (sum of angles of a trianlge)
C = 180 - 90 - 47
C = 43
hence
A + 43 = 180
A = 180 - 43
A = 137
A + B + 90 + 40 = 360 (sum of angles of a quadrilateral )
37 + B + 90 + 40 = 360
B = 360 - ( 137 + 90 + 40 )
B = 93
Read more on quadrilaterals here: https://brainly.com/question/16691874
Find the value of x. Write answer in simplest form.
Answers
Answer:
x=8
Step-by-step explanation:
x²+x²=(8 root2)²
2x²=128
÷2 on both sides
=x²=64
square root each side
so x=8
Apply Pythagorean theorem
P²+B²=H²x²+x²=(8√2)²2x²=(8√2)²2x²=128x²=128/2x²=64x=√64x=8Problem 1: Verify whether these two functions are inverses: (x + 5) f(x) = (2x + 1) and g(x) = (5 - x) (2x - 1) What is g(x))? Use your keyboard and the keypad to enter your answer. Then click Done
Answers
g(f(x)) = x
What is inverse function?
An inverse function is defined as a function, which can reverse into another function.
[tex]f(x)= \frac{(x + 5)}{(2x + 1)}[/tex]
[tex]g(x)= \frac{(5 - x)}{(2x - 1)}[/tex]
[tex]g(f(x))=g( \frac{(x+5)}{(2x +1)})[/tex]
Substitute the value of f(x),
[tex]g(f(x))= \frac{(5 - \frac{(x + 5)}{(2x + 1)})}{(2 \frac{(x + 5)}{(2x + 1)} - 1)}[/tex]
[tex]g(f(x))= \frac{\frac{10x+5-x-5}{2x+1} }{ \frac{2x+10-2x-1}{2x+1}}[/tex]
[tex]g(f(x)) = \frac{9x}{9}[/tex]
g(f(x)) = x
Hence, g(f(x)) = x
Learn more about inverse function
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Use the following table to find the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in
on-campus housing. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Students on the Student Government Board
Classification
On-Campus Housing Off-Campus Housing
Freshman
1
4
Sophomore
2
0
Junior
1
2
Senior
2
0
Graduate Student
2
3
Prey
Next
Copy Data
Answer How to enter your answer opens in new window) 2 Points
Keypad
Keyboard Shortcuts
56°F
Answers
Using it's concept, it is found that there is a [tex]\frac{11}{17}[/tex] probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, a total of 1 + 4 + 2 + 0 + 1 + 2 + 2 + 0 + 2 + 3 = 17 students were sampled.
Of those, 1 + 2 + 1 + 2 + 2 = 8 live in on campus housing, and 3 live off campus but are graduate students, hence there are 11 desired outcomes and the probability is given by:
[tex]\frac{11}{17}[/tex]
More can be learned about probabilities at https://brainly.com/question/14398287
The length of a rectangle is 2ft longer than it’s width. If the perimeter of the rectangle is 32 ft, find it’s area
Answers
Answer:
Area of rectangle is 63 feet²Step-by-step explanation:
Given:
The length of a rectangle is 2ft longer than it’s width. If the perimeter of the rectangle is 32 ftTo Find:
Area of the rectangle.Solution:
Let's assume Width of rectangle be x feet and length be 2 +x. to Find the are of the rectangle firstly we need to the length and width of the Rectangle:
Using formula:
Perimeter of rectangle = 2(L + B)→ 32 = 2(x + 2 + x)
→ 32 = 2(2x + 2)
→ 32 = 4x + 4
→ 32 - 4 = 4x
→ 28 = 4x
→ 28/4 = x
→ 7 = x
Hence,
Length of the rectangle = 2 + x = 9 feetWidth of the rectangle = x = 7 feet.Now,
→ Area of rectangle = Length × Width
→ Area fo rectangle = 9 × 7
→ Area of rectangle = 63 feet²
Hence, Area of the rectangle is 63 feet²Answer:
63 sq.ft⠀
Step-by-step explanation:
⠀
As it is given that, the length of a rectangle is 2ft longer than it’s width and perimeter of the rectangle is 32 ft.⠀
So, let us assume the width of the rectangle as w ft and therefore the length will (w + 2) ft .
⠀
Now,
⠀
[tex]{\longrightarrow \qquad{ {{\boldsymbol {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad {\rm{2(w + 2 + {w})= 32 \ }}}[/tex]
⠀
[tex]{\longrightarrow \qquad {\rm 2({2w + 2= 32 ) }}}[/tex]
⠀
[tex]{\longrightarrow \qquad {\rm{4w +4= 32 \ }}}[/tex]
⠀
[tex]{\longrightarrow \qquad {\rm{4w = 28\ }}}[/tex]
⠀
[tex]{\longrightarrow \qquad {\rm{w = \dfrac{28}{4} }}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ \mathfrak{{\pmb{w = 7 }}}}}[/tex]
⠀
Therefore width of the rectangle is 7 ft .⠀
Now, We are to find the length of the rectangle:
[tex]{\longrightarrow \qquad{ {{\rm{Length = w + 2 }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ {{ \rm{Length = 7 + 2 }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ { \frak{ \pmb{Length = 9}}}}}[/tex]
⠀
Now, we are to find the area of the rectangle :
⠀
[tex]{\longrightarrow \qquad{ {{\boldsymbol{ Area_{(Rectangle)} = Length \times Breadth }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ {{ \rm{ Area_{(Rectangle)} = 9 \times 7 }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ { \pmb{\boldsymbol{ Area_{(Rectangle)} = 63 }}}}}[/tex]
⠀
Therefore,
The area of the rectangle is 63 ft².⠀
how many three-letter "words" can Bob make using just these letters?
Answers
Answer:
two
Step-by-step explanation:
the two "words" Bob can make using the three letters t, o, and a are;
oat and tao
hope this helps
Find a degree 3 polynomial whose coefficient of x^3 equal to 1. The zeros of this polynomial are -5, -4i, and 4i. Simplify your answer so that it has only real numbers as coefficients.
I got an answer by solving (x^3+5x^2-16x-80) but it says thats incorrect.
Answers
Answer:
x^3+5x^2+16x+80
Step-by-step explanation:
You know that you can write your polynom this way : (x-r1)(x-r2)(x-r3) with r1,r2 and r3 the roots so you get :
(x+5)(x+4i)(x-4i)
Simplify (x+4i)(x-4i) with the formula (a-b)(a+b)=a²-b²
so you have (x^2+16)=(x+4i)(x-4i)
Your polynom looks like this :
(x^2+16)(x+5) just expand it
and you get x^3+5x^2+16x+80
Help me please For your points! Thanks
Answers
Answer:
Step-by-step explanation:
you will read the directions 2x before solving the problem then solve the problem
Due today pls helpp I will give brainlist
Answers
Answers:
jamal has 30 stickers in total.
chris has 7 stamps in each group.
Step-by-step explanation:
1. use multiplication, 6*5=30
2. use division, 56/8=7
hope this helped! ♡
Answer:
jamal has 30 stickers in total.
chris has 7 stamps in each group.
Step-by-step explanation:
The cheeseburger in Alan's kid's meal has 300 calories. His fries have 101 and his drink has 150. How many tota calories
are in his meal?
Answers
300+150 = 450
450 + 101 = 551
Answer:
551 calories
Step-by-step explanation:
Given the number of calories in each part of his food you can add:
300 + 101 +150
to equal the total amount of calories in his food, which would be:
551 calories
In conclusion, there would be a total of 551 calories if Alan's kid's meal.
Have a great rest of your day
#TheWizzer
What is the measure of Zx?
Angles are not necessarily drawn to scale.
Answers
Answer:
17°
Step-by-step explanation:
First, see what's the angle of "AOC"
Here, it's 90° (since it shows the Box at the bottom of the angle instead of a semicircle.
Now, lets subtract 90 by 73
that will be 17
so hence, the value of X is 17°
--------------------------------------௹﷼---------------------------------------------------------------
If you see someone without a simle, give them one of yours!
Thanks!
Have a great day!
:D
express the confidence interval 0.255 plus or minus 0.045
Answers
Answer:
0.255+45=0.300
or
0.255 - 0.045 = 0.210
what is
A two-column proof
Answers
Answer:
A two-column geometric proof consists of a list of statements, and the reasons that we know those statements are true. The statements are listed in a column on the left, and the reasons for which the statements can be made are listed in the right column.
Solve the quadratic equation by using either a numeric or a graphic approach. x squared + 2 x minus 3 = 0 a. x = -1.1 or x = -2 c. x = 2 or x = -5 b. x = 2.3 or x = -0.82 d. x = 1 or x = -3
Answers
[tex]x^2+2x-3=0\\\\\implies x^2 +3x -x -3 =0\\\\\implies x(x+3) -(x+3)=0\\\\\implies (x-1)(x+3)=0\\\\\implies x =1 ~ \text{or}~ x = -3[/tex]
Find the solution to the system of equation by using either graphing or substitution
y=4x and y + x=5
Answers
Answer:
x=1, y=4
Step-by-step explanation:
sub y=4x into second equation
4x + x=5
5x=5
x=1
now sub x=1 into the first equation
y = 4 x 1
y=4
A group of friends go out for a meal and the meal costs £148.
They are given a discount of 25% because of a mix-up on their orders.
How much discount did the group of friends receive?
£
Answers
you would multiply by the percent off they get.
Find MQ in parallelogram LMNQ .
Answers
Answer:
MQ = 16.4
By the Parallelogram Diagonals Theorem , MP = PQ
So MQ = 2 · MP
Step-by-step explanation:
Parallelogram Diagonals Theorem
The diagonals of a parallelogram bisect each other, i.e. they divide each other into two equal parts.
P is the point of intersection of the diagonals.
Therefore, MP = PQ and LP = PN
If MP = 8.2, then PQ = 8.2
⇒ MQ = 8.2 + 8.2 = 16.4
I do not understand how they got this answer. I am stuck on the exponent party- Please see attached
Answers
Looking at the question, the answer gotten is:$4316.55. The question is related to compound interest.
What is compound interest?Compound interest is known to be the interest that is earned on a principal sum in addition to the accumulated interest previously. It is as a result of reinvesting interest.
To find the compound interest, the formula used is:
A= P(1+r/n)^nt.
Where
P is the principal sum= $3500
r is the rate = 0.035
n is the compounding period = 12 months.
t is the time = 6 years.
Substituting them in the equation, we have:
A = 3500 ( 1 + 0.035/12)^12×6
Working out the one in the bracket and multiplying the exponent, we have:
A = 3500 (1.00291667)^72
Note: We got 72 by multiplying 12 by 6.
1.00291667 raised to the power of 72 = 1.23330133
A = 3500× 1.23330133 = $4,316.55
Ans: $4,316.55
Learn more about compound interest on https://brainly.com/question/24274034
Each of 7 students reported the number of movies they saw in the past year. This is what they reported.
13, 8, 6, 6, 18, 11, 4
Find the median and mean number of movies that the students saw.
If necessary, round your answers to the nearest tenth.
(a) Median:
(b) Mean:
Answers
Answer:
A is 6
B is 9.4
Step-by-step explanation:
First you put the numbers in order. then you take the middle number of the data set. This is how you find the median. For the mean you add all of the number in the data set then divide by how many numbers are there
help me please mark U as BRAINLIEST
Answers
Hope this helps. Good luck
Find the volume. Use 3.14 for π where necessary. Round the answer to two decimal places.
Answers
Answer:
25.12 feet cubed ~ 25ft^3
Step-by-step explanation:
You're doing a volume for a cone.
Volume of cone formula: 1/3 π r^2 h
You have given me the diameter of 4ft
Height of 6ft.
In order to solve this, you need to divide 4ft by 2ft because we need the radius rather than the diameter.
**The radius is half of the diameter.**
Our new radius is 2ft.
Formula: 1/3π2^2(6)
Now do the exponent first, 2 to the second power or 2 squared is 4.
You need to pull out your calculator.
Steps to calculate the volume:
Do 1 divided by 3 first
Then multiply that by 3.14
Multiply 4
Finally multiply 6
Your Volume for the cone is 25.12 feet cubed
One natural number is 4 more than another one. The product of the two numbers is three times the square of the lesser
number. Find the numbers.
Answers
Answer:
2 and 6
Step-by-step explanation:
Assume you have two six-sided dice - both numbered 1 to 6 - and add the total of the dice after each roll. Leave all answers as a fraction a/b. What is the probability of rolling a 4
Answers
How many square meters are there in a floor that is 9 meters long by 12 meters wide?
99
108
109
117
Answers
Answer:
108
9×12
Step-by-step explanation:
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Find the mass of an object that has a weight of 910kg
Answers
Answer:
91kg
Step-by-step explanation:
weight= mass × gravitational force
910kg = m× 10ms^-2
m= 910÷ 10
m= 91
250 gram as a percentage of 1 kg
Answers
Hey there!
Answer: 25%
[tex] \rightarrow \: (\sf{ \frac{250}{1000} ) \times 100}[/tex]
[tex] \rightarrow \: ( \sf{0.25) \times 100}[/tex]
[tex] \rightarrow \: \sf{ = 25\%}[/tex]
Answer:
25%
Step-by-step explanation:
the quantities must have the same units
1 Kg = 1000 grams
express the quantities as a fraction and multiply by 100%
[tex]\frac{250}{1000}[/tex] × 100% = 0.25 × 100% = 25%
Determine the measure of the interior angle at vertex C.
Answers
Answer:
B. 120 Degrees
Step-by-step explanation:
We know that the total interior angle of any five sided polygon is 540 Degrees.
The total interior angle of this polygon is
4x + 4x + 4x + 3x + 3x = 18x 540 = 18x
Divide by the lowest ratio 540/18 = 30
30 = x
C = 4x
4X30 = 120
C = 120 Degrees
Sancho paints the new sign for his bike shop. One quart of paint covers 200 square feet, and Sancho plans on applying three coats of paint. One quart of paint cost $8.97. What is the square footage of his sign and ow much must Sancho spend to paint the sign?
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