Consider the variable coefficient linear second order non-homogeneous ODE x²+yⁿ – 2xy' + (x² +2)y = 3x³ for 1 > 0. 1. Write down the associated homogeneous equation.
2. Show that y₁(x) = x sin x and y₂(x) = xcosx soulutions of the associated homogeneous equation.
3. Use the Wronskian test to determine if y₁ and y₂ are linearly independent for x > 0.

The estimated probability that the sum of five dice will be 26 is 0.0053

Estimated Probability: Estimated probability is an approximation, or estimate, of theoretical probability. The larger the number of trials, the more accurate we expect this approximation to be. If E consists of a single outcome s, we refer to P(E) as the probability of the outcome s, and write P(s) for P(E)

N = Number of Repeated Process = 10,000

n = Number of times the sum of the five tosses equaled 26 = 53

The estimated probability that the sum of the five dice will be 26 = n/N

Where n = 53

And N = 10,000

Using the above formula, we have the following:-

n/N becomes

n/N = 53/10,000

n/N = 0.0053

Hence, the estimated probability that the sum of five dice will be 26 is 0.0053

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Answer: C. 28

Step-by-step explanation:

It is simple: x + 62°=90° (right angle)

Therefore, x=38

Answer:

B=28°

Step-by-step explanation:

X+62°=90°(right angle)

X=90°-62°

X=28°

Answer:

No, I think and yes.

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

no cap

If on january 1, year 1, billy co signed a three-year lease for office space The amortization expense on this leasehold improvement that Billy should  record for Year 2 is: $1,000.

Since we were told that the new overhead lighting fixtures is the amount of $2,000 now let determine the  Amortization expense using this formula

Amortization expense = New overhead lighting fixtures / 2 years

Let plug in the formula

Amortization expense =  $2,000 /2

Amortization expense = $1,000

Therefore the  Amortization expense  is the amount of $1,000.

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The complete question:

On January 1 , Year 1, Billy Co. signed a three year lease for office space. The lease required monthly rent of 8,000 for the first year. 8,100 for the second year and 8,200 for the 3rd year. Billy has the option to renew the lease for a fourth year at 8,300 per month. On January 1, Year 2, Billy permanently installed new overhead lighting fixtures at a cost of $2,000. How much amortization expense on this leasehold improvement should Billy record for Year 2?

True , Every matrix transformation is a linear transformation.

Is there a linear transformation for every matrix operation?

Despite the fact that every linear transformation is a matrix transformation, not all linear transformations are matrix transformations.      

                                    Because of this, it's possible that we'll encounter a linear transformation in which we're unable to locate a matrix to carry out the mapping.

What alteration does matrix entail?

In a two-dimensional or three-dimensional space, the transformation matrix converts one vector into another vector, which may be comprehended geometrically.

                                    Stretching, squeezing, rotation, reflection, and orthogonal projection are some of the often utilized transformations.

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The value of the angle 7 is 80 degrees. Option B

A transversal line can be defined as a line that intersects two or more lines at distinct points.

It is important to note that corresponding angles are equal.

Also, the sum of angles on straight line is equal to 180 degrees.

From the information given, we have that;

Angle 3 and angle 7 are corresponding angles

Also, we have that

Angle 3 and angle 4 are on a straight line

equate the angles

<3 + 100 = 180

collect the like terms

<3 = 180 - 100

<3 = 80 degrees

Then, the value of <7 is 80 degrees

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The man can expect the population standard deviation for his weekly grocery cost to lie between 16.96 to 25.33 with 95% confidence.

Solution:In this question, the following values are given:Mean x = $113.52Standard deviation s = $23.75Sample size n = 52a) Construct a 95% confidence interval for the population standard deviation σ.The formula for the confidence interval for the population standard deviation (σ) when the sample size is large is given below:$$\large (\sqrt{\frac{(n-1)s^2}{\chi^2_{\frac{\alpha}{2},n-1}}},\sqrt{\frac{(n-1)s^2}{\chi^2_{1-\frac{\alpha}{2},n-1}}})$$where, $\chi^2_{\frac{\alpha}{2},n-1}$ and $\chi^2_{1-\frac{\alpha}{2},n-1}$ are the chi-square critical values with degree of freedom (df) = n-1 at α/2 and 1-α/2 levels of significance respectively.Here, sample size n = 52 which is greater than 30. Thus, the distribution of the sample standard deviation (s) is approximately normal.

Now we need to find the critical values of chi-square which is shown below:Degrees of Freedom (df) = n-1 = 52-1 = 51Level of Significance, α = 1 - Confidence level = 1 - 0.95 = 0.05α/2 = 0.025 and 1-α/2 = 0.975Now, we will find the critical values using the chi-square table or calculator which are:$$\chi^2_{0.025,51} = 71.420$$and$$\chi^2_{0.975,51} = 32.357$$Using the above values, the 95% confidence interval for the population standard deviation (σ) can be calculated as follows:$$\large (\sqrt{\frac{(n-1)s^2}{\chi^2_{\frac{\alpha}{2},n-1}}},\sqrt{\frac{(n-1)s^2}{\chi^2_{1-\frac{\alpha}{2},n-1}}})$$$$\large (\sqrt{\frac{(52-1)(23.75)^2}{71.420}},\sqrt{\frac{(52-1)(23.75)^2}{32.357}})$$$$\large (\sqrt{\frac{(51)(23.75)^2}{71.420}},\sqrt{\frac{(51)(23.75)^2}{32.357}})$$$$\large (16.96, 25.33)$$Hence, the 95% confidence interval for the population standard deviation σ is (16.96, 25.33) with a sample standard deviation s=$23.75. The man can expect the population standard deviation for his weekly grocery cost to lie between 16.96 to 25.33 with 95% confidence.

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The values of x when f(z) = 3 are x = -2 and x = -8.

The two points on the graph  are (-2, 3) and (-8, 3).

The function f(x) = x^2 + 10x + 19 is given.

Let's find when f(a) = 3.

To find the value of x when f(a) = 3, we substitute f(x) = 3 into the equation:

3 = a^2 + 10a + 19

Rearranging the equation:

a^2 + 10a + 16 = 0

Now, we can solve this quadratic equation by factoring or using the quadratic formula.

However, upon inspection, we can see that the equation cannot be factored easily.

Hence, we will use the quadratic formula:

a = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = 10, and c = 16.

Substituting these values into the formula:

a = (-10 ± √(10^2 - 4(1)(16))) / (2(1))

Simplifying:

a = (-10 ± √(100 - 64)) / 2

a = (-10 ± √36) / 2

a = (-10 ± 6) / 2

So, we have two possible values for a: a = (-10 + 6) / 2 = -2 and a = (-10 - 6) / 2 = -8.

Therefore, the values of x when f(z) = 3 are x = -2 and x = -8.

Now, let's find two points that lie on the graph of f(x) using the values we found.

Substituting x = -2 into f(x), we get:

f(-2) = (-2)^2 + 10(-2) + 19 = 4 - 20 + 19 = 3

So, one point on the graph is (-2, 3).

Substituting x = -8 into f(x), we get:

f(-8) = (-8)^2 + 10(-8) + 19

f(-8) = 64 - 80 + 19 = 3

So, another point on the graph is (-8, 3).

Hence, the two points on the graph of f(x) are (-2, 3) and (-8, 3).

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The expected number of unaffected kittens should be 84

Find the below calculation of chi square:

Category   Affected Unaffected Total

Observed values   44                 84                 128

Expected Ratio         1                  3                   4

Expected Values, E  32             96

Deviation, D              12              -12

Deviation Squared     14            144

D^2/E                           4.5      1.5                  6

X^2                               6  

Degrees of freedom                       -                  1

Unaffected number of kittens:

Observed values for Affected=44

Total=128

25% of the 128 are affected.

The unaffected proportion is,

Total-Observed values for Affected kittens

=128-44

=84

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Answer:

8/3

Step-by-step explanation:

Divide 8/3

Answer:

Option D: 8/3

Step-by-step explanation:

(2 x 3 + 2)/3 = 2 2/3

(6 + 2)/3 = 2 2/3

8/3 = 2 2/3

The distance between the point A and B is 15 units.

The distance between two points can be found using Pythagoras's principle.

Point A is located at (7,4), and point B is located at (-8,4). Let's find the distance between point A and B as follows:

Therefore,

d = √(y₂ - y₁)² + (x₂ - x₁)²

Hence, using (7, 4) (-8, 4)

x₁ = 7

x₂ = -8

y₁ = 4

y₂ = 4

Hence,

d = √(4 - 4)² + (-8 - 7)²

d = √(0)² + (-15)²

d = √225

d = 15 units

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Answer:

The y-coordinates in quadrant IV are negative. Because y represents profit, negative values of y signify not making a profit. That is, negative values signify loss. The points in quadrant IV represent the baseball team losing money.

Step-by-step explanation:

I took the assignment :).

Answer:

The y-coordinates in quadrant IV are negative. Because y represents profit, negative values of y signify not making a profit. That is, negative values signify loss. The points in quadrant IV represent the baseball team losing money.

Step-by-step explanation:

Answer:

-17

Step-by-step explanation:

the patter is minus 5

3 - 5=-2

-2 - 5=-7  

-7 - 5=-12

-12 - 5=-17

Answer:

I dont see a

Step-by-step explanation:

Main answer: The majority of respondents who favored the legalization of marijuana identified as liberal or very liberal.

Supporting explanation: The table shows that out of the 486 respondents who favored the legalization of marijuana, 296 identified as liberal and 120 identified as very liberal. This means that 616 out of the 826 respondents who answered both questions identified as liberal or very liberal. On the other hand, only 60 respondents who favored the legalization of marijuana identified as conservative or very conservative. This suggests that there is a correlation between political leaning and views on the legalization of marijuana, with those on the left end of the political spectrum more likely to support it.

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There are 10 students on the school bus who sing in the chorus but do not play in the band.To determine the number of students on the school bus who sing in the chorus but do not play in the band, we can analyze the given information.

Let's break down the information provided:

To find the number of students who sing in the chorus but do not play in the band, we can use the principle of inclusion and exclusion. The principle states that the number of elements in the union of two sets is the sum of the number of elements in each set minus the number of elements in their intersection.

Total students on the school bus: 30

Students who play in the school band or sing in the chorus (combined): 24

Students who play in the school band only: 6

Students who sing in the chorus and play in the school band: 14

To find the number of students who sing in the chorus but do not play in the band, we need to subtract the number of students who both sing and play from the total number of students who sing.

Number of students who play in the band or sing in the chorus = Number of students who play in the band + Number of students who sing in the chorus - Number of students who play in the band and sing in the chorus

Total students who sing in the chorus: Students who play in the band and sing + Students who sing only

Students who sing in the chorus only = Total students who sing - Students who play in the band and sing

Students who sing in the chorus only = 24 - 14 = 10

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∠FED and ∠DEW are complementary because it is a sum of 90 degrees.

By the law of addition of complementary angles,m∠FED + m∠DEW = 90°

m∠FED + m∠DEW = m∠FEW by the Angle addition postulate.

By the substitution property of equality, m∠FEW = 90°.

The ∠FEW is a right angle by the definition of right angles.

Complementary Angles defined as angles that sum up to 90 degrees.

Now, we are given that;

∠FED and ∠DEW are complementary.

We want to prove that ∠FEW is a right angle. Thus;

∠FED and ∠DEW are complementary because it is a sum of 90 degrees.

By the law of addition of complementary angles, we can say that;

m∠FED + m∠DEW = 90°

Also,

m∠FED + m∠DEW = m∠FEW by the Angle addition postulate.

By the substitution property of equality, m∠FEW = 90°.

The ∠FEW is a right angle by the definition of right angles.

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The value of "m" represents the length of side G F in the kite F G H K. The value of "m" is 3.5. Given that sides G F and F K are congruent, we can conclude that their lengths are equal.

We are given that the length of side G H is 5 m 1 and the length of side H K is 3 m 7.

To find the value of "m," we need to find the length of side G F.

Since G F and F K are congruent, we can set up an equation:

5 m 1 = 3 m 7

To solve for "m," we need to subtract 3 m from both sides of the equation:

5 m - 3 m = 3 m - 3 m + 7

This simplifies to:

2 m = 7

Now, we can solve for "m" by dividing both sides of the equation by 2:

m = 7 ÷ 2

m = 3.5

Therefore, the value of "m" is 3.5.

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A ray has only one endpoint. A segment has two endpoints.

What is a line?

A line is an object in geometry that is infinitely long and has neither width nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional spaces, they are one-dimensional objects. In everyday language, a line segment with two points designating its ends is also referred to as a "line."

A ray and a segment are parts of a line.

This line segment has two fixed-length endpoints, A and B. The distance between this line segment's endpoints A and B is its length.

In other words, a line segment is a section or element of a line with two endpoints. A line segment, in contrast to a line, has a known length.

A line segment's length can be calculated using either metric units like millimeters or centimeters or conventional units like feet or inches.

Ray has only one endpoint and the other ends go infinity.

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Answer:

26 miles * 5280 ft/ 1 mile

Step-by-step explanation:

We know there are 5280 ft in 1 mile

26 miles * 5280 ft/ 1 mile

Answer:

C

Step-by-step explanation:

Answer:

11 unit

Step-by-step explanation:

Applying,

s = √[(y₂-y₁)²+(x₂-x₁)²]...................... Equation 1

Where s = length of the side formed.

From the question,

Given: x₁ = -2, x₂ = 9, y₁ = 5, y₂ = 5

Substitute these values into equation 1

s = √[(9+2)²+(5-5)²]

s = √(11²)

s = 11 unit.

Hence the length of the side formed by the vertices is 11 unit

The Volume of the rectangular prism with a length of 214 inches, width of 412 inches, and height of 5 inches is 443,280 cubic inches.

The volume of a rectangular prism, we multiply the length, width, and height of the prism. In this case, the given dimensions are:

Length (l) = 214 inches

Width (w) = 412 inches

Height (h) = 5 inches

The formula for the volume (V) of a rectangular prism is:

V = l * w * h

Substituting the given values into the formula:

V = 214 * 412 * 5

Calculating the product:

V = 44,3280

Therefore, the volume of the rectangular prism is 44,3280 cubic inches.

In summary, the volume of the rectangular prism with a length of 214 inches, width of 412 inches, and height of 5 inches is 443,280 cubic inches.

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Shirley is incorrect because regardless of how the expressions are grouped they would produce the same output or result.

In Mathematics and Geometry, the standard form for a difference of two (2) squares is modeled or represented by this mathematical equation:

a² - b² = (a + b)(a - b) or a² - b² = (a - b)(a + b).

Where:

a and b represent numerical values (numbers or numerals).

Based on the information provided, we have the following mathematical equation:

(x - 15)(x + 15) = x² + 15x - 15x - 225

(x - 15)(x + 15) = x² - 225

By rewriting the product, we have the following;

(x + 15)(x - 15) = x² - 15x + 15x - 225

(x + 15)(x - 15) = x² - 225

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Answer:

5 bouquets

4 roses 2 tulips 1 daisy

Step-by-step explanation:

Find a number that can be divided in to all the values given, that would be the number of groups or in this case bouquets you have. The number you get after you divide Ex: 20/5 is the amount in each group/bouquet

Answer:

The answer is C) 5x + 2y = 4

Step-by-step explanation:

Answer:

One of the earliest known humans is Homo-habilis, or “handy man,” who lived about 2.4 million to 1.4 million years ago in Eastern and Southern Africa.

The solution of the trigonometric equation is θ = π/6 radian

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles

2cosθ = √3

Divide both sides by 2:

cosθ = (√3)/2

θ = cos⁻¹[(√3)/2]

θ = 30°

Convert 30° to radian by multiplying it with π/180. That is:

θ = 30 × π/180

θ = π/6 radian

Thus, the solution is θ = π/6 radian

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