Find a solution of the following ODE.
xy" - 3y' + xy = 0 (y = x^2u)
Find a solution of the following ODE. xy" – 3y' + xy = 0 " - (y = x²u) =

The value of x must be between -18 and -6. The solution has been obtained using Triangle inequality theorem.

What is Triangle inequality theorem?

The triangle inequality theorem explains how a triangle's three sides interact with one another. This theorem states that the sum of the lengths of any triangle's two sides is always greater than the length of the triangle's third side. In other words, the shortest distance between any two different points is always a straight line, according to this theorem.

We are given three sides of a triangle as 8, 6 and x+20

Using Triangle inequality theorem,

⇒8+6 > x+20

⇒14 > x+20

⇒-6 > x

Also,

⇒x+20+6 > 8

⇒x+26 > 8

⇒x > -18

Also,

⇒x+20+8 > 6

⇒x+28 > 6

⇒x > -22

From the above explanation it can be concluded that x is less than -6 but greater than -22 and -18.

This means that x must lie between -18 and -6.

Hence, the value of x must be between -18 and -6.

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Using sample standard deviation formula and the provided sample mean value, The test statistic are $8,080(sample mean) and 125 (sample standard deviation).

Large-scale numerical data collection and analysis, especially with the aim of extrapolating proportions in the total from those in a representative sample.

A population is the entire set of people in a group, whether that group is a country or a collection of people who share a certain trait.

A sample is a condensed, controllable representation of a larger group. It is a subgroup of people with traits from a wider population. When population sizes are too big for the test to include all potential participants or observations, samples are utilized in statistical testing.

Sample mean= $8,080

population standard deviation= $1,000

number of sample=64

sample standard deviation = \(\frac {1000}{\sqrt {64}}\)

=1000/8

=125

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Answer:

x>2

Step-by-step explanation:

first you collect like terms together so ,

u bring 5x to the other side to be 2x+5x-3>11 ,

you take -3 to the other side to be 2x+5x>11+3

therefore it will be 7x>14 ,so you divide both sides with 7 to get

x>2

Answer:

Step-by-step explanation:

Solving in steps

If the assumption for using the chi-square statistic, which specifies the number of frequencies in each category, is violated, the researcher has a few options to address this issue:

1. Combine categories: If some categories have very low expected frequencies, they can be combined with adjacent categories to increase the expected frequencies. This helps to meet the assumption of having a minimum expected frequency in each category.

2. Recategorize data: The researcher can also recategorize the data by collapsing categories or creating new categories that have more balanced frequencies. This can help to ensure an adequate number of observations in each category.

3. Use alternative statistical tests: If the assumptions for using the chi-square statistic cannot be met, the researcher can consider using alternative statistical tests. For example, if the data have a small sample size or violate the assumption of expected frequencies, Fisher's exact test or Monte Carlo simulation can be used as alternatives.

It is important for the researcher to carefully consider the specific circumstances and consult with a statistician to determine the most appropriate approach when the assumptions for using the chi-square statistic are violated.

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The total surface area of the cube is 150 square units.

A cube is a three-dimensional solid object that has six square faces, where each face is perpendicular to the adjacent face, and all faces are of equal size. It is a regular polyhedron, which means all its faces are congruent regular polygons, and all its edges are congruent. A cube has 12 edges, eight vertices, and six faces. The distance from one vertex to the opposite vertex, passing through the center of the cube, is called the diagonal of the cube. The length of the diagonal is equal to the square root of three times the length of one side of the cube. A cube is a fundamental shape in geometry and is commonly used in mathematics, architecture, and engineering.

The cube has 6 square faces, each with an area of (5 units)^2 = 25 square units. Therefore, the total surface area of the cube is:

6 x 25 = 150 square units

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The cube has 6 square sides, each of which is \((5\ units)^{2} =25\) square units in total. As a result, the cube's entire surface area is: 150 square units.

A cube is a solid three-dimensional object with six square sides that are all of the same size and perpendicular to one another. Since it is a regular polyhedron, all of its sides and edges must be congruent regular polygons. Eight vertices, six sides, and twelve edges make up a cube.

The diagonal of the cube is the distance traversing the centre of the cube from one vertex to the opposing vertex. The square root of three times the length of one cube side is equivalent to the length of the diagonal. A cube is a basic geometric shape that is frequently used in engineering, building, and mathematics.

The cube has 6 square sides, each of which is \((5\ units)^{2} =25\) square units in total. As a result, the cube's entire surface area is:

150 square units.

6 x 25 = 150 square units

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Answer:

325.58

Step-by-step explanation:

so im not good at explaining but JUST their DINNER costed $262.57. so you also have to ADD TAX because everything has tax so to find the 4% sale tax you need to set up the equation 262.57 x .04 (which is 4%). you will get 10.50 if you round. now you need to ADD TIP which is 20%. so to find that you need to do 262.57 x .20 (which is 20%). you will get 52.51. so now take BOTH 52.51 and 10.50 and ADD them. when you get this you also add it to the 262.57 and it gets you to 325.58

The probability of drawing a queen first and then a heart second without replacement is 1/51.

In this case, the probability of drawing a queen first and then a heart second is:

P(Queen and Heart) = P(Queen) * P(Heart | Queen)

The probability of drawing a queen first is 4/52, since there are 4 queens in a standard deck of 52 cards. The probability of drawing a heart second, given that a queen has already been drawn, is 13/51, since there are 13 hearts in the deck and now only 51 cards remaining after the first draw.

Therefore, the probability of drawing a queen first and then a heart second without replacement is:

P(Queen and Heart) = (4/52) * (13/51) = 52/2652 = 1/51

So the probability of drawing a queen first and then a heart second without replacement is 1/51.

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The value of f(5)(0) for the given Maclaurin series is -1/750.

The Maclaurin series for a function f(x) is given by the formula:

f(x) = Σn=0 to infinity [f^(n)(0) / n!] x^n

where f^(n)(0) is the nth derivative of f evaluated at x=0.

In this case, we are given the Maclaurin series for the function f(x) as:

f(x) = x * Σn=1 to infinity (-1)^n (1 / (x^n * 3n^2 * (n+5)))

To find the 5th derivative of f(x) evaluated at x=0, we need to differentiate the series 5 times and then evaluate it at x=0.

f(1)(x) = Σn=1 to infinity (-1)^n (1 / (x^(n-1) * 3n^2 * (n+5)))

f(2)(x) = Σn=1 to infinity (-1)^n * (n-1) / (x^n * 3n^2 * (n+5))

f(3)(x) = Σn=1 to infinity (-1)^n * (n-1) * (n+2) / (x^(n+1) * 3n^2 * (n+5))

f(4)(x) = Σn=1 to infinity (-1)^n * (n-1) * (n+2) * (n+7) / (x^(n+2) * 3n^2 * (n+5))

f(5)(x) = Σn=1 to infinity (-1)^n * (n-1) * (n+2) * (n+7) * (n+12) / (x^(n+3) * 3n^2 * (n+5))

Substituting x=0, we get:

f(5)(0) = Σn=1 to infinity (-1)^n * (n-1) * (n+2) * (n+7) * (n+12) / (0^(n+3) * 3n^2 * (n+5))

Simplifying the denominator, we get:

f(5)(0) = Σn=1 to infinity (-1)^n * (n-1) * (n+2) * (n+7) * (n+12) / (3n^2 * (n+5))

To evaluate this series, we can use partial fraction decomposition and then use the formula for the sum of the series 1/n^2.

After simplifying, we get:

f(5)(0) = -1/750

Therefore, the value of f(5)(0) is -1/750, which is option (C).

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Answer:

3/40

Step-by-step explanation:

Walter and Denise ordered a dessert to share at a restaurant. If Denise ate 1/8 of the dessert and Walter ate 4/5 of the dessert, what fraction of the dessert was left over?

Let the total dessert be represented as = 1

The fraction of the dessert left over =

1 - (4/5 + 1/8)

Lowest Common Denominator = 40

1 - (4 × 8 + 1 × 5/40)

1 - (32 + 5/40)

1 - 37/40

Lowest Common Denominator = 40

40 × 1 - 37 × 1/40

40 - 37/40

= 3/40

Therefore, the fraction of dessert that is left over = 3/40

Answer:

x=32

Step-by-step explanation:

Answer: x= -1 y= 13, x = 0 y= 10, x=4 y= -2

Step-by-step explanation:

Answer:

this makes no sense

Step-by-step explanation:

The number that when multiplied by 3, equals the sum of the number and 5 is 2.5.

First assume that the number we are looking for is x.

One side of the equation will be:

= 3 × x

= 3x

The other side of the equation would be:

= 5 + x

Equating these numbers gives:

3x = 5+ x

3x - x = 5

2x = 5

x = 5/ 2

x = 2.5

In conclusion, the number is 2.5.

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Answer:

Step-by-step explanation:

Given the population of yeast modelled by the function f(t)=a/1+be^-0.7t where t is measured in hours.

If at time t = 0 the population is 20 cells, then the equation becomes:

20 = a/1+be^-0.7t

20 = a/1+be^-0.7(0)

20 = a/1+be^-0

20 = a/1+b(1)

a/1+b = 20

a = 20(1+b) ........ equation 1

Also if the population is increasing at a rate of 12 cells/hour, then d(f(t)/dt = 12

Differentiate the expression with respect to time

f(t)=a(1+be^-0.7t)^-1

d(f(t)/dt =

a{-(1+be^-0.7t)^-2×(-0.7be^-0.7t)

a{-(1+be^-0.7t)^-2×(-0.7be^-0.7t) = 12

0.7abe^-0.7t/(1+be^-0.7t)² = 12 ..... equation 2

at t = 0, the equation becomes

0.7abe^-0/(1+be^-0)² = 12

0.7ab/(1+b)²= 12

0.7ab = 12(1+b)²

Substitute 1 into 2

0.7×20(1+b)b = 12(1+b)²

14(1+b)b = 12(1+b)²

Divide both sides by 1+b

14b = 12(1+b)

14b = 12+12b

14b-12b = 12

2b = 12

b = 6

Substitute b= 6 into the equation a = 20(1+b) to get a.

a = 20(1+6)

a = 20×7

a = 140

For us to be able to determine what happens to the yeast population in the long run. we will take the limit of f(t) as t approaches infinity.

Lim t -->/infty a/1+be^-0.7t

= a/1+be^-(infty)

= a/1+b(0)

= a

Since a = 140, hence the population of the yeast tends to 140 on the long run

The correct answer is not given in the options.

To find the values of c and d, we can use the formula for the inverse of a 3x3 matrix:

A^-1 = 1/det(A) x [adj(A)],

where det(A) is the determinant of matrix A and adj(A) is the adjugate matrix of A.

First, we need to find the determinant of matrix A:

det(A) = 1(1 x 4 - (-2)(0)) - 0(1 x 4 - 0(-2)) + 0(1 x 1 - 0(0)) = 4.

Next, we need to find the adjugate matrix of A, which is the transpose of the matrix of cofactors of A:

adj(A) = [{begin{array}{cc} 4&0&2 \ 0&4&0 \-2&0&1 \end{array}\right].

Therefore, we have:

A^-1 = 1/4 x [{begin{array}{cc} 4&0&2 \ 0&4&0 \-2&0&1 \end{array}\right)]

Multiplying out, we get:

A^-1 = [{begin{array}{cc} 1&0&1/2 \ 0&1&0 \-1/2&0&1/4 \end{array}\right)]

Comparing this with the given formula for A^-1:

A^-1 = 1/6(a^2 + cA + dI)

We can see that the diagonal elements of A^-1 correspond to the values of dI, so d = 1/4.

Also, the (1,3) entry of A^-1 corresponds to the value c in cA, so c = 2 x 6 = 12.

Therefore, the correct answer is not given in the options.

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Answer:

then there won't be a fair enough poll

Step-by-step explanation:

I think but at least  I tried

If the student council decides to randomly sample 5% of the student body instead of 10%, they may receive less reliable feedback about the theme they have chosen.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

If the student council decides to randomly sample 5% of the student body instead of 10%, the sample size would be smaller.

A smaller sample size may lead to less accurate or representative results.

In other words, the feedback received from the 5% sample may not be as reliable as the feedback from the 10% sample.

The smaller sample size may not capture the diversity of opinions within the student body, and the results may be more susceptible to chance variation.

Therefore, if the student council decides to randomly sample 5% of the student body instead of 10%, they may receive less reliable feedback about the theme they have chosen.

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Answer:

x=15°,  ∠A=75°,  ∠B=60°,  ∠C=45°

Step-by-step explanation:

As we know that sum of the angle of a triangle is 180°

Therefore ∠A+∠B+∠C=180°

                5x+4x+3x=180°     {  ∵ ∠A=5x   ∠B=4x ∠C=3x   }

              ⇒   12x=180°

              ⇒      x=15°

Hence ∠A=5x=5×15°=75°

           ∠B=4x=4×15°=60°

and      ∠C=3x=3×15°=45°

to verify your answer 75°+60°+45°=180°

Answer:

The solution is 8

The length of PQ in terms of MO if ∠POQ = 120° is PQ = -x * √3/3.

Let MO = x.

Since MO is perpendicular to plane α, MP and MQ form right angles with MO.

Using the Pythagorean Theorem, we have:

MP = x * tan(30°) = x * √3/3

MQ = x * tan(60°) = x * √3

Since ∠POQ = 120°, we have:

PQ = MP * 2 * cos(120°)

= 2 * x * √3/3 * -1/2

= -x * √3/3

Therefore, the length of PQ in terms of MO is PQ = -x * √3/3.

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EXPLANATION

Since the vertex is at (-1, -3), the only appropriate option is to translate the function one unit to the left, and again translating 3 units down, with the following form:

g(x) = |x+1| - 3

Therefore, the solution is the last option.

Answer: it’s actually -285

Step-by-step explanation: took test

The negative angle equivalent to a 75 angle is -285 angle.

We are given a 75 angle and we need to find a negative angle that is equivalent to the 75 angle.

A negative angle is defined as an angle generated in a clockwise direction from its given base.

We have a 75 angle which is in an anti-clockwise direction from the base AB as shown in the figure.

Now we will draw an angle in a clockwise direction from the base AB such that the angle reaches angle 75 which means it is equivalent to angle 75

We have,

Adding the angle from base AB till angle 75.

90° + 90° + 90° + 15° = 285°

Since the angle is measured in a clockwise direction we have,

285° =  - 285°

The negative angle equivalent to a 75 angle is -285 angle.

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Of the 180 students in a college course, of the 4 1 students earned an a for the course, of the students 3 earned a b for the course, and the rest of the students earned a c for the course. So, 136 students earned a C for the course.

To find the number of students who earned a C in the course, we'll follow these steps:

1. Determine the total number of students in the course.
2. Find out how many students earned an A and how many earned a B.
3. Subtract the number of A and B students from the total to find the number of C students.

We are given that there are 180 students in the course. It is also mentioned that 41 students earned an A and 3 students earned a B.

Now let's perform the calculations:

Step 1: We know that the total number of students is 180.

Step 2: We need to find the combined number of A and B students. We are given that 41 students earned an A, and 3 students earned a B. So, to find the total number of A and B students, we simply add these two numbers:

41 (A students) + 3 (B students) = 44 (A and B students)

Step 3: To find the number of C students, we subtract the total number of A and B students (44) from the total number of students (180):

180 (total students) - 44 (A and B students) = 136 (C students)

So, 136 students earned a C for the course.

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Answer:

I think 144.44 is the answer

Answer:

58.4

Step-by-step explanation:

To find the circumference of a circle, multiply the diameter by pi.

\(circumference=\pi d\)

In this case, the diameter is 18.6, and 3.14 is the substitute for pi.

\(18.6*3.14=58.404\)

\(58.404\) ≈ \(58.4\) (nearest tenth).

Answer:

to find the least common denominator list out the multiples of both denominator until you find the smallest multiple that is shared by both

4: 4,8,12,16,20,24,28,32,

7:14,21,28,35,

because 28 is the first shared multiple of 4 and 7,it most be the least common denominator for these two fractions.

Step-by-step explanation:

hope its help po

Answer:

Below.

Step-by-step explanation:

You can find this by first finding the prime factors of the numbers.

For example, find the LCD of 12 and 16:

12 = 2 * 2 * 3

16 = 2 * 2 * 2 * 2

There are 2 pairs of 2's in the list so only 2 of these four are included in the calculation. All other factors are included.

The LCD is:

2 * 2 * 2 * 2 * 3

= 16*3

= 48.

Find the LCD of  3 and 6

6 = 2 * 3

3 = 3

- so only one of the 3's is included:

LCD = 2*3 = 6.

The measure of RS to the nearest hundredth is 23.09 m

From the given figure, we have the following parameters

Adjacent to <R = RS

hypotenuse = 20cm

Using the theorem;

cos theta = opp/hyp

cos<R = RS/20
cos 30 = RS/20
RS = 20/cos30

RS =23.094 m

Hence the measure of RS to the nearest hundredth is 23.09 m

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