A city has a population of 340, 000 people. Suppose that each year the population grows by 3.75%. What will the population be after 10 years ? Use the calculator provided and round your answer to the nearest whole number.

The formula for the number of edges in a complete graph with n vertices is given by E= (n * (n-1))/2. We can simplify this expression as follows:E = (n2 - n)/2. So, the answer to the question is (N2 - 1)/2.

In a complete graph, each vertex is connected to all other vertices. Therefore, to find the number of edges in a complete graph, Kn, we need to consider the number of ways of choosing two vertices from the set of n vertices and connecting them.So, the formula for the number of edges in a complete graph with n vertices is given by E= (n * (n-1))/2. We can simplify this expression as follows:E = (n2 - n)/2So, the answer to the question is (N2 - 1)/2. Therefore, the correct option is (D).Answer in 120 wordsA complete graph is one in which each pair of distinct vertices is connected by a unique edge. The number of edges in a complete graph is determined by the number of vertices in the graph. To find the number of edges in a complete graph with n vertices, we must first consider the number of ways to choose two vertices from the set of n vertices. After that, we must connect those two vertices.

Each pair of vertices produces an edge in a complete graph, and since the edges are undirected, we must divide by two to avoid double-counting. The formula for the number of edges in a complete graph with n vertices is given by E= (n * (n-1))/2. We can simplify this expression as follows:E = (n2 - n)/2. So, the answer to the question is (N2 - 1)/2.

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The larger conclusion that can be reached by stringing together the sentences is:

If Henry goes to the library, the world is a better place.

This can be derived by combining the statements given as follows:

Therefore, if Henry goes to the library and reads a book, he becomes smarter, happier, and the world is a better place.

So, the final conclusion is that if Henry goes to the library, the world is a better place. None of the other statements can be derived from the given sentences.

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The moment of inertia of the solid cylinder grinding wheel is 0.014J.

Given values; Mass of grinding wheel, m = 2.80 kg

Radius of grinding wheel, r = 0.100 m

For calculating the moment of inertia of a solid cylinder about its central axis, the formula is;

I = (1/2)mr²

Here, m = Mass of cylinder r = Radius of cylinder I = Moment of inertia

Substitute the given values in the above formula to get the moment of inertia;

I = (1/2)mr²

I = (1/2)(2.80 kg)(0.100 m)²

I = (1/2)(2.80 kg)(0.010 m²)

I = 0.014 J

The moment of inertia of the given solid cylinder grinding wheel is 0.014 J.

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The type of distribution for the proportion of 100 college graduates who believe their degree was a good investment is a binomial distribution.

A binomial distribution is used to describe the outcome of a binomial experiment. A binomial experiment is one that satisfies the following four conditions:

1. The experiment consists of n repeated trials.

2. Each trial results in an outcome that may be classified as a success or a failure (hence the name, binomial).

3. The probability of a success, denoted by P, is the same on every trial.

4. The trials are independent; that is, the outcome of one trial does not influence the outcome of any other trial. In this case, the binomial experiment is the number of college graduates who believe their degree was a good investment out of a sample size of 100.

Each graduate can be classified as either a success (believes their degree was a good investment) or a failure (does not believe their degree was a good investment).

The probability of success is not specified, but it is assumed to be constant across all graduates. The trials (graduates) are also assumed to be independent of each other.

Therefore, the proportion of graduates who believe their degree was a good investment follows a binomial distribution.

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Answer:

x = 121°

Step-by-step explanation:

The lower left interior angle of the triangle is adjacent to 115° and are supplementary, thus

interior angle = 180° - 115° = 65°

The angle round a point is 360°

The vertex interior angle = 360° - 304° = 56°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle of the triangle, thus

x = 65° + 56° = 121°

Enzo's net worth = Enzo's assets - Enzo's liabilities. The resulting number is his net worth.

Enzo's net worth = (Enzo's cash + Enzo's investments + Enzo's property + Enzo's other assets) - (Enzo's loans + Enzo's credit card debt + Enzo's other liabilities)

Enzo's net worth is calculated by subtracting his liabilities from his assets. Enzo's assets include cash, investments, property and other assets he may own. His liabilities include any loans he has taken out, any credit card debt, and any other liabilities he may have. To find Enzo's net worth, you would add up all of his assets and subtract from that all of his liabilities. The resulting number is his net worth.

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The vector 57 - 4j + 3k can be expressed in the form [57, -4, 3].The vector 57 - 4j + 3k is represented by an arrow extending from the origin to the point (57, -4, 3).

To express the vector 57 - 4j + 3k in the form [a, b, c], we can simply write down the coefficients of the vector components. The vector consists of three components: the x-component, y-component,

and z-component. In this case, the x-component is 57, the y-component is -4, and the z-component is 3. Therefore, we can express the vector as [57, -4, 3].

To plot the vector on a Cartesian plane, we can use a 3D coordinate system. The x-coordinate corresponds to the x-component, the y-coordinate corresponds to the y-component, and the z-coordinate corresponds to the z-component.

First, draw a 3D Cartesian plane with three perpendicular axes: x, y, and z. Label each axis accordingly.

Next, locate the point (57, -4, 3) on the Cartesian plane. Start at the origin (0, 0, 0) and move 57 units along the positive x-axis. Then, move -4 units along the negative y-axis. Finally, move 3 units along the positive z-axis. Mark this point on the Cartesian plane.

Label the x-coordinate, y-coordinate, and z-coordinate of the point to indicate the values associated with each axis.

The vector 57 - 4j + 3k is represented by an arrow extending from the origin to the point (57, -4, 3). Draw the arrow to visually represent the vector on the Cartesian plane.

By following these steps, you can accurately express the vector in [a, b, c] form and plot it on a Cartesian plane, ensuring that you label the coordinates correctly and draw the vector accurately.

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Answer:

  a) "common multiplier" is 3

  b) both reduce to 1/2

Step-by-step explanation:

  \(\dfrac{30}{60}=\dfrac{3\cdot10}{3\cdot20}=\dfrac{3}{3}\cdot\dfrac{10}{20}=1\cdot\dfrac{10}{20}=\dfrac{10}{20}\)

Perhaps your "common multiplier" is 3. It multiplies both numerator and denominator in 10/20 to give you 30/60.

__

  \(\dfrac{10}{20}=\dfrac{10}{10}\cdot\dfrac{1}{2}=\dfrac{1}{2}\\\\\dfrac{30}{60}=\dfrac{30}{30}\cdot\dfrac{1}{2}=\dfrac{1}{2}\)

The simplest form of both fractions is 1/2.

Answer:

\(\left[A]\) The ratios \(\frac{10}{20}\) form a proportion by common multiplier 3 to get \(\frac{30}{60}\)

\(\left[B]\) Both ratio are equal to \(\frac{1}{2}\) in simplest form

Step-by-step explanation:

\(\left[A]\) We need to show both fraction of same proportion.

Ratio 1:  \(\frac{10}{20}\)

If we multiply by 3 at numerator and denominator

\(\frac{10*3}{20*3}\)

\(\frac{30}{60}\)

Therefore \(\frac{30}{60}\) is equivalent ratio to second one 30/60

Hence, The ratio 10/20 form a proportion by common multiplier 3 to get 30/60

∴-----------------------------------------------------------------------------------------------------∴

\(\left[B]\) Now we simplify both ration into simplest form

→ \(\frac{10/10}{20/10} =\frac{1}{2}\)

→ \(\frac{30/30}{60/30} =\frac{1}{2}\)

→ \(\frac{1}{2} =\frac{1}{2}\)

Hence, Both ratio are equal to \(\frac{1}{2}\) in simplest form.

The calculated length of the segment WX given that TU = 20, UV = 26, and XY = 39 is 30 units

From the question, we have the following parameters that can be used in our computation:

TU = 20, UV = 26, and XY = 39

The length WX can be calculated using the following equivalent ratio

TU : UV = WX : XY

Substitute the known values in the above equation, so, we have the following representation

20 : 26 = WX : 39

Express the ratio as fraction

So, we have

20/26 = WX/39

Make WX the subject

WX = 39 * 20/26

Evaluate the products

WX = 30

Hence, the length is 30 units

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Complete question

If TU = 20, UV = 26, and XY = 39, find the length of WX. Round your answer to the nearest tenth if necessary.

Figures are not necessarily drawn to scale

Yes, this sample of the homework problems assigned likely to be representative.

A representative sample is a portion of a population that attempts to accurately reflect the characteristics of a larger group. For example, a classroom of 30 students with 15 boys and 15 girls might have a representative sample of 6 students.

3 boys and 3 girls. A sample contains a smaller, more manageable version of a larger cohort, which is useful for statistical analysis when the population size is large.

A representative sample is a technique that can be used to gain insight and observations about a particular population. A representative sample is a small group of subsets that seeks to proportionally reflect a particular trait exemplified in the target population.

A representative sample often gives the best results, but can be the type of sample that is most difficult to obtain.

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Answer:

A, w=12

Step-by-step explanation:

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

Work Shown:

2.25% = 2.25/100 = 0.0225

2.25% of 56 dollars = 0.0225*56 = 1.26

The amount of sales tax is $1.26

Side note: The total bill is 56 + 1.26 = 57.26 dollars.

Answer:

$1.26

Step-by-step explanation:

So you just have to find 2.25% of 56.

To find a certain percentage of something, you multiply it. Let's write out a sentence explaining what you need to do. You have to find:

2.25% of 56

Whenever you've got a sentence like this, all you've got to do is change the word "of" to a multiplication symbol. And now you've got an expression:

2.25% × 56

Let's convert the percentage to a decimal. To do this, you simply remove the percent symbol, then move the decimal point 2 places to the left.

2.25% = 0.0225

And now you have:

0.0225 × 56

Then you just do the math! I am assuming you already know how to do decimal multiplication so I'm not going to explain the process here.

But once you multiply 0.0225 × 56, you get an answer: 1.26

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The probability is 0.01 that the sample variance is less than or equal to 2.57% of the population variance.

Probability that the sample variance is greater than or equal to what percentage of the population variance is 0.10:From the given information,

Random sample of n = 13 components was taken.

The duration of timing signals follow normal distribution.

The population variance is unknown.

Let S² be the sample variance and σ² be the population variance.

The quantity (n - 1)S²/σ²

follows a chi-square distribution with (n - 1) degrees of freedom.

Using the given information, we can say that:

(n - 1)S²/σ² ~ χ²(12)

We need to find the value of k such that P((n - 1)S²/σ² ≥ k) = 0.10.

Using the chi-square distribution table, we find that k = 20.96 (approximately).

Hence, the probability is 0.10 that the sample variance is greater than or equal to 20.96% of the population variance.b. Probability that the sample variance is less than or equal to what percentage of the population variance is 0.01:

We need to find the value of k such that P((n - 1)S²/σ² ≤ k) = 0.01.

Using the chi-square distribution table, we find that k = 3.82 (approximately).(n - 1)S²/σ² ~ χ²(12)

Let's solve for σ²:σ² = (n - 1)S²/k = 12S²/3.82 = 3.14S²

Now we need to find the value of S² such that P((n - 1)S²/σ² ≤ 3.82) = 0.01.

This is equivalent to P((n - 1)S²/3.14S² ≤ 3.82) = 0.01.Simplifying, we get P((n - 1)/3.14 ≤ 3.82) = 0.01.This is equivalent to P(n ≤ 13.69) = 0.01.Using the normal distribution table, we find that the value of n is approximately 4.

Using this value of n, we can find the value of S² as follows:

(n - 1)S²/σ² = 3.82S²/3.14S² = 1.22S² = 3.14/1.22 = 2.57

Hence, the probability is 0.01 that the sample variance is less than or equal to 2.57% of the population variance.

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Answer:

6

Step-by-step explanation:

3! = 3 x 2 x 1 = 6

We solved the following equation using an appropriate cofunction identity as x = π/18 and x = -π/18.

To solve the equation sin(4π/9) = cos(x) using an appropriate cofunction identity, we can start by recognizing that the sine and cosine functions are cofunctions of each other. This means that the sine of an angle is equal to the cosine of its complement, and vice versa.

In other words, sin(x) = cos(π/2 - x) and

cos(x) = sin(π/2 - x).

In this case, we have

sin(4π/9) = cos(x),

so we can rewrite the equation as

cos(π/2 - 4π/9) = cos(x).

Now, we need to find the value of π/2 - 4π/9. To simplify this, we can find a common denominator for π/2 and 4π/9, which is 18.

So, π/2 - 4π/9 can be written as

(9π/18) - (8π/18) = π/18.

Therefore, the equation simplifies to

cos(π/18) = cos(x).

Since the cosine function is an even function,

cos(x) = cos(-x),

we can say that

x = π/18 or x = -π/18.

Hence, the solutions to the equation sin(4π/9) = cos(x) using an appropriate cofunction identity are x = π/18 and x = -π/18.

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The amount of storage required to represent a simple graph with n vertices and m edges can vary depending on the chosen representation. Here's the storage requirement for each representation:

a) Adjacency lists:

In an adjacency list representation, we typically use an array of size n to store the vertices, and for each vertex, we maintain a linked list or an array to store its adjacent vertices. The space complexity of this representation is O(n + m), where n is the number of vertices and m is the number of edges.

Each vertex requires constant space, and each edge is represented by a link or entry in the adjacency list.

b) Adjacency matrix:

In an adjacency matrix representation, we use a 2D matrix of size n x n to represent the graph. Each entry (i, j) in the matrix represents whether there is an edge between vertices i and j. The space complexity of this representation is O(n^2), as we need to store n^2 entries for the complete matrix. However, if the graph is sparse (few edges compared to vertices), the space complexity can be reduced to O(n + m) by only storing the entries corresponding to the existing edges.

c) Incidence matrix:

In an incidence matrix representation, we use a 2D matrix of size n x m, where n is the number of vertices and m is the number of edges. Each entry (i, j) in the matrix represents whether vertex i is incident to edge j. The space complexity of this representation is O(n * m), as we need to store n * m entries for the matrix.

Similar to the adjacency matrix, if the graph is sparse, the space complexity can be reduced to O(n + m) by storing only the entries corresponding to the existing edges.

In summary:

a) Adjacency lists: O(n + m)

b) Adjacency matrix: O(n^2) or O(n + m) for sparse graphs

c) Incidence matrix: O(n * m) or O(n + m) for sparse graphs

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Answer:

Step-by-step explanation:

8% of $125 = 0.08×$125 = $10

If you have a right triangle, then you have 2 legs and 1 hypotenuse. The hypotenuse is the longest side across from the 90 degree angle. Pythagoras came up with the theorem for right triangles that states that the sum of the squares of the 2 legs is equal to the hypotenuse squared.

d) No.In this context, the term "average" is commonly used to refer to the mean, which is the sum of all incomes divided by the number of families. While the term "mean" could be more specific, it is not incorrect to use the term "average" in this case.

The mean is a commonly used measure of central tendency to represent the typical value of a set of data.

However, it's worth noting that depending on the distribution of income data, the median could also be a relevant measure.

The median represents the middle value when the incomes are sorted in ascending order, and it is less sensitive to extreme values compared to the mean. So, if the distribution of family incomes is highly skewed or has outliers, the median could provide a different perspective on the change in family income.

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Expected gain/loss with survey = (p * (probability of success given favorable survey * gain from success + probability of failure given favorable survey * loss from failure)) + ((1-p) * (probability of success given unfavorable survey * gain from success + probability of failure given unfavorable survey * loss from failure))
= (0.4 * (0.6 * $540,000 + 0.1 * -$450,000)) + (0.6 * (0.2 * $540,000 + 0.7 * -$450,000))

he company is considering whether to market a new product. They assess that the probabilities of the outcomes - success or failure - are p and 1-p, respectively. If the product is marketed and it fails, the company will have a net loss of $450,000. If the product is marketed and it succeeds, the company will have a net gain of $540,000. If the company decides not to market the product, there is no gain or loss.
The company can conduct a survey of prospective buyers to determine the market potential. The survey results can be classified as favorable, neutral, or unfavorable. Based on similar surveys for previous products, the company assesses the probabilities of favorable, neutral, and unfavorable survey results to be 0.6, 0.3, and 0.1 for a product that will evntually be a success, and 0.1, 0.2, and 0.7 for a product that will eventually be a failure.
The total cost of conducting the survey is c dollars. The question asks for which values of c, if any, would the company choose to conduct the survey, given that p=0.4.
To determine whether to conduct the survey, we need to compare the expected gains/losses from marketing the product with and without the survey.
If the company markets the product without the survey, the expected gain/loss can be calculated as follows:
Expected gain/loss without survey = (p * gain from success) + ((1-p) * loss from failure)
= (0.4 * $540,000) + (0.6 * -$450,000)
If the company markets the product with the survey, the expected gain/loss can be calculated as follows:
Expected gain/loss with survey = (p * (probability of success given favorable survey * gain from success + probability of failure given favorable survey * loss from failure)) + ((1-p) * (probability of success given unfavorable survey * gain from success + probability of failure given unfavorable survey * loss from failure))
= (0.4 * (0.6 * $540,000 + 0.1 * -$450,000)) + (0.6 * (0.2 * $540,000 + 0.7 * -$450,000))

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Answer:

20

Step-by-step explanation:

63 - 43 = 20

Answer:

20 students

Step-by-step explanation:

because 43+s=63

63-43=20

s=20

so it have 20 students on the playground

Answer:

40 is correct answer.its ok if wrong sorry

Answer:

\(\large \boldsymbol {} 6x^2 -5x-14 =0 \\\\ D=25+14\cdot 4\cdot 6 =361=19^2 \\\\ x_1= \dfrac{5+19}{12} =2 \\\\\\ x_2 =\dfrac{5-19}{12} =-\dfrac{7}{6} \\\\ and \ \ we \ \ \ know \ \ that \\\\\ 6x^2 -5x-14 =6 (x-x_1) ( x- x_ 2) = 6 ( x-(-\frac{7}{6} ))\boldsymbol { ( x-2 ) } \\\\ as \ we \ can \ see \ , \ the \ \ expansion \ is \\\\\ x-2 ; therefore \ \ , \ \ the \ \ answer \ \ is \ \ yes\)

Answer: Yes: divisible

Step-by-step explanation:

\(P(x)=6x^2-5x-14\\\\P(2)=6*2^2-5*2-14=24-10-14=0\\\\P(x)\ is\ exactly\ divisible\ by\ x-2\\\)

The bottom of the ladder is 9 feet from the wall.

Using the Pythagorean Theorem, we can calculate the distance from the wall. The Pythagorean Theorem states that for a right triangle, the sum of the squares of the sides is equal to the square of the hypotenuse. In this case, the hypotenuse is 15 feet and the side adjacent to the wall is 12 feet.

The formula for the Pythagorean Theorem is a^2 + b^2 = c^2.

We can solve for the distance from the wall (a). a^2 = c^2 - b^2, so a^2 = 15^2 - 12^2, which equals a^2 = 225 - 144, so a^2 = 81. Taking the square root of both sides, a = 9 feet.

Therefore, the bottom of the ladder is 9 feet from the wall.

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Answer:

8x + 2x (4)

Step-by-step explanation:

If you are trying to simplify or isolate the variables, its 4. Please tell me if this answer is wrong

Answer: 8x + 2x (4)

The correct answer is 8x + 2x (4)

Step-by-step explanation:

Hope this helps =)

The general solution of the given differential equation is y(x) = C₁e^-x + 4xe^-x. The largest interval over which the general solution is defined is (-∞, ∞). There are no transient terms in the general solution.

The differential equation given can be rearranged into the form dy/dx + (x + 2)/(x + 1)y = 8xe^-x, which is a linear first order differential equation. Using the integrating factor method, an integrating factor of e^(x + 1) can be used to obtain the general solution y(x) = C₁e^-x + 4xe^-x.

The integration constant C₁ can be determined by supplying the appropriate initial conditions. As the equation is a linear first order differential equation, the general solution is valid over the entire domain of x, which is (-∞, ∞). As the equation does not involve any terms that provide a particular value for y at any point in the domain, there are no transient terms in the general solution.

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Therefore, the circumference of the circle is 24π feet.

Circumference is the distance around the edge of a circular object. It is the measurement of the perimeter of a circle. To find the circumference of a circle, you can use the formula C = 2πr, where C is the circumference, π is the mathematical constant pi (approximately equal to 3.14), and r is the radius of the circle (the distance from the center of the circle to any point on its edge).

The formula for the circumference of a circle is:

C = 2πr

Where C is the circumference, π is pi, and r is the radius.

Substituting the given value of radius into the formula, we get:

C = 2π(12) = 24π

Therefore, the circumference of the circle is 24π feet.

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Answer:

The answer is 0.45 or if you want to put as a fraction 9/20

Step-by-step explanation:

You can use this equation to figure out for any number of seconds how many items the cashier can ring up.

For instance if you wanted to know if 100 seconds how many items could be rung up:

y = .45x

y = .45(100)  This would be 45 items.

If you wanted to know how many items could be rung up in 10 seconds:

y = .45(10) This would be 4.5 items.

You could use this equation for any amount of time to figure out how many items could be rung up.