Mathematics College

The volume of a cylinder is 24(pi) ft3. What is the volume of a cone that has the same base and height?

Answers

Answer 1
[tex]\bf \begin{array}{llll} \textit{volume of a cylinder}\\\\ V=\pi r^2 h \end{array}\qquad \qquad \qquad \begin{array}{llll} \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\implies \cfrac{1}{3}(\pi r^2 h) \end{array}[/tex]

now, if you notice there, for a cylinder with radius "r" and height "h", that is its volume.

and for a cone that has the same "h" and "r' as the cylinder's, that is its volume, however, notice, the cone's volume is one third of that of the cylinder's.

so if the cylinder has a volume of 24, well, you already know what is the cone's.

Related Questions

The circumference of a circle is 31.4 inches. What is the circle's diameter? C=31.4 in Use 3.14 for ​.

Answers

We will use the circumference formula to find the radius and then multiply it by 2 to find the diameter.

C = 2πr
31.4 = (2)(3.14)(r)
31.4 = 6.28r
5 = r

So our radius is 5 in.

We can multiply it by 2 to get the diameter.

5*2 = 10

So the diameter is 10 inches

49.3
this can be calc for a form

What is the area of this triangle?
Picture below, will give brainliest!!!! please help


can you give it to me in a decimal? Thank you

Answers

[tex]\text {Area = } \dfrac{1}{2} ABsin C[/tex]

[tex]\text {Area = } \dfrac{1}{2} (3.2)(4.7)sin (62 \textdegree)[/tex]

[tex]\text {Area = } 6.64 \ yd^2[/tex]

For ΔABC, the measure in degrees of angles A, B, and C are 60, 55, and x + 20 respectively. What is the value of x?

Answers

60 + 55 + x + 20 = 180
135 + x = 180
x = 180 - 135 = 45 degrees Answer.

Answer:

45

Step-by-step explanation:

60 + 55 + x + 20 = 180

135 + x = 180

x = 180 - 135 = 45

Answer: 45

If the rules for the lottery game powerball required participants to choose 5 unique numbers (ranging from 1 to 59) in any order along with one "powerball" (ranging from 1 to 35), what is the probability of winning the jackpot under these game rules?

Answers

59C5 = 5,006,386

5,006,386 x 35 = 175,223,510

probability 1: 175,223,510
Final answer:

To calculate the probability of winning the Powerball, you need to identify all possible combinations for drawing 5 unique numbers from a set of 59, then multiply that with the separate 35 options for the 'powerball'. Your chance of winning equals one (the exact match to your ticket) divided by the total possible combinations.

Explanation:

The probability of winning the Powerball jackpot can be determined using the concept of combination in probability theory. Probabilities are calculated by taking the total number of successful outcomes or combinations and dividing it by the total number of possible outcomes or combinations.

In the case of Powerball, there are 5 unique numbers to be drawn from a pool of 59 (ignoring order), and 1 'powerball' from a pool of 35. For the 5 unique numbers, there are C(59,5) combinations where C(n,r) = n! / [r!(n-r)!], n being the total number of options available and r being the number of options chosen at a time.

For the 'powerball', since it is a separate pool of 35 numbers and only 1 is chosen, the number of combinations is simply 35. As such, you multiply the two outcomes for total possible combinations: C(59,5)*35.

For the probability of winning, you want to know combinations that match exactly your selection, of which there is only one. Therefore the probability is 1 / [C(59,5)*35], resulting in extremely low chances of winning.

Learn more about Powerball Probability here:

https://brainly.com/question/33176496

#SPJ12

Lydia drove 302 miles in 10 hours. on average, how fast did she drive in miles per hour? express your answer in simplest form.

Answers

I think it is 30.2. I am not 100% sure though.

Answer:

30.2 mph

Step-by-step explanation:

Hello, I think I can help you with this

the speed average is the  is the quotient of the distance traveled and the time used to do it,  mathematical speaking

[tex]Average\ speed =\frac{distance}{time}\\[/tex]

Step 1

Put the values into the equation

Let

Distance:302 miles

Time:10  hours

[tex]Average\ speed =\frac{distance}{time}\\\\Average\ speed =\frac{302\ miles}{10\ hours}\\Average\ speed =30.2 \frac{miles}{hour} \\[/tex]

Average speed=30.2 mph

Have a great day.

There are a total of 26 students in Tom's class. There are 4 more boys than girls.

Which system of equations represents this situation? Let g be the number of girls, and let b be the number of boys.

A
g+b=26

g=4+b

B
g+b=26

b=4+g

C
g+b=26

g=4b

D
g+b=26

b=4g

Answers

The answer is B
4 more boys than girls so:
b = g + 4
And the total number of student is 26 so:
g + b = 26

what is the correct answer to this question?
a
b
c
d

Answers

The price of the item will change
.. from 275/6.58 = $41.79
.. to 275/6.25 = $44.00

which is a change of $2.21.

Find a linear differential operator that annihilates the given function. (use d for the differential operator.) e−x + 8xex − x2ex

Answers

Answer: [tex](d - 1)^3(d + 1)[/tex]

Explanation:

Let 

[tex]f(x) = e^{-x} + 8xe^x - x^2 e^x[/tex].
[tex]d^n (f(x))[/tex] = nth derivative of f

Note that 

[tex](d + 1) (e^{-x}) = d (e^{-x}) + e^{-x} = -e^{-x} + e^{-x} = 0 \\ \boxed{\Rightarrow (d + 1)e^{-x} = 0} [/tex]

So, (d + 1) annihilates [tex]e^{-x}[/tex]. 

Note that 

[tex](d + 1) (8x e^x - x^2 e^x) = d(8x e^x - x^2 e^x) + (8x e^x - x^2 e^x) \\ = (8e^x + 8x e^x - 2x e^x - x^2 e^x) + (8x e^x - x^2 e^x) \\ \boxed{(d + 1) (8x e^x - x^2 e^x) = 8e^x + 14x e^x - x^2 e^x}[/tex]

Let [tex]g(x) = 8e^x + 14x e^x - x^2 e^x[/tex]

For any real number [tex]\alpha[/tex] and positive integer n, 

[tex](d - \alpha)^n (c_1 e^{\alpha x} + c_2 xe^{\alpha x} + c_3 x^2 e^{\alpha x} + ... + c_n x^{n - 1} e^{\alpha x}) = 0 [/tex]      (1)

So, for g(x), [tex]\alpha = 1, n = 3[/tex]. Thus, using equation (1),

[tex](d - 1)^3 (8e^x + 14x e^x - x^2 e^x) = 0[/tex]     (2)

Since, [tex]8e^x + 14x e^x - x^2 e^x = (d + 1) (8x e^x - x^2 e^x)[/tex] , 

[tex](d - 1)^3 ((d + 1) (8x e^x - x^2 e^x)) = (d - 1)^3 (8e^x + 14x e^x - x^2 e^x) = 0[/tex]

Moreover, since [tex](d + 1) (e^{-x}) = 0[/tex]

[tex](d - 1)^3(d + 1) (e^{-x}) = (d - 1)^3 (0) [/tex]
[tex]\\ \boxed{(d - 1)^3(d + 1) (e^{-x}) = 0 }[/tex]     (3)

Hence based on equations (2) and (3),

[tex](d - 1)^3(d + 1) (e^{-x} + 8xe^x - x^2e^x) \\ = (d - 1)^3(d + 1)(e^{-x}) + (d - 1)^3(d + 1)(8xe^x - x^2e^x) \\ = 0 + 0 \\ \boxed{(d - 1)^3(d + 1) (e^{-x} + 8xe^x - x^2e^x) = 0}[/tex]

Therefore, the linear operator [tex](d - 1)^3(d + 1)[/tex] annihilates [tex]e^{-x} + 8xe^x - x^2e^x[/tex].



Final answer:

To find the differential operator that annihilates the given function e^(-x) + 8xe^x - x^2e^x, we individually find differential operators for each term. The operators d^2, d^3, and d^4 annihilate e^(-x), 8xe^x, and x^2e^x respectively. The least common multiple of these operators is d^4, which is the common operator that annihilates the entire function.

Explanation:

To find a linear differential operator that annihilates the function e−x + 8xex − x2ex, we must apply an operator that, when used on these functions, yields zero. For simplicity, we can use d to represent the differential operator d/dx. We annihilate each term independently and find a differential operator common to all terms.

Starting with the first term e−x, we note that d(e−x) = −e−x. Applying d again gives us d(d(e−x)) which is e−x. Thus, applying d2 annihilates e−x.

Annihilating 8xex and x2ex

Next, consider the second term 8xex. Applying the operator d3 to 8(xex) would be: d3(8xex) = d3(8(ex + xex))= d3(8ex) + d3(8xex) which results in zero.

For the third term x2ex, applying d4 annihilates the term, following the pattern: d4(x2ex) = d(d(d(d(x2ex)))) = 0.

The common differential operator that annihilates all three terms is the least common multiple of the individual operators for each term, in this case, d4.

hello, Can someone please help me with this math problem? thanks!

Answers

I believe it's A) because the conjugate of any number is basically inverted signs when multiplying a binomial, so [-2 - √b][-2 + √b]. It's A).

What is the approximate volume of the come 8cm and 12cm use 3.14 for pie

Answers

the answer would be 339 cm3

A fleet of vehicles is comprised of 60 vans, 20 limos, and X sedans. If 10% of all vehicles are limos, how many sedans are in the fleet?

Answers

Answer:

120 sedans are in the fleet.

Step-by-step explanation:

A fleet of vehicles is comprised of 60 vans, 20 limos and X sedans.

It is given that 10% of all vehicles are limos.

Let all vehicles be n

10% × n = 20

0.10n = 20

n = [tex]\frac{20}{0.10}[/tex]

n = 200

Now we have to calculate the number of sedans.

So  60 vans + 20 limos + x sedans = 200

80 + x = 200

x = 200 - 80

x = 120

Therefore, 120 sedans are in the fleet.

Final answer:

By knowing that 10% of the fleet are limos and that there are 20 limos, we determine that the fleet has 200 vehicles. Subtracting the known number of vans and limos from the total, we find there are 120 sedans in the fleet.

Explanation:

To solve the problem, we need to determine the total number of vehicles in the fleet and use the information that 10% of all vehicles are limos. We know there are 60 vans and 20 limos already, and we want to find the number of sedans, denoted as X.

Since 10% of the vehicles are limos and there are 20 limos, that means there must be 200 vehicles in total (because 20 is 10% of 200).

So the equation to find the total number of vehicles is: 60 vans + 20 limos + X sedans = 200 vehicles.  We already know that there are 60 vans and 20 limos, so we can say: 60 + 20 + X = 200. Solving for X, we subtract 60 and 20 from 200: X = 200 - 80 = 120.

Therefore, there are 120 sedans in the fleet.

write a whole number as a fraction the number 5

Answers

A whole number is technically the number over 1. So the whole number 5 is technically:

5/1, as 5 divided by 1 = 5


Hope this helps
5 as a fraction is 5/1. It’s like saying there are five of one stick. That means there are 5 sticks.

Hope this helped!

what is equivalent to (81m^6)^1/2

Answers

= 81^(1/2) * (m^6)^(1/2)
= 9 * m^(6*1/2)
= 9m^3

Answer: 9m^3

Step-by-step explanation:= 81^(1/2) * (m^6)^(1/2)

= 9 * m^(6*1/2)

= 9m^3

A pond is freshly stocked with 6 brown trout and 18 lake trout. The first fisherman in the area catches and releases a trout. He catches another trout a while later. What is the probability that the fisherman caught brown trout each time?

Answers

The possibility is 1 out of 8. You get this from adding up all trout (24), and then you divide that by what you are looking for (6 brown, so 24/6=4). If you have anything that says he caught # times, or something like that, multiply it by the denominator. This altogether is shown as

   24÷6= 4 so probability of  1 out of 4. times 2 because he caught 2 fish.  so then that would be 1 out of 8. :)

a taxi ride costs $3 plus $2.50 per mile. write and graph an equation in two variables that represents the total cost of a taxi ride.

Answers

we are asked to graph an equation using 2 variables.
the 2 variables in the equation are as follows;
y = total cost of taxi ride 
x = number of miles travelled per taxi ride 
we need to write the equation in slope- intercept form
y = mx + c
m = gradient /slope
mx = cost per mile travelled x number of miles travelled
c= intercept.  a fixed cost for every taxi ride 
m = $2.50 per mile
c = $3
the graph equation is as follows;
y = 2.50x + 3

Milo wants to make a mixture that is 50% lemon juice and 50% lime juice.

How much 100% lemon juice should he add to a juice mixture that is 20% lemon juice and 80% lime juice to make 4 gallons of the 50% lemon/50% lime juice mixture?

A. 0.5 gallon

B. 1.5 gallons

C. 2 gallons

D. 2.5 gallons

Answers

its actually 1.5 but ok


Answer:

The correct option is B.

Step-by-step explanation:

It is given that Milo wants to make a mixture that is 50% lemon juice and 50% lime juice.

Milo has a juice mixture that is 20% lemon juice and 80% lime juice. Milo add a 100% lemon juice.

Let the 100% lemon juice added by milo be x.

In 4 gallon of mixture contains 50% lemon juice and 50% lime juice. It means 2 gallon  lemon juice and 2 gallon lime juice.

If we add 100% lemon juice, then the quantity of lime juice will remains same.

80% of the fist mixture is 2 gallon.

20% of the first mixture is 0.5 gallon.

It means the first mature contains 2 gallon lime juice and 0.5 gallon lemon juice.

Milo will add 100% lemon juice

[tex]2-0.5=1.5[/tex]

Therefore option B is correct.

Solve log2 ( x - 1 ) + log2 ( x + 1 ) = 3

check answers are in domain

Answers

The answer is x=3, It doesn't have any domain restrictions, Therefore it covers all real numbers x∈R

Jean adds 35 and 9.how can she solve using only equations to model her thinking?

Answers

She can break up 9 three times and add it to 35 or add 35 and 9.

Hope this helps! ;)

Answer:

Step-by-step explanation: 35+(5+4)=35+5+4=40+4=44

Nacir is buying school supplies. He purchases 8 notebooks for $12.48. How much does Nacir pay for 1 notebook?

Answers

12.48/8= 1.56 per notebook

$1.56 for one notebook

if f(x) varies directly with x2, and f(x) = 96 when x = 4, find the value of f(6).

Answers

f(x)=kx
96=k(4)
k=24

f(x)=kx
f(6)=24(6)
f(6)=144

1/3 equivalent first 2 fractions

Answers

Hey there!

1/3 is equivalent to 2/6
Here is why:

1 x 2 = 2
3 x 2 = 6
You can do this by cross multiplying 1/3 and 2/6
That's how you get 2/6 as an equivalent fraction.

1/3 is also equivalent to 3/9
Here is why:
3 x 1 = 3
3 x 3 =9
You can also do this by cross multiplying 1/3 and 3/9
That's how you get 3/9 as an equivalent fraction.

There are also many other fractions that are equal to 1/3, but these are the first two.

Hope this helps you.
Have a great day!

delia spent 45 minutes working on her book report she finished at 6:10 p.m. at what time did delia start working on her paper

Answers

Delia started working on her paper at 5:25 p.m.

6:10 - 10 = 6:00

6:00 - 35 =5:25

When she finished the work, the time was 6:10 p.m. In other words, 6 hours and 10 minutes.

It says that she took 45 minutes to complete the work.

We need to find the time when she started working on it.

Start Time = Finish Time - time taken to complete work.

Start Time = (6 hours and 10 minutes) - 45 minutes

(Hint:- 1 hour = 60 minutes)

Start Time = (5 hours and 70 minutes) - 45 minutes

Start Time = 5 hours and 25 minutes i.e. 5:25 p.m.

It means that she started the work at 5:25 p.m.

is 7/8×6/6 greater then, equal to, or less than 7/8

Answers

7/8*6/6 is equal to 7/8
7/8 times 6/6 is equal to 7/8.

6/6 simplified equals 1.
7/8 times 1 would equal 7/8.
Therefore, 7/8 times 6/6 is equal to 7/8.

The length of a rectangle is 7 m less than triple the width. if w represents the width, write an expression for the length, l. question 13 options:

Answers

EHDGFSYGEVA‰ wetywrty

how much water do you add  to make 12% sugar syrup using 5g sugar?

Answers

so the syrup is just water and sugar, we know that the sugar percent is just 12%, and that happens to be 5grams.

now 100% - 12% is 88%, so the 88% leftover will just be water.

if 12% is 5g, how much is 88%?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 5&12\\ x&88 \end{array}\implies \cfrac{5}{x}=\cfrac{12}{88}\implies \cfrac{5}{x}=\cfrac{3}{22}\implies 110=3x \\\\\\ \cfrac{110}{3}=x\implies 36\frac{2}{3}=x[/tex]

Answer:

[tex]36\dfrac{2}{3}[/tex] g of water.

Step-by-step explanation:

You know that 5 g of sugar form 12%. Let x g be the amount of water needed. The total amount of syrup will be x+5 g. Then

5 g - 12%,

x+5 g - 100%.

Mathematically, you can write a proportion:

[tex]\dfrac{5}{x+5}=\dfrac{12}{100}\Rightarrow 500=12(x+5),\ 500=12x+60,\ 12x=440, \\ \\x=\dfrac{440}{12}=\dfrac{110}{3}=36\dfrac{2}{3}.[/tex]

Simplify (SecX-TanX)(1+sinX) X stands for theta

Answers

[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\ -------------------------------[/tex]

[tex]\bf [sec(\theta )-tan(\theta )][1+sin(\theta )]\implies \left[ \frac{1}{cos(\theta )}-\frac{sin(\theta )}{cos(\theta )} \right][1+sin(\theta )] \\\\\\\ \left[\frac{1-sin(\theta )}{cos(\theta )} \right][1+sin(\theta )]\implies \cfrac{\stackrel{\textit{difference of squares}}{[1-sin(\theta )][1+sin(\theta )]}}{cos(\theta )} \\\\\\ \cfrac{1^2-sin^2(\theta )}{cos(\theta )}\implies \cfrac{cos^2(\theta )}{cos(\theta )}\implies cos(\theta )[/tex]

Please help with the question. For some reason, I find it confusing and I need some assisstance. Thank you!

Answers

All you have to do is plug in the tables to T. Since there's 5 tables, your new equation will be C=4x5+2. Then, you solve using pemdas.
C=4x5+2.
C=20+2
C=22

You need 22 chairs. 

Answer: i think it is 22

Step-by-step explanation:

Assume you have a poker chip set containing blue, red, and white chips, all of the same size. you place 15 blue chips, 10 red chips, and 25 white chips in a bag. as you are about to randomly draw a chip from the bag, you bet your friend you will pick a red chip from the bag because you feel that red is your lucky color.

Answers

Is the question what is the probability that you draw a red chip? If it is, the answer is 10/50, which can be simplified to 1/5, 0.2 or 20%.

The graph below shows the solution set to which system of inequalities?

Answers

we have that

using a graph tool
I proceed to verify each case to get the answer
see the attached figure

case A) 
y> 2x-4    y>=-x     y<=3

case B) 
y> 2x-4    y>=-x     y<3

case C) 
y< 2x-4    y>=-x     y<=3

the answer is the option A)
y> 2x-4    y>=-x     y<=3


Evaluate. 134 × -7
A)-2,158
B)-828
C)-938
D)938

Answers

It's C
Because you are multiplying a positive and a negative your answer should be negative
The answer to the question is -938 
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