The population of a town in 2000 was 120,000 people. The town grew at a rate of 3% annually. How many people live in the town in 2018?

The inverse of the matrix [tex]\left[\begin{array}{cc}2&-7\\-2&5\end{array}\right][/tex] is [tex]-\frac 14 \left[\begin{array}{cc}5&7\\2&2\end{array}\right][/tex]

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

[tex]\left[\begin{array}{cc}2&-7\\-2&5\end{array}\right][/tex]

The determinant (D) of the matrix is

D = 2 * 5 + 7 * -2

Evaluate

D = -4

The inverse, I is then calculated as

[tex]I = -\frac 14 \left[\begin{array}{cc}5&7\\2&2\end{array}\right][/tex]

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The theoretical probability of choosing List A is less than the experimental probability of choosing List A.

The theoretical probability of choosing List B is greater than the experimental probability of choosing List A.

For a fair coin, the theoretical probability of obtaining a head or tail is 0.5 or 50% each.

Therefore, theoretically, the probability of choosing List A is 0.5, and the probability of choosing List B is also 0.5.

The experimental probability of choosing List A or List B is obtained using the formula below:

Experimental probability of List A = 37/70

Experimental probability of List A = 0.529

The experimental probability of choosing List B is:

Experimental probability of List B = 33/70

Experimental probability of List B = 0.471

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Answer:

  x ∈ {π/4, π/3, 2π/3, 3π/4}

Step-by-step explanation:

You want the solutions on the interval [0, 2π) of the equation ...

  [tex]-4\cos^2(x)-2(\sqrt{3}+\sqrt{2}\sin(x)+\sqrt{6}+4=0[/tex]

Replacing the cosine function with its equivalent, we have a quadratic in sin(x).

  [tex]-4(1-\sin^2(x))-2(\sqrt{3}+\sqrt{2}\sin(x)+\sqrt{6}+4=0\\\\4\sin^2(x)-2(\sqrt{3}+\sqrt{2})\sin(x)+\sqrt{6}=0\\\\(2\sin(x)-\sqrt{3})(2\sin(x)-\sqrt{2})=0\\\\x\in\left\{\dfrac{\pi}{2}\pm\dfrac{\pi}{4},\dfrac{\pi}{2}\pm\dfrac{\pi}{6}\right\}\\\\\boxed{x\in\left\{\dfrac{\pi}{4},\dfrac{\pi}{3},\dfrac{2\pi}{3},\dfrac{3\pi}{4}\right\}}[/tex]

__

Additional comment

It is helpful to have the solutions provided by a graphing calculator. This gives a useful clue as to how the equation factors.

The graph was created using Desmos.

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The correct answer is: "The second job offer is better by $21,840."

Let's calculate the total value of the second offer after 4 years:

Yearly salary: $63,000

Total gross income after 4 years: $63,000 x 4 = $252,000

For the 401k contributions, the company matches 5% of the employee's salary, so the employee contributes 5% of $63,000 = $3,150 per year, and the company contributes an additional 5% of $63,000 = $3,150 per year.

After 4 years, the total contributions and company matches are:

Employee contributions: $3,150 x 4 = $12,600

Company matches: $3,150 x 4 = $12,600

Total 401k contributions: $12,600 + $12,600 = $25,200

Therefore, the total value of the second offer after 4 years is:

Total value: $252,000 + $25,200 = $277,200

Now, let's compare this to the total value of the first offer, which is given as $255,360.

Therefore, the second job offer is better by:

$277,200 - $255,360 = $21,840

So the correct answer is: "The second job offer is better by $21,840."

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Answer:

3 feet

Step-by-step explanation:

Circumference of circle = d · π

Circumference = 3π

Let'solve

3π = d · π

d = 3 feet

So, the diameter is 3 feet.

Answer:

21.9

Step-by-step explanation:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]   If 18 is the whole base then 1/2 would be 9

[tex]9^{2}[/tex] + [tex]20^{2}[/tex] = [tex]c^{2}[/tex]

81 + 400 = [tex]c^{2}[/tex]

481 = [tex]c^{2}[/tex]

[tex]\sqrt{481}[/tex] = [tex]\sqrt{c^{2} }[/tex]

21.9 ≈ c Rounded to the nearest tenth

The radius of the cylinder is approximately 5.077 inches.

The volume of a cylinder is given by the formula:

V = πr²h

where V is the volume, r is the radius, and h is the height.

Substituting the given values, we get:

81 = πr²(1)

Simplifying this equation, we get:

81 = πr²

Dividing both sides by π and taking the square root, we get:

r = √(81/π)

r ≈ 5.077

Therefore, the radius of the cylinder is approximately 5.077 inches.

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Here are three sets of variables:

The level of physical activity and heart rate constitute a causal association wherein one's heart rate is directly affected by the exercised performed.

Likewise, the correlation between studying time and grades earned showcases another causal relationship that asserts how higher study hours lead to better academic scores.

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the relatedness of a son to a maternal aunt in a haplodiploid system is 0.25, or 1/4.

In a haplodiploid system, males develop from unfertilized haploid eggs and are haploid, while females develop from fertilized diploid eggs and are diploid. This means that sons inherit all their genes from their mothers, while daughters inherit half their genes from their fathers and half from their mothers.

To calculate the relatedness of a son to a maternal aunt, we need to consider the genetic relatedness between the son and his mother, and the genetic relatedness between the mother and her sister (the maternal aunt).

The son shares half of his genes with his mother, and his mother shares half of her genes with her sister. Therefore, the son shares one quarter (0.5 x 0.5) of his genes with his maternal aunt.

So, the relatedness of a son to a maternal aunt in a haplodiploid system is 0.25, or 1/4. Therefore, the correct answer is 0.25.

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Sine and cosine have defined amplitudes, while tangent, cosecant, secant, and cotangent do not have defined amplitudes.

The trigonometric functions that have a defined amplitude are sine and cosine. These functions have an amplitude of 1, as their maximum and minimum values lie between -1 and 1. The other functions (tangent, cosecant, secant, and cotangent) do not have a defined amplitude, as their values can approach infinity.

The trigonometric functions in mathematics are real functions that connect the angle of a right-angled triangle to the ratios of its two side lengths. They are also known as circular functions, angle functions, or goniometric functions. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others. Since they are some of the most basic periodic functions, Fourier analysis is frequently employed to examine periodic events.

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Answer:

180

Step-by-step explanation:

rotate it 90 degrees 2 times

The solution of the equation is x = 7, so the correct option is C

Here we want to find the solution of the equation:

3*(x + 9)^(3/4) = 24

First divide both sides by 3 to get:

(x + 9)^(3/4) = 24/3 = 8

Now we can pass the exponent to get:

(x + 9) =8^(4/3) = 2^4 = 16

x + 9 = 16

Now subtract 9 in the left side.

x = 16 - 9

x  =7

The correct option is C.

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The point (0, 4) is not a solution of the given system of equations.

The given system of equations,

-x + 4y = 16 [Equation 1]

3x - 4y = -19 [Equation 2]

We have to find the solution of the system of equations.

From [Equation 1],

4y = x + 16 [Equation 3]

From [Equation 2],

3x + 19 = 4y [Equation 4]

From [Equation 3] and [Equation 4],

x + 16 = 3x + 19

2x = -3

x = -3/2

So x = 0 is not possible.

Hence (0, 4) is not a solution.

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The cost of one ounce of peanuts and one ounce of cashews cost are $0.25 for peanuts and $0.45 for cashews

We can represent the cost of the peanut and cashew as

p=cost per ouce of peanuts

c=cost per ounce of cashews

We can represent the mixture according to the question can be expressed as

15p+5c=6

5p+15c=8

Then we can divide the equations with 5

3p + c = 1.2

p + 3c = 1.6

We can multiply first equation by -3 and add to 2nd to eliminate c's

-9p-3c=-3.6

 p + 3c = 1.6

-8p = -2

p= 0.25

Then from   3p + c = 1.2

c = 1.2 - 3(0.25)

=0.45

Therefore, $0.25 for peanuts and $0.45 for cashews

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The quadratic equations that are taller, that is, with a greater dilation factor:

Case A: y = 10 · x²

Case B: y = x²

Case C: y = 3 · x²

Case D: y = x²

In this problem we find four pairs of quadratic equations of the form:

y = k · x², k > 0

Where:

A quadratic equation is taller when it has a greater dilation factor. Now we proceed to determine the function for each case:

Case A: y = x² and y = 10 · x²

y = 10 · x²

Case B: y = x² and y = (1 / 7) · x²

y = x²

Case C: y = x² and y = 3 · x²

y = 3 · x²

Case D: y = x² and y = (1 / 12) · x²

y = x²

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A) True. The source term in a partial differential equation (PDE) represents a forcing function or external input to the system being modeled.

A) True. The source term in a partial differential equation (PDE) represents a forcing function or external input to the system being modeled. In the finite element method (FEM), the PDE is discretized into a set of algebraic equations, and the source term appears in each of these equations.

Specifically, for each algebraic equation resulting from the discretization of the PDE, the source term contributes to the coefficient of the dependent variable on the left-hand side of the equation, and it is taken to the right-hand side of the equation. The resulting coefficient and right-hand side term are then used to construct the corresponding row of the global coefficient matrix and the right-hand side vector, respectively.

Therefore, the source term affects all algebraic equations in the finite element method and is an essential component of the mathematical model. Changing the source term will affect the solution obtained from the ANSYS solver and can result in a different physical behavior of the system being modeled.

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The probability of a healthy adult having a body temperature greater than 97.60°F is approximately 91%.

To find the probability of a healthy adult having a body temperature greater than 97.60°F, we can use the Z-score formula to standardize the temperature value. The Z-score formula is:
Z = (X - μ) / σ

Where X is the value we are interested in (97.60°F), μ is the mean (98.60°F), and σ is the standard deviation (0.73°F).
Z = (97.60 - 98.60) / 0.73 = -1.37
Now, we can use the Z-score to find the probability. A Z-score of -1.37 corresponds to a percentile of approximately 0.0853, which means there is an 8.53% chance that an adult will have a body temperature lower than 97.60°F. Since we are interested in the probability of a temperature greater than 97.60°F, we need to subtract this value from 1:
1 - 0.0853 = 0.9147
As a whole number percentage, this would be 91%.

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The solution to the multiplication of the table is:

A) -205

B) -67

C) -7.93

D) 1

E) -121

Multiplication is an order of operation used in mathematical operations or algebraic problems.

Now, when we multiply two numbers, the answer is called product. The number of objects in each group is called multiplicand, and the number of such equal groups is called the multiplier. Thus:

We have that we are to find the solution for x * y and this gives:

A) -205 * 1 = -205

B) 67 * -1 = -67

C) 1 * -7.93 = -7.93

D) -1 * -1 = 1

E) 11 * -11 = -121

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Answer: To determine how many more of the shortest paper chains Rico has than the longest paper chains, you need to know how many paper chains he has of each length. Once you know that, you can subtract the number of longest paper chains from the number of shortest paper chains to find the difference.

For example, if Rico has:

- 10 paper chains that are 3 inches long

- 8 paper chains that are 5 inches long

- 6 paper chains that are 7 inches long

Then the shortest paper chains are the ones that are 3 inches long, and the longest paper chains are the ones that are 7 inches long. To find the difference, you can subtract the number of longest paper chains (6) from the number of shortest paper chains (10):

10 - 6 = 4

Therefore, Rico has 4 more of the shortest paper chains than the longest paper chains.

Step-by-step explanation:

To find the p-value for the test examining the positive linear relationship between speed and jump height, you need to calculate the Pearson correlation coefficient, determine the degrees of freedom, and then find the corresponding p-value.

To determine the p-value for this test, we would need to conduct a hypothesis test using a linear regression model. The null hypothesis would be that there is no linear relationship between speed and jump height, while the alternative hypothesis would be that there is a positive linear relationship between the two variables.

After running the regression model and performing the hypothesis test, we would look for the p-value associated with the slope coefficient for speed. If this p-value is less than the chosen significance level (usually 0.05), we can conclude that there is convincing evidence of a positive linear relationship between speed and jump height for students like these.

Without actually running the regression model and hypothesis test, it is not possible to provide an exact p-value for this scenario.

To determine if there is convincing evidence of a positive linear relationship between speed (mph) and jump height (in) for students like these, you need to conduct a correlation test, specifically a Pearson correlation test. The p-value will help you determine the significance of the relationship.

Step-by-step explanation:

1. Gather the data: Obtain the values for speed (mph) and jump height (in) for each student.

2. Calculate the Pearson correlation coefficient (r): This value will help you measure the strength and direction of the linear relationship between the two variables. You can use statistical software or a calculator for this.

3. Determine the degrees of freedom (df): Calculate this by subtracting 2 from the total number of data points (n). Formula: df = n - 2.

4. Calculate the p-value: Using the Pearson correlation coefficient (r) and the degrees of freedom (df), you can find the p-value in a t-distribution table or by using statistical software.

5. Interpret the p-value: If the p-value is less than your chosen significance level (commonly 0.05), there is convincing evidence of a positive linear relationship between speed and jump height. If the p-value is greater than 0.05, there is not enough evidence to suggest a significant positive linear relationship.

In summary, to find the p-value for the test examining the positive linear relationship between speed and jump height, you need to calculate the Pearson correlation coefficient, determine the degrees of freedom, and then find the corresponding p-value. Comparing this p-value to your chosen significance level will help you conclude if there is convincing evidence of a positive linear relationship between the two variables.

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The probability of getting in the trapezoid or in the triangle is 0.13.

From the given figure,

Sum of parallel sides of a trapezium is 13+8=21 m

Height of trapezium is 4 m.

Here, area of trapezium is 1/2 ×21×4

= 42 square meter

Base of a triangle = 4 m

Height of a triangle = 7 m

Area of a triangle = 1/2 ×4×7

= 14 square meter

Area of a rectangle = Length×Width

= 25×17

= 425 square meter

Probability of getting trapezium = 42/425

Probability of getting triangle = 14/425

Probability of getting in the trapezoid or in the triangle

= 42/425 + 14/425

= 56/425

= 0.13

Therefore, the probability of getting in the trapezoid or in the triangle is 0.13.

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The matching of the accounting terms will be:

It should be noted that in accountancy, depreciation is a term that refers to two aspects of the same concept: first, the actual decrease of fair value of an asset, such as the decrease in value of factory equipment each year.

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In the scenario where exactly half the time the element x is not in the list and if x is in the list it is equally likely to be in any position.

The average-case performance of the linear search algorithm would be O(n/2), where n is the size of the list.
This is because in the worst case scenario, the algorithm would have to search through the entire list to find the element x, which would take n operations. However, since half the time x is not in the list, the algorithm would only need to search through half the list, on average. Therefore, the average-case performance would be O(n/2).

To analyze the average-case performance of the linear search algorithm, given that exactly half the time the element x is not in the list and if x is in the list it is equally likely to be in any position, please follow these steps:
1. Consider the two scenarios: element x is in the list and element x is not in the list.
2. For the case when x is in the list, as it is equally likely to be in any position, the average number of comparisons required would be (n+1)/2, where n is the total number of elements in the list.
3. For the case when x is not in the list, the linear search algorithm will go through all the elements in the list and make n comparisons before determining that x is not present.
4. To calculate the average-case performance, take into account the probabilities of each scenario. As the element x is not in the list exactly half the time, the probabilities are 0.5 for each scenario.
5. The average-case performance would be the weighted average of the comparisons in both scenarios: 0.5*((n+1)/2) + 0.5*n.
So, the average-case performance of the linear search algorithm in this situation is given by the expression: 0.5*((n+1)/2) + 0.5*n.

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Answer:  B (4, 8)

Step-by-step explanation:

6x + 3y=48

5x+y= 28

these functions are lines.  "Solving a system of questions" means to find the point where they intersect, where the x's are the same and the y's are the same.

You want to multiply an entire equation to eliminate a variable.

6x + 3y=48

5x+y= 28

6x + 3y=48     multiply the 2nd equation by -3 so you can eliminate the y's

-3(5x+y= 28)   multiply all terms by -3

6x + 3y=48    

-15x-3y= -84       add like terms of the equations  and the y goes away

-9x       = -36        divide both sides by -9 to solve for x

x=4   now substitute back into one of the original equations

5(4)+y=28

20+y28

y=8

x=4,  y=8

(4, 8) is your point where they intersect.

The number of square inches which make up half of the cookie cake is approximately 100.48 inches².

Given that,

The diameter of a circular cookie cake is 16 inches.

Cookie cake is circular.

We have to find the area of the half of the cookie cake.

Diameter = 16 inches

Radius = 16/2 = 8 inches

Area of a circular figure = πr²

Total area of the cookie cake = π(8)² = 64π

Area of half the cake = 64π /2 = 32π = 100.48 square inches

Hence the area of half of the cookie cake is 100.48 inches².

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a)he margin error for a 95% confidence interval to estimate the population proportion is 0.0506., b) the 95% confidence interval for the population proportion is approximately (0.337, 0.423).

a) To find the margin error for a 95% confidence interval to estimate the population proportion, we need to use the following formula:

Margin error = z * sqrt(p * (1 - p) / n)

where z is the z-score for the desired confidence level (in this case, 95% confidence level), p is the sample proportion (given as 0.38), and n is the sample size (not given).

To find the sample size, we can use the formula:

n = (z^2 * p * (1 - p)) / (margin error)^2

where z and p are the same as above, and margin error is given as the value we want to find.

Using a z-score of 1.96 for a 95% confidence level, we can plug in the values and solve for the margin error:

Margin error = 1.96 * sqrt(0.38 * (1 - 0.38) / n)

Now we need to find n by solving the second formula:

n = (1.96^2 * 0.38 * (1 - 0.38)) / (margin error)^2

Plugging in the values for margin error and solving for n, we get:

n = 547.896

Rounding up to the nearest integer, we get a sample size of n = 548.

Plugging in this value for n, we can solve for the margin error:

Margin error = 1.96 * sqrt(0.38 * (1 - 0.38) / 548) = 0.0506

Therefore, the margin error for a 95% confidence interval to estimate the population proportion is 0.0506.

b) To find the confidence interval for a 95% confidence level, we can use the formula:

Confidence interval = sample proportion +/- margin error

where sample proportion is the given value of p (0.38), and margin error is the value we just calculated (0.0506).

Plugging in the values, we get:

Confidence interval = 0.38 +/- 0.0506

Simplifying, we get:

Confidence interval = (0.3294, 0.4306)

Therefore, the confidence interval for a 95% confidence level is (0.3294, 0.4306). This means that we can be 95% confident that the true population proportion falls within this range.
Hello! I'd be happy to help with your question.

a) To find the margin of error for a 95% confidence interval when estimating the population proportion, you'll need the following formula:

Margin of error = z * √(p * (1 - p) / n)

Where:
z = 1.96 (for a 95% confidence interval)
p = 0.38 (given proportion)
n = 500 (sample size)

Now, let's plug in the values and calculate the margin of error:

Margin of error = 1.96 * √(0.38 * (1 - 0.38) / 500)
Margin of error = 1.96 * √(0.38 * 0.62 / 500)
Margin of error = 1.96 * √(0.0004768)
Margin of error ≈ 0.043

So, the margin of error for the 95% confidence interval is approximately 0.043 or 4.3%.

b) To find the 95% confidence interval for the population proportion, use the following formula:

Confidence interval = p ± margin of error

Using the proportion (p) and margin of error calculated in part a:

Confidence interval = 0.38 ± 0.043

Lower limit = 0.38 - 0.043 = 0.337
Upper limit = 0.38 + 0.043 = 0.423

So, the 95% confidence interval for the population proportion is approximately (0.337, 0.423).

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The volume of the given rectangular prism is 13.5 units³

Given that the area of the base of a rectangular prism is 27/5 units², and the height is 5/2 units, we need to find the volume,

Volume = base area x height

= 27/5 x 5/2

= 13.5

Hence, the volume of the given rectangular prism is 13.5 units³

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The independent variable in a relationship between two variables is the variable that is used to predict or explain the variation in the other variable.

It is the variable that is manipulated or controlled by the researcher. For example, if we are investigating the relationship between temperature and ice cream sales, temperature would be the independent variable, as we would expect changes in temperature to predict changes in ice cream sales.

On a scatter diagram, the independent variable is typically represented on the horizontal axis (x-axis) and the dependent variable is typically represented on the vertical axis (y-axis). This is because the independent variable is typically plotted along the horizontal axis, with its values placed at regular intervals, and the dependent variable is then plotted along the vertical axis, with its values plotted based on their relationship to the corresponding independent variable values.

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