Given the differential equation: dy/dx -yx = x2 - e^x sin (y) with the initial condition y(0) = 1, find the values of y corresponding to the values of Xo+0.1 and Xo+0.2 correct to four decimal places using the Fourth-order Runge-Kutta method.

Answer:

C. $80

Step-by-step explanation:

A. $70

B. $65

C. $80

D. $75

When he pays $70 monthly

Number of months = $2330 / $70

= 33.3 months

When he pays $65 monthly

Number of months = $2330 / $65

= 35.9 months

When he pays $80 monthly

Number of months = $2330 / $80

= 29.1 months

When he pays $75 monthly

Number of months = $2330 / $75

= 31.1 months

The monthly amounts that will allow Arthur to pay off his balance the fastest is $80 per month

Answer:

16

Step-by-step explanation:

Given the definitions of f(x) and g(x) below,

f(x) = x^2+ x + 10

g(x) = -5x-3

f(g(x)) = f(-5x-3)

f(-5x-3) = (-5x-3)²+((-5x-3)+10

f(-5x-3) = 25x²+30x+9-5x-3+10

f(-5x-3) = 25x² +25x+16

f(g(x)) = 25x² +25x+16

f(g(-1)) = 25(-1)² +25(-1)+16

f(g(-1)) = 25-25 + 16

f(g(-1)) = 16

Hence f(g(-1)) is 16

1. The population is increasing for 0 < P < 4100. The answer in interval notation is (0, 4100).

2. The population is decreasing for P > 4100. The answer in interval notation is (4100, ∞).

3. The equilibrium solutions are P = 0 and P = 4100.

To determine when the population is increasing or decreasing, we need to examine the sign of the derivative dP/dt.

1. For what values of P is the population increasing?

The population is increasing when dP/dt > 0.

In this case, we have dP/dt = 1.1P(1 - P/4100).

To find the values of P for which the population is increasing, we need to solve the inequality 1.1P(1 - P/4100) > 0.

To do this, we can consider the sign of each factor:

1.1 is positive.

P is the variable.

(1 - P/4100) is positive when P < 4100 and negative when P > 4100.

From this, we can determine the intervals where the population is increasing:

When P < 0 (since P cannot be negative in a population context), the term 1.1P is negative, so the entire expression is negative. The population is not increasing in this interval.

When 0 < P < 4100, both 1.1P and (1 - P/4100) are positive, so the entire expression is positive. The population is increasing in this interval.

When P > 4100, 1.1P is positive, but (1 - P/4100) is negative. The entire expression is negative. The population is not increasing in this interval.

Therefore, the population is increasing for 0 < P < 4100. The answer in interval notation is (0, 4100).

2. For what values of P is the population decreasing?

The population is decreasing when dP/dt < 0.

In this case, we have dP/dt = 1.1P(1 - P/4100).

To find the values of P for which the population is decreasing, we need to solve the inequality 1.1P(1 - P/4100) < 0.

Using the same analysis as in the previous part, we can determine the intervals where the population is decreasing:

When P < 0, the population is not decreasing.

When 0 < P < 4100, the population is not decreasing.

When P > 4100, the population is decreasing.

Therefore, the population is decreasing for P > 4100. The answer in interval notation is (4100, ∞).

3. What are the equilibrium solutions?

Equilibrium solutions occur when the population remains constant, meaning dP/dt = 0.

In this case, we have dP/dt = 1.1P(1 - P/4100)

                                             = 0.

To find the equilibrium solutions, we solve the equation 1.1P(1 - P/4100) = 0.

This equation is satisfied when either 1.1P = 0 or (1 - P/4100) = 0.

From 1.1P = 0, we have P = 0.

From (1 - P/4100) = 0, we have P = 4100.

Therefore, the equilibrium solutions are P = 0 and P = 4100.

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To find the value of the constant k, we need to integrate the probability density function (PDF) over its entire range and set it equal to 1, since the total area under the PDF should be 1.

(a) Calculating the value of the constant K:

∫[from -1 to 1] kx² dx = 1

Integrating, we get:

(k/3) [x³] from -1 to 1 = 1

(k/3)(1³ - (-1)³) = 1

(k/3)(1 + 1) = 1

(2k/3) = 1

2k = 3

k = 3/2

Therefore, the value of the constant k is 3/2.

(b) Calculating the mean and variance of X:

To find the mean (μ), we need to calculate the expected value of X. Since the PDF is symmetric around x = 0, the mean will be 0.

μ = 0

To find the variance (σ²), we need to calculate the second moment of X around its mean.

σ² = ∫[from -1 to 1] x² * f(x) dx

Substituting the PDF f(x) = (3/2)x²:

σ² = ∫[from -1 to 1] x² * (3/2)x² dx

σ² = (3/2) ∫[from -1 to 1] x^4 dx

σ² = (3/2) * (1/5) [x^5] from -1 to 1

σ² = (3/2) * (1/5) * (1^5 - (-1)^5)

σ² = (3/2) * (1/5) * (1 - (-1))

σ² = (3/2) * (1/5) * 2

σ² = 3/5

Therefore, the mean of X is 0, and the variance is 3/5.

(c) The cumulative distribution function (CDF) of X is found by integrating the PDF from negative infinity to x:

F(x) = ∫[from -∞ to x] f(t) dt

For the given PDF f(x) = (3/2)x², the cumulative distribution function can be calculated as follows:

F(x) = ∫[from -∞ to x] (3/2)t² dt

F(x) = (3/2) ∫[from -∞ to x] t² dt

F(x) = (3/2) * (1/3) [t³] from -∞ to x

F(x) = (1/2) x³

Therefore, the cumulative distribution function (CDF) of X is F(x) = (1/2) x³.

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The probability that the events do not occur is 0.6778`.

The probability that the events do not occur is given by `P(Ac)=1-P(A)` and `P(Bc)=1-P(B)`.

The given probabilities are `P(A)=0.2272` and `P(B)=0.4506`.

Using the formula `P(A∪B)=P(A)+P(B)-P(A∩B)`, we have `P(A∩B) = P(A) + P(B) - P(A∪B)`

Using the fact that the two events are mutually exclusive, we get `P(A∩B) = 0`.

Thus, `P(A∪B) = P(A) + P(B) = 0.2272 + 0.4506 = 0.6778`.

The probability that either A or B but not both occurs is given by `P(AΔB) = P(A∪B) - P(A∩B) = 0.6778 - 0 = 0.6778`.

Hence, the required probability is `P(AΔB) = 0.6778`.

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Answer

picture below of order. Not entirely

Step-by-step explanation:

Answer:

B. Ten less than five times a number is greater than twenty-six.

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

n > 36 /5

Interval Notation:

( 36 /5 , ∞ )

Answer:

55

Step-by-step explanation:

The component of the displacement vector are: Horizontal component = -75 m Vertical component = 129.9 m (approx)

Given that the superhero flew 150 m at an angle of 120° with respect to the positive x-axis. We need to find the components of displacement vector.

Let's consider the given figure: Here, AB represents the displacement vector. AC represents the horizontal component of displacement vector and BC represents the vertical component of displacement vector.

The horizontal component can be calculated as: AC = AB cos θ

Here, θ = 120° and AB = 150 mAC = 150 cos 120°AC = -75 m (Negative sign indicates that the displacement is in the negative direction of the x-axis)

The vertical component can be calculated as: BC = AB sin θHere, θ = 120° and AB = 150 mBC = 150 sin 120°BC = 129.9 m (Approx)

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Given information: A superhero flew 150 m at a 120-degree angle with respect to the positive x-axis. The x-component of the displacement vector is 75 m and the y-component of the displacement vector is 129.9 m.

Components of displacement vector: The component of displacement vector with respect to the x-axis is called the x-component of displacement vector.

Similarly, the component of displacement vector with respect to the y-axis is called the y-component of displacement vector.

As per the given information, the angle of displacement vector is 120 degrees with respect to the positive x-axis.

So, the angle of the vector with respect to the negative x-axis is 180 - 120 = 60 degrees (supplementary angles).

Now, the horizontal component (x-component) of the vector is given by the product of the magnitude and the cosine of the angle with respect to the x-axis.

Let the x-component of displacement vector be x.

Then, x = 150 cos 60°

x = 75 m.

The vertical component (y-component) of the vector is given by the product of the magnitude and the sine of the angle with respect to the x-axis.

Let the y-component of displacement vector be y.

Then, y = 150 sin 60°

y = 129.9 m.

Therefore, the x-component of the displacement vector is 75 m and the y-component of the displacement vector is 129.9 m.

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Answer: 3.125

Step-by-step explanation:

Given

Triangle is dilated by a factor of [tex]\frac{1}{4}[/tex] i.e. each side multiplies to 0.25.

Side E'F' becomes 0.25 times the original length

[tex]\Rightarrow E'F'=\dfrac{1}{4}\times 12.5=3.125[/tex]

Answer: a = -7.68

STEPS:

- Subtract 13.61 from both sides

- Simplify

- Divide both sides by 3

Answer:

A.) The base is 5 and the exponent is 3

B.) The base is 4 the exponent is 7

C.) The base is 3 the exponent is 4

D.) The base is 6 the exponent is 8

Step-by-step explanation:

Answer:

x does not equal - 49.

x = 49

Step-by-step explanation:

To find the square you multiply the square root.

- 7 × - 7 = 49

x ≠ - 49

x = 49

Answer:

We can use the formula for the nth term of an arithmetic sequence to find n:

an = a1 + (n - 1)d

Substituting the given values, we get:

52 = 132 + (n - 1)(-4)

Simplifying and solving for n, we get:

n = 21

So, the sequence has 21 terms.

We can use the formula for the sum of the first n terms of an arithmetic sequence to find Sn:

Sn = n/2(2a1 + (n - 1)d)

Substituting the given values, we get:

Sn = 21/2(2(132) + (21 - 1)(-4))

Simplifying, we get:

Sn = 21/2(264 - 80)

Sn = 21/2(184)

Sn = 1932

Therefore, the sum of the first 21 terms of the arithmetic sequence is 1932.

The function f(x) is more steeply increasing at all points x than it is at x=1.

If the rate of change of f at x=c is twice its rate of change at x=1, then f(x) is said to be more steeply increasing at x=c than at x=1.

The rate of change of a function f(x) at any point x can be calculated by differentiating the function f(x).

That is, the derivative of the function f(x) gives the rate of change of the function at any point x.

If the rate of change of f(x) at x=1 is f'(1), and its rate of change at x=c is f'(c), then we have f'(c) = 2f'(1)

We can see that f(x) is more steeply increasing at x=c than at x=1 if and only if f'(c) > f'(1).

Since f(x) is twice as steep at x=c than at x=1, we can conclude that f'(c) > f'(1) for all c.

That is, the rate of change of f(x) is greater at any point x=c than at x=1.

Therefore, the function f(x) is more steeply increasing at all points x than it is at x=1.

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The probability that the event E does not happen is:

P(not E) = 0.61

First, remember that for any experiment with N outcomes, the sum of the N probabilities for these outcomes must be 1.

Then if we have two outcomes, E happens or E does not happen, we have:

P(E) + P(not E) = 1

Replace the value that we know:

0.39 + p(not E) = 1

Solve for the probability we want:

P(not E) = 1 - 0.39

P(not E) = 0.61

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Answer: 64%

75% of adults use some sort of vision correction. About 64% of them wear eyeglasses, and about 11% wear contact lenses, either exclusively, or with glasses. Over half of all women and about 42% of men wear glasses.

63.8% of Americans are predicted to wear glasses

The given parameters are:

The percentage of Americans that wear glasses is calculated as:

Percentage = Glasses/Sample size

This gives

Percentage = 638/1000

Evaluate the quotient

Percentage = 0.638

Express as percentage

Percentage = 63.8%

Hence, 63.8% of Americans would wear glasses

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Answer:

I cannot solve it step-by-step because like I'm helping other people cuz I'm busy with my homework so just I'm going to direct you the question you're supposed to solve simultaneous equation by any method example elimination method substitution method then you get the answer if you get stuck you can inform me

Answer:

200

Step-by-step explanation:

15% is 0.15

0.15x = 30

x = 30/0.15 = 200

Joanne's plan pays $2400 for her July losses, as she is responsible for 20% of the covered expenses during that month.

Joanne's health insurance plan with a $1000 deductible, 80% coinsurance, and a $5000 out-of-pocket cap requires her to pay for her medical expenses until she reaches the deductible.

After reaching the deductible, she is responsible for 20% of the covered expenses, up to the out-of-pocket cap. The plan pays the remaining percentage of covered expenses.

To calculate how much the plan pays for Joanne's July losses, we need to consider her deductible, coinsurance, and out-of-pocket cap.

In March, Joanne incurs $1000 in covered medical expenses.

Since this amount is equal to her deductible, she is responsible for paying the full amount out of pocket.

In July, Joanne incurs $3000 in covered expenses. Since she has already met her deductible, the coinsurance comes into play.

According to the plan's coinsurance rate of 80%,

Joanne is responsible for 20% of the covered expenses.

Therefore, Joanne is responsible for paying 20% of $3000, which is $600.

The plan will pay the remaining 80% of the covered expenses, which is $2400.

In December, Joanne incurs $30,000 in covered expenses. Since she has already met her deductible and reached her out-of-pocket cap, the plan pays 100% of the covered expenses.

Therefore, the plan will pay the full $30,000 for her December losses.

To summarize, Joanne's plan pays $2400 for her July losses, as she is responsible for 20% of the covered expenses during that month.

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Both the stores together donated 65.5 dozen cookies.

Answer:

Financial Literacy = 25

Model with mathematics:

a) cranes = 40 panthers = 40

b) yes, finding the mean is a good way of determining which team has the better record, because "finding the mean" is just finding the average.

Step-by-step explanation:

Financial Literacy:

24 = [tex]\frac{x+15+20+10+12+20+16+80+18}{9}[/tex] → [tex]24 = \frac{191}{9}[/tex]

24×9=x · 191

→ 216 = x · 191

→ 216-191=x

x = 25

Model with Mathematics:

Add all six wins and divide by how many seasons there are. (do it for both sides. Also, I'm too lazy to type it out.)

The confidence interval for the population mean, μ is y ± t*n-1sn, where y is the sample mean, s is the sample standard deviation, and n is the sample size.

The critical value t*n-1 depends on the confidence level, C, and the number of degrees of freedom, n-1.Critical value t*n−1:The critical value t*n-1 refers to the value of t that separates the middle 100C% of the t distribution from the extreme (tail) regions, where C is the specified confidence level.

The number of degrees of freedom is n - 1. A t-value can be used to determine the confidence interval for a population mean with unknown standard deviation if the sample size is less than 30 or the population is not normally distributed.

Confidence interval:If y is the sample mean and s is the sample standard deviation, the confidence interval for the population mean μ is y ± t*n-1sn, where n is the sample size. The confidence interval is a range of values around the sample statistic that is likely to contain the true population parameter. The confidence interval is used to estimate the value of an unknown parameter, such as a population mean or proportion, and to quantify the level of uncertainty surrounding that estimate.

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Answer:

m = 3/4

Step-by-step explanation:

slope of a line equation:

[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

m = (3-0)/(2-(-2))

m = 3/4

Answer:

c

Step-by-step explanation: