A cylinder has a volume of 60cm what is the volume of a cone with the same radius and height.
Answer:
20 cm³
Step-by-step explanation:
Since the volume of a cylinder is 60 cm³, which we can express it as:
[tex]\displaystyle \large{\pi r^2 h=60}[/tex]
Keep in mind that [tex]\displaystyle \large{\pi r^2 h}[/tex] is the cylinder’s volume formula, and we want to find the volume of a cone with same radius and height. When they say same radius and height, they mean that the radius and height are the same as cylinders’.
But since no values of radius and height are given, we know that the volume of a cone is:
[tex]\displaystyle \large{\frac{1}{3}\pi r^2 h}[/tex]
Compare both formulas:
[tex]\displaystyle \large{\pi r^2h}[/tex] — cylinder’s volume
[tex]\displaystyle \large{\frac{1}{3}\pi r^2h}[/tex] — cone’s volume
See how they are quite similar except that cone’s volume has 1/3. That means cone’s volume is 1/3 of cylinder’s volume
Finding cone’s volume, multiply both sides by 1/3:
[tex]\displaystyle \large{\pi r^2h=60}\\\displaystyle \large{\frac{1}{3}\pi r^2h=\frac{1}{3}\cdot 60}\\\displaystyle \large{\frac{1}{3}\pi r^2h=20}[/tex]
Therefore, the volume of a cone with same radius and height from cylinder is 20 cm³.
__________________________________________________________
Summary
Volume (Cone) (1/3 of cylinder’s volume):
[tex]\displaystyle \large{V=\frac{1}{3}\pi r^2 h}[/tex]
Volume (Cylinder):
[tex]\displaystyle \large{V=\pi r^2h}[/tex]
They are quite related!
__________________________________________________________
Others
Let me know if you have any doubts about my answer, explanation or this question through comment!
x^3 + 3x^2 -10x factor polynomial and find zero
Answer:
x(x - 2)(x + 5)x = 0, x = 2, x = -5Step-by-step explanation:
x^3 + 3x^2 - 10x
~Factor
x(x - 2)(x + 5)
Solve for the zero.
x(x - 2)(x + 5) = 0
We know that; x = 0, x - 2 = 0, and x + 5 = 0
x = 0
x - 2 = 0
x = 2
x + 5 = 0
x = -5
Best of Luck!
Here we are provided with an polynomial of degree 3 and we have to factorise it first and then we have to compute it's zeroes.
Given Polynomial:
x³ + 3x² - 10xTaking common x from all the 3 terms,
➝ x(x² + 3x - 10)
Factorising through Middle term factorisation,
➝ x(x² + 5x - 2x - 10)
➝ x{x(x + 5) - 2(x + 5)}
➝ x(x - 2)(x + 5)
Hence, Factorised !!
Now equating to 0 to find the zeroes of the poly.
➝ x(x - 2)(x + 5) = 0
That means,
x = 0x - 2 = 0x + 5 = 0So, the zeroes of the polynomial is 0, 2 or -5
And we are done....
Carry On Learning [tex]![/tex]
1. Data with two variables is called *
A double data.
.
B bivariate data.
C split data
D bipedal data
Answer:
B. "bivariate data"
Quizlet fortunately had the same question with this answer, so here you go! :)
Which inequality compares 2/4 and 5/6?
Answer:
2/4 is greater
Step-by-step explanation:
if you reduce 2/4 its 1/2 and 5/6 cant be reduced so therefor 2/4 is greater
Which two fixed points define the shape of an ellipse?
A. Center and focus
B. Focus and directrix
C. Two foci
D. Vertex and focus
An object starts from rest and accelerates at a rate of 3.0 meters per second2 for 6.0 seconds. The velocity of the object at the end of this time is
a= v-u/t
3 = v-0/6
3 = v/6
v=18 m/s
A bee population is measured each week and the
results are plotted on the graph. What is the bee
population when it is first measured?
Answer:
500 bees
Step-by-step explanation:
The initial value is the y-intercept, where a point crosses the y-axis when x=0.
(0, x) = (0, 500)
Hope this makes sense :]
There are 500 bees in the population when it is first measured.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
Every week, a bee population is counted, and the findings are illustrated on the given graph.
According to the given graph, the initial value is the y-intercept, where a point intersects the y-axis when x = 0.
(0, x) = (0, 500)
This means the bee population is 500 when it is first measured.
Learn more about exponential function here:
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PLEASE HELP ME ON THAT I REALLY NEEDED. Tell be the statement and the reason please also please do it in order because is on aleks. THANKS!
Answer:
CD = EC ⇒ proved down
Step-by-step explanation:
If a point lies on a segment, then it divides the segment into two parts, the sum of their length equals the length of the segment
Example:
If point Z lies on the segment XY, then Z divides XY into segments XZ and ZY, where XY = XZ + ZY
Let us use this fact to solve the question
∵ BD and EF intersected at point C
∴ C divides BD into two segments BC and CD
∴ C divides EF into two segments EC and CF
→ By using the fact above
∴ BD = BC + CD
∴ EF = EC + CF
∵ BD = EF ⇒ given
→ Equate their right sides
∴ BC + CD = EC + CF
∵ BC = CF ⇒ given
→ That means their adding segments are equal
∴ CD = EC ⇒ proved
A circle has a diameter that measures 20 inches. What is the area of the circle to the nearest 10th? Used 3.14 for pi
Answer:
A≈314.16
Step-by-step explanation:
a circle's diameter is 2 x radius
20/2 = radius
Area formula: A=πr^2
A=π 10^2
A≈314.16
Which equation is a direct variation? PLEASE HELP
The lid of a box is 43 cm² an area the volume of the box is 420 cm3 what is the height of the box?
Answer: 9.77 cm
Step-by-step explanation:
The volume of the box is length x width x height (V = l*w*h). The area of the lid of the box is the length x width (A = l*w). So, to find the height, you can change the equation to volume / (length x width) = height (V/(l*w) = h). Divide the volume by the area (420/43), to get the answer of 9.77 cm.
REE A manufacturer of window frames knows from past experience that 10 per cent of the production will have some type of minor defect that will require adjustment. Suppose 20 window frames are selected at random: a. How many window frames would you expect to have minor defects? (2 points) b. Calculate the standard deviation for the number of window frames to have minor defects in this random sample of 20 window frames. (2 points) c. Calculate the probability that exactly 2 window frames will need minor . adjustment. (2 points) d. What is the probability that more than 3 window frames will need minor adjustments? (7 points)
Answer:
10% to decimal is equal to 0.1.
Therefore 20 x 0.1 = 2
Step-by-step explanation:
Each window is independently probable for having minor defects. The expected number of window frames having minor defects = 2.
Other figures are:
Standard deviation for the number of windows frames to have minor defects in this random sample of 20 window frames = 1.34 approx.P(Exactly 2 windows will need minor adjustment) = 0.285 approx.P(More than 3 windows will need minor adjustment) = 0.1329 approx.How to find that a given condition can be modeled by binomial distribution?Binomial distributions consists of n independent Bernoulli trials.
Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
The expected value and variance of X are:
[tex]E(X) = np[/tex][tex]Var(X) = np(1-p)[/tex]For the considered case, we can assume that each window is independent of each other for having defects or being perfect.
Each window can be having defects (call it success) or no defects(call it failure).
Then, we can take:
X = number of windows out of 20 windows being perfect (no defect).
Then we get:
Success = window having defectn = 20p = 10% = 0.10 (as given in the problem)[tex]X \sim B(n=20,p=0.1)[/tex]Evaluating each sub parts one by one:
Case a: How many window frames would you expect to have minor defects?Expect number of defective windows = E(X) = np = 20 × 0.1 = 2
Case b: Calculate the standard deviation for the number of window frames to have minor defects in this random sample of 20 window frames.Standard deviation is the positive root of variance.
Standard deviation of number of windows (out of 20 windows of sample) having defects = [tex]\sqrt{Var(X)} = \sqrt{np(1-p)} = \sqrt{2(0.9)} \approx 1.34[/tex]
Case c: Calculate the probability that exactly 2 window frames will need minor adjustment.P(X = 2) = [tex]^{20}C_2(0.1)^2(0.9)^{18} \approx 0.285[/tex]
Case d: What is the probability that more than 3 window frames will need minor adjustments?P(X > 3) = 1 - P(X ≤ 3)
[tex]P(X > 3) = 1 -[ P(X = 0) + P(X = 1) +P(X= 2)+ P(X = 3)]\\\\P(X > 3) = 1- [^{20}C_0(0.1)^0(0.9)^{20} +^{20}C_1(0.1)^1(0.9)^{19} +\\\: \:\: ^{20}C_2(0.1)^2(0.9)^{18} +^{20}C_3(0.1)^3(0.9)^{17} ]\\\\P(X > 3) \approx 1-[ 0.1216 + 0.2702 + 0.2852 + 0.1901]=1-0.8671=0.1329 \\\\P(X > 3) \approx 0.1329[/tex]
Thus, the needed figures are:
Expected number of window frames having minor defects = 2Standard deviation for the number of windows frames to have minor defects in this random sample of 20 window frames = 1.34 approx.P(Exactly 2 windows will need minor adjustment) = 0.285 approx.P(More than 3 windows will need minor adjustment) = 0.1329 approx.Learn more about binomial distribution here:
https://brainly.com/question/13609688
PLEASE HELP
Driving 75 mph, it takes Alicia 3 hours to reach the airport to go on a vacation. It then takes her 3 hours to get to her destination with
the jet traveling at a speed of 350 mph. How many miles does Alicia travel to get to her destination?
OA. 1,275 miles
OB. 1,375 miles
OC. 1,125 miles
OD.
425 miles
Sorry I was wrong I searched up the wrong one but I would go with option C
Brainliest if correct
Answer:
[tex]\frac{5}{10}, \frac{4}{10}, \frac{1}{10}[/tex] are the numbers you need
Step-by-step explanation:
The least common denominator of those two numbers is 10.
[tex]\frac{1}{2} * \frac{5}{5} = \frac{5}{10} \\\\\frac{2}{5} * \frac{2}{2} = \frac{4}{10} \\\\\frac{5}{10} - \frac{4}{10} = \frac{1}{10}[/tex]
I hope this helps! Have a lovely day! :)
Consider a line whose slope is 6 and which passes through the point (8.–2).
3. Write the equation of the
4. Write the equation of the
line in point-slope form.
line in slope-intercept form.
Answer:
[tex]y=6(x-8)-2\qquad\text{point-slope form}[/tex]
[tex]y=6x-50\qquad\text{slope-intercept form}[/tex]
Step-by-step explanation:
The equation of a line can be written in several forms. Two of the most-used forms are the point-slope and the slope-intercept forms.
The point-slope form requires to have one point (xo, yo) through which the line passes and the slope m. The equation expressed in this form is:
[tex]y=m(x-xo)+yo[/tex]
The slope-intercept form requires to have the slope m and the y-intercept b, or the y-coordinate of the point where the line crosses the y-axis. The equation is:
[tex]y=mx+b[/tex]
The line considered in the question has a slope m=6 and passes through the point (8,-2). These data is enough to find the point-slope form of the line:
[tex]\boxed{y=6(x-8)-2\qquad\text{point-slope form}}[/tex]
To find the slope-intercept form, we operate the above equation:
[tex]y=6x-48-2[/tex]
[tex]\boxed{y=6x-50\qquad\text{slope-intercept form}}[/tex]
The cost of an air conditioner is $
130
. The cost to run the air conditioner is $
0.25
per minute for the first
400
minutes. Write the function that models the total cost of running the air conditioner for the first
400
minutes and determine the key features of the function.
Function:
Domain:
Range:
y−
intercept:
x−
intercept(s):
A function that models the total cost of running the air conditioner for the first 400 minutes is [tex]T=130 +0.25m[/tex].
Let the number of minutes be m.Let the total cost be T.Given the following data:
Cost of air conditioner = $130Running cost = $0.25 per minuteTime = 400 minutes.To write a function that models the total cost of running the air conditioner for the first 400 minutes:
How to solve a word problem.First of all, we would write an equation to models the total cost of running the air conditioner for the first 400 minutes:
For the total time:
[tex]0.25m[/tex]
For the total cost:
[tex]T=130 +0.25m[/tex]
For the domain:
The value of m is the domain and it can be chosen from 0 to 130.
Domain (m) = [0, 130].
For the range:
A range represents the minimum and maximum value of a data set.
Thus, the value of T would be between 130 and 230.
Range = [130, 230].
For the intercept:
when x = 0, we have:
[tex]y=130 +0.25(0)[/tex]
y = 130.
Intercept = [0, 130]
Read more on word problems here: https://brainly.com/question/13170908
Evaluate the expression 24(20*14)
What is this answer and how?
( 1 + 1 ) + ( 1 + 1 + 1) in standard form
Answer:
if im correct the answer should be 5 x 10
Step-by-step explanation:
3x-2(x+3)=4x-7
Please help me solve this
Answer:
x = 1/3
Step-by-step explanation:
First distribute the 2 to the (x + 3) and get 3x-2x-6 = 4x - 7.
Combine like terms and get x- 6 = 4x - 7.
Subtract x from either side and get -6 = 3x - 7
Now add 7 to both sides and get 3x = 1
Now divide 3 from both sides and get x = 1/3
20 Points for an answer! Please help! I have unlimited tries for the practice test, but I got this one wrong from an answer on here, Letter B doesn't work for the answer, I tried that already.
Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. If Beth places the swings at point D, how could she prove that point D is equidistant from the jungle gym and monkey bars?
Question options:
A.) If segment AC ≅ segment BC, then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.
B.) If segment AD ≅ segment CD, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
This one is incorrect according to my practice test I took.
C.) If segment AC ≅ segment BC, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
D.) If segment AD ≅ segment CD, then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.
Answer:
Well, according to the question, option D is the main answer
The points (1, 6) and (r, -6) lie on a line with slope - 4. Find the missing coordinate r.
Answer:
49
Step-by-step explanation:
By the definition of slope, as vertical change over horizontal change, we get
[tex]-4=m = \frac{\Delta y }{\Delta x} = \frac{r-1}{-6-6} = -\frac{r-1}{12}[/tex]
By checking the first and the last step of that chain
[tex]-4=-\frac {r-1}{12} \rightarrow r-1=48\rightarrow r= 49[/tex]
Find the area of the polygon.
Answer:
66 cm²
Step-by-step explanation:
As you know from the area formulas, the area of a triangle is equivalent to half the area of a rectangle with the same base and height. Another way to say that is the area of a triangle is equivalent to the area of a rectangle with the same base and half the height.
The triangle added to the side of the square is equivalent in area to a rectangle with the same 6 cm base (vertical dimension), and half the 10 cm height (horizontal dimension). That is, the total area of the polygon is the same as the area of one that is 6 cm high and 6+5 = 11 cm wide.
A = LW = (6 cm)(11 cm) = 66 square centimeters
__
If you want to figure the area more conventionally, it is the sum of the area of a 6 cm square and a 6×10 cm triangle:
6² +1/2(6)(10) = 36 +30 = 66 . . . square centimeters
the cost of computer was rs 65000 the price of computer was depreciated 12% compounded yearly how much amount was depreciated in 2 years?find it
Answer:
50336
Step-by-step explanation:
The cost deprecates by 12% each year. If we have to find how much it deprecated for 2 years, we will have to calculate how much is 12% of the current price, subtract it, then find how much is 12% equal to again and subtract it once again. Not sure if that's the smartest way to do it though.
Anyway, we have
65000, 12% of 65000 is equal to (65000 * 12) / 100 = 650 * 12 = 7800
After the first year, the price will be:
65000 - 7800 = 57200
Now we do the same thing:
12% of 57200 = 57200 * 12% = 57200 * 12/100 = 57200 / 1 * 12/100 = (57200 * 12) / 100 * 1 = 572 * 12 / 1 = 572 * 12 = 6864
After the second year the price will be:
57200 - 6864 = 50336
Determine the absolute value. Type the numerical answer only. |10|
Answer:
10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
The answer is 10 because:
1) Absolute value makes all negative or positive numbers positive (unless there is a negative sign outside the absolute value sign).
2) Therefore, the absolute value of 10 is positive 10.
Hope this helps! :D
What is the slope intercept form of (-4,-5); and slope 1/2
Answer:
Step-by-step explanation:
Slope intercept form is y = mx + b where m is the slope and b is the y intercept.
We are given m = 1/2
Plug the point (-4,-5) in for x and y and the given slope in for m.
y = mx + b
-5 = 1/2(-4) + b
Now solve for b.
-5 = -2 + b
b = -3
Now plug m and b back in to get your slope intercept form.
y = 1/2x -3
Hope this helps!
Testing for a disease can be made more efficient by combining samples. If the samples from two people are combined and the mixture tests negative, then both samples are negative. On the other hand, one positive sample will always test positive, no matter how many negative samples it is mixed with. Assuming the probability of a single sample testing positive is 0.2, find the probability of a positive result for two samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely necessary?
Answer:
The probability of a negative is 0.64 but the probability of a positive is 0.36
Step-by-step explanation:
What is the area of a section 10 ft wide and 50 yd long? Give your answer in square feet.
Answer:
1,500 square feet
Step-by-step explanation:
you have to convert yards to feet and multiply
True or false 49 is a irrational number
Answer:
FalseStep-by-step explanation:
49 is a rational number.
Hope this helps:)
Ray BD bisects ABC so that m
Answer:
Step-by-step explanation:
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