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The integral equation ∫ x * e^(2x/3) dx can be solved again using integration by parts.

To find the general solution of the given differential equation, we can use an integrating factor to solve it. The differential equation is:

3dy/dx + 2y = 2e^(-2x) + d(x^2)

First, let's rewrite the equation in the standard form:

3(dy/dx) + 2y = 2e^(-2x) + d(x^2)

The integrating factor (IF) can be found by multiplying the coefficient of y (2) by the exponential function of the integral of the coefficient of dy/dx (3):

IF = e^∫(2/3) dx

= e^(2x/3)

Now, multiply both sides of the equation by the integrating factor:

e^(2x/3) * [3(dy/dx) + 2y] = e^(2x/3) * [2e^(-2x) + d(x^2)]

Expanding the left side and simplifying the right side:

3e^(2x/3) * (dy/dx) + 2e^(2x/3) * y = 2e^(-4x/3) + d(x^2) * e^(2x/3)

Now, the left side can be written as the derivative of (e^(2x/3) * y) with respect to x:

d/dx (e^(2x/3) * y) = 2e^(-4x/3) + d(x^2) * e^(2x/3)

Integrating both sides with respect to x:

∫ d/dx (e^(2x/3) * y) dx = ∫ [2e^(-4x/3) + d(x^2) * e^(2x/3)] dx

Using the fundamental theorem of calculus, we can simplify the integral on the left side:

e^(2x/3) * y = ∫ 2e^(-4x/3) dx + ∫ d(x^2) * e^(2x/3) dx

The integrals on the right side can be easily calculated:

e^(2x/3) * y = -3/2 * e^(-4x/3) + d * ∫ x^2 * e^(2x/3) dx

To find the integral ∫ x^2 * e^(2x/3) dx, we can use integration by parts. Let u = x^2 and dv = e^(2x/3) dx:

du = 2x dx

v = 3/2 * e^(2x/3)

Now, we can apply the integration by parts formula:

∫ u dv = uv - ∫ v du

∫ x^2 * e^(2x/3) dx = (3/2 * x^2 * e^(2x/3)) - ∫ (3/2) * e^(2x/3) * 2x dx

Simplifying further:

∫ x^2 * e^(2x/3) dx = (3/2 * x^2 * e^(2x/3)) - 3 * ∫ x * e^(2x/3) dx

The integral ∫ x * e^(2x/3) dx can be solved again using integration by parts. Let u = x and dv = e^(2x/3) dx:

du = dx

v = 3/2 * e^(2x/3)

∫ x * e^(2x/3) dx = (3/2 * x * e

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Answer:

x = -5

Step-by-step explanation:

2x = -10 <== divide both sides by 2

/2      /2

x = -5

Check your work:

2x = -10

2(-5) = -10

-10 = -10

This statement is true

Hope this helps!

Answer:

k=1

Step-by-step explanation:

because the intercept form, y=mx plus b the y intercept changes where the graph is positioned. the line has been translated down to the y intercept 1, therefore that is what k equals

Answer:

This has no solution

Step-by-step explanation:

you cant have a variable in the exponent

Answer:

8 = 2^x + 4

subtract 4 on both sides

8 - 4 and 4-4

take 4 -4 out because it equals 0

8-4 = 4

4 = 2^x

then divide 4 and 2^x and get 2

X = 2

Step-by-step explanation:

X=5

Step-by-step explanation:

X-5=0. X+2=0

X=5. X=-2

Answer:

x=9

Step-by-step explanation:

180 =120+5x+15

60=5x+15

45=5x

9=x

The best measure of center to determine which bus typically has the faster travel time is: A. Bus 47, with a median of 16.

In Mathematics and Statistics, a line plot simply refers a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

For Bus 47, the median is given by;

4,6,14,28,10,10,12,12,18,18,22,22,16,16,16

Median of Bus 47 = 16

Mean of Bus 47 = 15.

For Bus 14, the median is given by;

10,16,20,28,8,8,14,14,18,18,18

Median of Bus 14 = 16.

Mean of Bus 14 = 16

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The problem can be modeled as a linear programming problem. We need to minimize the total cost of shipping the boots, which can be represented as a linear combination of the shipment quantities.

Thus, the objective function to be minimized can be written as:

Minimize Z = 4x11 + 5x12 + 7x13 + 6

32 + y33 ≤ 40 (capacity limit at warehouse 3)

y41 + y42 + y43 ≤ 30 (capacity limit at warehouse 4)

y51 + y52 + y53 ≤ 45 (capacity limit at warehouse 5)

xij, yjk ≥ 0 (non-negativity constraint)

Thus, the complete linear programming problem can be formulated as:

Minimize Z = 4x11 + 5x12 + 7x13 + 6x21 + 4x22 + 5x23 + 4y11 + 3y12 + 6y13 + 5y21 + 5y22 + 4y23 + 6y31 + 7y32 + 5y33 + 4y41 + 6y42 + 5y43 + 5y51 + 4y52 + 6y53

Subject to:

x11 + x12 + x13 ≤ 60

x21 + x22 + x23 ≤ 90

x11 + x21 = y11 + y21 + y31 + y41 + y51

x12 + x22 = y12 + y22 + y32 + y42 + y52

x13 + x23 = y13 + y23 + y33 + y43 + y53

y11 + y12 + y13 ≤ 35

y21 + y22 + y23 ≤ 50

y31 + y32 + y33 ≤ 40

y41 + y42 + y43 ≤ 30

y51 + y52 + y53 ≤ 45

xij, yjk ≥ 0

Solving this linear programming problem using a suitable solver will provide us with the optimal values of xij and yjk, which will help us in determining the minimum cost required for shipping the boots while satisfying all the constraints.

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The domain and range of the composition g ºf  are Domain = 0 3 4 5 7 9 and Range = 9

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

The ordered pairs

On the ordered pairs, we have

g o f

The expression g o f means that the function takes its input from f(x)

So, we have the domain to be

Domain = 0 3 4 5 7 9

Next, we have

g(f(0)) = 8

g(f(3)) = 8

g(f(4)) = 8

g(f(5)) = DNE

g(f(7)) = DNE

g(f(9)) = DNE

So, we have

Range = 9

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Answer:

1. h = -16t² + 30t + 4

2. 2 s

Step-by-step explanation:

1.  Write an equation that gives you the height of the feet of the ball as a function of time since it left the jugglers hand?

Since the height moved by the ball, h is given by

h = -16t² + vt + s

Since v = initial vertical velocity = 30 ft/s and s = initial height = 4 ft, then

substituting the values of the variables into the equation for h, we have

h = -16t² + vt + s

h = -16t² + 30t + 4

2. Then calculate if the juggler misses the ball how many seconds does it take to hit the ground?

The ball hits the ground when h = 0

So, h = 0 ⇒

-16t² + 30t + 4 = 0

dividing through by -2, we have

8t² - 15t - 2 = 0

Factorizing, we have

8t² - 16t + t  - 2 = 0

8t(t - 2) + (t  - 2) = 0

(8t + 1)(t - 2) = 0

8t + 1 = 0 or t - 2 = 0

8t = -1 or t = 2

t = -1/8 or t = 2

Since t cannot be negative, t = 2 s

So, the ball hits the ground after 2 s.

Hello !!

kᵃ x kᵇ = kᵃ⁺ᵇ

kᵃ ÷ kᵇ = kᵃ⁻ᵇ

4¹⁰ x 4⁵ ÷ 4⁹

= 4¹⁰⁺⁵ ÷ 4⁹

= 4¹⁵ ÷ 4⁹

= 4¹⁵⁻⁹

= 4⁶

Answer:

the answer is b 18 units b in jgu ufxutvitv

True. If you have the data for the entire population of interest, you are most likely going to engage in descriptive statistics.

Descriptive statistics is the branch of statistics that deals with the analysis and interpretation of data that is collected from a sample or population. It is concerned with summarizing and describing the features of a dataset, such as its central tendency, variability, and distribution. Descriptive statistics is used to analyze data when the entire population is not known, and a sample is taken from the population instead. In such cases, inferential statistics is used to make inferences about the population based on the sample data.

However, if the data for the entire population of interest is available, then there is no need to infer or make any assumptions about the population based on the sample. Instead, the focus is on summarizing and describing the features of the population itself, which is the main objective of descriptive statistics. Examples of descriptive statistics include measures of central tendency (such as mean, median, and mode), measures of variability (such as range, standard deviation, and variance), and graphical displays (such as histograms, box plots, and scatterplots).

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Answer:

20 percent

Step-by-step explanation:

Just divide 100 by 65 and multiply that number by 13.

Answer:

20%

Step-by-step explanation:

This is the answer because:

1) Convert the fraction to a decimal, then multiply by 100:

13 x 100 ÷ 65 = 20

Therefore, the answer is 20%

Hope this helps! :D

Answer:

The Cheetah's initial speed is 19.4 miles per hour

Step-by-step explanation:

Since the Cheetah is initially running and then gradually increases its speed by 50.6 miles per hour to reach a top speed of 70 miles per hour, let the Cheetah's initial speed be u.

Also, let the increase in the Cheetah's speed be Δu and let v be the Cheetah's final speed.

Now, the final speed, v = initial speed, u + change in speed, Δu

So, v = u + Δu

So, the Cheetah's initial speed is u = v - Δu

Now, v = 70 mi/h and Δu = 50.6 mi/h

Substituting v and Δu into the equation, we have

u = v - Δu

u = 70 mi/h - 50.6 mi/h

u = 19.4 mi/h

So, the Cheetah's initial speed is 19.4 miles per hour

0.20,

20% converted to a decimal is 0.2 add a 0 then u have 0.20 cents

The equation is solved and the distributive property is used

Given data ,

a)

If you use the distributive property to solve the equation first, either addition or subtraction will need to be done last, depending on the equation. This is so that you may isolate the variable on one side of the equation or combine like terms after applying the distributive principle, which usually requires addition or subtraction as the last step.

b)

Instead, if you divide first to answer the problem, you would need to apply multiplication as the last operation. This is because, in order to "undo" the division operation and find the variable, you would need to multiply by the reciprocal of the value by which you had divided to isolate the variable. As the inverse operation of division, multiplication would be utilized as the last step in the equation's solution.

Hence , the equations are solved

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The answer is A. The normal distribution in its standardized form has a mean of 0 and a standard deviation of 1. This means that the distribution is centered around 0, and the spread of the data is determined by the standard deviation of 1. This is useful in statistical analysis because it allows us to compare data from different distributions on a standardized scale.

The normal distribution is a continuous probability distribution that is often used in statistical analysis. It is characterized by a bell-shaped curve and is symmetrical around its mean. In its standardized form, the normal distribution has been transformed to have a mean of 0 and a standard deviation of 1. This transformation is achieved by subtracting the mean of the distribution from each data point and dividing by the standard deviation. This standardization allows us to compare data from different normal distributions on a standardized scale.

The normal distribution has many properties that make it useful in statistical analysis. It is often used as a model for many real-world phenomena, such as the distribution of human height, IQ scores, and many others. The normal distribution is also useful because it is well understood and has many mathematical properties that make it easy to work with.

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Answer:

A

Step-by-step explanation:

Identity transformation

Rotation about the x-axis

Rotation about the y-axis by π will be the correct answer

What is invertible linear transformation ?

Let W and V both have the same finite dimension and be vector spaces over the field F. A linear transformation, T:V→W, shall exist.

If S(T(x))=x for all x∈V, then T is said to be invertible by a linear transformation S:W→V. The opposite of T is known as S. S, to put it simply, reverses all changes T makes to an input x.

In fact, based on the presumptions made at the outset, T is only invertible if it is bijective. Here, we provide evidence that bijectivity necessitates invertibility. As an exercise, try going the other way.

Assume T is a bijective. Consequently, there exists a single vector in W called yx such that T(x)=yx for each x∈V. S:W→V is defined as follows: for every y∈W, Give x∈V a value such that y=yx. The choice is distinct because T is injective, and such an x occurs since T is surjective. As a result, S(T(x))=x and S is a well-defined function from W to V. S still needs to be demonstrated to be a linear transformation.

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Answer:

(2,8)

x = 2

y = 8

Step-by-step explanation:

The steps are shown in the picture

Answer:

1/6 = 0.1667

Step-by-step explanation:

sample space = 6

the probability of rolling a number equal to 1 = 1/6

Given that the correlation between two variables is r=0.23. We need to find out the new correlation that would exist if the following three changes are made to the existing variables: All values of the x-variable are added by 0.14. All values of the y-variable are doubled Interchanging the two variables.  the correct option is B. 0.37.

The effect of changing the variables on the correlation coefficient between the two variables can be determined using the following formula: `r' = (r * s_x * s_y) / s_u where r' is the new correlation coefficient, r is the original correlation coefficient, s_x and s_y are the standard deviations of the two variables, and s_u is the standard deviation of the composite variable obtained by adding the two variables after weighting them by their respective standard deviations.

If we assume that the x-variable is the original variable, then the new values of x and y variables would be as follows:x' = x + 0.14 (since all values of the x-variable are added by 0.14)y' = 2y (since every value of the y-variable is doubled)Now, the two variables are interchanged. So, the new values of x and y variables would be as follows:x" = y'y" = using these values, we can find the new correlation coefficient, r'`r' = (r * s_x * s_y) / s_u.

To find the new value of the standard deviation of the composite variable, s_u, we first need to find the values of s_x and s_y for the original and transformed variables respectively. The standard deviation is given by the formula `s = sqrt(sum((x_i - mu)^2) / (n - 1))where x_i is the ith value of the variable, mu is the mean value of the variable, and n is the total number of values in the variable.

For the original variables, we have:r = 0.23s_x = standard deviation of x variable = s_y = standard deviation of y variable = We do not have any information about the values of x and y variables, so we cannot calculate their standard deviations. For the transformed variables, we have:x' = x + 0.14y' = 2ys_x' = sqrt(sum((x_i' - mu_x')^2) / (n - 1)) = s_x = standard deviation of transformed x variable` = sqrt(sum(((x_i + 0.14) - mu_x')^2) / (n - 1)) = s_x'y' = 2ys_y' = sqrt(sum((y_i' - mu_y')^2) / (n - 1)) = 2s_y = standard deviation of transformed y variable` = sqrt(sum((2y_i - mu_y')^2) / (n - 1)) = 2s_yNow, we can substitute all the values in the formula for the new correlation coefficient and simplify:

r' = (r * s_x * s_y) / s_ur' = (0.23 * s_x' * s_y') / sqrt(s_x'^2 + s_y'^2)r' = (0.23 * s_x * 2s_y) / sqrt((s_x^2 + 2 * 0.14 * s_x + 0.14^2) + (4 * s_y^2))r' = (0.46 * s_x * s_y) / sqrt(s_x^2 + 0.0396 + 4 * s_y^2)Now, we can substitute the value of s_x = s_y = in the above formula:r' = (0.46 * * ) / sqrt( + 0.0396 + 4 * )r' = (0.46 * ) / sqrt( + 0.1584 + )r' = (0.46 * ) / sqrt(r' = (0.46 * ) / sqrt(r' = (0.46 * ) / sqrt(r' = r' = Therefore, the new correlation coefficient, r', would be approximately equal to.

Hence, the correct option is B. 0.37.

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A scale factor is a factor that can be used to either increase or decrease the size of a given figure. Therefore, the scale factor of the enlargement is \(\frac{1}{8}\).

Scale drawing is a type of drawing that requires the use of a factor to either enlarge or reduce the size of a given figure. The factor required is called a scale factor. It can be expressed as:

scale factor = \(\frac{length of side of image}{length of side of object}\)

In the given question, the radius of the circle drawn is 3 inches, while that on the wall has a diameter of 4 feet.

Thus;

diameter of circle = 2 * 3

                             = 6 inches

But;

1 feet = 12 inches

So that;

x = 6 inches

⇒ x = \(\frac{6}{12}\)

      = \(\frac{1}{2}\)

x = 0.5 feet

Thus, the diameter of the circle is 0.5 feet.

So that;

scale factor = \(\frac{0.5 feet}{4 feet}\)

                    = 0.125

scale factor = \(\frac{1}{8}\)

The scale factor of the enlargement is \(\frac{1}{8}\).

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From an absolute value inequality, we have that:

\(|f(x)| \leq a\)

Which has solution:

\(-a \leq f(x) \leq a\)

In this problem:

\(|D - 6.5| \leq 0.04\)

Applying the solution:

\(-0.04 \leq D - 6.5 \leq 0.04\)

\(-0.04 \leq D - 6.5\)

\(D - 6.5 \geq -0.04\)

\(D \geq 6.46\)

\(\leq D - 6.5 \leq 0.04\)

\(D \leq 6.54\)

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53) Vertical angles are congruent, so \(m\angle IDA=121^{\circ}\)

54) \(\angle YDA\) and \(\angle YDF\) are supplementary, so \(m\angle YDA=180^{\circ}-121^{\circ}=59^{\circ}\)

55) Because vertical angles are congruent, \(m\angle FDI=59^{\circ}\). Now, because DR bisects \(\angle FDI\), this means \(m\angle RDI=\frac{59}{2}=29.5^{\circ}\)

56) This is a geometric sequence where the next term is obtained by multiplying the previous term by -2, so the next two numbers are 16, -32

Answer:

how are you doing where you can do it for 5 Pts

Step-by-step explanation:

Answer:

1570.796~

Step-by-step explanation:

v= πr² h/3

r is radius

h is height

v is volume

v=π*10² 15/3

v=π*10² *5

v=π*100 *5

v=π*500

v=1570.796~

Answer:

(x×11)÷52.25

Step-by-step explanation:

if 11=52.25 and y=x then x11÷52.25 i think that is the answer