The volume of a rectangular prism with a cone shaped hole in it is approximately 163.22cm³ (as shown below).
✏️ What is the height of the cone?

The Volume Of A Rectangular Prism With A Cone Shaped Hole In It Is Approximately 163.22cm (as Shown Below).

Answers

Answer 1

Answer:

Height of the cone = 5 cm

Step-by-step explanation:

Volume of the rectangular prism with a cone shaped hole = Volume of the rectangular prism - Volume of the cone

Volume of the rectangular prism = Length × Width × Height

                                                       = 5 × 5 × 7

                                                       = 175 cm³

Volume of the cone = [tex]\frac{1}{3}\pi r^{2}h[/tex]

Here, r = Radius of the cone

h = Height of the cone

Volume of the cone = [tex]\frac{1}{3}\pi (\frac{3}{2})^{2}(h)[/tex]

                                 = 0.75πh cm³

Volume of the rectangular prism with a hole = 163.22 cm³

175 - 0.75πh = 163.22

0.75πh = 175 - 163.22

0.75πh = 11.78

h = 5 cm


Related Questions

State the leading coefficient of -7x+10x^3-9x^5+3x^2+3?

Answers

Answer:

-9

Step-by-step explanation:

-7x+10x^3-9x^5+3x^2+3

We need to write the terms from highest power to smallest power

-9x^5+10x^3+3x^2-7x+3

The leading coefficient is the number in front of the highest power

-9

Three consecutive integers have a sum of -42. Write and solve an equation to find the three integers.​

Answers

Let the first integer be x.

Let the second integer be x + 1 .

Let the third integer be x + 2 .

According to the question

x + ( x + 1 ) + ( x + 2 ) = -42

Opening the brackets and simplifying :

x + x + 1 + x + 2 = -42

3x + 3 = -42

Now , solving equation :

[tex]\bf \rightarrow \: \:3x \: + \: 3 \: = \: -42[/tex]

[tex]\bf \rightarrow \: \: 3x \: = \: -42 \: - 3[/tex]

[tex]\bf \rightarrow \:3x \: = \: -45 \: [/tex]

[tex]\bf \rightarrow \:x \: = \: \frac{ - 45}{ \: 3} \\ [/tex]

[tex]\bf \rightarrow \:x \: = \: \cancel\frac{ - 45}{ \: 3} \: \: ^{ - 15} \\ [/tex]

[tex]\bf \rightarrow \:x \: = \: - 15[/tex]

[tex]{\boxed{ \Large{ \red{ \rm{ \underline{ Now \: \: substitute}}}}}}[/tex]

[tex]\bf \implies \: \:x \: = \: - 15[/tex]

[tex]\bf \implies \: \:x \: + \: 1 \: = \: - 15 \: + \: 1 \: = \: - 14[/tex]

[tex]\bf \implies \: \:x \: + \:2 \: = \: - 15 \: + \: 2 \: = \: - 13[/tex]

-15 , -14 and -13 are the three consecutive integers.

**URGENT PLEASE HELP**
Find g(x), where g(x) is the translation 2 units right and 13 units down of f(x) = -2x + 5.​

Answers

Answer:

g(x)=x+9

Step-by-step explanation:

When translating a graph, adding the number of units shifts the graph to the left and subtracting the number of units shifts it to the right. Since you need the graph translated 9 units to the left, you will need to add that many units to x

therefore, g(x)=x+9

Answer:

g(x)=x-8

Step-by-step explanation:

-2+2 = 0, so g(x) = x

5-13 = -8

Help please fast geometry surface area!

Answers

Answer:

SA=2πrh+2πr2=2·π·12·3+2·π·122≈282.7cm2

6
с
2
3.
43
In the figure, which angle has the same measure as 22?
A. 21
B. 23
C. 24
D. 25

Answers

I think the answer is 5 not sure tho

In parallelogram ABCD, m∠B = 105°.



What is the value of x. (Round your answer to the nearest tenth, if necessary.)

Answers

Answer:

x=52.5

Step-by-step explanation:

Since ABCD is a parallelogram, B= ADC. So angle ADC is 105. Next since ED=AD, angle EAD=angle AED=x and ADE=75. So 2x+75=180, 2x=105, x=105/2

In parallelogram ABCD, m∠B = 105° then the value of x = 52.5

What is a parallelogram?

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

Since ED ≈ AD,

∆AED is an isosceles triangle where ∠EAD and ∠AED has the same angle measurement

Now, ∠B = 105°, since ABCD is a parallelogram,

∠B = ∠D

∠ADC = 105°

∠ADE = 180°-105° = 75°

Now, ∠EAD + ∠AED+ ∠ADE = 180°

∠AED+∠AED+∠ADE = 180°

x+x+75°=180°

2x=180+75°

2x = 105°

x = 52.5°

Learn more about parallelogram;

https://brainly.com/question/1563728

#SPJ2

Amy bakes and sells cupcakes out of her home. She uses baking pans that hold 12 cupcakes and 36 cupcakes to fill her orders. Amy needs to fill her biggest order of 504 cupcakes for a special event.
a. Write an equation to represent the number of 12-cup and 36-cup baking pans for her
order.

b. Amy needs to use a combination of the 12-cup and 36-cup baking pans to fill the order. With only eighteen 12-cup baking pans in her shop, how many of the 36-cup baking pans does she need to complete the order?

Answers

Answer:

Below

Step-by-step explanation:

a) let's say that x represents the number of 12 pan cupcakes and y represent the number of 36 pan cupcakes. For her larger order she needs 504 cupcakes so that is the total. This can be demonstrated by the equation below!

    12x + 36y = 504

b) here we know that x = 18, so...

     12(18) + 36y = 504

      216 + 36y = 504

                36y = 288

     Divide both sides by 36

                     y = 8

Amy needs 8 of the 36 cup baking pans in order to complete her order.

Hope this helps! Best of luck <3

Evelyn earned a score of 86 on Exam A that had a mean of 71 and a standard deviation of 20. She is about to take Exam B that has a mean of 550 and a standard deviation of 40. How well must Evelyn score on Exam B in order to do equivalently well as she did on Exam A? Assume that scores on each exam are normally distributed.

Answers

Answer:

580

Step-by-step explanation:

Assuming that the answer should be in terms of z scores, we can calculate the z score as

z = (observed value - mean)/(standard deviation)

For the first exam, the observed value is 86, the mean is 71, and the standard deviation is 20. The z score fot that exam is

z = (86-71)/20 = 0.75

Then, for the second exam, Evelyn has to do equivalently well, so the z score must be the same. Therefore, we have

0.75 = (observed score - 550)/40

multiply both sides by 40 to remove a denominator

0.75 * 40 = observed score - 550

add 550 to both sides to isolate the observed score

0.75 * 40 + 550 = observed score = 580

Maya is learning to drive, so this weekend she practiced driving 1/2 of a mile with her mother and another 3/4 of a mile with her father. How far did Maya drive in all?

Answers

Step-by-step explanation:

1/2 + 3/4

= 2/4 + 3/4

= 5/4

= 1 and 1/4 miles

The population of valleytown is also 5,000 with an annual increase of 1,000. Can the expected population for Valleytown be modeled with an exponential growth fu nction ? Explan

Answers

Answer:

An annual increase of 1000 means that the number by which the population increases is constant, which means that the population cannot be modeled with an exponential growth function, it is modeled by a linear growth function.

Step-by-step explanation:

Linear growth:

The number by which it increases is constant.

Exponential growth:

The rate which it increases is constant, that is, a proportion of population.

Annual increase of 1,000.

An annual increase of 1000 means that the number by which the population increases is constant, which means that the population cannot be modeled with an exponential growth function, it is modeled by a linear growth function.

after allowing a 15% discount on the Marked price of a radio becomes rupees 1997 find the Marked price of the radio​

Answers

Answer:

after discount sales price is rs 1997 which is 85 % of market price the market price = 1997/85×100 = 2350 ans.

Discount 15% find the marked price

The population of a large U.S. city is 2,707,210. Which of the following best expresses this population?
A 2.7 × 106 C 2.707 × 106
B 2.7 × 107 D 27.07 × 106

Answers

Answer:

2.707 * 10^6

i think it is the best expression

here is another question i need help

Answers

the one you have selected is correct

Find the missing length the triangles are similar.

Answers

Answer:

Step-by-step explanation:

The missing length is 13 because,

Lets say the top triangle is A and the bottom triangle is B.

Triangle A gives us the side GF, and Triangle B gives us the sides TU and ST. Since the triangles are similar(as stated in the problem), we can pair 2 sides GF(A) and TU(B) which is 11:22.(one way I usually figure which sides are similar is by first- matching the hypotenuse, then checking which of the remaining two is longer.. if that made any sense). You can see that their relationship is x2 or /2 (In another word, from A to B is multiplication- ex: 11 * 2 is 22, and from B to A is division- ex 22/2 is 11.) Since the missing number is the hypotenuse of triangle A and you know the Hypotenuse of triangle B all you have to do is divide side TS by 2 to get side SF. So the missing side is 13.

Answer: 13

A basketball team won 8 games and lost 7 games. Based on these results what is the probability of winning a game

Answers

the probability is made of the desired outcome divided by the total outcome.

desired = wins = 8

total = wins and losses = 15

8/15 is the probability (approx. 53%)

hope it helps :)

The speed of a car as a function of time is shown in the figure(attached up) . Find the distance travelled by the car in 8 seconds and its acceleration .

Answers

______________________________

[tex]\sf\bold{The\:above\:graph\:says:}[/tex]

$\sf\bold\red{a=slope\:of\:v-t\:graph}$

$\space$

$\sf\bold{here:}$

$\sf\bold\red{a=acceleration}$

$\space$

$\sf\bold{Find\:acceleration\:by\:v-t\:graph:}$

$\mapsto$ $\sf\small{TanØ =}$ $\sf\dfrac{slope\:of\:y}{slope\:of\:x}$= $\sf\dfrac{20}{8}$ $\sf{m/s^2}$

$\space$

$\mapsto$ [tex]\sf\underline\bold\purple{a=2.5m/s^2}[/tex]

$\space$

$\sf\bold{Now,calculate\:the\:distance:}$

$\sf\bold{By\:equation\:of\:motion.}$$\sf{s=}$ $\sf{ut+}$ $\sf\dfrac{1}{2}$ $\sf{at^2}$

$\space$

$\sf\bold{Given\:parameters:}$

$\sf\bold{u=0}$$\sf\bold{a=5/8}$$\sf\bold{t=8}$

$\space$

$\sf\bold{Substituting \: the\:values:}$

$\mapsto$ $\sf\small{s=0+}$ $\sf\dfrac{1}{2}$ $\times$ $\sf\dfrac{5}{8}$ $\sf\small{8^2}$

$\space$

$\longmapsto$ $\sf\underline\bold\purple{S=80m}$

$\space$

❍Therefore , the acceleration is $\sf\bold{2.5m/s^2}$ and the distance traveled by car is $\sf\bold{80m.}$

_______________________________

80 m is distance ! Please mark as brainliest


Last year, Mary opened an investment account with $5400. At the end of the year, the amount in the account
had decreased by 6%.

Answers

6/100*5400
324
5400-324
5076 final answer

Triangle ABC with vertices A(-4, 2), B(4,7), and
C(5, 1) in the x-axis.
A’
B’
C’
D’

Answers

9514 1404 393

Answer:

  A'(-4, -2), B'(4, -7), C'(5, -1)

Step-by-step explanation:

Reflection in the x-axis changes the sign of each y-coordinate.

  (x, y) ⇒ (x, -y)

  A(-4, 2) ⇒ A'(-4, -2)

  B(4, 7) ⇒ B'(4, -7)

  C(5, 1) ⇒ C'(5, -1)

Is the equation below written in standard form? If not, select which explanation best applies to why the equation
is not written in standard form.
12 = 2x + 4y
A. the requirement that A 20 is not satisfied
B. the requirement that A and B are not both zero is not satisfied
C. A, B, and C do not have a greatest common factor of 1
D. the equation is written in standard form

Answers

Answer:

D

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers

12 = 2x + 4y , that is

2x + 4y = 12 ← is in standard form

PLS HELP MEE

1st equation: a^2 + b^2 = c^2
2nd equation: a^2 + b^2 = n^2

Since the equations for both triangles have a^2 + b^2, you can think of the two equations for c^2 and n^2 as a system of equations. Substitute what a^2 + b^2 equals in the first equation for a^2 + b^2 in the second equation. After you substitute, what equation do
you get?

Answers

Answer:

c² = n²

Step-by-step explanation:

Given the 2 equations

a² + b² = c² → (1)

a² + b² = n² → (2)

Substitute a² + b² = c² into (2)

c² = n²

Writing equations in standard form:

(1,-6) and (-7,2)

How would I write this in standard form? I already tried but I keep getting x+y=7 and it says it’s wrong so could someone help?

Answers

Answer:

[tex]x + y = - 5[/tex]

Step-by-step explanation:

hopefully it is clear and makes sense

:)

Plz help me out with this ;)

Answers

I have the same problem with you

What is 3x^2-5x-13=0

Answers

Answer:

D. 58

Step-by-step explanation:

Given, 3x+8x+4x=6x+63

⇒15x=6x+63

⇒9x=63

⇒x=7

Then 5x+23=5(7)+23

=35+23

=58

A rectangular box contain 782 apples. If there are 23 rows in a box, how many columns are there?

Answers

Answer:

34

Step-by-step explanation:

This is because you will have to simply divide 782 by 23.

782 / 23 =

34 :D

[tex]\sqrt{\\\frac{9+\sqrt{17} }{2}[/tex]

Answers

[tex]\huge\underline\pink{✏ANSWER}[/tex]

Hello and sorry but it's a Gatheted Question Can you fix it Can you?

Sorry for answering a nonsense

#BrainliestBunch

What is the area of the circle?

Answers

Diameter = radius x 2

So, the radius is half of the denominator.

10 / 2 = 5

A = pi x r^2

A = pi x 5^2

A =  3 x 25

A = 75 ft^2

Hope this helps!

the first three terms of an arithmetic progression are m,12 and n . Find the value of m+n​

Answers

Answer:  24

===========================================

Explanation:

There are a few approaches. Here's one way to solve.

Let d be the common difference between the terms.

We add d to each term of this arithmetic sequence to get the next term.

First term = mSecond term = 12 = m+dThird term = n = (m+d)+d = m+2d

Focusing on the second equation, we can solve for d like so

m+d = 12

d = 12-m

This is then plugged into the third equation

n = m+2d

n = m+2(12-m)

n = m+24-2m

n = 24-m

Therefore,

m+n = m+(24-m) = 24

It turns out that it doesn't matter what m and n are because m+n is always equal to 24 in this case.

-----------------

A more concrete example:

Let's say m = 2. We won't set up n just yet but we'll be able to compute it fairly soon.

Since m = 2, this means d = 12-m = 12-2 = 10. This is the gap between adjacent or neighboring terms.

If d = 10, then the third term must be n = 12+d = 12+10 = 22

We can then see that m+n = 2+22 = 24

-----------------

I'll do another example:

m = 5

d = 12-m = 12-5 = 7

n = 12+d = 7 = 19

m+n = 5+19 = 24

Whenever in doubt, or if you get stuck, it helps to come up with actual numeric values to hopefully clear things up.

-----------------

An alternative way to get the answer:

Let's try to determine what m+n is actually saying. We have 12 right in the middle of the first term (m) and third term (n). Because the gap between the numbers is the same (that being d), we know that 12 is the midpoint of m and n. It might help to draw out a number line to see what's going on.

The midpoint of m and n is (m+n)/2

Set this equal to 12 and isolate the "m+n"

(firstTerm+thirdTerm)/2 = second term

(m+n)/2 = 12

m+n = 2*12

m+n = 24

So in general, if the first three terms of the arithmetic sequence are m, k, n, then m+n = 2k.

Write an equation of the graph (shown below) in slope intercept form.

Answers

Answer:

Step-by-step explanation:

Okay! so first, let's specify the components of a slope intercept form equation.

We got y=mx+b as a general formula, where m is slope and b is the y intercept.

The graph gives us two points on the line at (0, 5) and (-6, 7)

To find slope, we can use this slope equation. I suggest you memorize it-it helps a lot with future problems!

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1} }[/tex]

Plugging in the points into the equation, we get 2/-6, or -1/3

we really don't need to do much work anymore, since the choices are given. There is only one choice left with -1/3 as slope m, which is D.

The y intercept can be found at wherever the line intersects the y axis. In this line, it crosses 5, which means b=5.

y=mx+b

y=-1/3x+5

For his long distance phone service, tony pays $3 monthly fees plus 11 cents per minute. Last month, Tony's long distance bill was $22.03. For how many minutes was tony billed

Answers

Answer:

11+11= 22 answer is $ 22.03

Emília ganhou 350 reais de sua avó. Com esse dinheiro, ela comprou um sapato, e uma roupa que custou o dobro do preço do sapato. Os 200 reais que sobraram foram depositados por Emília em sua conta poupança.

Qual é a equação eu permite determinar o preço x, em reais, que Emília pagou por esse sapato?

A) x + 2× = 350
B) x + 2× 200 = 350
C) x + (x + 2) + 200 = 350
D) x + ײ + 200 = 350

Answers

The answer is going is B: x + 2 x 200 = 350
Other Questions
2. Dentre as formas de representar um nmero decimal, a mais comum a que utiliza vrgula. Valor como 0,25 est presente nos comrcios, nos hospitais, nas lanchonetes e em muitos outros lugares. Esse valor tambm pode ser representado por A. ( ) 25/10 B. ( ) 1/4 C. ( )1/25 D. ( ) 1/25 A viral music video is spreading to many parts of the world as children love to watch and sing along with the song. What type of diffusion would this represent?relocationexpansioncontagious Which symbol and unit of measurement are used for electric current? symbol. A, unit: 1 symbol: C, unit: A symbol l; unit C symbol: 1; unitA Consecutive numbers are whole numbers that follow in order such as 7, 8, 9, 10, and so forth. Suppose the average of 15 consecutive numbers is 15. What is the average of the first five numbers of the set? How did the Battle of Bunker Hill impact colonists?? Why can't an average annual temperature and average annual precipitation tell you about climate? Because a single average does not show you a pattern over the course of years, Because climate only concerns precipitation and not temperature Because climate only concerns temperatures and not precipitation. Because it doesn't reveal the actual location on the surface. Can I get some help please How to think like psychological scientist? PLS HELP!! EXTRA POINTS FOR THE QUICKEST REPSONSE, AS WELL AS THE MOST HELPFULL (AND RELEVANT) ANSWER (BRAINLIEST) !!!I appreciate any help given!!Write one complete paragraph in which you reflect on the impact of the changing nature of labor and land ownership in the post-Civil War era. Be sure to write a topic sentence that addresses all parts of the prompt, support it with examples and evidence, and leave your readers with a thoughtful conclusion. What are the steps to understanding this problem as well as the answers. What is the slope of the line in the graph? Aaron is 63 inches tall. In order to ride a roller coaster at an amusement park, a person must be 5 feet tall. Is Aaron tall enough to ride a roller coaster? How many inches shorter or taller is he than 5 feet Circle the letter of the correct answer Yes. He is 3 inches taller than 5 feet Yes. He is 13 inches taller than 5 feet No. He is 7 inches shorter than 5 feet No. He is 17 inches shorter than 5 feet Tina chose A as the correct answer. How did she get that answer? If 5 and 12 are the two smallest values in a Pythagorean triple, what is the largest value, c, in the triple? Firm A has a 21 percent marginal tax rate, and Firm Z has a 28 percent marginal tax rate. Firm A owns a controlling interest in Firm Z. The owners of Firm A decide to incur a $9,500 deductible expense that will benefit both firms.Required:Compute the after-tax cost of the expense assuming that:a. Firm A incurs the expenseb. Firm Z incurs the expense what is the theme of "freeing the pike" short story by Richard Wagamese If a company spends $80 million to build facility space sufficient to hold 5 million pairs of footwear-making equipment at a site in Latin America, then the company's annual depreciation costs for this facility space will be Your grandfather put some money in an account for you on the day you were born. You are now years old and are allowed to withdraw the money for the first time. The account currently has in it and pays an interest rate.Required:a. How much money would be in the account if you left the money there until your twenty-fifth birthday?b. What if you left the money until your sixty-fifth birthday?c. How much money did your grandfather originally put in the account? Traduzca la siguiente frase. Sabes si habr mucha gente en la conferencia sobre energa renovable?A. Do you know if there are a lot of people at the conference on renewable energy? B. Do you know if there will be a lot of people at the conference on renewable energy? C. Do you know if there were a lot of people at the conference on renewable energy? D. Will there be a lot of people at the conference on renewable energy? Select the market segment that looks the most promising? 1. Luxury trenfollowers Segment size 5,000(5%)Growth rate 7%2. School children Segment size 35,000 (35%) Growth rate 1%3. University students Segment size 24,099(24%) Growth rate 5%4. Outdoor enthusiasts Segment size 14,000 (14%) Growth rate 5%5. Urban commuters Segment size 20,000 (20%) Growth rate 3% Good afternoon. Kindly assist on the following please. Assignment due by 4:30pm Mike bookshop had the following structure. Share capital 500000 ordinary shares of $1 each. 300000 10% preference of $1 each. Reserves Share premium 200 000 General reserves 100 000 Retained earnings 400 000 8% debenture 100 000 During the year the following transaction took place. 01 January issue of 200 000 $1 ordinary shares at$1,20 and 100 000 preference shares at $2 each. 01 June a 1 for 4 right issue at a premium of $0,10c each per share. 01 December 1 for 5 bonus shares fully paid. All shares issued during the year qualified for bonus and the company wishes to leave the reserves in their flexible form. Required. Balance sheet extract.