The circumference of a circle can be found using the formula C = 2r.

Which is an equivalent equation solved for r?

r = C
r = C(2)
r = r equals StartFraction C Over 2 pi EndFraction.
r = r equals StartFraction 2 pi Over C EndFraction.

Therefοre, the savings plan balance after 12 mοnths is $2,480(rοunded tο the nearest cent).

The fοllοwing equatiοn can be used tο determine interest: Calculating interest is dοne using the fοrmula P x R x T. The primary value is P. (the beginning balance). what the interest rate is (usually per year, expressed as a decimal). T denοtes the number T. (generally οne-year time periοds).

Accοrding tο the given infοrmatiοn:

\(\rm FV = Pmt \times [(1 + r/n)^{(n \times t) }- 1] / (r/n)\)

In this case, Pmt = $200, r = 9%, n = 12 (since we are making monthly payments), and t = 1 (since we are saving for 12 months). Plugging in these values, we get:

\(\rm FV = 200 x [(1 + 0.09/12)^{(12 x 1) }- 1] / (0.09/12)\)

FV = 200 x (1.0075¹² - 1) / 0.0075

FV = 200 x( 1.093 - 1) / 0.0075

FV =2,480

Therefore, the savings plan balance after 12 months is $2,480(rounded to the nearest cent).

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Step-by-step explanation:

Did you mean :

f(x) = 5(4 - x)

f(16) = 5(4 - 16)

f(16) = 5(-12)

f(16) = -60

Answer:

          Statement                                                      Reason

Answer:

The equation of perpendicular bisector is:

\(y = 2x-2\)

Step-by-step explanation:

Given the points

First, we need to find the midpoint of the points (-4, 3) and (8, -3)

\(\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\)

\(\left(x_1,\:y_1\right)=\left(-4,\:3\right),\:\left(x_2,\:y_2\right)=\left(8,\:-3\right)\)

\(=\left(\frac{8-4}{2},\:\frac{-3+3}{2}\right)\)

\(=\left(2,\:0\right)\)

Thus, the midpoint of the points is: (2, 0)

Now, finding the slope between (-4, 3) and (8, -3)

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(\left(x_1,\:y_1\right)=\left(-4,\:3\right),\:\left(x_2,\:y_2\right)=\left(8,\:-3\right)\)

\(m=-\frac{1}{2}\)

Therefore, the slope m = -1/2

The slope of the line perpendicular to the segment = [-1] / [-1/2] = 2

Using the point-slope form of the equation of the line, the equation of perpendicular bisector is:

\(y-y_1=m\left(x-x_1\right)\)

where m is the slope of the line

substituting the slope 2 and the point (2, 0)

\(y-y_1=m\left(x-x_1\right)\)

\(y - 0 = 2 (x-2)\)

\(y = 2x-2\)

Therefore, the equation of perpendicular bisector is:

\(y = 2x-2\)

The following given task is an experiment.

So,

The following given task is an experiment.

Therefore, the following assignment is an experiment.

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Answer:

9x3

Step-by-step explanation:

x+9

/4

9x=8

x=2

+2=4

x=1+4234

Answer:CED

Step-by-step explanation:

Answer:

C, E, and D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Solve through logic and brain rather than lengthy calculations

Trick to be used

See

Only option D contains y≤4

Option D is correct

Answer:

(3,-2)

Step-by-step explanation:

Rewrite in vertex form and use this form to find the vertex

The prefix associated with the multiplier 0.001 is "milli-."

The International System of Units (SI) uses prefixes to denote decimal multiples and submultiples of units. The prefix "milli-" corresponds to a multiplier of 0.001. Here's a stepwise explanation of how this prefix is determined:

1. Identify the multiplier: The given multiplier is 0.001.

2. Understand the prefix: The prefix "milli-" represents a factor of 1/1000 or 0.001.

3. Determine the prefix symbol: The symbol for "milli-" is "m." It is written in lowercase.

4. Attach the prefix: To express a unit with the multiplier 0.001, you attach the prefix "milli-" to the base unit. For example, if the base unit is meter (m), the millimeter (mm) represents 0.001 meters.

5. Other examples: The milligram (mg) represents 0.001 grams, the millisecond (ms) represents 0.001 seconds, and the milliliter (mL) represents 0.001 liters.

By using the "milli-" prefix, we can conveniently express values that are a thousandth of the base unit, allowing for easier comprehension and communication in various scientific and everyday contexts.

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To know if the classmate’s family is actually wealthy, one will need to know their assets and their debt.

In financial accounting, an asset means a resource that is owned or controlled by a business or an economic entity. An asset is anything that can be used to produce positive economic value.

Assets represent the value of ownership that can be converted into cash and the examples of personal financial assets include cash and bank accounts, real estate, personal property like furniture and vehicles, and investments such as stocks, mutual funds, and retirement plans.

In this case, through the assets, one will be able to know that they're wealthy. The debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. This is the money that they owe.

The asset should more than the debt.

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Answer:

l = 40 m

Step-by-step explanation:

The formula for area of a rectangle is

A = lw, where

Step 1:  Since we're given the area and width, we plug in these two values for A and w and to solve for l (length):

360 = 9l

Step 2:  Divide both sides by 9 to solve for l

(360 = 9l) / 9

40 m = l

Optional Step 3:  We can check our answers by checking that the product of 40 and 9 is 360

40 * 9 = 360

360 = 360

Answer:

1/3

Step-by-step explanation:

The exponent -1 indicates that we need to take the reciprocal of the base 3.

So, 3^(-1) = 1/3

Therefore, the answer is 1/3.

Answer:

1/3

Step-by-step explanation:

Rewrite the expression using the negative exponent rule \(b^{-n}\) = \(\frac{1}{b^{n} }\)

The answer is 1/3

Answer: 20 questions

Step-by-step explanation:

Answer:

15/x*100=75

75/100*15=x

x=20

total no. of questions

Answer:

4 red marbles

Step-by-step explanation:

r is the number of red marbles then green marbles is 9r , so

r + 9r = 40

10r = 40 ( divide both sides by 10 )

r = 4

there are 4 red marbles

Answer:

15%

Step-by-step explanation:

To find the radius of convergence, we use the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges absolutely. If the limit is greater than 1, then the series diverges. If the limit is equal to 1, then the test is inconclusive.

In this case, we have the series (-1)^(n-1)/n5^n. Taking the absolute value of the ratio of consecutive terms, we get |((-1)^n)/(n+1)(5^(n+1))) / ((-1)^(n-1)/n5^n)| = 1/(5(n+1)). Taking the limit as n approaches infinity, we get 1/5. Since the limit is less than 1, the series converges absolutely.

The radius of convergence is equal to the reciprocal of the limit we just found, which is 5. Therefore, the series converges for all x values between -5 and 5.

To find the interval of convergence, we need to test the endpoints. When x=5, the series becomes (-1)^(n-1)/(5n), which is an alternating series. The alternating series test tells us that the series converges if the absolute value of the terms decreases and approaches zero. In this case, the terms are decreasing in absolute value but do not approach zero, so the series diverges at x=5.

When x=-5, the series becomes (-1)^(n-1)/(-5n), which is also an alternating series. The same reasoning as above tells us that the series converges at x=-5.

Therefore, the interval of convergence is [-5,5).

The radius of convergence of the series (-1)^(n-1)/n5^n is 5, and the interval of convergence is [-5,5). To find the radius of convergence, we used the ratio test and found that the limit of the absolute value of the ratio of consecutive terms is 1/5. To find the interval of convergence, we tested the endpoints and found that the series converges at x=-5 and diverges at x=5.

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The interval of convergence is [-5,5). We apply the ratio test to determine the radius of convergence. The ratio test asserts that the series converges absolutely if the limit of the absolute value of the ratio of consecutive terms is smaller than 1.

The series diverges if the limit is bigger than 1. The test is not convincing if the limit is equal to 1.The series in question is (-1)(n-1)/n5n. The result is |((-1)n)/(n+1)(5(n+1))] / ((-1)(n-1)/n5n)| = 1/(5(n+1) when we take the absolute value of the ratio of successive words. When we take the limit as n gets closer to infinity, we get 1/5. Since 1, the limit, the series completely converges.

The radius of convergence is equal to the reciprocal of the limit we just found, which is 5. Therefore, the series converges for all x values between -5 and 5.

To find the interval of convergence, we need to test the endpoints. When x=5, the series becomes (-1)\(^(n-1)/(5n)\), which is an alternating series. The alternating series test tells us that the series converges if the absolute value of the terms decreases and approaches zero. In this case, the terms are decreasing in absolute value but do not approach zero, so the series diverges at x=5.

When x=-5, the series becomes (-1)\(^(n-1)/(-5n),\)which is also an alternating series. The same reasoning as above tells us that the series converges at x=-5.

Therefore, the interval of convergence is [-5,5).

The radius of convergence of the series (-1)^(n-1)/n\(5^n\) is 5, and the interval of convergence is [-5,5). To find the radius of convergence, we used the ratio test and found that the limit of the absolute value of the ratio of consecutive terms is 1/5. To find the interval of convergence, we tested the endpoints and found that the series converges at x=-5 and diverges at x=5.

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Answer:

yes

by SAS

Step-by-step explanation:

Yes, they are congruent by SAS.

Answer:

You will not win in the wrong run

Step-by-step explanation:

if you pay $51.00 to play one game and won you would have $2.00 back and you would have payed $49.00 to play a game

Answer:

1). 1/9 - 1/12 = 1/t

2). 36 minutes

3). 24 hours

4). 30 quarts of Type A cream and 60 quarts of Type B cream are needed

Step-by-step explanation:

Answer:

\(\{-2,2\}\)

Step-by-step explanation:

\(~~~~~~2|p| = 4\\\\\implies |p| = \dfrac 42\\\\\implies |p| = 2\\\\\implies p =\pm2\)

The pressure inside the reactor once equilibrium is V₁ = 12.7 dm³ and V₂ = 9.20 dm³

The ideal gas law equation is given by:

PV = nRT

Where:

P = pressure of the gas

V = volume of the gas

n = number of moles of the gas

R = ideal gas constant

T = temperature in Kelvin

In your case, we have the initial conditions at equilibrium in a vessel with a volume of 12.7 dm³. The number of moles of the three gases present at equilibrium are:

HCONH₂: 0.298 moles

NH₃: 5.71 moles

CO: 3.43 moles

However, we don't have the temperature (T) mentioned in the problem. To solve for pressure, we need to know the temperature as well. Once we have the temperature, we can calculate the initial pressure using the ideal gas law equation.

Let's assume we have the temperature as T. Now, let's calculate the initial pressure (P₁) using the initial volume (V₁ = 12.7 dm³) and the number of moles of the three gases.

For HCONH₂:

PV = nRT

P₁ * V₁ = (0.298 moles) * R * T

For NH₃:

PV = nRT

P₁ * V₁ = (5.71 moles) * R * T

For CO:

PV = nRT

P₁ * V₁ = (3.43 moles) * R * T

Since all three gases are present in the same volume and at the same temperature, we can add the equations together:

P₁ * V₁ + P₁ * V₁ + P₁ * V₁ = (0.298 moles + 5.71 moles + 3.43 moles) * R * T

(3 * P₁ * V₁) = (9.508 moles) * R * T

Now, let's calculate the final pressure (P₂) when the volume is changed to 9.20 dm³. We will use the same number of moles for each gas as given in the problem.

For HCONH₂:

P₂ * V₂ = (0.298 moles) * R * T

For NH₃:

P₂ * V₂ = (5.71 moles) * R * T

For CO:

P₂ * V₂ = (3.43 moles) * R * T

Again, we can add the equations together:

P₂ * V₂ + P₂ * V₂ + P₂ * V₂ = (0.298 moles + 5.71 moles + 3.43 moles) * R * T

(3 * P₂ * V₂) = (9.508 moles) * R * T

Now, we have two equations:

(3 * P₁ * V₁) = (9.508 moles) * R * T

(3 * P₂ * V₂) = (9.508 moles) * R * T

To find the ratio of P₂ to P₁, we can divide the second equation by the first equation:

(3 * P₂ * V₂) / (3 * P₁ * V₁) = (9.508 moles) * R * T / (9.508 moles) * R * T

Canceling out the common terms, we get:

P₂ * V₂ / (P₁ * V₁) = 1

Now, substitute the given values:

V₁ = 12.7 dm³

V₂ = 9.20 dm³

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Answer:

  ln(x)/2 -3.810930

Step-by-step explanation:

The relevant rules of logarithms are ...

  ln(ab) = ln(a) +ln(b)

  ln(a^b) = b·ln(a)

  ln(a/b) = ln(a) -ln(b)

  ln(e) = 1

__

Your expression expands to ...

  \(\ln\left(\dfrac{4\sqrt{x}}{9e^3}\right) = \ln(4\sqrt{x})-\ln(9e^3)=\ln(4)+\dfrac{1}{2}\ln(x)-(\ln(9)+3\ln(e))\\\\=\dfrac{1}{2}\ln(x)+\ln(4)-\ln(9)-3\\\\\approx\dfrac{\ln(x)}{2}-3.810930\)

Answer:

66cm²

Step-by-step explanation:

The figure shown is actually a parallelogram

The area of a parallelogram can easily be calculated by multiplying the base length by the height

For this parallelogram the height given is 6 cm and the base length given is 11cm

so area = 6 * 11

6 * 11 = 66

hence the area of the parallelogram is 66cm²

the mean score for a critical reading test, using Excel, the probability that a random sample of 500 students will have a mean score of more than 590 can be calculated to be approximately 0.408.

To calculate the probabilities using Excel, we can utilize the standard normal distribution. First, we need to convert the sample means to z-scores by using the formula: z = (sample mean - population mean) / (population standard deviation / sqrt(sample size)). For the sample mean of more than 590, we can calculate the probability of z being greater than the corresponding z-score using the formula "=1-NORM.S.DIST(z-score,TRUE)". In this case, the z-score is (590 - 580) / (115 / sqrt(500)), which gives approximately 0.408.

Similarly, for the sample mean of less than 575, we calculate the probability of z being less than the corresponding z-score using the formula "=NORM.S.DIST(z-score,TRUE)". The z-score is (575 - 580) / (115 / sqrt(500)), which gives approximately 0.084.

Therefore, the probability that a random sample of 500 students will have a mean score of more than 590 is approximately 0.408, and the probability that the sample mean is less than 575 is approximately 0.084.

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The Laplace transform of the solution to the given initial value problem is Y(s) = (3πe^(-3s))/(s^2+9π^2), and the solution in the time domain is y(t) = (π/3)(1 - cos(3πt)) for 0 ≤ t < 3, and y(t) = (π/3)(e^(3-3t) - cos(3πt)) for t ≥ 3. The solution is piecewise-defined, with a continuous change in behavior at t = 3.



To find the Laplace transform of the solution, we apply the Laplace transform operator to the given differential equation. Using the properties of the Laplace transform, the Laplace transform of y''(t) is s^2Y(s) - sy(0) - y'(0), where Y(s) represents the Laplace transform of y(t). By substituting the initial conditions y(0) = 0 and y'(0) = 0, we have s^2Y(s) = 3π/s - 0 - 0. Solving for Y(s), we obtain Y(s) = (3πe^(-3s))/(s^2+9π^2).

To obtain the solution in the time domain, we use the inverse Laplace transform. By employing partial fraction decomposition and applying inverse Laplace transform techniques, we find y(t) = (π/3)(1 - cos(3πt)) for 0 ≤ t < 3, and y(t) = (π/3)(e^(3-3t) - cos(3πt)) for t ≥ 3. This solution is piecewise-defined, indicating that the behavior of the solution changes at t = 3.

At t = 3, there is a sudden change in the solution due to the presence of the delta function. Before t = 3, the solution follows a periodic oscillation, represented by (π/3)(1 - cos(3πt)). After t = 3, the solution starts to decay exponentially, given by (π/3)(e^(3-3t) - cos(3πt)). The graph of the solution is continuous but has a distinct change in slope at t = 3, reflecting the impact of the delta function and the subsequent decay of the system.

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The equation of the line parallel to y = -5x - 3 and passing through the point (2, -12) can be found by using the point-slope form of a linear equation. The equation of the line is y = -5x - 2.

To find the equation of a line parallel to a given line, we know that the slopes of the two lines must be equal. In this case, the given line has a slope of -5.

Using the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can substitute the given point (2, -12) and the slope -5 into the equation.

The equation becomes y - (-12) = -5(x - 2), which simplifies to y + 12 = -5x + 10.

To isolate y, we subtract 12 from both sides, giving y = -5x - 2.

Therefore, the equation of the line parallel to y = -5x - 3 and passing through the point (2, -12) is y = -5x - 2.

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This equation implies that the intercept of the scatter plot for the rich school is at (0, 45) and the slope of the line is 3. This means that for every additional million dollars allocated to the rich school.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

To plot the relationships between scores and additional spending for the two schools, we can use a scatter plot with the x-axis representing additional spending (in millions of dollars) and the y-axis representing the average test score.

For the poor school, the equation for the relationship is:

Spoor = 40 + Xpoor

This equation implies that the intercept of the scatter plot for the poor school is at (0, 40) and the slope of the line is 1. This means that for every additional million dollars allocated to the poor school, the average test score will increase by 1 point.

For the rich school, the equation for the relationship is:

Srich = 45 + 3xrich

This equation implies that the intercept of the scatter plot for the rich school is at (0, 45) and the slope of the line is 3. This means that for every additional million dollars allocated to the rich school.

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Answer:

approximately 1.732

Step-by-step explanation:

To solve this expression, we need to start by performing the operations inside the parentheses first. The square root of 8 is equal to 2, so 3 minus 2 is equal to 1. Then, we can divide 1 by the square root of 3, which is equal to approximately 1.732. Therefore, the expression 3 minus square root of eight divided by square root of 3 is equal to approximately 1.732.

Answer:

7

Step-by-step explanation:

The highest power of the given polynomial is 7. Therefore, the degree of the given polynomial is 7.