What is the equation given a slope of 5 and a y-intercept of 12?​

Main Answer: The value of f(n) = 16(f(k))^4 when n = 3k.

Supporting Question and Answer:

How can we determine the value of f(n) when n = 3k using the given recurrence relation and initial condition?

By analyzing the given recurrence relation f(n) = 2f(n/3)^4 and the initial condition f(1) = 1, we can recursively calculate the value of f(n) for n = 3k. Using the recurrence relation, we can express f(n) in terms of f(n/3) and apply it iteratively. The value of f(n) when n = 3k is given by f(n) = 16(f(k))^4, where f(1) = 1 is used as the base case.

Body of the Solution:To find the value of f(n) when n = 3k, where f satisfies the recurrence relation f(n) = (2f(n/3))^4 with f(1) = 1, we can use the recurrence relation to recursively calculate the values of f(n).

Given that f(1) = 1, we can calculate the values of f(n) for n = 3, 9, 27, and so on.

f(3) = (2f(3/3))^4

= ((2f(1)))^4

= 2^4(1)^4

= 16

f(9) = (2f(3))^4

= (2(16))^4

= 1048576

f(27) =(2f(9))^4

= (2(1048576))^4

=(2097152)^4

Therefore, f(n) when n = 3k is given by:

f(3K)  =16(f(k))^4

So, f(n) =16(f(k))^4  when n = 3k, where f satisfies the given recurrence relation and f(1) = 1.

Final Answer:Therefore, f(n) =16(f(k))^4 when n = 3k.

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The percentage of Earth's freshwater is found in lakes, rivers, and streams as surface water is 69%. Therefore, option A is the correct answer.

We need to find the percentage of Earth's freshwater is found in lakes, rivers, and streams as surface water.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Over 69 percent of the fresh water on Earth is found in icecaps and glaciers, and just over 30 percent is found in ground water. Only about 0.3 percent of our fresh water is found in the surface water of lakes, rivers, and swamps.

The percentage of Earth's freshwater is found in lakes, rivers, and streams as surface water is 69%. Therefore, option A is the correct answer.

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The center of mass of the region is (21/20, 10/3).

To find the center of mass of the area formed by the curve \(x+3=(y-1)^2\) ans the line y=2, we need to first find the area of the region and then find the coordinates of the center of mass.

To find the area , we integrate the curve between the y-values of 2 and 3:

\(A = \int\limits^3_2 [(y-1)^2 - 3] dy \\ = > \int\limits^3_2 (y^2 - 2y - 2) dy \\ = > [\frac{1}{3} y^3 - y^2 - 2y]_2^3\\ = > \frac{1}{3} (27 - 4 - 6) - \frac{1}{3} (8 - 4 - 4) = \frac{5}{3}\)

So , the area of the region is 5/3 square units.

To find the coordinates of the center of mass , we need to compute the moments about the x and y axes and divide by the total area:

\(Mx = \int\limits^3_2[(y-1)^2 - 3] * y dy \\ = > \int\limits^3_2 (y^3 - 3y^2 + 2y) dy \\ = > [1/4 y^4 - y^3 + y^2]_2^3 \\ = > 1/4 (81 - 27 + 9) - 1/4 (16 - 8 + 4) = 7/4My = 1/2 \int\limits^3_2 [(y-1)^2 - 3] dx \\\\= > 1/2 \int\limits^3_2 [(y-1)^2 - 3] (dy/dx) dx \\\\\)

\({using dx = (dy/dx) dy}\\ = 1/2 \int\limits^3_2 [(y-1)^2 - 3] (2(y-1)) dx \\ {using dy/dx = 2(y-1)} \\ = \int\limits^3_2 (y-1)^2 (y-2) dx \\ = \int\limits^2_1u^2 (u+1) du \\ {using[ u = y-1], and[ dx = (1/2(y-1)) dy]} \\ = [1/3 u^3 + 1/4 u^4]_1^2 \\ = 1/3 (8 + 4) - 1/3 (1 + 1) = 7/3X = Mx / A = (7/4) / (5/3) = 21/20Y = My / A = (7/3) / (5/3) + 1 = 10/3\)

Therefore , the center of mass of the region is (21/20, 10/3).

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Answer:

(4,4)

Step-by-step explanation:

The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.

x^2 - 6x + 12 = 2x - 4

x^2 - 8x + 16 = 0

(x - 4)^2 = 0

x = 4

Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.

y = 2x - 4 = 2(4) - 4 = 4

Therefore, the solution of this system of equations is (4, 4).

Therefore, the correct answer is (4, 4).

Answer:

107

Step-by-step explanation:

2675 ÷ 25 = 107

Answer:

107 haircuts

Step-by-step explanation:

25x \(\geq\) 2,675

25x/25  \(\geq\) 2,675/25

x \(\geq\) 107

The three major chords built on white notes without accidentals are:

1. C major chord (C, E, G)

2. F major chord (F, A, C)

3. G major chord (G, B, D)

These chords are formed by taking the root note, skipping one white note, and adding the next white note on top. For example, in the C major chord, the notes C, E, and G are played together to create a harmonious sound.

Similarly, the F major chord is formed by playing F, A, and C, and the G major chord is formed by playing G, B, and D. These three major chords are commonly used in various musical compositions and are fundamental building blocks in music theory.

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Answer: Mr. Nut

Step-by-step explanation: Divide the price by the amount of oz. are in each brand to find the price of one oz of nuts. Round it to the nearest 100th because we're talking about money, Then compare the prices, then you have your answer! If my calculations are correct.

Answer:

number 19 is letter B.hence express P(x) as the product of it's linear factors

Answer:

a

Step-by-step explanation:

Identifying a proportion Which proportion resulted in the equation 3a = 7b

Answer:

B

Step-by-step explanation:

Answer:

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

We have a repeating decimal 4.6(1).

Let's express it as a GP:

Fund the sum of infinite GP, with the first term of a = 0.01 and common ratio of r = 0.1:

Add 4.6 to the sum:

Hence the fraction is 4 11/18.

Answer: 2

Step-by-step explanation:

5 consecutive integers with an average means the middle number will be the average since they are consecutive and even (increasing by 2/decreasing by 2). Because the middle number is 6, then the highest number will be 4 more and the lowest number will be 4 less. The consecutive numbers will be 2, 4, 6, 8, 10 and the lowest numbers is 2.

Answer:

4

Step-by-step explanation:

Consecutive numbers are numbers that increment by 1 (Ex. 1,2,3,4,5)

If the mean is 6, we know that the middle number has to be 6 and since these numbers are consecutive we can set 6 as "x" and write the following:

(x - 2, x - 1, x, x + 1, x + 2)

Plugging in 6 into the data set:

(4, 5, 6, 7, 8)

The least of these 5 integers is 4

Answer:

54π

Step-by-step explanation:

The volume for a cone is πr²h/3, which if we replace the number in, we get :

π6²4,5/3, which is approximately 54π

Hope it helps :)

Set c = {north america, south america, europe, asia, australia, africa, antarctica}. Set-builder notation: c = {x | x is continent and x ∈ {north america, south america, europe, asia, australia, africa, antarctica}}.

What is set ?

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines,etc.

a) The set c = {north america, south america, europe, asia, australia, africa, antarctica} can be written in set-builder notation as:

c = {x | x is a continent and x ∈ {north america, south america, europe, asia, australia, africa, antarctica}}

b) The set-builder notation can be read as "the set c, such that x is a continent and x is an element of the set {north america, south america, europe, asia, australia, africa, antarctica}".

Set c = {north america, south america, europe, asia, australia, africa, antarctica}. Set-builder notation: c = {x | x is continent and x ∈ {north america, south america, europe, asia, australia, africa, antarctica}}.

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Answer:

5x + 2y = p

5x - 5x + 2y= p - 5x

2y = p+ 5x

we divide both sides by 2

2y/2 = p + 5x/2

y = p + 5x/2

Step-by-step explanation:

hope that will help you

Answer:

y= 1/2p + −5/2x

Step-by-step explanation:

5x + 2y + −5x = p + −5x

2y = p −5x

2y/2 = p -5x/2

y= 1/2p + −5/2x

Answer:

$296.55

Step-by-step explanation:

3 $10 = $30

3 $5 = $15

3 $0.25 = $0.75

4 $0.01 = $0.04

The money in her purse adds up to be $45.79

Add that to her savings account to get her total money.

$250.76

$ 45.79

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

$296.55

Answer: \(y=\frac{2}{5}, \frac{6}{5}\)

Step-by-step explanation:

When answering a problem like this, you first isolate the absolute value.  TO do this, first subtract 8 from both sides, to get –2|4–5y|=-4.  Then divide both sides of the equation to get |4–5y|=2.  The next thing you do is split the equation into 4-5y=2 and 4-5y=-2, because the contents of the absolute value could be negative or positive, and simplifying both into y = 2/5, and y = 6/5y.

Hope it helps <3

Answer:

You add similar  fraction by adding the numerators together but since the denominators are the same u keep them as they are

1. Similar fractions are those which have the same denominator. To change dissimilar fraction to similar fractions, you express them as a equivalent with a common denominator. For example 2/12, 3/12

2. To add similar fraction one should ensure that both the numerator are same and then add the numerator and put that on the denominator. If there is need to simply the fraction then you should first simplify the fraction.

For example:- 1/4+4/4= 5/4

Here as we see that bot number denominator are same so it's addition is done easily

a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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The 300 Mexican Pesos is worth $15.94 USD.

It depends on the exchange rate used, the exchange rate is the price a currency will be exchanged at to another. Usually, we use the official exchange rate set by the Mexican central bank (Banco de Mexico),the current exchange rate is 0.0531. So, (300×0.0531)=15.94$. In the US, Mexican Pesos (MXN) are usually accepted as a form of payment. One cent is equal to 1/100 of a dollar so if you have to convert €1 into MXN then you have to multiply by ten and add 1.

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Answer:

$1015.11

Step-by-step explanation:

Compounded interest rate formula: A = P(1 + r/n)^t

Step 1: Plug in known variables

A = 1000(1 + 0.005/12)^36

Step 2: Multiply it all together

1000(1.00042)^36

1000(1.01511)

1015.11

This is a pretty bad bank considering only giving you .5% interest per month.

Answer:

22$

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Answer:

Step-by-step explanation:

cot²(3x)=y

y²-3y+2=0

y²-y-2y+2=0

y(y-1)-2(y-1)=0

(y-1)(y-2)=0

y=1,y=2

cot3x=1

tan 3x=1=tan (π/4)=tan (nπ+π/4)

3x=nπ+π/4=(4nπ+π)/4=(4n+1)π/4

x=(4nπ+1)π/12,n is an integer.

cot 3x=2

tan 3x=1/2

3x=tan^{-1}(1/2)≈26.57°+360n

x≈8.86°+120n

Answer:

Step-by-step explanation:

4,536

Answer:

335 Miles

Step-by-step explanation:

804/12 = 67 MPH

5 × 67 = 335

An MIS differs from a TPS in that it creates databases is True.

An MIS (Management Information System) does indeed differ from a TPS (Transaction Processing System) in that it creates databases. The main purpose of an MIS is to collect, process, store, and disseminate information to support managerial decision-making within an organization. It involves the use of technology and various information systems to manage and analyze data for strategic planning, monitoring, and control.

One of the key components of an MIS is the creation and management of databases. Databases are structured collections of data that are organized, stored, and accessed in a systematic way. They serve as a central repository for storing relevant information that can be utilized by the MIS. These databases can contain data from various sources within the organization, such as sales records, customer information, inventory data, financial data, and more.

On the other hand, a TPS focuses primarily on the processing of transactions. It is designed to capture, process, and record day-to-day operational transactions, such as sales transactions, inventory updates, customer orders, and so on. While a TPS may store and retrieve data related to these transactions, its main focus is on efficiently processing and ensuring the accuracy and integrity of transactional data.

In summary, an MIS goes beyond the functionalities of a TPS by not only processing transactions but also creating and managing databases to support the informational needs of managers.

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