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The solution to the given differential equation is \(y = a_0x^{[0]} + a_1x^{[1]} + a_2x^{[2]}\), where a_0, a_1, and a_2 are constants.

To fathom the given differential equation, xy'' + y' = 0, we will begin by expecting a control arrangement of the frame y = ∑(n=0 to ∞) a_nx^n, where a_n speaks to the coefficients to be decided.

Separating y with regard to x, we get:

\(y' = ∑(n=0 to ∞) a_n(nx^[(n-1))] = ∑(n=0 to ∞) na_nx^[(n-1)]\)

Separating y' with regard to x, we get:

\(y'' = ∑(n=0 to ∞) n(n-1)a_nx^[(n-2)]\)

Presently, we substitute these expressions for y and its subsidiaries into the differential condition:

\(x(∑(n=0 to ∞) n(n-1)a_nx^[(n-2))] + (∑(n=0 to ∞) na_nx^[(n-1))] =\)

After improving terms, we have:

\(∑(n=0 to ∞) n(n-1)a_nx^[(n-1)] + ∑(n=0 to ∞) na_nx^[n] =\)

Another, we compare the coefficients of like powers of x to zero, coming about in a boundless arrangement of conditions:

For n = 0: + a_0 = (condition 1)

For n = 1: + a_1 = (condition 2)

For n ≥ 2: n(n-1)a_n + na_n = (condition 3)

Disentangling condition 3, we have:

\(n^[2a]_n - n(a_n) =\)

n(n-1)a_n - na_n =

n(n-1 - 1)a_n =

(n(n-2)a_n) =

From equation 1, a_0 = 0, and from equation 2, a_1 = 0.

For n ≥ 2, we have two conceivable outcomes:

n(n-2) = 0, which gives n = or n = 2.

a_n = (minor arrangement)

So, the solution to the given differential equation is \(y = a_0x^{[0]} + a_1x^{[1]} + a_2x^{[2]}\), where a_0, a_1, and a_2 are constants.

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We accert H1 alternative that is result is population mean greater than 400.

There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

What is standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

We have given: μ = 14, x bar = 16, n = 40, s = 6,  α = 5%, = 0.05

To test μ0 : μ = 14   Vs  H1: μ > 14

Test statistics = (X bar - μx)√n / sx = (2 x 6.3245) / 6 = 2.1081

So, P value = 0.021

Conclusion: There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

P value for the hypothesis test

n = 50, x bar = 420, sx = 81, μ = 400,

To test:  H0: μ 400    Vs   H1:  μ > 400

It is right tail test

Test statistics =  (X bar - μx)√n / sx = (420 - 400) √50 / 81 =

z = 1.7459

P value = 0.04093

Declsion: We reject H0 is p value < α

Here α = 0.05

Hence P value < α

Conclusion: We accert H1 alternative that is result is population mean greater than 400.

Hence, we accert H1 alternative that is result is population mean greater than 400.

There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

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The solution to the given system of equations is x = 2, y = -1, and z = 1.

To solve the system of equations, we can use methods such as substitution or elimination. Here, we will use the method of elimination to find the values of x, y, and z.

First, let's eliminate the variable x by multiplying equation (1) by 2 and equation (3) by -1. This gives us:

2x + 4y - 2z = -6 (4)

-x + y - z = -4 (5)

Next, we can subtract equation (5) from equation (4) to eliminate the variable x:

5y - z = 2 (6)

Now, we have a system of two equations with two variables. Let's eliminate the variable z by multiplying equation (2) by 2 and equation (6) by 1. This gives us:

4x - 2y + 2z = 10 (7)

5y - z = 2 (8)

Adding equation (7) and equation (8), we can eliminate the variable z:

4x + 5y = 12 (9)

From equation (6), we can express z in terms of y:

z = 5y - 2 (10)

Now, we have a system of two equations with two variables again. Let's substitute equation (10) into equation (1):

x + 2y - (5y - 2) = -3

x - 3y + 2 = -3

x - 3y = -5 (11)

From equations (9) and (11), we can solve for x and y:

4x + 5y = 12 (9)

x - 3y = -5 (11)

By solving this system of equations, we find x = 2 and y = -1. Substituting these values into equation (10), we can solve for z:

z = 5(-1) - 2

z = -5 - 2

z = -7

Therefore, the solution to the given system of equations is x = 2, y = -1, and z = -7.

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The Multi-Step Campers can cut approximately 15 kite lines from the roll of string.

To determine the number of kite lines that can be cut from the roll of string, we need to convert the measurements to a consistent unit. Let's convert the length of the string roll and the kite line to yards.

Since 1 yard is equal to 3 feet, we have:

50 feet = 50/3 yards ≈ 16.67 yards (rounded to two decimal places)

Now, we can calculate the number of kite lines that can be cut from the string roll:

Number of kite lines = Total length of string roll / Length of each kite line

Number of kite lines = 250 yards / 16.67 yards ≈ 15

Therefore, the Multi-Step Campers can cut approximately 15 kite lines from the roll of string.

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Answer:

9.28 liters

Step-by-step explanation:

The unit rate is 1.6 liters per hour.

You multiply it by the number of hours

1.6 x 5.8 = 9.28

Answer:

9.28.

Step-by-step explanation:

We're trying to find out how much gas Luis uses in 5.8 hours. It states that Luis uses 1.6 liters of gasoline EACH HOUR. So, we just multiply 1.6 and 5.8.

Answer:

The statement is true is for any \(n\in \mathbb{N}\).

Step-by-step explanation:

First, we check the identity for \(n = 1\):

\((2\cdot 1 - 1)^{2} = \frac{2\cdot (2\cdot 1 - 1)\cdot (2\cdot 1 + 1)}{3}\)

\(1 = \frac{1\cdot 1\cdot 3}{3}\)

\(1 = 1\)

The statement is true for \(n = 1\).

Then, we have to check that identity is true for \(n = k+1\), under the assumption that \(n = k\) is true:

\((1^{2}+2^{2}+3^{2}+...+k^{2}) + [2\cdot (k+1)-1]^{2} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}\)

\(\frac{k\cdot (2\cdot k -1)\cdot (2\cdot k +1)}{3} +[2\cdot (k+1)-1]^{2} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}\)

\(\frac{k\cdot (2\cdot k -1)\cdot (2\cdot k +1)+3\cdot [2\cdot (k+1)-1]^{2}}{3} = \frac{(k+1)\cdot [2\cdot (k+1)-1]\cdot [2\cdot (k+1)+1]}{3}\)

\(k\cdot (2\cdot k -1)\cdot (2\cdot k +1)+3\cdot (2\cdot k +1)^{2} = (k+1)\cdot (2\cdot k +1)\cdot (2\cdot k +3)\)

\((2\cdot k +1)\cdot [k\cdot (2\cdot k -1)+3\cdot (2\cdot k +1)] = (k+1) \cdot (2\cdot k +1)\cdot (2\cdot k +3)\)

\(k\cdot (2\cdot k - 1)+3\cdot (2\cdot k +1) = (k + 1)\cdot (2\cdot k +3)\)

\(2\cdot k^{2}+5\cdot k +3 = (k+1)\cdot (2\cdot k + 3)\)

\((k+1)\cdot (2\cdot k + 3) = (k+1)\cdot (2\cdot k + 3)\)

Therefore, the statement is true for any \(n\in \mathbb{N}\).

Answer:: the equation is 7m + 19

Step-by-step explanation:

21 inch²

we splitthe two shapes, find the areas by multiplying the two sides and we add both of the answers, 15+6

Answer:

2(3) + 2(6) = 6 + 12 = 18 square feet

From the given ANOVA table, we can see that the test statistic for the analysis of variance (ANOVA) is 4.0105, and the corresponding P-value is 0.0208.

The test statistic in ANOVA measures the ratio of the variability between the groups to the variability within the groups.

The P-value is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the data, assuming that the null hypothesis is true.

A P-value of 0.0208 means that if the null hypothesis were true (i.e., the group means are equal), there would be only a 2.08% chance of obtaining a test statistic as extreme as or more extreme than 4.0105.

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The work done by Francesca is incorrect as the solved final answer and the final answer given in the question don't matches.

As per the given data, we have to determine whether the evaluation made by Francesca is either correct or wrong.

The given expression is \(3(5)^{2} -18 \div3\)

We have to follow the BODMAS rule for evaluating the expressions.

B - Brackets

O - Of

D - Division

M - Multiplication

A - Addition

S - Subtraction

Steps for solving the given expression:

Step 1: Solve for square value in brackets

= 3(25) – 18 ÷ 3

Step 2: Remove the brackets between the terms 3 and 25.

= 75 – 18 ÷ 3

Step 3: Divide the terms 18 and 3.

= 75 - 6

Step 4: Subtract the terms 75 and 6.

= 69.

As the final answer is given in the question and the final answer which we have done are not matching Francesca's work is incorrect.

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Answer:

14, 18, 20

Step-by-step explanation:

You have to replace the number in the "s" column with the "s" in the problem. For example the first number in the table is 2 so you have to put 2 into the problem then add it with 12 and you get 14.

Let x = hours that he worked

4x + 20 = 80

- 20. - 20

4x = 60

--- ----

4 = 4

x = 15

Hope that helps :)

Answer:

15 hours

Step-by-step explanation:

\((4 \times n) + 20 = 80 \\ (4 \times n) = 80 - 20 \\ (4 \times n) = 60 \\ 60 \div 4 = n \\ 15 \: hours\)

answer:

step by step explanation:

make all numbers the same decimal,fraction or percentage and then compare

3/8=37.5%

-2.8=20.8%

0.053=5.3%

-2.8%

ascending means from smallest to biggest so the answer would be 0.053

Answer: True

Step-by-step explanation:

Cost = 15 + 3t

22.5 = 15 + 3(2.5)

22.5 = 15 + 7.5

22.5 = 22.5 <— true

Answer:

true

Step-by-step explanation:

2.50 x 3 = 7.50

15 + 7.50 = 22.50

22.50 = 22.50

Answer:

B

Step-by-step explanation:

Using the method of cross- multiplication

\(\frac{a}{b}\) = \(\frac{c}{d}\) ⇒ ad = bc

If ad ≠ bc then equation is not true

A

\(\frac{10}{12}\) = \(\frac{5}{6}\) , then

10 × 6 = 12 × 5 = 60 ← equation is true

B

\(\frac{69}{100}\) = \(\frac{6}{10}\) , then

69 × 10 = 690 and 100 × 6 = 600

690 ≠ 600 ← equation not true

C

\(\frac{10}{5}\) = \(\frac{200}{100}\) , then

10 × 100 = 5 × 200 = 1000 ← equation is true

D

\(\frac{12}{4}\) = \(\frac{6}{2}\) , then

12 × 2 = 4 × 6 = 24 ← equation is true

Hi!

I can help you with joy! :)

• Here, we need to determine if each equation is true by simplifying fractions.

• The 1st equation states that

10/12 = 5/6

Is it true?

Let’s simplify 10/12 to find out.

Divide 10 and 12 by 2:

5/6

Thus. The 1st equation is true.

How about the next one?

We have 3 options left.

69/100=6/10

Is that correct?

Nope!

Why?

If we simplify 69/100, we will not get 6/10.

In fact, 69/100 cannot be simplified.

Thus, the second equation is not true.

Now, how about Options C and D?

Well, both of these equations ARE true.

Thus, the second equation is not true.

Hope it helps.

Do ask if you have any query.

~Silent~

Answer:

third one

Step-by-step explanation:

can you help me with my question In the extended simile of the underlined passage from Paragraph 15 of "A Wagner Matinee," the narrator makes an observation about the soul that aring rokol been A. it is like a strange moss on a dusty shelf that, with excruciating suffering, can wither and die y for I the be B though after excruciating suffering it may seem to wither, the soul never dies, C. excruciating, interminable suffering that goes on for half a century can kill the soul.

Laplace transforms are an essential mathematical tool used to solve differential equations. These transforms transform differential equations to algebraic equations that can be solved easily.

To solve the differential equations given in the question, we will use Laplace transforms. So let's start:Solution:a) y" – y = t y(0) = 1, y'(0) = 1First, we take the Laplace transform of the given differential equation.L{y" - y} = L{ty}

Taking the Laplace transform of both sides gives:L{y"} - L{y} = L{ty}Using the formula, L{y"} = s²Y(s) - s*y(0) - y'(0), and L{y} = Y(s) then we get:s²Y(s) - s - 1 = (1/s²) + (1/s³)Rearranging the above equation, we get:Y(s) = [1/(s²*(s² + 1))] + [1/(s³*(s² + 1))]Now, we apply the inverse Laplace transform to find the solution.y(t) = (t/2)sin(t) + (cos(t)/2)

The solution of the differential equation y" – y = t, with initial conditions y(0) = 1, y'(0) = 1 is y(t) = (t/2)sin(t) + (cos(t)/2).

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Answer:

what do you mean

Step-by-step explanation:

Answer:

9/6

Step-by-step explanation:

6 (4r + 3 ) : 8 (2 + 3r) + 2

6 (4r - 3r) : 8 ( 2 - 3) + 2

6 (r) : 8 (-1) + 2

6r : 8 + 1

6r : 9

r = 9/6

Answer:

i think it's c but I'm rly not sure on this one...

Answer:4,050

Step-by-step explanation:

The volume of the rectangular prism is 4050 centimeter cube

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

In geometry, a rectangular prism can be defined as a 3-dimensional solid shape which has six faces that are rectangles

Height of the rectangular prism =15 cm

Area of the base =270 centimeter square

Volume of the rectangular prism = Area of the base × Height

=270×15

=4050 centimeter cube

Hence, the volume of the rectangular prism is 4050 centimeter cube

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Answer:

2

Step-by-step explanation:

The basic annual salary of Martha is R576 000. She is entitled to an annual bonus of 90% of her basic monthly salary. Her employer contributes 8% of her basic salary to her pension fund. She works for 45 hours per week Martha's hourly recovery tariff for 17 March 2022 can be calculated by adding her monthly basic salary, bonus amount, and pension fund contribution, and dividing it by the total number of working hours in a year.

To calculate Martha's remuneration for 17 March 2022. It involves determining her basic monthly salary, annual bonus, pension fund contribution, and the number of working hours on that specific day. By combining these factors and using the given information, the hourly recovery tariff can be calculated.

To calculate Martha's remuneration for 17 March 2022, we need to consider her basic annual salary, annual bonus, pension fund contribution, and the number of working hours on that specific day.

Basic Annual Salary: R576,000

Annual Bonus: 90% of her basic monthly salary

Basic Monthly Salary = Basic Annual Salary / 12

Annual Bonus = Basic Monthly Salary * 90%

Pension Fund Contribution: 8% of her basic salary

Pension Fund Contribution = Basic Annual Salary * 8%

Number of Working Hours on 17 March 2022: Since it is not specified, we'll assume the standard working hours for that day, which is 8 hours.

Now, let's calculate Martha's remuneration for 17 March 2022:

Step 1: Calculate the Basic Monthly Salary

Basic Monthly Salary = Basic Annual Salary / 12

Step 2: Calculate the Annual Bonus

Annual Bonus = Basic Monthly Salary * 90%

Step 3: Calculate the Pension Fund Contribution

Pension Fund Contribution = Basic Annual Salary * 8%

Step 4: Calculate the Hourly Recovery Tariff

Hourly Recovery Tariff = (Basic Monthly Salary + Annual Bonus + Pension Fund Contribution) / (52 weeks * 45 hours per week)

Finally, substitute the calculated values into the formula to find the Hourly Recovery Tariff for Martha's remuneration on 17 March 2022.

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Answer:

294

Step-by-step explanation:

We will take our equation, and substitute in 7 for s, wherever we see it, so we have:

\(6 * 7^{2}\)

Simplifying, we have:

\(6 * 49\)

Which finally we multiply to:

6 * 49 = 294

So, your answer is 294.

Hope this helped!

The true proportion of the side lengths of the quadrilaterals is A'B'/AB

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

Quadrilaterals ABCD and A'B'C'D

These quadrilaterals are similar

So, it means that the corresponding side lengths are proportional

So. we have

Side length = AB

Corresponding side length = A'B'

The true proportion is then represented as

k = Corresponding side length/Side length

Substitute the known values in the above equation, so, we have the following representation

k = A'B'/AB

Hence, the proportion is A'B'/AB

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Answer:

Step-by-step explanation:

The inequality is x > 45.

This is so because the dot is not shaded which tells us that the value of x is not equal to 45.

Also, the direction of the arrow is going to the right on the positive side of the number line which means it's greater than 45.

Lisa's situation could be represented by just reversing the arrow on the above graph.

Hope this helps! :)

Answer:

The rule used to reflect Δ ABC to its image is Reflect over y = x ⇒ B

Step-by-step explanation:

From the given figure

∵ The coordinates of point A are (-4.5, 6)

∵ The coordinates of point A' are (6, -4.5)

→ The coordinates are switched ⇒ 3rd rule

∴ Point A is reflected over the line y = x

∴ Δ ABC is reflected over the line y = x

∴ The rule used to reflect Δ ABC to its image is Reflect over y = x

Note: Point B' on the graph should be C' and point C' should be B' (correct it)