what is the sum of all the possible 3 digit numbers that can be constructed using the digits 3, 4, and 5 if each digit can only be used once in each number

the general solution of the given differential equation is:

y = [(1/3) x^3 + 2x^2 + 4x + C1] / |x^2 - 4|

To find the general solution of the given differential equation:

(x^2 - 4) dy/dx + 4y = (x + 2)^2

We can rearrange the equation to isolate the derivative term:

dy/dx = [(x + 2)^2 - 4y] / (x^2 - 4)

First, let's simplify the numerator:

[(x + 2)^2 - 4y] = (x^2 + 4x + 4) - 4y

= x^2 + 4x + 4 - 4y

= x^2 + 4x - 4y + 4

Now, substitute this simplified expression back into the differential equation:

dy/dx = (x^2 + 4x - 4y + 4) / (x^2 - 4)

This is a first-order linear homogeneous differential equation. To solve it, we can use the integrating factor method.

First, let's write the equation in the standard form: dy/dx + P(x)y = Q(x)

dy/dx + (4x / (x^2 - 4))y = (x^2 + 4x + 4) / (x^2 - 4)

The integrating factor is given by the exponential of the integral of P(x):

μ(x) = exp ∫ (4x / (x^2 - 4)) dx

To find the integral, we can use substitution. Let u = x^2 - 4, then du = 2x dx:

μ(x) = exp ∫ (2x dx) / (x^2 - 4)

= exp ∫ (du / u)

= exp(ln|u|)

= |u|

Substituting back u = x^2 - 4:

μ(x) = |x^2 - 4|

Now, multiply the entire differential equation by the integrating factor:

|x^2 - 4| dy/dx + (4x / (x^2 - 4)) |x^2 - 4|y = (x^2 + 4x + 4) |x^2 - 4| / (x^2 - 4)

The left side can be simplified using the product rule for differentiation:

d/dx [ |x^2 - 4|y ] = (x^2 + 4x + 4) |x^2 - 4| / (x^2 - 4)

Now, integrate both sides with respect to x:

∫ d/dx [ |x^2 - 4|y ] dx = ∫ (x^2 + 4x + 4) |x^2 - 4| / (x^2 - 4) dx

Integrating the left side gives:

|x^2 - 4|y = ∫ (x^2 + 4x + 4) dx

= (1/3) x^3 + 2x^2 + 4x + C1

where C1 is the constant of integration.

Finally, divide both sides by |x^2 - 4| to solve for y:

y = [(1/3) x^3 + 2x^2 + 4x + C1] / |x^2 - 4|

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The approximate probability of having 11 or more serious Vespa scooter accidents in Redondo Beach this summer break is approximately 0.3085.

To approximate the probability of having 11 or more serious Vespa scooter accidents in Redondo Beach during the summer break, we can use the Central Limit Theorem (CLT). The CLT states that the sum or average of a large number of independent and identically distributed random variables will be approximately normally distributed, regardless of the underlying distribution.

In this case, we can consider the number of serious Vespa scooter accidents as a random variable following a Poisson distribution with an average of 9 accidents during the summer break. The Poisson distribution can be approximated by a normal distribution when the average is sufficiently large.

To apply the CLT, we need to calculate the mean and standard deviation of the Poisson distribution:

Mean (μ) = average = 9

Standard Deviation (σ) = square root of average = √9 = 3

Now, we want to find the probability of having 11 or more accidents. We can use the normal approximation by considering the continuity correction. Since the Poisson distribution is discrete, we adjust the boundaries by subtracting 0.5:

P(X ≥ 11) ≈ P(X > 10.5)

Now, we standardize the value using the Z-score formula:

Z = (X - μ) / σ

Z = (10.5 - 9) / 3 ≈ 0.5

Next, we find the probability of Z being greater than 0.5 using a standard normal distribution table or calculator:

P(Z > 0.5) ≈ 0.3085

Therefore, the approximate probability of having 11 or more serious Vespa scooter accidents in Redondo Beach this summer break is approximately 0.3085.

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The path of the Presidential Inaugural Parade is defined as a straight line that runs west from the U.S. Capitol Building, located at the eastern end of the National Mall in Washington D.C., to the White House, located just a few blocks to the north.

The parade typically follows Pennsylvania Avenue, which is the main ceremonial route used for many official processions in the nation's capital. The path is lined with grandstands for spectators and is closed to vehicle traffic during the parade. The parade route is flanked by some of Washington D.C.'s most important landmarks, including the National Archives Building, the Department of Justice, the Old Post Office Pavilion, and the Trump International Hotel. The Presidential Inaugural Parade has been a tradition in the United States for over 200 years and  is a key part of the Inauguration Day ceremonies, which mark the peaceful transfer of power from one presidential administration to the next.

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When you graph a quadratic function, its shape is called a parabola.

Option C is the correct answer.

We have,

A parabola is a curve that is formed when graphing a quadratic function.

It is a U-shaped curve that can open upwards or downwards, depending on the coefficients of the quadratic equation.

A quadratic function is a polynomial function of degree 2, which can be expressed in the form y = ax² + bx + c, where a, b, and c are constants and x represents the variable.

The coefficient a determines whether the parabola opens upwards or downwards.

If coefficient a is positive, the parabola opens upwards, and if coefficient a is negative, the parabola opens downwards.

The vertex of the parabola is the highest or lowest point on the curve, depending on the orientation.

Thus,

A parabola is a specific shape that is formed when graphing a quadratic function, characterized by its U-shape.

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(A) x(t) = ln(t+1) + C, where C is a constant.

(B) dy/dt = 3x^2 - 3.

(C) At t = 8, the particle is located at x = ln(9) - 1 and has a speed of |3(3ln(9) - 3)^2 - 3|.

(A) To find x(t) in terms of t, we integrate dx/dt with respect to t. Integrating 1/(t+1) gives us ln(t+1) + C, where C is a constant. Since x(3) = -1, we can substitute t = 3 and x = -1 into the equation to solve for C. We get -1 = ln(3+1) + C, which gives us C = -1 - ln(4). Therefore, x(t) = ln(t+1) - ln(4) - 1.

(B) To find dy/dt in terms of t, we differentiate y = x^3 - 3x with respect to t using the chain rule. We have dy/dt = (dy/dx) * (dx/dt) = (3x^2 - 3) * (dx/dt). Substituting dx/dt = 1/(t+1), we get dy/dt = (3x^2 - 3)/(t+1).

(C) At t = 8, we can substitute t = 8 into x(t) to find the x-coordinate of the particle. We have x(8) = ln(8+1) - ln(4) - 1 = ln(9) - ln(4) - 1. To find the y-coordinate, we substitute this value of x into y = x^3 - 3x, giving us y(8) = (ln(9) - ln(4) - 1)^3 - 3(ln(9) - ln(4) - 1). To find the speed, we substitute x = ln(9) - ln(4) - 1 into dy/dt = (3x^2 - 3)/(t+1) and take the absolute value.

Therefore, at t = 8, the particle is located at the point (ln(9) - ln(4) - 1, (ln(9) - ln(4) - 1)^3 - 3(ln(9) - ln(4) - 1)), and its speed is given by |3((ln(9) - ln(4) - 1)^2 - 1)/(8+1)|.

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according to question the surface integral is (32π - 192)/15.

To evaluate the surface integral, we need to parameterize the surface and find the surface element ds.

Let's consider the parameterization:

x = y^2 + z^2

y = y

z = z

The surface element can be found as:

ds = √(1 + (dx/dy)^2 + (dx/dz)^2) dy dz

ds = √(1 + 4y^2) dy dz

Now, we can rewrite the integral as:

∫∫s z^2 ds = ∫∫R (y^2 + z^2)^2 √(1 + 4y^2) dy dz

where R is the projection of the surface S onto the yz-plane, which is the region 0 ≤ y ≤ 2, -√(4 - y^2) ≤ z ≤ √(4 - y^2).

Let's evaluate the integral:

∫∫s z^2 ds = ∫0^2 ∫-√(4-y^2)^√(4-y^2) (y^2 + z^2)^2 √(1 + 4y^2) dz dy

Using cylindrical coordinates, we can rewrite the integral as:

∫0^2 ∫0^π/2 ∫0^2r (r^2 cos^2θ + r^2 sin^2θ)^2 r √(1 + 4r^2 sin^2θ) dr dθ dy

Simplifying and solving the integral, we get:

∫∫s z^2 ds = (32π - 192)/15

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Answer:

approximately 6.4 meters

Answer:

400

Step-by-step explanation:

V= [tex]\frac{1}{3}[/tex]Bh

the base is a square, so B= [tex]10^{2}[/tex] or 100

h= 12

B= 100

Bh= 1200

[tex]\frac{1200}{3}[/tex] = 400

V=400

Answer:

(a) $ 7000

(b) $ 5600

Step-by-step explanation:

discount = 20%

20% = $1400

1% = 1400/20

original price = 100%

= 1400/20 × 100

= $7000

sale price = 80%

= 1400/20 × 80

= $5600

The true statement from the graph is this: D. The girls have a higher interquartile range but a lower mean than the boys.

The interquartile range of the girls' resting heart rate spans from 80 to 88 while the interquartile range of the boys spans from 84 to 90. So, the interquartile range for the girls is higher than that of the boys. Also, the mean of the girls is lower than that of the boys.

The mean of the girls is the sum of the rates divided by 8 = 11/8 = 1.375

The mean for the boys is the sum of the rates divided by 6 = 11/6 = 1.833

Som the mean of the girls is lower than that of the boys.

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The Percentage error is 40%. This means that the recorded value is 40% lower than the true value. In other words, the recorded value is only 60% of the true value.

To find the percentage error, we need to calculate the difference between the recorded value and the true value, then divide that difference by the true value and multiply by 100 to get a percentage.

True value = 1,500

Recorded value = 900

Difference = True value - Recorded value

Difference = 1,500 - 900

Difference = 600

Percentage error = (Difference / True value) x 100

Percentage error = (600 / 1,500) x 100

Percentage error = 40

Therefore, the percentage error is 40%. This means that the recorded value is 40% lower than the true value. In other words, the recorded value is only 60% of the true value.

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When a point is reflected about the xy-plane, its z-coordinate is negated while its x and y-coordinates remain the same. the image of the point P(-2, 3, 5) after a reflection about the xy-plane is the point P'(-2, 3, -5).

what is coordinates ?

Coordinates are values used to indicate the position of a point in a coordinate system. A coordinate system is a system that uses one or more numbers, called coordinates, to determine the position of a point or object. For example, in a two-dimensional Cartesian coordinate system, a point is located by its distance from two perpendicular lines, the x-axis and the y-axis, which intersect at a point called the origin. The coordinates of a point are usually represented by an ordered pair (x, y) in this system. In a three-dimensional coordinate system, a point is located by its distance from three perpendicular planes, and its coordinates are usually represented by an ordered triple (x, y, z).

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Answer:

Scale factor is 2

Step-by-step explanation:

Not sure how to explain, just count the number of points the dilated figure is from the point of dillations compared to the original figure. 2/1=2.

The equation P (1 + r/100)n, wherein P = the principal, r = yearly rate of interest, and n = the number of years and time periods, yields the amount of money when interest is made worse annually.

Compound interest refers to the interest added to a loan or deposit. It is the concept that we use every day the most regularly. For an amount, compound interest is computed using either the principal and accrued interest. This is the primary distinction among compound and simple interest. The formula P (1 + r/100)n, where P = principal, r = yearly rate of interest, and n = the number of years or time periods, yields the amount if interest is compounded annually.

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[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=6\\ \theta =45 \end{cases}\implies A=\cfrac{(45)\pi (6)^2}{360} \\\\\\ A=\cfrac{9\pi }{2}\implies A=\cfrac{9(3.14) }{2}\implies A=14.13~yd^2[/tex]

Answer: -8

Step-by-step explanation:

13x+22=x-34+5x

13x+22=6x-34 (combine like terms)

13x-6x+22=6x-6x-34 (subtract 6x on each side)

7x+22=-34

7x-22+22=-34-22 (subtract 22 on each side)

7x=-56

7x/7x = -56/7 (divide 7 on each side)

x=-8

Answer:

0.09 l

Step-by-step explanation:

Given:

900 ml ⇒ 10s

Required:

Liters per second

Analyze:

Let the unknown amount be x.

900 ml ⇒ 10s

         x ⇒ 1s

Solve:

Use cross multiplication

900 × 1 = 10 × x

    900 = 10x

Divide both sides by 10.

90 ml = x

To covert the answer into liters divide it by 1000.

0.09 l = x

Paraphrase:

We breathe 0.09 liters of air per second

The probability that the sample mean will be between 295 and 305 can be determined using the Central Limit Theorem and the properties of the normal distribution.

According to the Central Limit Theorem, for a large sample size (n ≥ 30), the distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution. In this case, since the sample size is 64, we can assume that the sample mean will follow a normal distribution.

To find the probability that the sample mean will be between 295 and 305, we need to standardize the sample mean using the formula z = (x - μ) / (σ / sqrt(n)), where x is the given range (295 to 305), μ is the population mean (300), σ is the population standard deviation (12), and n is the sample size (64).

By calculating the z-scores for the lower and upper limits of the range and referring to the standard normal distribution table, we can find the corresponding probabilities. The probability can be calculated by subtracting the cumulative probability corresponding to the lower limit from the cumulative probability corresponding to the upper limit.

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Answer: £67.875

Step-by-step explanation:

€90.50 x 3/4 = £67.875

The set of data that provides the clearest difference between the two samples is option (c): One sample has M = 20 with s2 = 10 and the other has M = 30 with s2 = 10. The reason is that the standard deviation is higher in both samples compared to the other options, and the means of the two samples are also relatively far apart, making the difference between the two samples clearer. I

n options (a) and (b), the means are not far enough apart to provide a clear difference, and in option (d), while the means are farther apart than in option (b), the standard deviation is the same, which makes the difference less clear.

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To calculate the average number of employees per dealership, we need to first find the total number of employees working in both the dealerships and the head office. Let's assume that the total number of employees in August 2020 was 1000.

If 1.5% of the total number of employees worked at the head office, then the number of employees working in the head office would be 0.015 x 1000 = 15. To find the number of employees working in dealerships, we can subtract the number of employees working in the head office from the total number of employees, which is 1000 - 15 = 985.

Next, we need to calculate the average number of employees per dealership. To do this, we can divide the number of employees working in dealerships by the number of dealerships. Let's assume there are 10 dealerships in total. Therefore, the average number of employees per dealership would be 985/10 = 98.5.

So, on average, each dealership would have approximately 98.5 employees in August 2020.

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There is no general rule for the sequence as this is neither an arithmetic sequence nor a quadratic sequence.

If this is an arithmetic sequence, then there would be a constant difference between the consecutive terms.

Difference between term 2 and term 1 : 5 - 2 = 3

Difference between term 3 and term 2 : 7 - 5 = 2

Difference between term 4 and term 3 : 11 - 7 = 4

This is therefore not an arithmetic sequence.

We can check to see if it is quadratic with the second difference :

Difference between the second and first differences: 2 - 3 = -1

Difference between the third and second differences: 4 - 2 = 2

These are still not constant which means that there is no general rule given the terms.

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Answer:

[tex]\Large \textsf{$\boxed{\boxed{-1.702\leq x\leq4.702}}$}[/tex]

Step-by-step explanation:

The inequality required to solve:

[tex]\Large \textsf{$\Rightarrow$\ } \boxed{\Large \textsf{$x^2-3x-4\leq 4$}}[/tex]

[tex]\large \textsf{First, subtract 4 from both sides:}\\ \\\large \textsf{$\Rightarrow x^2-3x-8\leq 0$}\\\\\large \textsf{This is in the form of a quadratic equation, where $ax^2+bx+c=0$}\\\large \textsf{We need to consider the LHS as an equation, and solve for $x$:}\\\\\large \textsf{Using the quadratic formula:}\\\\\large \textsf{$\boxed{x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}$} \large \textsf{ , where $ax^2+bx+c=0$}\\\\[/tex]

[tex]\large \textsf{$x=\frac{-(-3)\pm\sqrt{(-3)^2-4(1)(-4)}}{2(1)}$}\\\\\large \textsf{$\therefore x=-1.702, 4.702$}[/tex]

Now, this is not the solution of the inequality yet. These are the x-intercepts (roots) of the graph of y = x² - 3x - 8. From the graph, we can apply the inequality sign, and solve for values below or equal to y = 0.

[see attached diagram of graph]

[tex]\large \textsf{From the graph, we can conclude that:}\\\\\Large \textsf{$\boxed{\boxed{-1.702\leq x\leq4.702}}$}[/tex]

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Answer:

3/28

Step-by-step explanation:

5 + 3 = marbles in total.

P(first blue) = 3/8

P(second blue) = (3-1) / (8-1)  = 2/7

P(selecting 2 blue) = (3/8) X (2/7) = 6/56 = 3/28

The original equation  provided (74.94 * 1000), we can see that multiplying 74.94 by 1,000 is equivalent to adding three zeros to the end of the number. Now let's consider the number 10 with a 3 exponent, which we know is equal to 1,000.  So, the answer to the equation is simply 74,940.

we need to understand the concept of exponents and how they relate to the number of zeros in a number. An exponent is a way of showing how many times a number should be multiplied by itself. For example, 10 raised to the power of 3 (written as 10^3) means 10 multiplied by itself three times, which is equal to 1,000.
Now let's consider the number 10 with a 3 exponent, which we know is equal to 1,000. When this number is written without an exponent, we can simply write it as 1 followed by three zeros, which is 1,000. Therefore, the answer to your question is that the number 10 with a 3 exponent has three zeros when it is written without an exponent.
When you multiply 74.94 by 1000, you are essentially moving the decimal point three places to the right because the number 10 with a 3 exponent (10^3) has three zeros when it is written without an exponent.
1. Identify the number to be multiplied (74.94) and the exponent of 10 (3).
2. Convert 10^3 to its standard form, which gives us 1000 (three zeros).
3. Move the decimal point of the number (74.94) three places to the right due to the three zeros in 1000.
So, 74.94 * 1000 = 74940.

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The original equation  provided (74.94 * 1000), we can see that multiplying 74.94 by 1,000 is equivalent to adding three zeros to the end of the number. Now let's consider the number 10 with a 3 exponent, which we know is equal to 1,000.  So, the answer to the equation is simply 74,940.

The concept of exponents and how they relate to the number of zeros in a number. An exponent is a way of showing how many times a number should be multiplied by itself. For example, 10 raised to the power of 3 (written as 10^3) means 10 multiplied by itself three times, which is equal to 1,000.

Now let's consider the number 10 with a 3 exponent, which we know is equal to 1,000. When this number is written without an exponent, we can simply write it as 1 followed by three zeros, which is 1,000. Therefore, the answer to your question is that the number 10 with a 3 exponent has three zeros when it is written without an exponent.

When you multiply 74.94 by 1000, you are essentially moving the decimal point three places to the right because the number 10 with a 3 exponent (10^3) has three zeros when it is written without an exponent.

1. Identify the number to be multiplied (74.94) and the exponent of 10 (3).

2. Convert 10^3 to its standard form, which gives us 1000 (three zeros).

3. Move the decimal point of the number (74.94) three places to the right due to the three zeros in 1000.

So, 74.94 * 1000 = 74940.

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