Write an expression for the calculation 47 minus 3times the difference of 15 2

The units of measure for the rate of increase would be frogs per unit of time

(The largest rate of increase in the number of frogs in the pond would be when the growth rate is at its maximum. This can be determined by finding the derivative of the growth function and setting it equal to zero to find the maximum point.

Since we are not given a specific growth function, we cannot accurately determine the largest rate of increase. However, we can say that the largest rate of increase would occur at the point where the derivative of the growth function is at its maximum. The units of measure for the rate of increase would be frogs per unit of time (e.g. frogs per day or frogs per week).

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Answer:

B is the correct answer

Step-by-step explanation:

Hope this helps:)

The formula can be used to determine the area of the sector bounded by central angle MON is x/360*πr².

The correct option is (A).

The area of a sector of a circle is the amount of space enclosed within the boundary of the sector. A sector always originates from the center of the circle. The sector of a circle is defined as the portion of a circle that is enclosed between its two radii and the arc adjoining them.

Given: Central Angle= x , radius= r

We know the formula for Area of sector is

=\(\theta\)/360*πr²

= x/360*πr²

Hence,  Area of sector=  x/360*πr².

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Answer:

Step-by-step explanation:

7x > 7, o 7(x > 1).

es x>1

espero y te ayude esto

Check the picture below.

we know the diameter MK is 9 units, so the radius must be half that, or 4.5.

\(\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4.5\\ \theta =218 \end{cases}\implies \begin{array}{llll} s=\cfrac{(218)\pi (4.5)}{180}\implies s=5.45\pi \\\\\\ s\approx 17.1 \end{array}\)

Answer:

x=-3, y=-23

x=0, y=-8

x=4, y=12

Step-by-step explanation:

Step-by-step explanation:

\(2 - 2 \sqrt{3 \: \: \: \: } \div 3\)

Alternate form: 0.845299

The standard error of the sample mean, \(\bar{x}\) , is the standard deviation of the distribution of sample means.

The standard error is a measure of the amount of variability in the mean of a population. It is also defined as the standard deviation of the sampling distribution of the mean. This value is used to create confidence intervals or to test hypotheses. The formula to find the standard error is SE = s/√n, where s is the sample standard deviation and n is the sample size. This estimate shows the degree to which the sample mean is anticipated to vary from the actual population mean.

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The solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

To solve the given differential equation (DE), we can use the integrating factor method. The steps are as follows:

1. Multiply both sides of the DE by the integrating factor, which is the exponential of the integral of the coefficient of y. In this case, the coefficient of y is (x + 2), so the integrating factor is e^(∫(x+2)dx) = e^(x^2/2 + 2x).

So, we have: (x + 1) e^(x^2/2 + 2x) dy/dx + (x + 2) e^(x^2/2 + 2x) y = 2x e^(x^2/2 + 2x) e^(-xy)

2. Notice that the left-hand side of the DE is the product of the derivative of y with respect to x and the integrating factor, so we can apply the product rule of differentiation to obtain:

d/dx [ e^(x^2/2 + 2x) y ] = 2x e^(x^2/2 + 2x) e^(-xy)

3. Integrate both sides of the previous equation with respect to x to obtain:

e^(x^2/2 + 2x) y = - e^(-xy) + C

where C is the constant of integration.

4. Solve for y by dividing both sides by the integrating factor:

y = [- e^(-xy) + C] e^(-x^2/2 - 2x)

This is the general solution of the given DE.

Note that the solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

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Answer:

rational

Step-by-step explanation:

irrational numbers can not be expressed as a fraction

Given:

The number is \(\dfrac{5}{21}\).

To find:

Whether the given number is rational or irrational.

Solution:

Rational number: If a number can be defined in the form of \(\dfrac{p}{q}\) where \(p,q\) are integers and \(q\neq 0\), then it is called a rational number.

For example: \(2,\dfrac{1}{3},0.25\) etc.

Irrational number: If a number cannot be defined in the form of \(\dfrac{p}{q}\) where \(p,q\) are integers and \(q\neq 0\), then it is called an irrational number.

For example: \(\sqrt{2},\sqrt{3},\pi \) etc.

The given number is \(\dfrac{5}{21}\). It is in the form of \(\dfrac{p}{q}\) where \(p=5, q=21\) and both are non-zero integers.

By the definition of rational numbers, the number \(\dfrac{5}{21}\) is a rational number.

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Answer:

The answer is 5

Step-by-step explanation:

add all numbers up then divide by  how many numbers there are.

The rule for the function g(x) is g(x) = x - 5 when f(x) = 5 and vertical down to 5 units.

Functions:

Function refers the relationship from a set X to a set Y assigns to each element of X exactly one element of Y

Given,

Let g(x) indicated the transformation of f(x)

Here we need to write the rule for g(x) when f(x) = x, and vertical translation down 5 units.

Here we have the function f(x) = x.

Considering the normal graph, we know that, the graph has four parts.

And each part refers difference sign. That is,

Horizontal left indicates the positive where as the horizontal right refers the negative for x axis.

Similarly, vertical up refers the positive and the vertical down represents the negative.

Here we have the vertical down translation of 5 units which refers the negative 5.

So, the rule of g(x) = x - 5.

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9514 1404 393

Answer:

  20x -6y

Step-by-step explanation:

Parentheses can be eliminated and like terms combined.

  10x +y +10x -7y

  = x(10 +10) +y(1 -7)

  = 20x -6y

Answer:

1 hour and 5 minutes

Step-by-step explanation:

55+5=60 (this takes you to 11:00 o'clock)

plus 1 hour is 12:00 or noon

Hope this helps! :)

In the given angles, the values of R=31⁰, x=34⁰, m<S= 38⁰, m<Y = 111⁰

We know that a triangle is a polygon whose sum of angles is equal to 180 degress , with three sides and three vertices.

The given angles are

31⁰,  (x+4)⁰,  (3x+9)⁰

The sum of angles of the triangle

31+x+4+3x+9=180⁰

44+4x=180⁰

Collecting like terms

4x=136

Dividing by 4

x=34⁰

Substituting the value of x=34 in the given angles we have

R= 31⁰,             given

 (x+4)⁰   = 34+4=38⁰,  (3*34+9)⁰=111⁰

In conclusion the values of R= 31⁰, x=34⁰ , m<S=38⁰, m<T=111⁰

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The percent change of the annual investment in renewable energy sources increased by 308.77% from 2005 to 2018.

So the annual investment in renewable energy sources increased by 308.77% from 2005 to 2018.

The formula for calculating percent change is applicable to any source where you want to determine the change in value between two points in time. It can be used to compare growth or decline in a variety of fields including finance, economics, business, demographics, science, technology, and more. The formula is widely used to calculate changes in a variety of different metrics, such as stock prices, GDP, population, and energy consumption.

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For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, the process is still "in order," while for the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}, the process might be "out of order."

To determine whether the process is still "in order" or "out of order," we can compare the current sample of output to the known mean and standard deviation of the process.

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}:

Calculate the sample mean by summing up all the values in the sample and dividing by the number of values (n = 10):

Sample mean = (2.038 + 2.054 + 2.053 + 2.055 + 2.059 + 2.059 + 2.009 + 2.042 + 2.053 + 2.047) / 10 = 2.048.

Compare the sample mean to the known process mean (2.050):

The sample mean (2.048) is very close to the process mean (2.050), indicating that the process is still "in order."

Calculate the sample standard deviation using the formula:

Sample standard deviation = sqrt(sum((x - mean)^2) / (n - 1))

Using the formula with the sample values, we find the sample standard deviation to be approximately 0.019 liters.

Compare the sample standard deviation to the known process standard deviation (0.020):

The sample standard deviation (0.019) is very close to the process standard deviation (0.020), further supporting that the process is still "in order."

For the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}:

Calculate the sample mean:

Sample mean = (2.022 + 1.997 + 2.044 + 2.044 + 2.032 + 2.045 + 2.045 + 2.047 + 2.030 + 2.044) / 10 ≈ 2.034

Compare the sample mean to the process mean (2.050):

The sample mean (2.034) is noticeably different from the process mean (2.050), indicating that the process might be "out of order."

Calculate the sample standard deviation:

The sample standard deviation is approximately 0.019 liters.

Compare the sample standard deviation to the process standard deviation (0.020):

The sample standard deviation (0.019) is similar to the process standard deviation (0.020), suggesting that the process is still "in order" in terms of variation.

In summary, for the first sample, the process is still "in order" as both the sample mean and sample standard deviation are close to the known process values.

However, for the second sample, the difference in the sample mean suggests that the process might be "out of order," even though the sample standard deviation remains within an acceptable range.

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The equation of the tangent line to the parabola at the point (1,5) is y = 4x + 1.

To find the slope of the tangent line to the parabola at the point (1,5), we need to find the derivative of the equation y = 6x - x² and evaluate it at x = 1.

Taking the derivative of y with respect to x:

dy/dx = d(6x - x²)/dx

= 6 - 2x

Now, we can substitute x = 1 into the derivative to find the slope at that point:

slope = 6 - 2(1)

= 6 - 2

= 4

So, the slope of the tangent line to the parabola at the point (1,5) is 4.

To find the equation of the tangent line, we need to use the point-slope form of a line.

The equation is given by:

y - y₁ = m(x - x₁)

Substituting the values we have:

y - 5 = 4(x - 1)

Expanding and simplifying:

y - 5 = 4x - 4

Moving the constant term to the other side:

y = 4x + 1

Therefore, the equation of the tangent line to the parabola at the point (1,5) is y = 4x + 1.

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Complete question =

Find the slope of the tangent line to the parabola at the point (1,5). y = 6x-x². find an equation of the tangent line.

The 98% confidence interval for a sample of size 307 with 82% successes is (0.7487, 0.8913).

To find the confidence interval for a sample of size 307 with 82% success and 98% confidence interval,

The following steps should be followed:

Step 1: Calculate the standard error of the statistic. Standard error is given by; `

se= sqrt [(p*(1-p))/n]`Where `p` is the proportion of successes and `n` is the sample size.

So, `se= sqrt [(0.82*(1-0.82))/307]

          = 0.0306`

Step 2: Calculate the z-score associated with the confidence level of 98%. We can look up the z-score from the standard normal table or use the calculator. `

z=2.33`

Step 3: Calculate the margin of error. `ME= z*se = 2.33 * 0.0306 = 0.0713`

Step 4: Calculate the confidence interval. The interval is given by;

CI = (p - ME, p + ME)`

Substitute the values, CI = `(0.82 - 0.0713, 0.82 + 0.0713)

                                         = (0.7487, 0.8913)`

Therefore, the 98% confidence interval for a sample of size 307 with 82% successes is (0.7487, 0.8913).

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Answer:

Free fall acceleration 10m/s/s approx.

So in ten seconds after acceleration, it would be 100 m/s

Answer:

100 m/s

..........

1) Solve each inequality individually.

\(\dfrac{2x-3}5 - \dfrac{4x-9}6 > 1 \\\\ 6(2x-3) - 5(4x-9) > 30 \\\\ (12x-18) - (20x+45) > 30 \\\\ -8x > 3 \\\\ x < -\dfrac38\)

and

\(5(x-1) + 7(x+2) > 3 \\\\ (5x-5) + (7x+14) > 3 \\\\ 12x > -6 \\\\ x > -\dfrac12\)

Then the solution set is

\(-\dfrac12 < x < -\dfrac38\)

since -1/2 = -4/8 is smaller than -3/8.

2)

\(\dfrac{x+1}2 - \dfrac{x+2}3 < \dfrac{x+12}6 \\\\ 3(x+1) - 2(x+2) < x+12 \\\\ (3x+3) - (2x+4) < x + 12 \\\\ x - 1 < x + 12 \\\\ -1 < 12\)

This is true for all values of \(x\).

For the second inequality, (I use periods in place of commas because it renders better as TeX)

\(0.3x - 19 \le 1.7x - 5 \\\\ -1.4x \le 14 \\\\ x \ge -10\)

Taken together, the solution set is

\(\boxed{x\ge-10}\)

3)

\((x-6)^2 < (x-2)^2 - 8 \\\\ x^2 - 12x + 36 < (x^2 - 4x + 4) - 8 \\\\ -8x < -40 \\\\ x > 5\)

and

\(3(2x-1) - 8 < 34 - 3(5x-9) \\\\ (6x - 3) - 8 < 34 - (15x - 27) \\\\ 21x < 72 \\\\ x < \dfrac{72}{21} = \dfrac{24}7\)

But \(x\) cannot be both larger than 5 = 35/7 and smaller than 24/7, so there are no solutions.

4)

\(\dfrac{3x-2}3 - \dfrac{4x+1}4 \le 1 \\\\ 4(3x-2) - 3(4x+1) \le 12 \\\\ (12x-8) - (12x + 3) \le 12 \\\\ -11 \le 12\)

This is true for all \(x\).

\((x-1)(x-2) > (x+4)(x-7) \\\\ x^2 - 3x + 2 > x^2 - 3x - 28 \\\\ 2 > -28\)

This is also true for all \(x\).

Any value of \(x\) is a solution.

Answer:

11x-9

Step-by-step explanation:

5+2(5x-7)+x=5+10x-14+x

                   = 11x-9

Answer:

-9+11x

Step-by-step explanation:

5+2(5x-7)+x

multiply (5x-7) by 2

5+ 10x-14+x

add like terms

-9+11x

Answer:

She paid $205 for the bike .

To find the expected value of the game, we need to calculate the expected value of the random variable X, which represents the image value of bills.Therefore, the expected value of the game to you is $16.50.

The probability distribution of X can be filled in as follows:

x   | $1   | $5   | $10  | $50

P(X) | 1/4  | 1/4  | 1/4  | 1/4

The probabilities are equal because each bill has an equal chance of being drawn.

To calculate the expected value, we multiply each value of X by its corresponding probability and sum them up:

E(X) = (1/4 * $1) + (1/4 * $5) + (1/4 * $10) + (1/4 * $50)

    = $0.25 + $1.25 + $2.5 + $12.5

    = $16.5

Therefore, the expected value of the game to you is $16.50.

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Answer:

D i think

Step-by-step explanation:

Answer:

44

Step-by-step explanation:

96 divided by 4 add 5 times 2 squared equals 44

Answer:

44

Step-by-step explanation:

BIDMAS

B: Brackets

I: Indices

D: Division

M: Multiplication

A: Addition

S: Subtraction

96 divided by 4 + 5 x 2^2

96 divided by 4 + 5 x 4

96 divided by 4 = 24

24 + 5 x 4

24 + 20

24 + 20 = 44

Answer:

0.0030796 to the ten thousandths place is 0.0031

Answer:

0.0031

Step-by-step explanation:

A $1,000 initial investment in Bank ABC's CD would be worth $1,628.89 at maturity.  A $1,000 initial investment in Bank XYZ's CD would be worth $1,622.82 at maturity.

The formula to calculate the value of a CD after a specific duration at a specific interest rate compounded annually is given by:

A = P(1 + r/n)^(nt)

where P is the principal,

r is the annual interest rate,

n is the number of times compounded per year,

t is the number of years, and

A is the value of the CD at maturity.

Here, we need to calculate the value of a $1,000 initial investment in each bank's CD at maturity.

Let's calculate the value of a $1,000 investment in Bank ABC's CD.

P = $1,000

r = 5.0% compounded annually

t = 10 years

n = 1

We have all the values; let's put them in the formula and solve:

A = $1,000(1 + 0.05/1)^(1x10)A = $1,628.89

Therefore, a $1,000 initial investment in Bank ABC's CD would be worth $1,628.89 at maturity.

Let's calculate the value of a $1,000 investment in Bank XYZ's CD.

P = $1,000

r = 4.95% compounded daily

t = 10 years

n = 365

We have all the values; let's put them in the formula and solve:

A = $1,000(1 + 0.0495/365)^(365x10)A = $1,622.82

Therefore, a $1,000 initial investment in Bank XYZ's CD would be worth $1,622.82 at maturity.

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To calculate the total charge within the cylinder with dimensions r=1.5 and h=3, we use the potential function V = 5r + 4 cos Ø in cylindrical coordinates.

The total charge can be obtained by integrating the charge density over the volume of the cylinder.

The potential V within the cylinder is given by V = 5r + 4 cos Ø, where r represents the radial distance from the axis of the cylinder and Ø represents the angle in the cylindrical coordinate system. To calculate the total charge within the cylinder, we need to integrate the charge density over its volume.

The charge density ρ can be related to the potential by ρ = -∇²V, where ∇² is the Laplacian operator. In cylindrical coordinates, the Laplacian operator takes the form:

∇² = (1/r) ∂/∂r (r ∂/∂r) + (1/r²) ∂²/∂ز + ∂²/∂z²

Since the potential function V does not depend on the z coordinate, the Laplacian reduces to:

∇² = (1/r) ∂/∂r (r ∂/∂r) + (1/r²) ∂²/∂ز

Applying this operator to the potential function V, we find:

∇²V = (1/r) ∂/∂r (r ∂V/∂r) + (1/r²) ∂²V/∂ز

To find the charge density, we substitute this expression into ρ = -∇²V:

ρ = -(1/r) ∂/∂r (r ∂V/∂r) - (1/r²) ∂²V/∂ز

To calculate the total charge, we integrate the charge density ρ over the volume of the cylinder:

Q = ∫∫∫ ρ dV = ∫∫∫ -(1/r) ∂/∂r (r ∂V/∂r) - (1/r²) ∂²V/∂ز dV

The integration is performed over the cylindrical coordinates r, Ø, and z, with appropriate limits. Evaluating this integral will give us the total charge within the cylinder.

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