Solve the differential equation by variation of parameters. y" + y = CSC X y(x) =sin(x)ln(|sin(x)|) + C2cos(x) + C1sin(x) + xcos(x)

The maximum number of oranges he can distribute to the ground would be = group C with a total of 115 oranges.

A maximum number is defined as the number that is equal to or greater than other values in a data set.

The various number of oranges distributed by Musa include the following:

Group A Students = 100 oranges

Remaining oranges from group A = 1

Total = 101 oranges

Group B students = 105 oranges

Remaining oranges from group B = 3

Total = 108 oranges.

Group c students = 110 oranges

Remaining oranges from group C = 115 oranges.

Therefore the maximum oranges he distributed was for group C which was 115 in total number.

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Population is the all 12th-grade students who took the National Assessment of Educational Progress year 2000 mathematics test. This can be solved using the concept of statistics.

Statistics is a discipline of applied mathematics concerned with the gathering, description, analysis, and derivation of inferences from quantitative data. Calculus of differential and integrals, linear algebra, and probability theory are key mathematical concepts in statistics.

Statistics provide us the knowledge we need to understand how things operate. To conduct research, assess results, foster critical thinking, and make wise judgements, statistics are utilized. Almost any subject of study may benefit from the application of statistics to explore the causes, timing, and predictability of events.

So, population is the all 12th-grade students who took the National Assessment of Educational Progress year 2000 mathematics test.

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A type II error in this context would be when the inspector incorrectly fails to reject the null hypothesis (H0), meaning they accept the null hypothesis that the humidity level absorbed is 3% when it is actually more than 3%.

A hypothesis test is a statistical procedure used to evaluate a hypothesis by using sample data. Brainly experts can use hypothesis tests to verify the accuracy of their answers by collecting sample data, analyzing it and making a conclusion. Hypothesis testing involves formulating a null and alternate hypothesis, generating a test statistic, and using the test statistic to make a decision. Brainly experts can use hypothesis testing to check the validity of their answers and to ensure that they are providing accurate information to their users.

This type of error would result in potentially hazardous components being approved for use and could lead to catastrophic accidents. In other words, if the inspector fails to reject H0 when it is false, it could lead to unsafe components being used and put the health and safety of people in danger.

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When Julie divides 98.6 by 12 , So by the rules of significant figures , the number that Julie should write down is  8.3  .

What are Significant Figures ?

The Significant figures can be defined as number of digits in a value, that is often a measurement, which contribute to degree of accuracy of value. The significant figures is counted from first non zero digit .

The Rule of Significant figures says that , when a number "a" that have 3 significant figures is divided by number "b" having 2 significant figures , then the quotient will have the minimum of the two significant figure that is 2 .

Here 98.6 is divided by 12 ,

the number 98.6 has 3 significant figures ; the number 12 has 2 significant figures ,

So , the result can have maximum of 2 significant figures ,

On dividing 98.6 by 12 , we get the result as 8.2166666..  ;

since the result can have at most 2 sig. figure , So , the result is 8.3 .

Therefore , Julie should write down 8.3   .

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If you want to make 1/2 the recipe, then [tex]1\frac{11}{16}[/tex] tablespoon of sugar you need.

In the given question, a recipe calls for [tex]3\frac{3}{8}[/tex] tablespoons of sugar.

If you want to make 1/2 the recipe, then we have to find how much sugar you need.

As given that;

1 recipe = [tex]3\frac{3}{8}[/tex] tablespoons of sugar

Before solving the question, we convert the mixed fraction into simple fraction.

To convert in simple fraction we multiply 3 by 8 then we add 3 on the result of multiplication of 3 and 8.

1 recipe = 27/8 tablespoons of sugar

We have to find sugar need for making 1/2 recipe.

1/2 recipe = [tex]\frac{27}{8}\times\frac{1}{2}[/tex] tablespoons of sugar

1/2 recipe = 27/16 tablespoons of sugar

1/2 recipe = [tex]1\frac{11}{16}[/tex] tablespoons of sugar

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The artist should divide the region with vertical lines at x1 = 0.5000, x2 = 0.7500 and x3 = 1.0000 to get 3 pieces with equal areas.

Let the length of the region be l. Then, the area of the region = l x l = l^2

To divide the region into 3 equal areas, let the 3 divisions be at x1, x2, and x3 such that x1 < x2 < x3.

Then, the area of each division = (x2-x1) x l = l x (x2-x1) = l^2/3

Therefore,

l x (x2-x1) = l^2/3

or, x2 - x1 = l/3

Using this equation, we can find the values of x1, x2, and x3 that divide the region into 3 equal areas:

x1 = 0, x2 = l/3 and x3 = 2l/3

Therefore, for the given region, the artist should divide it with vertical lines at x1 = 0.5000, x2 = 0.7500 and x3 = 1.0000 to get 3 pieces with equal areas.

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Answer:

14

Step-by-step explanation:

Answer:

We can start by multiplying the first equation by 3:

12x + 24y = 120

Then we can multiply the second equation by 4:

12x - 8y = 56

Now, we have:

12x + 24y = 120

12x - 8y = 56

If we subtract the first equation from the second equation:

32y = 64

y = 64/24

y = 2

Now that we know the value of y, we can substitute it back into one of the original equations to find the value of x.

Let's use the first equation:

4x+8(2) = 40

4x+16 = 40

4x = 24

x = 24/4

x =6

So, the solution of the system of equations is x = 6, y = 2.

Answer:

68823600

Step-by-step explanation:

Using linear functions, we have that:

a) The equation for the line is: y = -500x + 5000

b) The prediction is 2250 sales with a price of $6.50.

The equation of a line is given by:

y = mx+ b

In which

Item a:

In this problem:

[tex]m = \frac{1500-2500}{7-5} = - \frac{1000}{2} = -500[/tex]

Thus:

y = -500x + b

Point (5,2500) means that when x=5, y = 2500, which we use to find b.

y = -500x + b

⇒2500 = -500* (5) +b

⇒2500 = -2500 +b

⇒b = 2500 +2500

⇒b = 5000

Thus

y = -500x + 5000

∴The equation for the line is: y = -500x + 5000

Item b:

y = -500*(6.5) + 5000

y = 2250

The prediction is 2250 sales with a price of $6.50.

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We can conclude the sample obtained is an SRS because the final sample was obtained by simple random sampling. not an SRS because the first sample was not balanced between men and women

an SRS?

the leader of a student organization wishes to form a committee that will consist of 5 of the 50 members.

he decides to take an SRS of size five from the members and those selected will comprise the committee.

he chooses an SRS of size five and all are men.

he would like to have some women on the task force, so he decides to take another SRS.

this time there are three women and two men in the sample, so he decides these five will form the committee.

we can conclude the sample obtained is an SRS because the final sample was obtained by simple random sampling.

an SRS because all members had the same chance of being in the final sample.

not an SRS because a sample consisting entirely of men is not allowed.

not an SRS because the first sample was not balanced between men and women.

we can conclude the sample obtained is an SRS because the final sample was obtained by simple random sampling. not an SRS because the first sample was not balanced between men and women.

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Answer:

SohCahToa

Step-by-step explanation:

Answer: 17

Step-by-step explanation:

First, change everything to ascending order.

14, 15, 16, 17, 18, 20, 25

Now, select the middle number, in this case, it is 17.

To find the median of a data set, you must put the numbers in order from least to greatest and find the middle (center) number.

The following data set: 16, 14, 15, 18, 17, 20 and 25 can be organized into the following order: 14, 15, 16, 17, 18, 20, 25.

Now, simply find out the middle number.

17 is the middle number, therefore the median.

1 is the quantity cosine of x to the power of two plus sine of x to the power of two divided by quantity cotangent of x to the power of two minus cosecant of x to the power of two

The given expression is as follows

(cos^2(x) + sin^2(x))/(cot^2(x) - csc^2(x))

This expression is equal to 1, because of the identity cos^2(x) + sin^2(x) = 1.

Cosecant is the reciprocal of sine, so csc^2(x) = 1/sin^2(x)

Cotangent is the reciprocal of tan, so cot^2(x) = 1/tan^2(x)

As tan^2(x) = sec^2(x) - 1, we can write the expression as:

1/(1/sin^2(x) - (sec^2(x) - 1))

Further on  simplifying this using the identity sec^2(x) = 1/cos^2(x) we get:

1/(1/sin^2(x) - (1/cos^2(x) - 1))

The denominator is now:

1/((sin^2(x) - cos^2(x))/cos^2(x)sin^2(x))

on Using the identity sin^2(x) + cos^2(x) = 1 we can simplify this as:

1/(cos^2(x)sin^2(x))

Canceling out the sin^2(x) and cos^2(x) we get 1

therefore  the final answer is 1.

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[tex]\displaystyle\\Answer:\ c.\ \frac{y-b}{x}[/tex]

Step-by-step explanation:

Given:  y=mx+b

y-b=mx+b-b

y-b=mx

Divide both parts of the equation by x:

[tex]\displaystyle\\\frac{y-b}{x}=m\\ Thus,\ m=\frac{y-b}{x}[/tex]

The number of ways in which we can choose four members of the club to serve on the executive committee is 12650 ways.

The act of placing all the components of a set into a certain sequence or order is known as permutation in mathematics. In other terms, the process of permuting is the reordering of the elements of a set if the set is already ordered. Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method.

Given that the total number of members in the club is 25.

To choose four executive members for the committee we use the formula of combinations given as follows:

[tex]nCr = \frac{n!}{(n-r)! r!}[/tex]

Substituting the value of n= 25 and r = 4:

[tex]25C 4 = \frac{25!}{(25 -4)! 4!}\\\\\\25C 4 = 12650\\[/tex]

Hence, the number of ways in which we can choose four members of the club to serve on the executive committee is 12650 ways.

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Each tray will have 18 pieces after they have been cut to the same size.

To find the number of pieces on each tray after they have been cut to the same size, we need to find the least common multiple (LCM) of 3, 6, and 9. This will give us the smallest number of pieces that all three trays can be divided into without any remainder.

The LCM of 3, 6, and 9 is 18. This means that all three trays can be divided into 18 equal-size pieces without any remainder.

So, each tray will have 18 pieces after they have been cut to the same size. It is important to note that this is the smallest number of pieces that all three trays can be divided into, and any larger number would also work.

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The complete question is -

One tray of granola bars was cut into 3 equal-size pieces. A second tray was cut into 9 equal-size pieces, and a third was cut into 6 equal-size pieces. Jan wants to continue cutting until all three trays have the same number of pieces. How many pieces will there be on each tray?

Elasticidad es la forma de recobrar la forma original (banda elástica), dureza es la capacidad de resistir el rayado (mesa), permeabilidad es la propiedad de dejar pasar un liquido (camiseta) y tenacidad es la capacidad de resistir fuerzas.

Esta es una propiedad de un material que se puede definir como la capacidad de mantener su forma original o recobrar la forma después de una fuerza. Algunos ejemplos son cauchos, bandas elásticas, una licra.

Se refiere a la propiedad de un material para resistir el rayado y el corte. Materiales como los metales tienen esta propiedad, otro ejemplo de esto es una mesa pues no es fácil cortar o rayar la misma.

Se refiere a la capacidad de un material para permitir el paso de líquidos especialmente agua, por ejemplo una camiseta es muy permeable pero una bolsa de plástico no lo es.

Se refiere a la capacidad de resistencia si se somete el material a fuerzas. Un serrucho tiene gran tenacidad pues a pesar de someterlo a fuerza mecánica este la resiste.

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The sample space is given as: S = { MEV, MEH, MSV, MSH, AEV, AEH, ASV, ASH }

The total number of sample points is 8

A sample point is one of the experiment's potential outcomes in a probabilistic experiment. Sample space is the collection of all sample points.

There are two results when you toss a coin: head (H) or tail (T) (T). There are four possible results when tossing two coins: HH, HT, TH, and TT, where the first letter denotes the result of the first toss and the second, that of the second. Each result is referred to as a sample point.

The list of all potential outcomes of an experiment is referred to as the sample space. Regardless of the number of ways an event might occur, each potential result is represented by a single point in the sample space.

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So on solving the provided question we cans say that  sides of a square are given as 18 units, area = 324 cm sq.

A square is an equilateral quadrilateral with four equal sides and four equal angles according to Euclidean geometry. It is also known as a rectangle with two neighboring sides that have the same length. Having all four equal sides and all four equal angles, a square is an equilateral quadrilateral. 90 degree or straight angles are square angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. a neighboring rectangle with two equal sides. a quadrilateral with four right angles and four sides of equal length. a parallelogram having two adjacent, equal sides that form a right angle. straight-sided rhombus.

here,

sides of a square are given as 18 units

so area will be s^2 18*18 = 324 cm sq.

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Answer: .

Step-by-step explanation:

67.002 - 67.020 - 67.200

Answer:

67.002, 67.020, 67.200

Step-by-step explanation:

I think this is the answer

We can see that the vertices, ko vertices and foci are related by the formula c2=a2+b2. This formula can also be rewritten as b2=c2-a2. This relationship is used to describe the equation given the coordinates of the hyperbolic foci and vertices.

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Answer: For the first geometric sequence, the missing value is:

1 = -3/2, -2 = 7

To find the missing value, we can use the formula:

an = ar^(n-1)

Where a1 is the first term, r is the common ratio, and n is the term number.

So we know that:

a1 = 1, r = -3/2, n = 3

Plugging these values into the formula:

an = ar^(n-1)

an = 1 * (-3/2)^(3-1) = 1 * (-3/2)^2 = 1 * 9/4 = 9/4

So the missing value is 9/4.

For the second geometric sequence, the missing value is:

2 = 6, 7 = 192

To find the missing value, we can use the formula:

an = ar^(n-1)

Where a1 is the first term, r is the common ratio, and n is the term number.

So we know that:

a1 = 2, r = 7/6, n = 11

Plugging these values into the formula:

an = ar^(n-1)

an = 2 * (7/6)^(11-1) = 2 * (7/6)^10 = 2 * (7/6)^10 = 2 * 7^10 / 6^10 = 9261

So the missing value is 9261.

Step-by-step explanation:

Answer:  X or Y

Step-by-step explanation:

So, the fractional part of the regular passengers that are adult is 0.9404 or 94.04%.

We know that the cruise ship has 2,400 regular passengers, and that 120 of them are children and 23 are teenagers. To find the fractional part of the regular passengers that are adults, we need to subtract the number of children and teenagers from the total number of regular passengers.

First, add the number of children and teenagers: 120 + 23 = 143

Then, subtract this number from the total number of regular passengers: 2,400 - 143 = 2,257

This is the number of adult passengers. To find the fraction of adult passengers, divide the number of adult passengers by the total number of regular passengers and convert the result to a fraction.

2,257/2,400 = 0.9404

So, the fractional part of the regular passengers that are adult is 0.9404 or 94.04%.

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The quadrilateral is parallelogram, When the vertices of quadrilateral ABCD are given.

A parallelogram is a two-dimensional shape that has a pair of two parallel and congruent sides. It is the simplest type of quadrilateral that has opposite sides equal and parallel.

The opposite angles of a parallelogram are also equal and the sum of two consecutive angles is always supplementary. It has two unequal diagonals.

A point always represents the location of a particular place or position in a standard cartesian system, and the coordinates of the point represent the distances from the respective coordinate axis.

For example, consider a point P(x,y), in which the coordinates x and y are the perpendicular distances from the x-axis and the y-axis respectively.

The formula to find out the distance between two points is generally known as the Distance formula which can be expressed as:

d=√(x₂−x₁)²+(y₂−y₁)²

Given:

The vertices of the quadrilateral

A B C D: A(-2,3),B(-5,7),C(3,6), D(6,2).

The measure of the sides of the quadrilateral

d=√(x₂−x₁)²+(y₂−y₁)²

AB=√(-5-(-2))²+(7-3)²

Ab=√(-3)²+4²

AB=√25

AB=5units.

BC=√(3+5)²+(6-7)²

BC=√(8)²+1²

BC=√65 units.

CD=√(6-3)²+(2-6)²

CD=√3²+4²

CD=√25

CD=5 units.

AD=√(6-(-2))²+(2-3)²

AD=√(-8)²+1²

AD=√65 units.

The diagonals:

BC=√(3+5)²+(6-7)²

BC=√(8)²+1²

BC=√65 units.

AC=√(3+2)²+(6-3)²

AC=√(5)²+3²

AC=√25+9

AC=√34 units

Here, AB=CD and BC=AD and AC≠BC

Thus, the given quadrilateral is parallelogram.

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Jack's working is incorrect. To correctly find the product of 25 x 14.2 without a calculator, he should have used the distributive property of multiplication.

First, he should have broken down 25 into 20 and 5, which are easier numbers to multiply mentally. Then, he should have multiplied 14.2 by 20 to get 284, and 14.2 by 5 to get 71.

Finally, he should have added these two intermediate results, 284 and 71, to get the final answer of 25 x 14.2 = 355.

A correct working would be:

20 x 14.2 = 284

5 x 14.2 = 71

25 x 14.2 = 284 + 71 = 355

Therefore, Jack's final answer is incorrect, the correct answer is 355.

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The answer of 21 tracks is accurate since, once the membership cost has been paid, the store charges $1.50 by each song. Since the monthly charge is a one-time expense, it is deducted from the $50 price cap.

The characteristic that every input is associated to approximately one output defines a function as a relationship between a series of inputs but a set of allowable outputs. A mapping from Here to there B will only be a function if every piece in set A has one end and only the image in set B. Let A & B have been any two non-empty sets.

The number of songs that may be downloaded with the specified budget is then calculated by dividing the remaining balance by the price of each song. The outcome is an analytic sequence because each song's price is set. The outcome is then rounded down to the closest whole number, which in this example is 21.

1. Take the $50 budget and deduct the $18 membership fee:

$50 - $18 = $32

2. Take the leftover amount and divide it by the price of each song:

$32 ÷ $1.50 = 21.33

3. To the nearest full number, round down:

21 songs

As a result, you may purchase 21 tracks for $50.

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The three (3) true statements about the quadratic function and its graph include the following:

A. The value of f(–10) = 82

B. The graph of the function is a parabola.

D. The graph contains the point (20, –8).

Generally speaking, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. For this quadratic function, the graph is a upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero.

Next, we would determine the other true statements about the graph of this quadratic function:

At point (-10, 82), we have:

Quadratic function, f(x) = 1/5 x² – 5x + 12

Quadratic function, f(x) = x²/5 – 5x + 12

Quadratic function, f(-10) = -10²/5 – 5(-10) + 12

Quadratic function, f(-10) = 82

At point (20, -8), we have the following:

Quadratic function, f(x) = 1/5 x² – 5x + 12

Quadratic function, f(x) = x²/5 – 5x + 12

Quadratic function, f(20) = 20²/5 – 5(20) + 12

Quadratic function, f(20) = -8

In conclusion, we can logically deduce that the graph of this quadratic function does not contain the point (0, 0) as shown in the image attached below.

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Complete Question:

Consider the quadratic function f(x) = 1/5x² – 5x + 12. Which statements are true about the function and its graph? Select three options.

The value of f(–10) = 82

The graph of the function is a parabola.

The graph of the function opens down.

The graph contains the point (20, –8).

The graph contains the point (0, 0).

So on solving the provided question we can say that [tex]\sqrt{2} , \sqrt{18} \\[/tex], [tex]5.\sqrt{5} \\[/tex] none of them are rational number.

Any number that can be expressed as a ratio (or fraction) of two integers is said to be rational. A rational number is a fraction that has a nonzero denominator. 1/2, 1/5, and 3/4 are examples of rational numbers. Additionally a rational number, "0" may be expressed in a variety of ways, including 0/1, 0/2, and 0/3. However, 1/0, 2/0, 3/0, etc. The number seven is logical. When two integers are divided, the result is known as a rational number. Divide the whole number 7 by the whole number 1 to obtain the rational number 7. Since two integers may be divided to yield 7, it is known as a rational number.

here, we have

[tex]\sqrt{2} , \sqrt{18} \\[/tex]

[tex]5.\sqrt{5} \\[/tex]

none of them are rational number

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A cone with slant height 21 m and radius 4 m has a total surface area of 100 π m.

What is a cone?

A cone is a shape created by connecting the points on a circular base to a common point, known as the apex or vertex, using a series of line segments or lines (which does not contain the apex).

The formula for curved surface area of cone is = πrl

The formula for total surface area of cone is = πrl + πr²

The slant height value l = 21 m

The diameter is given d = 8 m

The radius is given as r = 4 m

The total surface area is -

TSA = πrl + πr²

TSA = πr (l + r)

TSA = π4 (21 + 4)

TSA = 4 π (25)

TSA = 100 π m

Therefore, the total surface area is 100 π m.

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