Given a soda can with a volume of 15 and a diameter of 2, what is the volume of a cone that fits perfectly inside the soda can?
Answers
so, a cone, that fits inside the cylinder, will have the same height "h" and radius "r". Thus
[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h\qquad \boxed{\pi r^2 h}=15 \\\\\\ \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\implies V=\cfrac{\boxed{15}}{3}[/tex]
Related Questions
If today is tuesday what day will it be in 100 days
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una pizzeria hace pizzas de varios tamaños y las vende en cajas hexagonales de 39 cm de lado y 4.7 cm de alto ¿que cantidad de cartón se anestesia para cada caja teniendo en cuenta q la caja esta formado por dos partes compuestas de una base lateral ?
Answers
Final answer:
To calculate the amount of cardboard used for each box, we need to find the surface area of the hexagonal base and the lateral surface area. We can use the formula for the surface area of a hexagon to find the base area. Then, we multiply it by the height of the box and add the two areas together.
Explanation:
To find the amount of cardboard used for each box, we need to calculate the surface area of the hexagonal base and the lateral surface area. The surface area of a hexagon can be found using the formula:
Surface Area = 3 x √3 x s^2
where s is the length of the side of the hexagon. Given that the side length is 39 cm, we can substitute this into the formula to find the surface area of the hexagonal base. Once we have the surface area, we can calculate the lateral surface area by multiplying it by the height of the box, which is 4.7 cm. Adding the two areas together will give us the total amount of cardboard used for each box.
Two spheres of the same density have a ratio of 4 to 9 in surface area. If the small sphere weighs 10 kg, what does the large sphere weigh?
Answers
Sphere Surface Area = 4 • π • r²
radius^2 = Surface Area / 4* PI
Let's say area of smaller sphere is 4 PI
radius^2 = 1
radius = 1
9/4 = 2.25
Area of the larger sphere = 4 * PI * 2.25
radius^2 = 2.25
radius = 1.5
Volume of a sphere = 4/3 • π • r³
Volume of larger sphere = 4/3 • π • 1.5^3
Volume of larger sphere = 3.375 times volume of smaller sphere
Mass of larger sphere = 3.375 * 10 kg
The larger sphere weighs 33.75 kg
Ship A receives a distress signal from the northeast and ship B receives a distress signal from the same vessel from the west. At what location is the vessel in distress located? Describe how you arrived at your conclusion using complete sentences.
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Second based on the two directions from the points you know that up is north, Right is east, West is left, and down is south on the graph.
Draw a line from the two points in the direction that it says the ship received the call from.
so the ship is at Ordered pair 3,3 :)
Coordinate geometry is the use of a 2D plane to represent the location of points. The position or location of the distress is in the first quadrant.
The coordinates of ship A and B are not given. So, I will give a general explanation.
On the four cardinal points,
North is upwardsEast is at the rightWest is at the leftSouth is downwardSo, if ship A receives a distress from the northeast, then it means that the distress is coming from a location at the top right of A. i.e. the first quadrant.
Also, ship B receives distress from the west. This means that ship B is at the right-hand side of the distress.
So, we can conclude that the position or location of the distress is at the first quadrant.
It is impossible to determine the actual coordinates of the distress because the coordinates are not given (see attachment possible illustration)
Read more about coordinate geometry at:
https://brainly.com/question/18269861
What is the equation of a circle with a center (-2, 3) and a radius r = 5?
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(x - h)^2 + (y - k)^2 = r^2
(h, k) is the center.
So the equation would be:
(x + 2)^2 + (y - 3)^2 = 5^2
or
(x + 2)^2 + (y - 3)^2 = 25
Your teacher is giving you a test worth 100 points containing 40 questions. there are two-point and four-point questions on the test. let the number of two-point questions be x and the number of four-point questions be y. how many of each type of question are on the test?
Answers
2x + 4y = 100
2(40 - y) + 4y = 100
80 - 2y + 4y = 100
-2y + 4y = 100 - 80
2y = 20
y = 20/2
y = 10 <=== there are 10 four-point q's
x + y = 40
x + 10 = 40
x = 40 - 10
x = 30 <=== there are 30 two-point q's
Answer:
t=30 f=10
Step-by-step explanation:
t= 100*1 - 40*4 = 30
2*1 - 1*4
f= 2*40 - 1*100 = 10
2*1 - 1*4
t=30 f=10
The variable Z is inversely proportional to X. When X is 6, Z has the value 2. What is the value of z . When x = 13
Round to at least the thousandths place if needed.
Answers
Z= k/x
when x is 6, Z= 2
2=k/6
k=2*6
k=12
Z=12/X
when x = 13
Z=12/13
Z=0.923
How to determine the direction of a vector?
Answers
Which complex number has a distance of √17 from the origin on the complex plane?
A;2 + 15i
B:17 + i
C:20 – 3i
D:4 – i
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Then by the pythagoras therem
17 = x^2 + y^2
D will satisfy this equation
4^2 + (-1)^2 = 17
answer is D 4 - i
Answer:
The complex number 4-i has distance [tex]\sqrt{17}[/tex] from origin.
D is correct
Step-by-step explanation:
We are given the absolute value of complex plane.
If complex number is a+ib then absolute value [tex]\sqrt{a^2+b^2}[/tex]
We have to check the absolute value of each option and check which is equal to [tex]\sqrt{17}[/tex]
Option A: 2+15i
[tex]d=\sqrt{2^2+15^2}=\sqrt{4+225}=\sqrt{229}\neq \sqrt{17}[/tex]
Option B: 17+i
[tex]d=\sqrt{17^2+1^2}=\sqrt{289+1}=\sqrt{290}\neq \sqrt{17}[/tex]
Option C: 20-3i
[tex]d=\sqrt{20^2+3^2}=\sqrt{400+9}=\sqrt{409}\neq \sqrt{17}[/tex]
Option D: 4-i
[tex]d=\sqrt{4^2+1^2}=\sqrt{16+1}=\sqrt{17}= \sqrt{17}[/tex]
Hence, The complex number 4-i has distance [tex]\sqrt{17}[/tex] from origin.
Suppose you draw a card from a well-shuffled pack of playing cards. What is the probability the card you draw will be an ace? A. 4/50 B. 1/13 C. 4/13 D. 1/52
Answers
Favorable outcome ={ 4 Aces}
P(drawing ONE Ace) = 4/52 = 1/13 = 0.0769 (answer B. 1/13)
What does b belong with?
Answers
b-5
C-6
D- 2
Explanation: To match the equations properly I just used the process is substitution and elimination.
please vote my answer brainliest. thanks!
Examine the graph at right. Then in a sentence suggest why the graph rises at 11:00am and drops at 1:15pm
Answers
Use the distributive property to expand the following expression. -3(6.3x + 7y - 2.5)
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The expression -3(6.3x + 7y - 2.5) expands to -18.9x - 21y + 7.5 using the distributive property by multiplying each term inside the parentheses by -3.
To use the distributive property to expand the expression -3(6.3x + 7y - 2.5), you multiply each term inside the parentheses by -3. The distributive property lets you reverse the distributive law and turn it into factors (multiples).
-3 × 6.3x = -18.9x
-3 × 7y = -21y
-3 ×-2.5 = 7.5
Once each term is multiplied, the expanded expression is: -18.9x - 21y + 7.5
if 5(3x-7)=20 then what is 6x-8
Answers
15x-35=20
15x= 55
x= 55/15
x= 11/3
Plug this x value in.
6(11/3)-8
66/3 -8
22-8
14
Final answer: 14
4xy - 9xy + -3xy Simplify the polynomial
Answers
Maggie’s brother is 12 years younger that three times her age . The sun of their ages is 44 . How old is Maggie
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Maggie's brother's age = b
Maggie's age = m
b = 12 - 3m
44 = 12-3m
12-3m = 44
-12 -12
-3m = 32
÷ 3 ÷3
m = 10.67
So this would be Maggie's age
I hope this helped :)
There are 10 people in a room. if each person shakes hands with exactly 3 other people, what is the total number of handshakes?
Answers
10x3=30
Which equation is not a quadratic equation?
y = 3x2 + 2
y = 5x - 2
y = -x2
y = 5x2 - 2x + 7
Answers
[tex]ax^{2} +bx +c[/tex]
where a, b and c are the coefficients of the expression and a ≠ 0.
If a = 0, the equation becomes a linear expression and is no longer quadratic.
Hence, in the above options; y = 5x -2 is the only one that is not a quadratic equation.
An acute angle θ is in a right triangle with sin θ = two thirds . What is the value of cot θ?
Answers
Answer:
six divided by the square root of thirteen
Step-by-step explanation:
hey there,
< sin θ = [tex]\frac{O}{H}[/tex]
So that means O = 2 and H = 3. In order to find cot θ, first let's find tan θ.
tan θ = [tex]\frac{O}{B}[/tex]
We only know what O is equal to, not B. So let's draw out a triangle.
7
◢ 6
B
As you can see (sorry for the poor triangle), this is a right triangle. In order to find an unknown part, use [tex]a^2 + b^2 = c^2[/tex]!
[tex]6^2 + B^2 = 7^2[/tex]
B = ±√13
Obviously, a side of a triangle can't be negative, so it stays positive. Now we can find tangent!
tanθ = [tex]\frac{6}{\sqrt{13} }[/tex]
But, we're not done here. We're trying to find cotθ.
cotθ = [tex]\frac{1}{tan}[/tex]θ
[tex]\frac{1}{\frac{6}{\sqrt{13} } }[/tex] = [tex]\frac{\sqrt{13} }{6}[/tex]
That's your final answer! >
Hope this helped! Feel free to ask anything else.
a(1)=20
a(n)=a(n−1)−17
Find the 3rd term in the sequence
Answers
----------------------------------------------
Explanation:
First term = A(1) = 20, which is given
Second term
A(n) = A(n-1) - 17
A(2) = A(2-1) - 17
A(2) = A(1) - 17 .... note: second term = (first term) - 17
A(2) = 20 - 17
A(2) = 3
Third term
A(n) = A(n-1) - 17
A(3) = A(3-1) - 17
A(3) = A(2) - 17 ... note: third term = (second term) - 17
A(3) = 3 - 17
A(3) = -14
Answer:
-14
Step-by-step explanation:
khan academy
A personal identification code consists of five digits (0 through 9). how many codes are possible?
a. 50
b. 252
c. 100,000
d. 30,240
Answers
on each place you have 10 possible digit,
so for 5 places it will be 10^5 = 100, 000
There are 30,240 codes that are possible which consist of five digits (0 through 9).
What is a permutation?A permutation is defined as a mathematical process that determines the number of different arrangements in a set of objects when the order of the sequential arrangements.
There are 10 options for each of the 5 digits in the personal identification code (0 through 9). Since the order of the digits matters, we can use the formula for the number of permutations of n items taken r at a time, which is:
n!/(n-r)!
In this case, n is the number of options (10) and r is the number of items (5). Plugging these values into the formula gives us:
10!/(10-5)! = 10!/(5!) = 109876 = 30,240
Therefore, the correct answer is (d) 30,240.
Learn more about permutation here:
brainly.com/question/1216161
#SPJ5
Which formula is used to find circular mil area?
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For example, a wire has a diameter of 6×10⁻⁵ inches. To find its area:
A = πr² = π( 6×10⁻⁵ /2)² = 2.83×10⁻⁹ in²
Since 1 mil = 1/1000 (inch) or 0.001 inch
A = (2.83×10⁻⁹ in²)* (1 mil/ 0.001 inch)²
A = 0.00283 circular mils
The lifetime of a supertough aaa battery is normally distributed with mean of 28.5 hours and standard deviation of 5.3 hours. for a battery selected at random, what is the probability that the lifetime will be 25 hours or less?
Answers
z-score = (x - μ) / σ
where x is the data, μ is the mean, and σ is the standard deviation.
Substituting the known values,
z-score = (25 - 28.5)/5.3
z-score = -0.66
This translates to a percentage equal to 25.46%.
Therefore, from the supertough aaa batteries, approximately 25.46% has a lifetime that is only about 25 hours or less.
Because the car that has a terrible oil leak not only as a new battery for the van but also slows him down because he needs the Atwell after every hundred miles of driving he drives 100 miles every two hours it takes him 15 minutes to add oil how long should it take him to drive 500 miles
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To drive 500 miles, taking into account both driving time and oil stop time, it would take 11 hours and 15 minutes.
He drives 100 miles every 2 hours, so to drive 500 miles he would take 10 hours (5 segments of 100 miles each).He needs to add oil every 100 miles, which takes 15 minutes each time. Therefore, for the 500-mile trip, he would spend an additional 75 minutes (5 segments x 15 minutes each).Adding the driving time and oil stop time, he would take 10 hours (driving) + 1 hour 15 minutes (oil stops) = 11 hours 15 minutes to drive 500 miles.Which of the following statements is the converse of the statement "If each of two angles has a measure of 28 degrees, then the two angles are equal in measure"?
Answers
If the 2 angles are equal in measure the each of the 2 angles has a measure of 28 degrees.
AS you see in this example , the converse is not necessarily true.
Answer:
If two angles are equal in measure then each of the two angles has a measure of 28 degrees.
Step-by-step explanation:
The converse of a statement is found by switching the hypothesis and conclusion of a conditional statement.
The hypothesis is the part that comes after "if" and the conclusion is the part that comes after "then."
This means the hypothesis is "each of two angles has a measure of 28 degrees" and the conclusion is "the two angles are equal in measure."
This gives us the converse "If two angles are equal in measure then each of the two angles has a measure of 28 degrees."
What are the discontinuities of the function f(x) = the quantity x squared minus 16 over the quantity 4x plus 24
Answers
--------
4x + 24
when x = -6 the denominator 4x+24 = 0 so there is a discontinuity at x = -6
This is a vertical asymptote x = -6
There is also a sloping asymptote - you find this by getting the quotient
which is y = 0.25x - 1.5 This is the equation of this asymptote.
Answer:
x= -6 is the point of discontinuity.
Step-by-step explanation:
We have been given the expression
[tex]\frac{x^2-16}{4x+24}[/tex]
The first thing to find the discontinuity is to factorize the given rational function:
After factorization we get:
We will use [tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]here, a=x\text{and}b=4[/tex] we will get:
[tex](x+4)(x-4)=x^2-4^2[/tex]
we will get:
[tex]\frac{(x+4)(x-4)}{4(x+6)}[/tex]
Discontinuity is the point where value of the function becomes not defined
Here, the point of discontinuity is -6 because when denominator becomes zero. function becomes not defined.
It has vertical asymptote but function is not defined.
Hence it is the point of discontinuity.
If you had 5 green marbles and 8 red marbles, what's the probability that you'll pull out a marble that is green?
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5+8 = 13 total marbles
5 are green
so you would have a 5/13 probability of picking a green one
Jorge bought a car for $41,902 . He paid for the car with a check. Round the price to the nearest:
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Two numbers, 3 and a, have a geometric mean of 9. Find the value of a.
Answers
So, if the geometric mean of 3 and a is 9 =>
9 = √(3a)
=> 9^2 = 3a
=> a = 9^2 / 3
a = 81 / 3
a = 27
Answer: the value of a is 27.
An experiment consists of dealing 5 cards from a standard 52-card deck. what is the probability of being dealt aa 10, jack, queen, king, ace, all in the same suit
Answers
The probability of getting a royal flush is 1/649740 = 0.00000153907717
---------------------------------------------
Explanation:
There are 4 ways to get a royal flush. Those ways are
* You have a royal flush with nothing but hearts
* You have a royal flush with nothing but diamonds
* You have a royal flush with nothing but spades
* You have a royal flush with nothing but clubs
This is out of 52 C 5 = (52!)/(5!*(52-5)!) = 2,598,960 different five cards hands
So we have 4/2598960 = 1/649740 = 0.00000153907717