A cone has a height of 11 yards and a radius of 7 yards. What is its volume? Use ​ ≈ 3.14 and round your answer to the nearest hundredth.

Answer:

7. m^21n^27

8. a^21b^28

Step-by-step explanation:

7. since m^7 raised to the 3rd power = m^( 7 * 3 ) = m^21

then  n^9 raised to the 3rd power = n^( 9 * 3 ) = n^27

your answer is m^21n^27

8. a^3 raised to the 7th power = a( 3 * 7 ) = a^21

b^4 raised to the 7th power = b( 4 * 7 ) = b^28

your answer is a^21b^28

hope this helps:)

Colin's new mean score, after getting 6 runs on Sunday, is approximately 20.09.

To calculate Colin's mean score, we need to sum up all his scores and divide by the number of scores.

a) Mean score:

16 + 11 + 25 + 27 + 11 + 25 + 20 + 26 + 29 + 35 = 215

Total scores: 10

Mean score = 215 / 10 = 21.5

Colin's mean score is 21.5.

b) To calculate his new mean score after getting 6 runs on Sunday, we need to add the new score to the previous total and divide by the new number of scores.

New total scores = 215 + 6 = 221

New number of scores = 10 + 1 = 11

New mean score = 221 / 11 = 20.09 (rounded to two decimal places)

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The given statement is true, according to the question.

Exponents with the same base have a ratio that is equal to the difference between their exponents with the same base. The division rule of exponents with the same base is another name for the quotient law of exponents with the same base.

According to the question,

Division in mathematics involves two exponents with the same base, however unlike dividing numbers, it is not possible to divide one exponential expression by another. As a result, the indices with the same base must be divided using a particular quotient rule.

By subtracting any two exponents with the same base, you may apply the property for dividing powers with the same base to calculate the quotient of any two exponents with the same base.

f'(x) equals [u(x)/v(x)]. '= [v(x) u'(x) - v'(x) u(x)] /[v(x)] 2

where,

The function of the form u(x)/v(x) for which the derivative must be determined is denoted by f(x).

u(x) = A differentiable function that serves as the function f's numerator (x).

Function derivative u'(x) equals u (x).

v(x) = A differentiable function that creates the supplied function f's numerator (x).

V'(x) = The function's derivative v(x).

The quotient rule says that when you are dividing x^m by x^n, you can simply subtract the two exponents (m-n) and keep the same base.

Therefore, the statement is true.

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The correct option is the last one, multiply the second equation by −2 to get −4x − 12y = −48.

Here we have the system:

4x + y = 4

2x + 6y = 24

One way to eliminate one of the variables is:

Adding the first equation and -2times the second one, then we will get:

4x + y + -2*(2x + 6y) = 4 + -2*24

4x + y - 4x - 12y = -44

-11y = -44

And we removed variable x, so the correct option is the last one.

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Answer:

48

Step-by-step explanation:

4/9 x 108 = number of students who voted for Millie

48 = number of students who voted for Millie

Answer:

48 students voted for Millie

Step-by-step explanation:

Based on the information given, you can set up a proportion:

\(\frac{4}{9}\)=\(\frac{x}{108}\)

To find the missing variable first cross multiply 108 and 4

108 x 4= 432

Next, divide your product by 9,

432÷9=48

So now you know that:

\(\frac{4}{9}\)=\(\frac{48}{108}\)

To argue why the liberal arts are so important in education and leisure, one must discuss its Greek origin and how it is received today.

The term "liberal arts" comes from the Latin word "liberalis," which means free. It was used in the Middle Ages to refer to topics that should be studied by free people. Liberal arts refers to courses of study that provide a general education rather than specialized training. It encompasses a wide range of topics, including literature, philosophy, history, language, art, and science.The liberal arts curriculum is based on the idea that a broad education is necessary for individuals to become productive members of society. In ancient Greece, education was focused on developing the mind, body, and spirit.  

The study of the liberal arts is necessary to create well-rounded individuals who can contribute to society in meaningful ways. While the importance of the liberal arts has been debated, it is clear that they are more important now than ever before. The study of the liberal arts is necessary to develop the skills that are required in a rapidly advancing technological world.

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Answer:

The inequality represented by the graph is y >  \(\frac{1}{2}\) x + 2

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

The rule of the slope is m = \(\frac{y2-y1}{x2-x1}\) , where

From the given figure

∵ The line passes through points (0, 2) and (2, 3)

∴ x1 = 0 and y1 = 2

∴ x2 = 2 and y2 = 3

→ Substitute them in the rule of the slope above

∵ m = \(\frac{3-2}{2-0}\) = \(\frac{1}{2}\)

∴ m =  \(\frac{1}{2}\)

→ b is the value of y at x = 0

∵ At x = 0, y =2

∴ b = 2

→ Substitute the value of m and b in the form of the equation above

∵ y =  \(\frac{1}{2}\) x + 2

∴ The equation of the line is y =  \(\frac{1}{2}\) x + 2

∵ The line is dashed

∵ The shaded area is over the line

∴ The sign of inequality is >

→ Replace = in the equation by >

∴ y >  \(\frac{1}{2}\) x + 2

∴ The inequality represented by the graph is y >  \(\frac{1}{2}\) x + 2

Answer:

7. adjacent (next to each other)

8. vertical (right across from each other)

9. vertical (right across from each other)

10. neither

11. adjacent (right next to each other)

12. neither

Before I go on: all these angles have the same measure as the one across, so ∠SYX has the same measure as ∠UYV (76°), ∠XYW has the same measure as ∠TYU (40°), and ∠WYV has the same measure as ∠SYT (64°)...

13. ∠SYX = 76°

14. ∠XYW = 40°

15. ∠WYV = 64°

These last three are angles added together. They look tricky, but you just note the endpoints and add the measures of the included angles together.

16. ∠SYW = ∠SYX + ∠XYW = 76° + 40° = 106°

    ∠SYW = 106°

17. ∠TYX = ∠SYX + ∠SYT = 76° + 64° = 140°

    ∠TYX = 140°

18. ∠VYX = ∠WYV + ∠XYW = 64° + 40° = 104°

    ∠VYX  = 104°

I hope this helps you understand the concept! Have a great day!

Answer:

2 computers

Step-by-step explanation:

Hope this helps :D

The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

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In a parallelogram, opposite angles are congruent.

Since angles z and 124° are opposite angles in the parallelogram, they are congruent angles.

Therefore we have:

Answer:

208

Step-by-step explanation:

If you multiply 2.08 by ten to the second power (100) Then you get 208

Scientific notations are the way through which a very small or a very large number can be written in shorthand.  The given expression can be written in the standard form as 208.

Scientific notations are the way through which a very small or a very large number can be written in shorthand.  In scientific notations when a number between 1 and 10s is multiplied by a power of 10.

For example, 6,500,000,000,000 can be written as 6.5e+12.

The given expression can be written in the form of an expression as shown below.

2.08 x 10²

= 2.08 × 100

= 208

Hence, the given expression can be written in the standard form as 208.

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Johnathan deposited money into an account that earns a 9.25% interest rate. The following explanation explores the details of this scenario and how the interest would accumulate over time.

When Johnathan deposits money into an account that earns a 9.25% interest rate, he can expect his balance to increase over time due to the interest earned. The interest rate of 9.25% signifies that for every dollar he deposits, the account will accrue an additional 9.25 cents per year. This interest can compound over time, meaning that not only the initial deposit but also the accumulated interest will earn further interest.

To calculate the growth of Johnathan's account, we need additional information such as the initial deposit amount and the duration of the investment. For example, if he deposited $10,000 into the account, after one year, the account would accrue $925 in interest, resulting in a total balance of $10,925. If the interest is compounded annually, the interest earned in the second year would be based on the new balance of $10,925.

Over an extended period, the compounding effect of the interest can significantly increase Johnathan's balance. However, the rate of growth would depend on factors such as the frequency of compounding (annual, semi-annual, quarterly, or monthly) and the duration of the investment. By utilizing compound interest, Johnathan has the potential to accumulate substantial earnings on his initial deposit over time, making it an advantageous choice for long-term savings or investments.

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Answer:

f[g(x)]

7(x^2)-9

Step-by-step explanation:

(fºg)(x) read: f of g of x. And can be seen written like in this format: f[g(x)]. Which I prefer.

The expression f[g(x)] means that you put the expression g(x) into the x variable for f(x). Comment if you need a better explanation :)

Answer:

Step-by-step explanation:

Step one:

given data

mass of harvested peanuts = 14,000kg

size of land = 8-acre

Step two:

Required:

mass of harvested peanuts for a 30-acre land

let the mass be x

so, for 8-acre land the harvested mass is 14,000

hence for 30-acre land the harvested mass is x

cross multiply we have

8x=14,000*30

divide both sides by 8

x=420000/8

x=52500 kg

8 over 1400=30 Over x

If on  Monday Tom work for 11 extra hours the total amount of money that tom made on Monday is £885.

As per the given data, the extra money he earns can be calculated as,

= [(11 - 7) × 15] × 13 + (7 × 15)]

= (4 × 15 × 13) + 105

= 780 + 105

= £885

Therefore, the amount of money  is £885.

Time and work are concerned with how long it takes a person or a group of people to finish a task and how well each of them completes it.

Indirect proportion is related to time and work. In both directions, when one quantity rises, the other falls, and vice versa. It takes less time to finish the same amount of work when people work more hours.

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The value is 24 square units is parallel to the face of the right rectangular prism.

We can see that the face of the given rectangular prism shows a width 4 and a height of 6. If we cut the figure at any point along the length 20, such that the cross-section is parallel to the face, the cross-section, which occurs at x length, will always have the same dimensions, which are 4 and 6.

So the area of the cross-section which is parallel to the face of the given rectangular prism is given by:

A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

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A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

Answer:

At first glance anyone would assume Amy would reach the school first because she is traveling at a faster rate. However, this is only true when both kids are in the same starting place. The question doesn't give us enough information to verify that answer because we don't know the location of the starting place. Perhaps Jeremy would reach the school first because his Aunt's house's closer to the school, even though he is traveling at a slower rate....

Step-by-step explanation:

Answer:

x=15, y=8

15 hats and 8 scarves

Step-by-step explanation:

hats=x

scarves=y

5x+3y=99

3x+5y=85

Answer:

Doc drove the fastest.

Step-by-step explanation:

The first thing you want to do is figure out how many milese they are traveling per hour. We know that Einstein has these two time stamps  (hour/miles) ; 3/240 and 4/320.

so divide the hour by the number of miles:

3÷240=80

just to make sure I did the four hour one as well;

4÷320=80

Do the same thing for doc and marty!

4÷340=85

4÷100=0.04

The answer that you get from the division problems is the number of miles that they travel each hour.

Hope this helps!

Answer:

4

Step-by-step explanation:

Answer:2+2 = 4.............

A minor treatment effect may nonetheless be significant under certain circumstances if the sample size is large and the sample variance is low.

Therefore, a minor treatment effect may nonetheless be significant under certain circumstances if the sample size is large and the sample variance is low.

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Answer:

yo congratulations on finishing 10th grade (congratulate me on finishing 8th)

hamood spelled backwards is doomah so...um...

also do u mean 7/2/21..bc 6/2/21 is like in June and we're in July

Justice is using a technique known as chunking.

Short-term memory can function more effectively thanks to chunking, however the quantity of chunks that can be stored efficiently declines as chunk size grows.

Large pieces of information may be divided into smaller bits and then grouped together using relevant information or attributes before being stored in order to improve retention of that information in the short term memory. To establish relational information or similarity between the information to be stored in order to improve retention and recall in the short term memory, information must be broken down before being regrouped. However, as chunk size grows, so does the efficiency of information chunking.

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The first column represents the coefficients of the variable \(x\), the second column represents the coefficients of the variable \(y\), the third column represents the coefficients of the variable \(z\), and the last column represents the constants on the right-hand side of each equation.

To write the augmented matrix for the system of equations:

\[

\begin{cases}

4x - 2y + 3z = -8 \\

x - 3y = -9 \\

x - 9z = -6 \\

\end{cases}

\]

We can represent the coefficients of the variables and the constants in matrix form. The augmented matrix is constructed by placing the coefficients and constants in a rectangular arrangement, separating the coefficients and the constants with a vertical line. Each row corresponds to an equation in the system.

The augmented matrix for the given system of equations is:

\[

\begin{bmatrix}

4 & -2 & 3 & -8 \\

1 & -3 & 0 & -9 \\

1 & 0 & -9 & -6 \\

\end{bmatrix}

\]

In this matrix, the first column represents the coefficients of the variable \(x\), the second column represents the coefficients of the variable \(y\), the third column represents the coefficients of the variable \(z\), and the last column represents the constants on the right-hand side of each equation.

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Answer:

6x+8y = 3

Step-by-step explanation:

we have 3x + 4y = 7

4y = -3x + 7

y = -3/4 x + 7/4

so slope is -3/4

2 parallel lines always have same slope

so the slope of our new line is -3/4

so y = -3/4 x + C

for c,

we have (x,y) = (-2/3,7/8)

7/8 = -3/4 * -2/3 + C

C = 3/8

so equation is

y = -3/4 x + 3/8

simplyfyig,

8y = -6x + 3

or, 6x+8y = 3

help please someone

The volume of the rectangular prism is given by the equation

A = 13 1/2 inches³

What is the Volume of a Rectangle?

The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle

Volume of Rectangle = Length x Width x Height

Volume of Rectangle = Area of Rectangle x Height

Given data ,

Let the volume of the rectangular prism be represented as A

Now , the equation will be

The length of the rectangular prism L = 1 1/2 inches

The length of the rectangular prism L = 1.5 inches

The width of the rectangular prism L = 2 1/4 inches

The width of the rectangular prism L = 2.25 inches

The height of the rectangular prism L = 4 inches

So , the volume of the rectangular prism A = Length x Width x Height

Substituting the values in the equation , we get

The volume of the rectangular prism A = 1.5 x 2.25 x 4

On simplifying the equation , we get

The volume of the rectangular prism A = 13.5 inches³

Hence , the volume of rectangular prism is  13.5 inches³

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The volume of the pyramid is 13 units³.

A pyramid is a 3-dimensional shape that is made up of a rectangular base and 4 triangular faces. The volume of a pyramid is one-third that of a prism.

Volume of a pyramid = 1/3 x prism

1/3 x 39 = 13

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