simplify the expression using the distributive property y(2+x)​

The expression for the difference of two linear functions is (f - g)(x) = 4x - 6.

A linear function is a type of function in mathematics that has the form f(x) = mx + b, where x is the independent variable, f(x) is the dependent variable, m is the slope of the line, and b is the y-intercept.

To find the expression for the difference of two linear functions, f(x) and g(x), denoted by (f - g)(x).

The expression for (f - g)(x) can be found by subtracting g(x) from f(x):

(f - g)(x) = f(x) - g(x)

Substituting the given functions f(x) = x - 2 and g(x) = -3x + 4, we get:

(f - g)(x) = f(x) - g(x)

= (x - 2) - (-3x + 4) [Substitute the given values of f(x) and g(x)]

= x - 2 + 3x - 4 [Distribute the negative sign in front of (-3x + 4)]

= 4x - 6 [Combine like terms]

Therefore, (f - g)(x) = 4x - 6.

Option D (-3x² - 2x - 8) is incorrect as it involves squaring a linear expression, which would result in a quadratic expression. Option A (which has no operation between 3 and 22) is not a valid expression. Option B (-3x - 8) and C (3x3x22 or 198) do not take into account the fact that each sundae can be made using one of 3 syrups and one of 3 candy toppings.

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In order to avoid double counting, statisticians just count the final goods and services.

According to the statement

we have to find the procedure which is used by statisticians to avoid the double counting.

final goods and services are the type of way which is used to avoid the double counting.

In other words, statisticians count only the final results rather than the efforts.

So, In order to avoid double counting, statisticians just count the final goods and services.

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The task involves finding the approximate solution to the Poisson equation on a unit square using finite difference approximation with a given equation. The solution is required at each grid point for a specific value of N.

To find the approximate solution to the Poisson equation on the unit square, we use the finite difference approximation method. The given equation provides the approximation formula for each grid point (xᵢ, yⱼ). The solution at each grid point is denoted by uᵢ,ⱼ.

For a specific value of N, we divide the unit square into (N+2) x (N+2) equally spaced grid points. The indices i and j represent the coordinates of the grid points, ranging from 0 to N+1. The grid spacing h is determined by h = 1/(N+1).

Using the approximation formula, we can calculate the solution uᵢ,ⱼ at each interior grid point (excluding the boundary) by substituting the neighboring grid points' values into the formula. The term Uxx represents the second derivative of u with respect to x, and Uyy represents the second derivative of u with respect to y. The factor sin(2x)sin(2πy) accounts for the spatial variation in the equation.

By applying the approximation formula to each interior grid point, with appropriate boundary conditions (u = 0 on the boundary), we can obtain the approximate solution uᵢ,ⱼ at each grid point for the given value of N. The grid spacing h determines the accuracy of the approximation, with smaller values of h leading to a more accurate solution.

Therefore, by using the provided finite difference approximation formula and applying it to each grid point with the given boundary conditions, we can find the approximate solution to the Poisson equation on the unit square for the specified N value.

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Let's start by setting up an equation to represent the problem.

Let's say Jake started with x amount of money.

After giving 1/3 to his wife, he has 2/3 left: (2/3)x

After giving 1/4 of that amount to his mother, he has $600 left: (1/4)(2/3)x = $600

We can solve for x by isolating it:

(1/4)(2/3)x = $600

Multiplying both sides by 12/2 gives:

(2/3)x = $3600

Dividing both sides by 2/3 gives:

x = $5400

So Jake started with $5400.

To find out how much he gave to his mother, we can take 1/4 of 2/3 of $5400:

(1/4)(2/3)($5400) = $900

So he gave his mother $900.

Step-by-step explanation:

x = original amount of money

the problem description tells us he gives 1/3 of his money to his wife and 1/4 of his money to his mother. and then he had still $600 left.

x - (1/3)x - (1/4)x = 600

so let's bring every fractional term to .../12.

12x/12 - (4/4)×(1/3)x - (3/3)×(1/4)x = 600

12x/12 - 4x/12 - 3x/12 = 600

5x/12 = 600

5x = 600×12

x = 600×12/5 = 120×12 = $1440

he gave to his mother

(1/4) × 1440 = $360

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

The slope of the tangent line to the graph of the function y = x^4 - 10x^2 + 9 at x = 1 can be found by taking the derivative of the function and evaluating it at x = 1. The equation of the tangent line can then be determined using the point-slope form.

Taking the derivative of the function y = x^4 - 10x^2 + 9 with respect to x, we get:

dy/dx = 4x^3 - 20x

To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative:

dy/dx (at x = 1) = 4(1)^3 - 20(1) = 4 - 20 = -16

Therefore, the slope of the tangent line is -16.

To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Given that the point of tangency is (1, y(1)), we substitute x1 = 1 and y1 = y(1) into the equation:

y - y(1) = -16(x - 1)

Expanding the equation and simplifying, we have:

y - y(1) = -16x + 16

Rearranging the equation, we obtain the equation of the tangent line:

y = -16x + (y(1) + 16)

To find the slope of the tangent line, we first need to find the derivative of the given function. The derivative represents the rate of change of the function at any point on its graph. By evaluating the derivative at the specific value of x, we can determine the slope of the tangent line at that point.

In this case, the given function is y = x^4 - 10x^2 + 9. Taking its derivative with respect to x gives us dy/dx = 4x^3 - 20x. To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative equation, resulting in dy/dx = -16.

The slope of the tangent line is -16. This indicates that for every unit increase in x, the corresponding y-value decreases by 16 units.

To determine the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1). We know the point of tangency is (1, y(1)), where x1 = 1 and y(1) is the value of the function at x = 1.

Substituting these values into the point-slope form, we get y - y(1) = -16(x - 1). Expanding the equation and rearranging it yields the equation of the tangent line, y = -16x + (y(1) + 16).

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

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Answer:

<PQR is 130 degrees

Step-by-step explanation:

When it says the line bisects the angle, that means the two smaller angles are equal to each other.

Therefore 3x+5 = 2x+25

Now rearrange to get x.

3x-2x=25-5

x=20

Now plug the x back into both phrases and them together to get the final answer for <PQR.

20 * 3 + 5 = 65

20 * 2 + 25 = 65

65*2 = 130

Answer:

<

Step-by-step explanation:

< because 10 is lower than 43

Also, can you please tell me 43 what quantity? like qt, or ml?

My gratitude attitude - THANKS!

Answer:

9.07 > 9.008

Step-by-step explanation:

If you do 9.070, 70 is more than 8 so the answer is B

Answer:

  28.2

Step-by-step explanation:

The perimeter of a plane figure is the sum of the lengths of its sides. Those lengths and their sum can be found a number of different ways.

__

The values computed by the graphing program in the attachment add up to 28.2 units.

__

The length of each side of the triangle can be computed using the distance formula or the Pythagorean theorem. For a given "rise" and "run", the length of a line segment is ...

  d = √(rise^2 +run^2)

  HI = √((-4)^2 +10^2) = √116 ≈ 10.770

  IJ = √(1^2 +12^2) = √145 ≈ 12.042

  JH = √(5^2 +2^2) = √29 ≈ 5.385

The perimeter is the total of the lengths of the sides:

  P = HI +IJ +JH = 10.770 +12.042 +5.385 = 28.197

To the nearest tenth, the perimeter is 28.2 units.

Answer:

The water level decreased by 1/18 inches each hour.

Step-by-step explanation:

A rate of change is a rate that describes how one quantity changes in relation to another quantity. Between 11 P.M. and 8:54 A.M.​, the water level in a swimming pool decreased by 11/20, for each hour it decreases by 33/554

A rate of change is a rate that describes how one quantity changes in relation to another quantity.

Given that,  Between 11 P.M. and 8:54 A.M.​, the water level in a swimming pool decreased by 11/20. Assuming that the water level decreased at a constant​ rate, we need to find the amount of water level drop each​ hour.

In an hour we will have sixty minutes.

We need to calculate the number of minutes between 11 pm and 8: 54 am.

The minutes between 11 P.M. and 8:54 A.M. is 594 minutes.

So in 554 min water level drop is 11/20.

So in 1 min=11/20×1/554

So in 60 min

We need to multiply with sixty

= 60(11/20×1/554)

We need to solve 60(11/20×1/554), we get

=3(11/554)

3 times of eleven  by five hundred fifty four.

=33/554

Hence 33/554  water level drop each​ hour when water level decreased at a constant​ rate.

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Answer:

Step-by-step explanation:

A flow network with supplies is a directed capacitated graph where each edge has a capacity indicating the maximum flow that can pass through it. The flow in the network represents the movement of a certain resource (e.g., water, electricity, goods) from sources to sinks.

In a flow network with supplies, there may be multiple sources, which are nodes that generate the resource and have outgoing edges, and multiple sinks, which are nodes that consume the resource and have incoming edges.

The sources and sinks can have different supply or demand values, indicating the amount of resource they generate or consume.

The edges in the flow network have capacities that restrict the maximum flow that can pass through them. The capacity represents the limit on the amount of resource that can traverse the edge. The flow through an edge cannot exceed its capacity.

The objective in a flow network is to determine the maximum flow that can be sent from sources to sinks while respecting the capacities of the edges. This is typically solved using algorithms such as the Ford-Fulkerson algorithm or the Edmonds-Karp algorithm.

The concept of a flow network with supplies is important in various applications, such as transportation networks, communication networks, and supply chain management, where resources need to be efficiently distributed from multiple sources to multiple sinks, taking into account the capacity constraints of the network.

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Let \(n=0\). Then \(0^3 = 0\) but 0 > 0 is a false statement.

The cash price of the refrigerator is $408.

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Given that, a new refrigerator has a price of $480.00.

The store will discount the price by 15% if the purchaser pays in cash.

Now, the discount is

15% of 480

= 15/100 ×480

= 0.15×480

= 72

Now, 480-72

= $408

Therefore, the cash price of the refrigerator is $408.

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Answer:

7.8 * 10^7

Step-by-step explanation:

Group coefficients together and exponents together to multiply numbers in scientific notation.

( 7.8  *  1 )  ( 10 ^3  * 10^4)

Multiply  7.8 times 1.

7.8 * (10^3 * 10^4)

Use the power rule  a^m * a^n = a^(m+n) to combine exponents. So, add 3 and 4

7.8 * 10^7

Among the given options, the description that best fits a frequency table is "a grouping of qualitative data into classes showing the number of observations in each class."

The best description of a frequency table is: "A grouping of qualitative data into classes showing the number of observations in each class."

A frequency table is a statistical tool used to organize and summarize qualitative data by grouping it into classes or categories and displaying the number of observations or frequency in each class.

It provides a clear and concise representation of how the data is distributed across different categories.

In a frequency table, the qualitative data is organized into classes or categories, which are mutually exclusive and exhaustive.

Each class represents a range or a distinct category, and the frequency column displays the count or number of observations that fall within each class.

The frequencies can be absolute frequencies (counts) or relative frequencies (proportions or percentages).

The purpose of a frequency table is to provide a visual summary of the data distribution, allowing for easy identification of patterns, gaps, or outliers.

It helps to understand the frequency or occurrence of different values or categories in the dataset.

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Answer:

the answer its 2/5

Step-by-step explanation:

hes rite

Answer:

A.

I hope it helps

There were the most observations of female tokoeka kiwis in the given frequency table so option (A) will be correct.

A frequency table is a list of objects with the frequency of each item shown in the table.

The frequency of an occurrence or a value is the number of times it happens.

Given the frequency table of kiwi birds with their gender.

Number of female tokoeka kiwis = 44

Now if we look at the table there is none of any bird that is greater than 44 which means it is the most observations in the research.

Hence  "There were the most observations of female tokoeka kiwis".

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The statement opportunity cost for Germany to produce 1 beer is 1/2 motorcycles is true.

The German economy would be better off if it produced beer and traded motorcycles with the US.

Germans would benefit from specializing in producing beer and engaging in trade with the United States since their opportunity cost is lower (1/2 is less than 3).

A country is said to be having a comparative advantage in producing a good if it can produce it at a lower opportunity cost. Germany has a lower opportunity cost in producing beer so it has a comparative advantage in making beer.

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2.25 kilometers on the ground is represented by 9cm on the map

According to the question, the scale on the map is in the ratio 1 : 25000

That is the     length on the map = length of the ground

                               1cm = 25000 cm

                                1 cm = 25000/100000 km

                                1 cm = 0.25 km

Now we have to find the length of the ground in kilometres which is represented by 9cm on the map

That is we have to find the ratio,  9cm : x km

As from above, we know that,

                          1cm = 0.25 km

                           9 cm = 0.25*9 km

                                    = 2.25 km

Hence 2.25 km on the ground is represented by 9 cm on the map

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Answer:

D y=2x

Step-by-step explanation:

Using slope formula change in y over change in x

\( \frac{2}{1} \)

the slope is 2 and when we plug the x value in it gives us our corresponding y value so the answer is D

With a 99% confidence level, we can say that the true proportion of all homes that have electrical/environmental problems is at least 8.3%.

To calculate a lower confidence bound using a confidence level of 99% for the percentage of all homes that have electrical/environmental problems, we need to have a sample of data on this issue. Let's assume that we have a random sample of 100 homes, and 20 of them were found to have electrical/environmental problems.

To calculate the lower confidence bound, we can use the formula:

Lower bound = p - zα/2 * sqrt(p * (1-p) / n)

where:

p = proportion of homes in the sample that have electrical/environmental problems = 20/100 = 0.2

zα/2 = z-score for the given confidence level of 99% = 2.576 (obtained from a standard normal distribution table or calculator)

n = sample size = 100

Plugging in these values, we get:

Lower bound = 0.2 - 2.576 * sqrt(0.2 * 0.8 / 100) = 0.083

Therefore, with a 99% confidence level, we can say that the true proportion of all homes that have electrical/environmental problems is at least 8.3%.

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This means we can be 99% confident that the true percentage of all homes with electrical/environmental problems is

at least 17.5%.

To calculate a lower confidence bound using a confidence level of 99% for the percentage of all homes that have

electrical/environmental problems, you would need a sample of homes and the number of homes in the sample that

have such problems. Using this information, you could calculate the sample proportion (p-hat) of homes with

electrical/environmental problems.

Then, using a formula or calculator, you could find the lower confidence bound by subtracting the margin of error (ME)

from the sample proportion.

The margin of error can be calculated using the sample proportion, sample size, and the chosen confidence level (in

this case, 99%).

For example, if the sample proportion is 0.25 and the sample size is 100, the margin of error would be 0.075 and the

lower confidence bound would be 0.175 (0.25 - 0.075).

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Answer:

use symbolab

Step-by-step explanation:

A house that has 2,100 sq ft of living area is more unusual than a house that sells for ​$125,000. This is because the probability of finding a house with 2,100 sq ft of living area is only 38.21% which is less than 5.86% which is the probability of finding a house that sells for ​$125,000.

A real estate agent has surveyed houses in twenty nearby zip codes in an attempt to put together a comparison for a new property that she would like to put on the market. The 1057 houses she surveyed have a mean price of ​$172,000, with a standard deviation of $30,000. The mean living area is 1567 sq​ ft, with a standard deviation of 210 sq ft. We are to find out which is more unusual, a house in that market that sells for ​$125,000 or a house that has 2,100 sq ft of living​ area? Let's answer this question step by step. We have,Mean of Price

= $172,000

Standard Deviation of Price

= $30,000

Mean of Living area

= 1567 sq ft

Standard Deviation of Living area

= 210 sq ft

The price of the house that is being sold is $125,000.The calculation to find the Z-score for the house that is selling at $125,000 is given by:

Z = (X- μ)/ σ

Where, X = Price of the house

= $125,000μ

= Mean Price

= $172,000σ

= Standard Deviation

= $30,000

Substitute the values and find the Z-score,

Z = (125,000-172,000) / 30,000 = -1.5667

We then look at the Z-table to find the probability of getting the Z-score value -1.5667. From the Z-table, we get the value of 0.0586 or 5.86%. The probability of finding a house that sells at $125,000 is 5.86% in that area.Now let's calculate the Z-score for a house that has 2,100 sq ft of living area using the formula,

Z = (X- μ)/ σ

Where, X = Living area

= 2100 sq ftμ

= Mean Living Area

= 1567 sq ftσ

= Standard Deviation

= 210 sq ft

Substitute the values and find the Z-score,

Z = (2100-1567) / 210

= 0.3

We then look at the Z-table to find the probability of getting the Z-score value 0.3. From the Z-table, we get the value of 0.3821 or 38.21%. The probability of finding a house with 2,100 sq ft of living area is 38.21% in that area.Therefore, a house that has 2,100 sq ft of living area is more unusual than a house that sells for ​$125,000. This is because the probability of finding a house with 2,100 sq ft of living area is only 38.21% which is less than 5.86% which is the probability of finding a house that sells for ​$125,000. Hence, a house with 2,100 sq ft of living area is more unusual in that area.

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The complete graph with 100 vertices will have \(\( \binom{100}{2} = 4950 \)\)edges. Therefore, the correct option is (a) 4950. A connected graph with 100 vertices must have at least 99 edges.

1. A complete graph with 100 vertices means that there is an edge between every pair of vertices. The number of edges in a complete graph with n vertices is given by the formula \(\( \binom{n}{2} = \frac{n(n-1)}{2} \)\). Substituting n = 100, we get\(\( \frac{100 \cdot 99}{2} = 4950 \)\) edges.

2. In a connected graph with n vertices, the minimum number of edges required to ensure connectivity is n - 1. Therefore, a connected graph with 100 vertices must have at least 99 edges.

3. The given algorithm has a loop that divides the value of k by 2 in each iteration. As long as k is greater than or equal to 1, the loop continues. Since the value of k is halved in each iteration, the loop will run approximately \log ntimes. Therefore, the complexity of the algorithm is \(\( O(\log n) \)\).

4. The Minimum Spanning Tree algorithm is a Greedy method because it makes locally optimal choices at each step to construct the minimum spanning tree.

5. A graph is called connected if there is a path between every pair of vertices. Therefore, if a graph has a path between each two vertices, it is a connected graph.

6. NP-Complete problems are a subset of problems in the NP-class and are also NP-Hard. Therefore, any problem in the NP-Complete class is in both NP-class and NP-Hard class.

7. The algorithm with linear complexity is the Max is in-place Algorithm, which finds the maximum element in an array by comparing each element with the current maximum and updating it if necessary.

8. The worst-case time complexity of Insertion Sort is\(\( O(n^2) \)\) because in the worst case, for each element, it may need to be compared and shifted with every element to its left.

9. Dijkstra's algorithm is an example of the Greedy method for finding the shortest path in a graph.

10. The correct option is not provided for question 10, as none of the given options

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Given statement solution is :- We cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).

The given sequence is: 5 2 1 4 0 0 7 2 8 1 m m 7 m 5 m A.

To find the missing value, let's analyze the pattern in the sequence. We can observe the following pattern:

The first number, 5, is the sum of the second and third numbers (2 + 1).

The fourth number, 4, is the sum of the fifth and sixth numbers (0 + 0).

The seventh number, 7, is the sum of the eighth and ninth numbers (2 + 8).

The tenth number, 1, is the sum of the eleventh and twelfth numbers (m + m).

The thirteenth number, 7, is the sum of the fourteenth and fifteenth numbers (m + 5).

The sixteenth number, m, is the sum of the seventeenth and eighteenth numbers (m + A).

Based on this pattern, we can deduce that the missing values are 5 and A.

Now, let's calculate the missing value:

m + A = 5

To find a specific value for m and A, we need more information or equations. Without any additional information, we cannot determine the exact values of m and A. Therefore, we cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).

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Answer:

False

Step-by-step explanation:

It does not have an equal sign, therefore making it a false equation

Answer:

4x-36

Step-by-step explanation:

3x+x=4x

Answer:

4(x - 9)

Step-by-step explanation:

x + 3x - 36 =

= 4x - 36

= 4(x - 9)

Answer:

The inequality that is true is -5 - 3x > 10.

Step-by-step explanation:

if x = -6

we can subtitution x to every inequality, so :

-5 - 3x > 10

-5 - 3(-6) > 10

-5 - (-18) > 10

-5 + 18 > 10

13 > 10 [true]

-3 - 5x < -14

-3 - 5(-6) < -14

-3 - (-30) < -14

-3 + 30 < -14

27 < -14 [false]

2 - x < -3

2 - (-6) < -3

2 + 6 < -3

8 < -3 [false]

So if x=-6, inequality true is -5 - 3x > 10.

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