Item 13
Which expressions represent the volume of the cone, where $r$ is the radius and $h$ is the height?




$\frac{\pi h^3}{48}$

$\frac{16\pi r}{3}$

$\frac{\pi h^2}{12}$

$\frac{4}{3}\pi r^3$

Answer:

61

Step-by-step explanation:

It should be 61

Square 60 and 11 and add them together to get 3271

Then square root 3271

You'll get 61

Which is the answer

Area of region A is equal to the sum of area of region B and area of region C when a right-angled triangle is formed by the diameters of three semi-circular regions A, B, and C.

Let the diameters of semicircle A, B and C be a, b and c respectively.

We know area of a semi-circular region of diameter d is

A = (1/2)(πd²/4)

A = πd²/8

Thus,

area of region A is πa²/8

area of region B is πb²/8

area of region C is πc²/8

The triangle formed is a right angled triangle, with hypotenuse a and legs b and c. By Pythagoras theorem

a² = b² + c²

Multiplying both sides by π/8

(π/8)a² = (π/8)(b² + c²)

πa²/8 = πb²/8 + πc²/8

Area of region A = Area of region B + Area of region C

Hence proved.

--The question is incomplete, answering to the question below--

"A right-angled triangle is formed by the diameters of three semi-circular regions A, B, and C as shown in the diagram. Show that area of region A = area of region B + area of region C."

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Answer:

A) 2.45 seconds

B)\(\begin{center}\begin{tabular}{ c c}\bold{Average Velocity} & \bold{Velocity at strike of water} \\ 39.18 & 78.4 \\ \end{tabular}\end{center}\)

Step-by-step explanation:

Distance \(s\) (in feet) from the top of cliff after \(t\) seconds when a rock is dropped off the edge of a cliff is given as:

\(s(t)=16t^2\)

Distance from the top of cliff to water = 96 ft

To find:

A) When will the rock strike the water

i.e. The time taken by the rock to travel the distance of 96 ft.

B) Table of Average Velocity and approximate velocity at which the rock strikes the water ?

Solution:

A) Given that distance traveled = 96 ft

To find the value of \(t\)

Putting the value of \(s\) in formula: \(s(t)=16t^2\) to find \(t\):

\(96 = 16t^2\\\Rightarrow t^2=6\\\Rightarrow \bold{t = 2.45\ sec}\)

B) The velocity at which the rock hits the water:

We need to differentiate \(s(t)\) w.r.to \(t\) in order to find the velocity at any instant.

\(s'(t) =\dfrac{d}{dt}s(t) = \dfrac{d}{dt}(16t^2)\\\Rightarrow v = 2\times 16t^{(2-1)}\\\Rightarrow v = 32t\)

The time taken to reach the water is 2.45 seconds.

Putting \(t\) = 2.45 seconds to find the velocity:

\(v = 32\times 2.45 = 78.4\ ft/sec\)

Average velocity is given as total distance traveled and total time taken.

\(\text{Average Velocity = }\dfrac{\text{Total Distance traveled}}{\text{Total Time Taken}}\)

\(\text{Average Velocity = }\dfrac{96}{2.45}\\\text{Average Velocity = 39.18\ ft/s}\)

\(\begin{center}\begin{tabular}{ c c}\bold{Average Velocity} & \bold{Velocity at strike of water} \\ 39.18 & 78.4 \\ \end{tabular}\end{center}\)

Answer:

2(x-3)

Step-by-step explanation:

2x² - 2x - 12= 2(x²-x+6)= 2(x²+2x- 3x+6)= 2(x-3)(x+2)

Step-by-step explanation:

use formula

volume of cone =1/3 πr²h

Answer:

50%

Step-by-step explanation:

Only 4 and 5 can be considered because 6 is not included, so the probability would be 2/4, or 50%.

Answer: 50%

Step-by-step explanation: It says if you pick a random card that is less than 6 or 4. That means that 4 and 5 are the ones you hope to get. 2/4 = 50%.

Answer:

Step-by-step explanation:

the first one is not a constance a constance is a number all by its self and if a letter is all by their self that counts as a constance two all you have to do next time is just search up the definition

Answer:

5/8

Step-by-step explanation:

7/8-1/4=5/8

7/8 stays the same

1/4 turns into 2/8

Therefore , the solution to the given problem of equation comes out to be the cost of carpet is $2072.

An equation is referred to as linear when all of the highest powers of the variables are equal to one. The components are interconnected. This kind of issue is also known as a one-degree equation. Learn how to solve a linear equation in one or two variables using the standard form, formula, graph, and instructions in the following paragraphs.

Here,

Given :

floor area of a square feet is 50a + 12h,

where h is the number of hours

Thus.

At t =6 and a =40

So ,

the cost of carpet

=> Cost =  50a + 12h

=> Cost =  50*40 + 12*6

=> Cost = 2000 + 72

=> Cost = 2072

Therefore , the solution to the given problem of equation comes out to be the cost of carpet is $2072.

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The difference between the two given temperature values is 24 °F

We have got an equation that can relate these three units of measurement of temperature, as given below:

c/5 = (F - 32)/9= (K - 273)/5

where C represents the measurement of a fixed temperature in celsius, F represents the measurement of that same intensity temperature in fahrenheit, and K represents the measurement of equally intense temperature in kelvin.

The given parameter the lowest temperature = -3 °F

the highest temperature = 21 °F

To determine the difference between the two given temperature values.

The range or difference between the two given temperature values is calculated as follows;

Range = highest - lowest

Range = 21 °F -(-3 °F)

Range = 24 °F

Thus, the difference between the two given temperature values will be 24 °F

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The term most likely to be considered an ordinal variable among the given options is:
c. Education level

How do you know if a variable is ordinal?

A purely nominal variable is one that simply allows you to assign categories but you cannot clearly order the categories. If the variable has a clear ordering, then that variable would be an ordinal variable.

Your answer: Education level (c) is most likely to be considered an ordinal variable because it involves a ranking or order, such as high school diploma, bachelor's degree, master's degree, etc., where each level has a specific order but the differences between levels are not numerically equal.

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Answer:

Solution given:

the area of the red triangle =½(a×b)unit²

So area

The volume of the second cone is gotten as; 56π m³

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor.

Volume of cone A = 24π m³

Height of cone A = 6 m

Volume of cone B = B

Height of cone B = 14 m

24π/B = 6/14

Cross multiply to get;

B = (24π * 14)/6

B = 56π m³

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0.0910, I think.

-

-

-

-

-

-

-

My dyslexia did not like theese numbers

Answer: 4 minutes and 10 seconds

To solve this equation you need to follow the BODMAS rule and also the rules of algebraic expressions as there is an x.

So the equation to be solved is 5(7-x)+32=106-1. 5(4x+18). Here the sign '.' is taken to be multiplication and not decimal, as there is space between '1' and '5'.

Forwarding with the sum: First solve L.H.S. 5(7-x)+32, = 35 - 5x + 32, = 67 - 5x. Now doing R.H.S. 106-1. 5(4x+18), = (105) (20x + 90), = 2100x + 9450.

Now, find the value of x. L.H.S. = R.H.S.

67 - 5x = 2100x + 9450.

-5x - 2100x = 9450 - 67

- 2105x = 9383. So we have the value of x. Where x= 9383+2105. Therefore x= 11488.

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Answer:

308

Step-by-step explanation:

this is the answer right

The total number of pages in the book is 180.

Total number of pages:

It refers the number of pages in the prescribed book.

And if we want to find the total number of pages, then we have to add the read pages and the remaining pages.

Given,

Jimmy read 2/15 of a book on Monday, 1/3 on Tuesday, 2/9 on Wednesday and 3/4 of the remainder on Thursday. If he still had 14 pages left to read on Friday.

Here we need to find the total number of pages in the book.

Let us consider x be the number of pages in the book.

The portion of book read by Jimmy on Monday is 2/15

The portion of book read by Jimmy on Tuesday is 1/3

The portion of book read by Jimmy on Wednesday is 2/9

The portion of book read by Jimmy on Thursday is 3/4

And the remaining pages to read on Friday is 14

So, the total of all is:

=> x (2/15 + 1/3 + 2/9)

=> x (6 + 15 + 10)/45

=> 31x/45

So, for Thursdays, he reads 3/4 of the remainder of the book.

He has (1 - 31/45)x left that is 14x/45.

So, he reads 3/4 of this; which is

=> 3/4(14x/45) = 42/180x.

Therefore, until Thursday he has read

=> 31/45x + 42/180x.

We know that here 180 would be a common denominator;

Now we have to convert these fractions,

Then we have,

124/180x + 42/180x = 166/180x

Up to this point, he has 14 pages left;

Therefore, this means he has read 14 pages less than x, the total number of pages.

Then the given equation is written as,

166/180x = x-14

0 = 14/180x - 14

Adding 14 to each side gives us, then we get,

14 = 14/180x

14(180)/14 = x

180 = x

Therefore, there are 180 pages in the book.

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Answer:

water=32 meters tall

Step-by-step explanation:

16/30=x/60

x=32

The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in (4 choose 3) = 4 ways.

The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in (6 choose 3) = 20 ways.

Therefore, the probability that there will be no graduate students on the subcommittee is:

Number of subcommittees with only undergraduate students / Total number of possible subcommittees

= 4 / 20

= 1/5

= 0.2

So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

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Answer:

D = (6, -4)

E = (2, 1)

F = (-3, -5)

x-axis makes the y coordinate negative

As we know 1 kilometer = 39370.079 inches

and, 8.39 kilometer = 330,315 inches.

Kilometers: - It is a unit of length in the international system of units (SI) equal to one thousand meters. It is now the measurement unit used for expressing distances between geographical places on land in most of the world.

Inches: - It is a unit of length in the British imperial and united states customary system of measurement. It is equal 1/36 yard or 1/12 of a foot.

To convert a kilometer measurement to an inch measurement, multiply the length by the conversion ratio.

Since 01 kilometer = 39,370.07874 inches,

We can use this simple formula to convert:

          inches = kilometers × 39,370.079

Now, according to the question:

inches = 8.39 × 39370.079

inches = 33.315

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If the store pays $2 for a Halloween mask and marks up the price by 35%, we can calculate the amount of the mark-up as follows:

Mark-up percentage = 35%

Cost of the mask = $2

Mark-up amount = Mark-up percentage x Cost of the mask

Mark-up amount = 0.35 x $2

Mark-up amount = $0.70

Therefore, the amount of the mark-up is $0.70. The store sells the Halloween mask for $2.70 ($2 + $0.70 mark-up).

Answer:Its F

Step-by-step explanation:

Answer:

Letter i

Step-by-step explanation:

BeCuAsE A rAtIoNaL NuMbEr Is A NuMbEr ThAt CaN Be MaDe InTo A FrAcTiOn AnD I CaNt Be MaDe InTo A FrAcTiOn.

Answer:

x = -1

Step-by-step explanation:

You have:

\(\frac{3}{2x-1} =\frac{1}{x}\)

Multiply both sides by 'x' to get:

\(\frac{3x}{2x-1} =1\)

Multiply both sides by (2x-1) to get:

\(3x=2x-1\)

Subtract 2x on both sides to get:

\(x=-1\)

The required equation will be 200-80h=20 as the statement says, "You want to take a bus to go visit your friend in a different city. The distance between two cities is 200 kilometers and the bus drives 80 kilometers per hour. If the bus is 20 kilometers away from your friend’s city".

In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. In mathematics, an equation is a relationship of equality between two expressions written on both sides of the equal to sign. 3y = 16 is an example of an equation. Equations can be classified into three types based on their degree:

Here,

The distance between two cities=200 KM

The speed of bus=80 KM/hour

Time travelled=h hours

The distance travelled by bus=80h

The difference between distance=20

200-80h=20

As stated in the statement, the required equation is 200-80h=20 "You want to take the bus to see a friend in another city. The distance between the two cities is 200 kilometers, and the bus travels at an average speed of 80 kilometers per hour. If the bus is 20 kilometers away from your friend’s city".

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