Find the general solution of the first-order linear differential equation y' - (ln x)y = 3 x^x.
y(x)=
Note: Use C for the arbitrary constant.

The 5th value is 15.5, and the 6th value is 15.7. The median is then (15.5 + 15.7)/2 = 15.6.

A Stem-Leaf plot is a graphical way to organize and summarize numerical data. It is composed of two columns, the stem and the leaf. The stem column contains the leading digits of the data values, while the leaf column contains the remaining digits.

For the given data set, the stem-leaf plot looks like this:

Stem  Leaf

14  8

15  2 8 5 7 9

16  0 1

To create this stem-leaf plot, the data values were first sorted in ascending order, and then the leading digits were placed in the stem column. The remaining digits were then placed in the leaf column, in increasing order. The key, 15|2=15.2, is an example of a data value from the set.

To calculate the median of the data set, we first need to find the number of values in the set. Since there are 10 values, the median will be the average of the 5th and 6th values.

The 5th value is 15.5, and the 6th value is 15.7. The median is then (15.5 + 15.7)/2 = 15.6.

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The three integers are 89,406, 89408 and 89410.

What are integers?

The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.

Let 'm' be a positive integer.

Then, 2m is an even integer ( as multiplying by 2 makes the number even)

So, 2m+2 is the next integer and 2m+4 is the next.

Now, we have three consecutive integers as 2m, 2m+2 and 2m+4.

We are given that twice the first integer added to the second is 2,68,220, this means

⇒2(2m) + (2m+2) = 2,68,220

⇒4m + 2m + 2 = 2,68,220

⇒6m + 2 = 2,68,220

⇒6m = 2,68,218

⇒m = 44,703

So, 2m = 89,406

2m+2 = 89408

2m+4 = 89410

Hence, the three integers are 89,406, 89408 and 89410.

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Step-by-step explanation:

We can prove without use of calculator.

Use exponent product rule:

[tex]a^{n+m} = a^{n}*a^{m}[/tex]

Rewrite with exponent power rule:

[tex](9*9*9*9)-(3^{2}*3^{2}*3^{2}*3)[/tex]

Since [tex]3^{2}=9[/tex], we can eliminate 3 pairs via subtraction, leaving us with:

[tex]9-3=6[/tex]

6 is divisible by 6.

Easy without calculator :)

Hope this helps.

The fixed point of the function f(x) = x^2 + 1 is c = 0.

f(x) = x^2 + 1

c = 0

To find the fixed point of the function f, we can set the equation f(x) = x^2 + 1 equal to x, since the fixed point is when f(x) is equal to x.

Therefore, we can solve for x by setting x^2 + 1 = x. Re-arranging the equation, we get x^2 - x + 1 = 0.

Using the quadratic formula, x = (-(-1) ± √(1 - 4(1)(1))/(2(1))

Simplifying this expression, x = (-1 ± √3)/2.

Since we are looking for a real number, we can eliminate the negative solution and set x = (1 + √3)/2.

Therefore, the fixed point of the function f is c = 0.

The fixed point of the function f(x) = x^2 + 1 is c = 0.

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The potential function for f(x,y) is given by f(x,y) = x^2 + y^2 + 2xy.

The potential function can be used to find the maximum value of f by taking the partial derivatives with respect to x and y, setting them equal to zero, and solving for the x and y values that correspond to the maximum. This will give the x and y values that will produce the maximum value of f.

To prove this, we can start by taking the partial derivatives of f(x,y), which are given by:

f_x = 2x + 2y

f_y = 2y + 2x

Therefore, the potential function for f(x,y) is equal to the integral of the partial derivatives with respect to x and y:

∫f_xdx + ∫f_ydy = x^2 + y^2 + 2xy

This shows that the potential function for f(x,y) is given by f(x,y) = x^2 + y^2 + 2xy.

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Complete question: What is the potential function for the function f(x, y) = x + y + xy?

The sentence into a mathematical equation is R = 160x

The sentence "The difference between a number and ten is four" can be translated into a mathematical equation as:

x - 10 = 4

To solve for x, we can add 10 to both sides of the equation. This will give us:

x - 10 + 10 = 4 + 10

x = 14

Therefore, the number is 14.

More generally speaking, we can say that the equation for this sentence is x - a = b, where a is the number we are subtracting (in this case 10) and b is the result of the subtraction (in this case 4). To solve for x, we add a to both sides of the equation, giving us x = a + b.

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Answer:

The distance that the baseball is from the pitching rubber, D, can be modeled using the equation:

D = V*t + 60.5

Where V is the horizontal velocity of the baseball in feet per second and t is the time in seconds that the baseball is in the air.

In this scenario, the baseball is thrown by the pitcher with a horizontal velocity of 132 feet/second, and then hit by the batter with a horizontal velocity of 141 feet/second. The baseball passes over the pitching rubber on its way out of the stadium and eventually passes over the center field fence, 450 feet away. So, the equation will be

D = (132+141) * t + 60.5

y = 30 ( 0.95 ) t y=30(0.95)^t y=30(0.95)t is an exponential decay function. Because 0.95 < 1 0.95<1 0.95<1. Therefore, 0.95 0.95 0.95 is the decay factor 1 − r 1-r 1−r.

What is meant by function ?

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Option A is correct i.e., Yes, the statement is an exponential function because the population decreases daily by a proportional rate.

Exponents in mathematics are usually defined as when a number or an expression is given a specific power. The number to which the power is assigned is multiplied power times itself to get the final value. It is depicted by raised symbol written beside the number or expression.

It is written as a∧b where a is the base and b is the power and is called b to the base a or a raised to bth power. An example of the same can be 2∧3= 2x2x2=8, [tex]a^{3}[/tex]=axaxa, etc.

There are some properties of exponents like

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The quantity of chlorine that has a 60% concentration is 310 ml.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given that,  60% chlorine solution must be mixed with an 18% chlorine solution to produce 542.5 mL of 42% solution

Let "x" be the quantity of chlorine that has a 60% concentration

So, the quantity of chlorine that has 18% concentration = 542.5 - x

thus, As per the given data expression formed as given below:

0.6 * x + 0.18 (542.5 - x) = 542.5 * 0.42

0.6x - 0.18x + 0.18 *542.5 = 542.5 *0.42

0.42x = 130.20

x = 310

therefore, the quantity of chlorine that has a 60% concentration is 310 ml.

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Answer:

9

Step-by-step explanation:

parenthesis

exponents

multiply

división

add

Subtract

do it in this order and it makes it 10 times easier

The linear combination of the general solution of system of equations is.

[tex]X=(7,-3,0)+S1(-2,0,1)\\[/tex].

A system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. A linear system in three variables determines a collection of planes The intersection point is the solution.

A linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results.

Write vector form of the equations, then the vector with variable can expressed as a linear combination of vectors on right sides.

[tex](x1,x2,x3)=(7-2S1,-3,S1)\\=(7,-3,0)+(-2S1,0,S1)\\\\=(7,-3,0)+S1(-2,0,1)[/tex]

So, the linear combination of vectors is.

[tex]X=(7,-3,0)+S1(-2,0,1)\\[/tex]

The complete question is,

the general solution to a linear system is given. express this solution as a linear combination of vectors.

x1=7-2S1

X2=-3

X3=S1.

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To determine how much effort the gas undergoes as it changes from its original condition to its final one, Nora and Bob utilize the area underneath the line separating the two states and the first rule of thermodynamics.

When a gas changes from its initial condition to its final state, Nora and Bob explain how to compute the work that is done. They talk about compressing gas, thus something is being done to the gas.

You suggest using the area under the line separating the final and initial states to calculate the work done as well as the application of the first equation of thermodynamics, q=w.

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Width of the rectangle is 14/3 feet.

Rectangle is a two dimensional figure which has four sides and four angles and all the angles are right angles.

Area of a rectangle = Length × Width

Length = 3/7 feet

Area = 2 feet²

Substituting in the equation for the area,

2 = 3/7 × Width

Width = (2 × 7) / 3

          = 14/3 feet

Hence the measure of width of the rectangle is 14/3 feet.

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S=72, P=108, Q=144, and R=36 are the degree measures for each quadrilateral angel.

Since the sum of all angles is 360.

∠S+∠P+∠Q+∠R=360

2y+3y+4y+y=360

10y=360

y=36.

Hence, we get ∠S=72, ∠P=108, ∠Q=144 and ∠R=36.

A polygon with four sides, four vertices, and four angles is called a closed quadrilateral. It is made by joining four non-collinear points together. In all cases, the inner angles of quadrilaterals add up to 360 degrees.

The fact that the sum of the interior angles is always equal to 360 degrees is a property shared by all of the above four-sided shapes. Each interior angle of a regular quadrilateral, such as a square, will be equal to: 90 degrees is 360/4.

They split in two directions. There are both regular and irregular quadrilaterals. The diagonals of a regular quadrilateral must cross each other and have four equal sides and angles. The only quadrilateral that meets all of these requirements is square

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Answer:

Jelly bean is 8 pound

Brach's variety is 4 pound

Step-by-step explanation:

jelly belly = x

brach's variety = y

5.99x + 3.99y = 63.88 _______(1)

x = 2y ______(2)

5.99x + 3.99y = 63.88

5.99(2y) + 3.99y = 63.88

11.98y + 3.99y = 63.88

15.97y = 63.88

15.97y/15.97 = 63.88/15.97

y = 4

Substitute y = 4 into equ 2

x = 2y

x = 2(4)

x = 8

Therefore, Steven bought 8 lb of jellybean and 4 lb of brach variety

The depth of snow in the yard one hour after the snow depth was 9 inches, obtained using the linear function used for finding the snow depth, D = 1.4·t + 3 is; 10.4

A linear function is a function that produces a straight line graph when plotted.

The function that can be used to calculate the depth of the snow D in inches is; D = 1.4·t + 3

Where;

D = The snow depth in inches

t = The time duration (hours)

The present depth of the snow = 9 inches

The depth of the snow one hour from now can be found as follows;

The function for the depth of the snow; D = 1.4·t + 3 is a linear function

Therefore, the slope, which is the coefficient of the input variable, t, when the coefficient of the output variable, D, is 1

Therefore, the slope = 1.4

The slope is the rate of change of the output variable D when the input variable increases by one unit

The slope therefore, indicates that the depth of the snow in the yard, increases by 1,4 inches per hour

If the depth of the snow is presently 9 inches, the depth of the snow 1 hour later is therefore; D = 9 inches + 1.4 inches = 10.4 inches

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If each code contains non-repeating digits there would be 720 possible gate codes.

What is a combination in mathematics?

Combination in mathematics is a way of selecting items from a set, without regard to the order in which they were chosen.

In your example, there are 10 possible digits (0-9) that can be used for each of the three numerical digits, but since the digits cannot repeat, the total number of possible gate codes is 1098 = 720. Since the "#" sign is not included in this calculation, the final answer is 720 possible gate codes.

Hence,  If each code contains non-repeating digits there would be 720 possible gate codes.

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The volumes of the hemisphere are (π/12)R³, 2π/3(R³) and π/3(R³)

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

x' + y' = R²

Using the disk method

Start by calculating the area of a single disk is given by the quarter circle of radius R in the first quadrant.

The area of the single disk is:

Area = π(R/2)²

The volume of the hemisphere using the disk method is given by:

V = ∫(π(R/2)² dx from 0 to R

This gives

V = (π/4) * ∫R^2 dx from 0 to R

Differentiate

V = (π/12)R³

Here, we first need to find the area of a single shell.

The area of the single shell is:

Area = 2πx * dx

The volume of the hemisphere using the single shell method is given by:

V = ∫(2π x * dx)dy from 0 to R

So, we have

V = 2π * ∫xdy*dx from 0 to R

Differentiate

V = 2π/3(R³)

Here, we can use any slicing method, such as slicing the hemisphere parallel to the y-axis.

The volume of the hemisphere using the general slicing method is given by:

V = ∫(π * (x^2) * dy) from 0 to R

So, we have

V = π * ∫(y^2)dy from 0 to R

Differentiate

V = π/3(R³)

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The mathematical sentence can be written as the equation below,

k + t = 11

Here we want to write the the mathematical sentence below:

"The sum of a number k and t is 11"

As an algebraic equation, so let's analyze each part of the mathematical sentence.

"sum" refers to an addition, in this case between two numbers represented by k and t, then we can write:

k + t

And that is equal to 11, then the equation will just be:

k + t = 11

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Transitivity: Assume that for some a, b, xRSy and yRSz, or xRaSy and yRbSz, exist. After that, aSRb, abbreviated as aSyRb. In light of the fact that SoR=RoS, we obtain aRSb, or, to use an example, aRcSb.

R and S should be two equivalence relations on X.

I want to demonstrate that the relationship RS is equivalent, but I am unable to demonstrate that it is transitive and reflexive.

regarding transitivity

There are random x and y with (x,y)RS, z with (x,z)R and (z,y)S, and what else?

Do I need to use R=S=S=R somewhere else?

As opposed to (x,y)R, I use the notation xRy. For some a, the term "xRSy" specifically refers to "xRaSy." Additionally, writing (xRy and yRz) is more convenient than writing xRySz. I would generally suggest drawing these relationships as graphs, with the vertices representing the points and the edges denoting the relationship.

assumption R=S=R.

Transitivity: Assume that for some a, b, xRSy and yRSz, or xRaSy and yRbSz, exist. After that, aSRb, abbreviated as aSyRb. In light of the fact that SoR=RoS, we obtain aRSb, or, to use an example, aRcSb. Then, as R,S are equivalence relations, xRcSz follows from xRaRcSbSz, and xRSz follows.

I'm sure you can now independently demonstrate reflexivity.

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∆AEC ≅ ∆AFC by reason of SAS. Thus, using CPCTC, we can prove that <AEC ≅ <AFC.

With the given information and the image attached below, we can state that the two triangles are congruent by SAS, and then go ahead to use the CPCTC to show that any of their corresponding parts are congruent as well.

The proof is given as:

Statement Reason

1. AB ≅ BC, AE ≅ FC 1. Given

2. AC ≅ AC 2. Reflexive property of congruence

3. <BAC ≅ <BCA 3. Base angles of isosceles ∆BAC

4. ∆AEC ≅ ∆AFC. 4. SAS

5. <AEC ≅ <AFC. 5. CPCTC

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Answer:

[tex]c > -1[/tex]

Step-by-step explanation:

[tex]2c-10 < 3c-9\\-10 < c-9\\-1 < c\\c > -1[/tex]

An absolute maximum point is where the function reaches its highest value.

A function may have more than one location (x values) or point (ordered pairs) where these values occur, but there can be only one absolute minimum value and one absolute maximum value (in a given closed interval).

A point where the function achieves its highest value is known as an absolute maximum point. Similar to this, an absolute minimum point is the location at which the function's maximum value is obtained.

Minimum refers to the bare minimum that can be done. For instance, if anything requires seven dollars as the minimum payment, you cannot make a payment of six or less (you must pay at least seven). More than the bare minimum is acceptable, but not less. Maximum refers to the greatest quantity of anything.

Therefore, the correct answer is option C) (3, h(3)) is neither an absolute maximum nor an absolute minimum.

The complete question is:

Suppose that h(x) is a continuous function and is defined for all x greater than or equal to 1. You are given that h(x) has critical points at x = 1, x = 3, and x = 5. If h'(x) is negative on the interval 1 < x < 3, positive on the interval 3 < x < 5, and positive on the interval x > 5, what can be said about the point (3, h(3))?

A) (3, h(3)) is an absolute maximum.

B) (3, h(3)) is an absolute minimum.

C) (3, h(3)) is neither an absolute maximum nor an absolute minimum.

d) Nothing can be determined about the point (3, h(3)).

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Picking a king from a deck of cards, swapping it out for a queen, then continuing. These occurrences would constitute Dependent events.

'What is dependent probability?'

A dependent variable is precisely what it sounds like, just like an independent variable. It is something on which other elements depend.

A test score, for instance, may be a dependent variable because it could vary based on a number of variables, including how much you studied, how much sleep you got the night before the test, and even how hungry you were. Typically, when attempting to establish a connection between two variables, the goal is to determine what causes the dependant variable to vary in the manner that it does.

Many people struggle to recall which variable is the independent variable and which variable is the dependent variable.

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The value of the missing length is 44.

Two or more triangles will be similar if on comparing their corresponding sides or measure of angles, some common properties can be observed. But when two or more shapes are similar, it do not imply that they are equal.

To find the value of the missing length, let the length LV be represented by s.

So that;

VN/ LN = NU/ MN

11/ (11 + s) = 8/ (24 + 8)

11/ (11 + s) = 8/ 32

cross multiply to have;

8(11 + s) = 11 *32

88 + 8s = 352

8s = 352 - 88

    = 264

s = 264/8

  = 33

Therefore, the missing length = 11 + 33

                        = 44

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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 19.37}}{\left( \cfrac{15}{100} \right)19.37} ~~ \approx ~~ 2.91[/tex]

The scientific method is a systematic set of method that scientists follow to gain information. we will explore how the scientific method is used in the study of nutrition.

To make the things simple, you might want to think of the scientific method as a pro way to ask questions and find answers. With this in mind, it makes sense that the stride of the scientific method starts when researchers ask questions.

For example, a research scientist might awe whether people who eat an apple a day visit their family doctor hardly times a year than those who do not eat apples.

The scientific method is a nice tool for analyzing nutrition. It has been used to set nutrition advice, understand how nutrients support health and learn how nutrition supports athletic account.

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10 number of hours khalil worked tutoring last week and 3 the number of hours khalil worked landscaping last week

given that

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a b indicates that an is smaller than b.

When a > b is used, it indicates that an is bigger than b.

A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities. Equivalence is not considered.

khalil is working two summer jobs, making $18 per hour tutoring

$9 per hour landscaping

last week khalil worked a total of 14 hours and earned a total of $180.

let x be number of hours khalil worked tutoring last week

y be the number of hours khalil worked landscaping last week

we can form equation by given information

x + y [tex]\leq[/tex] 13 - (1)

18x + 9y > 180 - (2)

the numbers that satisfy the above equations is (10,3)

10 number of hours khalil worked tutoring last week and 3 the number of hours khalil worked landscaping last week

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