Well, we would find the volume of both the cylinder and the cone.
The formula to find the volume of a cylinder is V = \pi r^{2} h.
The formula to find the volume of a cone is V = \frac{1}{3} \pi r^{2} h.
Now, when using pi (the symbol \pi ), if the problem asks to use the approximate value of pi as 3.14, we'll use 3.14 to represent pi. If the problem asks for the exact answer, then we'll just put the pi sign next to our final answer we've gotten.
We can do both ways to solve with pi. Tho let's solve using the approximate value of pi.
One more thing. When there's an exponent in the problem, (such as r^{2} in the problem), that just means you would multiply the base, (which is r in r^{2} ), by itself the number of times the exponent, (which is the number 2 in r^{2} ), shows. For example, if it was 3^{2} , that would just mean we would multiply 3 times itself twice. So 3^{2} would be the same as 3 times 3, which is 9. When you deal with variables in a problem, (the letters used to represent a value in the equation, such as a, b, c, d, etc.), they're solved in multiple ways. If a number is next to a variable, (for example, 3b), it would mean you are supposed to multiply the number times the variable. If a number is next to parenthesis, that would mean you would multiply the number times the answer from the parenthesis. In formulas, when all the letters and numbers are squished together in one line, that means you would multiply all of them times each other after they're individually solved. In this problem, r = radius and h = height.
So without further-a-do, let's begin! :)
So the question says that the radius of the cylinder is 10 centimeters, and the height is 20 centimeters. According to the formula given above, we would multiply the radius times itself twice, which would be 10 times 10, which equals 100, then multiply it by the height which is 20, so 100 times 20 = 2,000. If we were to find the exact volume, it would be 2,000 with the pi sign next to it, which would be 2,000 \pi . Though, let's find the volume with the approximate value of pi, 3.14. So 2,000 times 3.14 is 6280. The exact volume of the cylinder is 2,000 \pi and the approximate volume is 6280.
Now after we find the volume of the cone, we would need to find out how many times we'd need to use the cone to fill up the cylinder's volume.
To find the volume of the cone, we would do the same as last time. Since the cone's radius is 5 centimeters, and its height is 10 centimeters, we would first multiply the radius times itself twice, which would be 5 times 5, which is 25, then multiply that by the height, which would be 25 times 10, which is 250. The fraction part of the formula means this- the numerator "1" means you would multiply what you have so far times 1, and the denominator "3" means you will divide what you have so far NOW by 3. So 250 times 1 = 250, and 250 divided by 3 = 83.3333333333, though we'd say that answer up to the hundredths place, which would be 83.33. If you need the exact answer, we'd put the pi sign next to it as 83.33 \pi , and you're done.Tho we didn't find the approximate volume of the cone.So we'd trace back to what answer we had before moving on to the step with the fraction \frac{1}{3} . Since we were on 250, we'd multiply that by 3.14, which is 785, and continue with what we did with the fraction. 785 times 1 = 785, and 785 divided by 3 = 261.666666667, and saying the answer up to the hundredths place, the approximate volume of the cone would be 261.66
Now since we know the volume of the cylinder, exact = 2,000 \pi and approximate volume = 6280, this means this is how much of the cylinder should be filled when we use the cone to pour in the water.
We could easily determine this by division.
Finding with the exact volume, you would do 2,000 (from cylinder's volume) divided by 83.33 (from cone's volume), which is 24.0009600384, and since it's not a whole answer, you would move it up a whole number. Why you may ask? Well you can't pour 0.0009600384 of a cone's volume into the cylinder now can you? :P So it would take 25 times of pouring the cone filled with water into the cylinder in order for the cylinder to be full using the exact volumes of both objects.
Now finding with the approximate volumes of both objects, we'd do the same we did last time. The cylinder's volume divided by the cone's volume, which is 6280 divided by 261.66, would be 24.0006114805, and saying the answer up to the hundredths place, 24.00, but for the same reason as the last one when we were using the exact volumes, we'd round 24 up a whole number, so it would approximately take 25 times to fill the cylinder with the cone.
Either way, using exact or approximate volumes, your final answer would be 25 times. =DI hope I helped! ^-^
By calculating the volume of cone and cylinder, we find that one need to 24 times use the completely filled cone to completely fill the cylinder with water.
What is volume of cone and cylinder?
The volume of cylinder is equal to the product of the area of the circular base and the height of the cylinder.
The volume of cone will be equal to one-third of the product of the area of the base and its height.
For a cylinder, the formula is πr²h. For a cone it is 1⁄3πr²h.
Volume of cylinder = π[tex]r^{2}[/tex]h = π * 10* 10 * 20 = 2000π
Volume of cone = [tex]\frac{1}{3}[/tex]*π[tex]r^{2}[/tex]h = 1/3 * π * 5 * 5 * 10 = 250 π/3
Number of times one needs to use the completely filled cone to completely fill the cylinder with water =
= Volume of cylinder/Volume of cone
= 2000π / (250π/3) = 24
Learn more about volume of cone and cylinder here
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in a given year, the rate of flu infection for the general public was 8.3%. And sample of 200 people who receive the flu vaccine, the rate of flu infection was just 3.5%. What conclusion should you draw?
Answer:
[tex]\fbox{\begin{minipage}{10em}Option A is correct\end{minipage}}[/tex]
Step-by-step explanation:
Step 1: Define significance level
In this hypothesis testing problem, significance levels α is selected: [tex]0.05[/tex], the associated z-value from Laplace table:
Φ([tex]z[/tex]) = α - [tex]0.5 = 0.05 - 0.5 = -0.45[/tex]
=> [tex]z[/tex] = [tex]-1.645[/tex]
Step 2: Define null hypothesis ([tex]H_{0}[/tex]) and alternative hypothesis ([tex]H_{1}[/tex])
[tex]H_{0}[/tex] : rate of flu infection [tex]p[/tex] = 8.3% or 8.3/100 = 0.083
[tex]H_{1}[/tex] : rate of flu infection [tex]p[/tex] < 8.3% or 8.3/100 = 0.083
Step 3: Apply the formula to check test statistic:
[tex]K = \frac{f - p}{\sqrt{p(1 - p)} } * \sqrt{n}[/tex]
with [tex]f[/tex] is actual sampling percent, [tex]p[/tex] is rate of flu infection of [tex]H_{0}[/tex], [tex]n[/tex] is number of samples.
The null hypothesis will be rejected if [tex]K < z[/tex]
Step 4: Calculate the value of K and compare with [tex]z[/tex]
[tex]K = \frac{(\frac{3.5}{100}) - 0.083}{\sqrt{0.083(1 - 0.083)} } * \sqrt{200} = -2.46[/tex]
We have [tex]-2.46 < -1.645[/tex]
=>This is good evidence to reject null hypothesis.
=> The actual rate is lower. (As [tex]H_{1}[/tex] states)
Hope this helps!
:)
The y-intercept of the graph of y=(x-c)(x-d)^3 is
Answer:
Just Make x=0
[tex]y_i=(-c)(-d)^3=cd^3[/tex]
find the value of x,
Answer:
for the first one they are opposite angles so they are the same degrees so x=15 I forget adjacent angles so idk the second one sorry
Express 0.96 as an percent
Answer:
96%
Step-by-step explanation:
0.96 × 100/100
(0.96 × 100)× 1/100 = 96/100
percentage = 96%
Answer:
96%
Step-by-step explanation:
Me pueden ayudar en este problema de potencia antonio tiene3 cajas , en cada caja hay 3 botones que contienen 3 lapices cuantos lapices habra en total
Answer:
23 lapices
Step-by-step explanation:
Él tiene 3 cajas.
Cada caja contiene 3 botones.
Cada botón contiene 3 lápices.
La cantidad de lápices que tendrá en total es:
[tex]N = 3 * 3 * 3 = 3^3 = 27[/tex]
Tendrá 23 lápices
Angle measure and segment lengths: Find "Y" and do not round your answer. Please answer in under five minutes, thanks!
Answer:
y = 11.2 in.
Step-by-step explanation:
To solve this question we will use the theorem of intersecting secants and tangents.
"If a secant and a tangent are drawn to a circle from an external point then length of tangent is the geometric mean between the length of external segment of the secant and the length of the secant."
By this theorem,
5(5 + y) = (9)²
y + 5 = [tex]\frac{81}{5}[/tex]
y = 16.2 - 5
y = 11.2 in
Therefore, y = 11.2 in. will be the answer.
Answer:
11.2
Step-by-step explanation:
i got it right online
Please help! Correct answer only!
You can play a game with a wheel whose rim is divided into equal sections marked with the numbers from 1 to 20. If you play, the attendant will spin the wheel and a ball will land in a random section. If the number the ball lands on is even, you win $34. If the number the ball lands on is odd, you win nothing. If you play the game, what is the expected payoff?
Answer:
" Expected Payoff " - 17 Dollars ; Type in 17
Step-by-step explanation:
Consider the probability of landing in an odd section;
[tex]Sections of the Wheel - 20 Sections,\\Numbers Numbered On the Wheel - 1 To 20,\\\\Odd Numbers = Even Numbers,\\Odd Numbers = 20 / 2 = 10,\\Even Numbers = Odd Numbers = 10,\\\\Probability of Spinning Even - 10 / 20 = ( Simplified ) 1 / 2,\\Money Won = 34 Dollars,\\\\Proportionality - 1 / 2 = x / 34, Where, x = " Expected Payoff "\\1 / 2 = x / 34,\\2x = 34,\\x = 17 Dollars,\\\\Conclusion ; " Expected Payoff " = 17 Dollars[/tex]
Solution ; Provided Directly Above
Pls pls help me with this
A jar contains 3 black marbles, 4 white marbles and 5 striped marbles. If a marble is picked at random, what is the probability that it is not white? Give your answer as a fraction in lowest terms.
Please help!!!
Answer:
2/3
Step-by-step explanation:
The first person to make me become Brainliest wins the official contest!!! Hurry!
Answer:
I'm not sure but it might be 2/3????? That's just from looking at Spatrickfarley's answer. He deserves Brainliest!
Please explain and show work. In the function f(x)=cosx, f(x) is multiplied by a factor of 3, x is replaced with 4x and 5 is added to the function. Explain the effects this has on the graph of the function (i.e. horizontally, vertically, compressed, stretched, etc.).
Your graph will actually look like an oscillation (wave), it will be more compressed horizontally. As the value of x increases withe very whole number, your graph will compress horizontally. More like in the image below.
The perimeter of an equilateral triangle is 120mm.
State the length of one of its sides.
Answer:
[tex]40 \:mm[/tex]
Step-by-step explanation:
An equilateral triangle has 3 equal sides.
[tex]\frac{120}{3} =40[/tex]
Answer:
40mm
Step-by-step explanation:
Perimeter of an equilateral=3a
120=3a
a=120/3
a=40mm
When given a graph, the vertical line test can be used to determine functionality. Describe the vertical line test and explain the reasons why a graph would, or would not, represent a function.
Answer:
The vertical line test is a way for you to see if a graph represents a function. It allows you to identify if any x values have more than one y value.
A graph would be a function if every input (x) has exactly one output (y). A graph would not be a function if an input (x) has more than one output (y).
Step-by-step explanation:
In a function, every input within the domain of the function must have exactly one output. If the graph has an input that has more than one output, then it is not a function. The vertical line test is what allows you to see if a graph is a function or not.
Answer:
When given a graph, the vertical line test can be used to determine functionality. The vertical line test would represent a function if no more than one point of the graph of a relation, this shows that only one output value for each input value. If this doesn't apply or more than one point is on the line then it would not represent a function.
Step-by-step explanation:
Draw vertical lines to intersect on a graph.
The relation is a function if there’s only one point of intersection on a graph.
The relation is not a function if there’s more than one point of intersection on a graph.
The vertical line test is used to determine if each input has exactly one output.
please help!!!!!!! just click on picture to see question
Answer:
g(n) = - 19 + (n - 1)*6
Step-by-step explanation:
The way to do this is to try a couple and then see if you can make some sort of equation that follows the rule.
g(1) = - 19
=============
g(2) = g(2 - 1) + 6
g(2) = g(1) + 6
g(2) = -19 + 6
g(2) = -13
=============
g(3) = g(2) + 6
g(3) = -13 + 6
g(3) = - 7
==========
g(4) = g(3) + 6
g(4) = - 7 + 6
g(4) = - 1
==========
g(5) = 5
g(6) =11
===========
Now the hard part. You have to start with - 19
The nth term is g(n) = - 19 + (n - 1)*6
Now see if it works.
g(7) = - 19 + (7 - 1)*6
g(7) = - 19 + 6 * 6
g(7) = -19 + 36
g(7) = 17
Is that correct?
g(7) = g(n - 1) + 6
g(7) = g(6) + 6
g(7) = 11 + 6
g(7) = 17 Seems to be the same as the explicit formula gives.
13 is 23 less than 15 times a number
Answer:
13 = 15(x) - 23
x = 12/5 or 2 2/5
which two of the following is continuous data?
Answer:
B. Age of student
D. Time taken to run 1 mile
Step-by-step explanation:
From the list of given options, only B and D satisfy the required condition.
One unique determinant of continuous data is that; they are measured and not counted.
Now, let's categorize option A to D into two
1. Counted data
2. Measured data
Options that fall into the category of measured data are said to be continuous data.
A. Concert attendance; The number of people in a concert is counted
B. The age of a student is measured (in years)
C. Number of pens in a box is counted
D. Time taken to run 1 mile is measured (in units like seconds, minutes, hours, etc...)
In summary; we have
Counted
A. Concert Attendance
C. Number of pens in a box
Measured
B. Age of a student
D. Time taken to run 1 mile
Hence, the continuous data are Age of a student and Time taken to run 1 mile
Practice:
1. What is the product of – 2x^3 + 8 and - 4x?
2. What is the product of yx^2and (6y^2x - yx)?
WRITE THE ANSWERS TO YOUR WORK IN HERE!!
(2^8 • 5^negative5 • 19^0) • (5^negative2 / 2^3)^4 • 2^38
i need steps shown and a simplified answer please!
Answer:
6.872* 10^17
Step-by-step explanation:
(2^(8) * 5^(5) * 19^(0)) * ((5^(2))/(2^(3)) ) * 2^(38)
you add the exponent of the same number because it is multiplication
for number two 2 : 8+38=46
for division you subtract the exponents : 46-3=43
and for number 5 : 5+2=7
for 19^0=1
2^43*5^7=6.872*10^17
Given that Triangle ABC such that
a=8cm, b=7cm and c=9cm
tem and c= 9cm find Cos B
Answer:
We use cosine rule also called cosine law which states
c^2=a^2+b^2-2abcosC
given
a=8cm, b=7cm, c=9cm cos C?
9^2=8^+7^2-2*8*7 cos C
expand
81=64+49-112 cos C
like terms together
81-113=-112 cos C
-32=-112cos C
multiply both sides by -1
32=112cos C
divide both sides by 112
32/112=cos C
cosC=0.2857
find cos inverse of 0.2857
angle C= 73.40
Anna has 2 purple lipsticks, 3 red lipsticks and 3 pink lipsticks in her kit. She picks one lipstick, record its color, puts it back in the kit and draws another lipstick. What is the probability of taking out a purple lipstick followed by the red lipstick?
Answer:
9/64Step-by-step explanation:
This is a probability problem on selection with replacement, that is the sample size does not change after each selection or event.
Given data
2 purple lipsticks,
3 red lipsticks and
3 pink lipsticks
The sample space s=(2,3,3)
The sample size= 8
1. the probability of taking a purple lipstick Pr(purple)= [tex]\frac{3}{8} \\[/tex]
2.the probability of taking a red lipstick Pr(red)= [tex]\frac{3}{8}[/tex]
probability of taking out a purple lipstick followed by the red lipstick is
[tex]= \frac{3}{8} * \frac{3}{8} = \frac{9}{64}[/tex]
URGENT!!!!! LAST TWO QUESTIONS!!!!!!! WILL GIVE BRANLIEST!!!AT LEAST TAKE A LOOK!!!!!! PLS HELP!!!
14. Find the missing angle x. ( 155 degrees is on the top left side, FIRST pic below)
19. Triangles ABC and DEF are similar. Find x. SECOND PIC
A) 9.45
B) 6.12
C) 7.23
D) 8.57
Answer:
#14) x is 95 (155-180= 25, 180-25-60= 95)
#19) my best guess is 4 (DE=7 -> AB=11, a 4 unit increase)
7x + 14 - 17-3x = 6x - 4z + 2 - 5 find the value of x
3 5 3
Answer:
when z=3 or 5 , values of x is ; 6 or 10.
I think that there is a lack of information or misspelling in the question.
Step-by-step explanation:
4x-3=6x-4z-3
4z=2x
2z=x
z=3 => x=6
z=5 => x=10
Function g can be thought of as a translated (shifted) version of f(x)=x^2 Write the equation for g(x) g(x)=______
Answer:
g(x)=(x^2)-3
Step-by-step explanation:
f(x) is shifted down by 3 units
Need help with this problem
Answer:
Start at the top. Place the numbers below it in a triangular pattern. Each number is the added numbers directly above it.
Step-by-step explanation:
Start with "1" at the top, then continue placing numbers below it in a triangular pattern. Each number is the numbers directly above it added together.
The horizontal sum's double each time.
the weights of cars passing over a Bridge have a mean of 3550 lb and a standard deviation of 870 lb. Assume that the weights of the cars passing over the bridge, Lee distributed. Use the empirical rule to estimate the percentage of the cars going over the bridge whose weights are more than 4420 lbs.
Answer:
a. 16%
Step-by-step explanation:
The difference from the mean is ...
(x - µ) = 4420 lb -3550 lb = 870 lb
Then the minimum Z-score of the traffic of interest is ...
(x - µ)/σ = (870 lb)/(870 lb) = 1
__
The "empirical rule" tells you that 68% of a normal distribution is within 1 σ (Z = ±1) of the mean. If 68% is inside that range, then the remaining 32% is outside that range. The normal distribution is symmetrical about the mean, so half that quantity is below Z = -1, and the other half, 16%, is above Z=1.
About 16% of the cars have weights more than 4420 pounds.
In which number is the value of the 6 ten times the value of the 6 in the number
6,000?
Answer:
600
Step-by-step explanation:
the value of 6 in 6000 is thousands
600x10=6000
Answer:
Step-by-step explanation:
The product of Chau's height and 5 is 70.
Answer: 14
Step-by-step explanation: chau's height = x
x * 5 =70
5x = 70
x = 70/5
x = 14
Students in a political science course were asked to describe their politics as "Liberal", "Moderate", or "Conservative." Here are the results:
Politics
Liberal
Moderate
Conservative
Total
Female
40
34
14
88
Male
48
50
26
124
Total
88
84
40
212
Given that the student is male what is the probability that he considers himself to be a "Liberal"? Round your answer to three decimal places if necessary.
a.
0.226
c.
0.387
b.
0.415
d.
0.455
Please select the best answer from the choices provided
A
B
C
D
Answer:
Answer is a (A)
Step-by-step explanation:
Answer is a (A)
please could you help me with these questions! they would be quick
Answer:
Where are the questions....?
Answer:
Hey!
Well there aren't any question up here!!
Step-by-step explanation:
Maybe put another one!
Hope this helps!
Record 3 2/25 as a decimal. Please help!!!!!
Answer:
1.28 is the decimal form
Step-by-step explanation:
and 128/100 or 128% is the percentage for 32/25.
// have a great day //
3x^2 -5x -2=0
help factor left side please!!
y’all i didn’t sleep at all last night and i cannot remember how to factor the first half of the equation help me out asap please guys
Answer:
Step-by-step explanation:
1. Find two numbers that add to make the coefficient of x (in this case, -5) and that multiply to make the constant term multiplied by the coefficient of x^2 (in this case, -2 x 3 = -6)
Two numbers that work are -6 and +1
-6 x +1 = -6
-6 + -1 = -5
2. Split the middle term into the two numbers that you found.
3x^2 -6x +x -2 = 0
I've put the -6 on the left side because in our next step, when we factorise, it will be easier than having the numbers the other way around.
3. Factorise the left side by taking out common factors from each pair. The pairs I'm talking about here are '3x^2 and -6x', and 'x and -2'
3x (x-2) +1 (x-2) = 0
4. You now have two numbers both being multiplied by the term x-2. We can rearrange this equation to give us two brackets being multiplied by each other.
(3x + 1) (x-2) = 0
5. According to the Null Factor Law, if two terms are multiplied together and the result is 0, then one of those terms must be 0. Make both terms equal to 0 and solve each for x.
3x + 1 = 0 x-2 = 0
3x = -1 x = 2
x = -1/3
6. The solutions to this equation are x = 2 and x = -1/3
Answer:
Step-by-step explanation:
Start by separating (not factoring) -5x. For example, we might get {-2x, - 3x} (note how these combine to produce -5x). Might have to try several combinations to find the right one.
Then 3x^2 -5x -2=0 could possibly be x(3x - 2) - (3x - 2), or
x(3x - 2) - 1(3x - 2).
Notice how the factor (3x - 2) shows up twice. If we factor out (3x - 2) we are left with (x - 1). We check these results by multiplying (3x - 2) and (x - 1) together, so we can be sure that the result is the original 3x^2 -5x -2=0.
(3x - 2)(x - 1) = 3x^2 - 3x - 2x + 1 results in 3x^2 - 5x + 2. Unfortunately, the sign of that 2 is incorrect; we'd hoped for -2, not +2.
To check this further, I used synthetic division with 1 as divisor; the remainder is -4, which tells us that (x - 1) is not a factor of 3x^2 -5x -2=0.
Please double check to ensure that you have copied this problem down correctly.
