2. The figure shows a small rectangle cut out of a big rectangle. Find the area of the shaded figure.
7 cm
8 cm
3 cm
3 cm
Area of the shaded figure:
Area of the shaded figure:
square centimeters

The differential equation of y'' + 3y' + 2y = 1/4+ex is

               [tex]y=c_{1} e^-^2^x+c_{3} e^-^x+4e^-^2^xln(4+e^x)+e^xln(4+e^x)[/tex]

The given differential equation is y'' + 3y' + 2y = 1/4+ex

As we are considering the LHS part looks like a Quadratic equation.

y''+3y'+2y=m²+3m+2

m²+3m+2=0 ---(1)

finding the roots for eq(1)

m²+2m+m+2=0

m(m+2)+1(m+2)

(m+2) (m+1)=0

m=-2,m=-1

Yc=C₁e⁻²ˣ+C₂eˣ   ----(2)

equation (2) is called a complementary function.

A complementary function is only one part of the solution to a linear, and autonomous differential equation.

An ordinary differential equation (ODE) defines the sum of a function and its derivatives. When the explicit functions y = f(x) + cg(x) form the solution, g is called the complementary function; f is the particular integral.

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The required solution of the given inequality 2x < 8 is x < 4.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given:

The given  inequality is

2x < 8

According to given question we have

Write inequality

2x < 8

Divide both sides by 2 we get,

x < 4

Therefore, the required solution of the given inequality 2x < 8 is x < 4.

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The line parallel to Line 1 which is given by the equation: −6y + 3x = 12 and passes through (−1, − 5) is written in slope intercept form as

\y = 0.5x - 4.5

A linear function consists of functions where the variables has exponents of 1. the relationship is expressed in the slope intercept form as below.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

The given equation is rewritten in slope intercept form as follows

−6y + 3x = 12

−6y = 12 - 3x

y = 1/2 x - 2

the slope is 1/2

equation of the line of slope = 1/2 passing through point (-1, -5) is calculated using the point slope formula which is

(y - y') = m(x - x')

(y + 5) = 1/2(x + 1)

y + 5 = 1/2 x + 1/2

y = 1/2 x + 1/2 - 5

y = 0.5x - 4.5

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25.6

The question is asking for the difference between 4000 compounded interest and 4000 with simple interest.

So simply calculate 4000 compounded by 8% per annum for 2 years:

4000(1+0.08)^2=4665.6

Now calculate 4000 with simple interest of 8% per annum for 2 years:

4000(1+0.08×2)=4640.

Now subtract the simple interest amount from the compounded amount:

4665.6-4640=25.6

Hope that helps :)

Under the translation (x, y) (x-2, y-3) via transformation, the translation image of (2, -6) is (0, -9)

A point, line, or geometric object can be changed in four different ways that are all collectively referred to as transformations.  Each change must be carried out, and you must be able to tell which transformations have been carried out. The function translation and transformation guidelines are: F (x) + b moves the function up by b units. The function is moved downward by f (x) b. The function is moved left b units by the formula f (x + b).

given

(2 , -6 )

under this (x, y) → (x-2, y-3)

( 2 - 2, -6 , -3 )

(0 , -9)

Under the translation (x, y) (x-2, y-3) via transformation, the translation image of (2, -6) is (0, -9) .

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Answer:

[tex]c = \sqrt{74}[/tex]

Step-by-step explanation:

To find the distance between the two, we will use the Pythagorean theorem ([tex]a^{2} + b^{2} = c^{2}[/tex]). To find a and b, we need to subtract the distances between the y coordinates and the x coordinates respectively. For the x coordinates, we have 8 - 1 = 7 units. For the y coordinates, we have 7 - 2 = 5. Plugging this into our equation gives us:

[tex]7^{2} + 5^{2} = c^{2}[/tex]

We will simplify our exponents:

[tex]49 + 25 = c^{2}[/tex]

Then adding them together gives us:

[tex]74 = c^{2}[/tex]

Then, we square root both sides giving us:

[tex]\sqrt{74} = c[/tex]

Then, we cannot simplify past this, since 74's prime factorization doesn't allow it. So, [tex]c = \sqrt{74}[/tex].

Hope this helped!

Answer:

The first one

sorry if I'm wrong

The fifth term of the binomial expansion is; 76545x³y⁴

We are given the algebraic expression as; (3x - 3y)⁷

To solve this problem, we will make use of Pascals triangle which is the triangular array of numbers that begins with 1 on the top and with 1's running down the two sides of a triangle. Each new number will lie between two numbers and below them, and its value is the sum of the two numbers above it. It is expressed as;

                                 1

                        1              1

                 1              2              1

            1            3             3           1

      1         4             6            4           1

   1       5         10           10          5          1

1     6        15         20          15         6        1

1   7      21        35          35         21       7        1

Using binomial expansion, we have;

(3x - 3y)⁷ = 1(3x)⁷(-3y)⁰ + 7(3x)⁶(-3y)¹ + 21(3x)⁵(-3y)² + 35(3x)⁴(-3y)³ ...... 1(3x)⁰(-3y)⁷

= 2187x⁷ - 15309x⁶y + 45927x⁵y² - 76545x⁴y³ + 76545x³y⁴ - 45927x²y⁵......

The fifth term here is; 76545x³y⁴

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Answer:

y = 1/3x

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

The slope = rise/run

Let's pick 2 points (0,0) (3,1), we see the y increase by 1 and the x increase by 3, so the slope is

m = 1/3

The y-intercept is located at (0,0)

So, our equation is

y = 1/3x

numbers are 20 and 30 or 30 and 20.

A statement that represents the equality between two mathematical expressions. An equation can have one variable or two variables.

sum of two numbers = 50

sum of their reciprocal = 1/12

what is the 2 numbers.

let, one number is X and the other number is Y

as per the given condition, sum of X and Y is 50

X + Y =50 ...... equation 1

again, sum of the reciprocal of X and Y = 1/12

1/ X + 1/ Y = 1/12 ..... equation 2

 (X + Y)/ XY = 1 /12

(X + Y)12 = XY...  equation 3

from equation 1, we can write, Y = 50 - X

putting this value of Y in the equation 3

12X + 12(50 - X) = X(50 -X)

12X + 600 - 12X = 50X - X²

X² - 50X+600= 0

from the formula for quadratic equation, X = [50 ±√ (50² - 4×600)] / 2×1

                                                         X = (50±10) / 2

                                    X = 30, 20

          Y = 50 -30 = 20

      Y = 50- 20 = 30

hence, the 2 numbers are 20 and 30.

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19/6 * 3+2, expression is equivalent to 19÷6•3+2

Expressions that are equivalent do the same thing even when they have distinct appearances.

When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

We may be given equations with algebraic expressions on both sides in some situations.

The two expressions on either side of the equation must be comparable in order for the equation to hold true for all values of the variable. F

Hence, 19/6 * 3+2, expression is equivalent to 19÷6•3+2

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On solving the provided question we can say that the Volume of the sphere with radius 11.2 in is 5885 .

A sphere is a geometrical entity that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is equal to r, and the provided point is its center.

characteristics of a sphere

The symmetry of a sphere is flawless.

A polyhedron is not a sphere.

Each point on the surface is equally spaced from the center.

There is no surface of centers on a sphere.

The mean curvature of a sphere is constant.

The breadth and circumference of a sphere are fixed.

Radius of sphere = 11.2 in

Volume = 4 pi r ^ 2 = 4 X 3.14 X 11.2 X 11.2 = 5885 .

Volume of the sphere with radius 11.2 in is 5885 .

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On solving the provided question we can say that the Volume of the sphere with radius 11.2 in is 5885 .

A sphere is a geometrical entity that resembles a two-dimensional circle in three dimensions. In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is equal to r, and the provided point is its center.

characteristics of a sphere

The symmetry of a sphere is flawless.

A polyhedron is not a sphere.

Each point on the surface is equally spaced from the center.

There is no surface of centers on a sphere.

The mean curvature of a sphere is constant.

The breadth and circumference of a sphere are fixed.

Radius of sphere = 11.2 in

Volume = 4 pi r ^ 2 = 4 X 3.14 X 11.2 X 11.2 = 5885 .

Volume of the sphere with radius 11.2 in is 5885 .

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Classifying  the scenarios as an observational study, an experiment, or a sample survey.

Scenario A: Counties in eastern Iowa that received either an above typical or below typical rainfall in a given year are compared in terms of corn production - observational study.

Scenario B: Eight students were chosen at random from the cafeteria and asked if their favorite sport was soccer- a sample survey

Scenario C: To determine which drug is most effective in treating the common cold, drug A or drug B, cold patients were randomly given one of the two drugs and the results were compared-  a sample survey.

Scenario D: To determine which hair growth treatment was most effective in regrowing hair, GrowHair or ReGain, participants were assigned a treatment to determine which showed the most new hair growth- experiment.

Scenario E: Students who were taught reading by two different methods are compared in terms of their reading standardized test scores  observational study.

Scenario F: Ten employees are randomly selected and asked whether they would be in favor of a new management position in their department- a sample survey.

Sample Survey can be defined as the way in which people are randomly choose or pick from a large population so as to draw or reach a conclusion.

Observational study is a type of research method in which  people are be observed before conclusion are drawn.

Experiment study is research method in which something is been  tested before conclusion are reach.

Therefore Scenario A: Counties in eastern Iowa that received either an above typical or below typical rainfall in a given year are compared in terms of corn production - observational study.

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Answer:

the patient would receive 375 mL of fluid in 3 hours.

Step-by-step explanation:

To calculate the amount of fluid a patient would receive in 3 hours, we can use the formula:

Flow rate (mL/hr) = Total volume (mL) / Time (hr)

Flow rate = 1000 mL / 8 hr = 125 mL/hr

To find the amount of fluid a patient would receive in 3 hours, we can use the formula:

Volume = Flow rate x Time

Volume = 125 mL/hr x 3 hr = 375 mL

So the patient would receive 375 mL of fluid in 3 hours.

To add 2 1/2 + 4/5 using a number line, we can start by marking off the whole numbers along the number line. Then, we can divide each whole number into equal parts to represent the fractions. For example, if we divide each whole number into fifths, we can mark off 2 1/5, 2 2/5, 2 3/5, etc.

After the above, the next thing is that we can find the point on the number line that represents 2 1/2 by starting at 2 and moving 1/5 of the way to the right. Similarly, we can find the point that represents 4/5 by starting at 4 and moving 1/5 of the way to the right.

Finally, to add the two numbers, we can simply move from the point that represents 2 1/2 to the point that represents 4/5. The final point we reach will be the sum of 2 1/2 + 4/5. In this example, the final point will be 3 3/10.

Therefore, 2 1/2 + 4/5 will be 3 3/10.

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In the above equation, swap out BD = 7x-10, BC = 4x-29, and CD = 5x-9.

BD = 88

BC = 27

CD = 61.

Given that BD is equal to 7x, BC is equal to 4x, and CD is equal to 5x,

It is evident from the above figure that Points B, C, and D are parallel. On line segment BD, point C is located.

BD = BC + CD

In the above equation, swap out BD = 7x-10, BC = 4x-29, and CD = 5x-9.

7x - 10 = (4x - 29) + (5x - 9)

When we combine similar phrases, we obtain

7x - 10 = (4x + 5x) + (-29 - 9 )

7x - 10 = 9x - 38

38 plus 38 on either side.

7x - 10 + 38 = 9x

7x + 28 = 9x

Take 7x away from both sides.

28 = 9x - 7x

28 = 2x

By 2, divide both sides.

14 = x

Consequently, x has a value of 14.

BD  = x - 10 = 7(14) - 10 = 88

88 units are BD's worth.

BC = 4x - 29 = 4(14) - 29 = 27

BC has a value of 27 units.

CD = 5x - 9 = 5(14) - 9 = 61.

The CD is worth 61 units.

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The approximate number of packets containing blades with no defective is :  9802

We are given the probability of defect per blade = 1/500 = 0.002

The general formula for Poisson distribution is;

Pₓ (k) = (x^k)/k × e⁻ˣ

Where;

k = The number of defective blades in a packet.

For a packet of 10 blades the mean number of defect is;

x = 0.002 × 10

x = 0.02

When there is no defective in a consignment, then it means k = 0

Thus;

Pₓ(0) = (0.02⁰ / 0!) × e^(-0.02) = 0.980199

The approximate number of packets containing blades with no defective is : 10000 × 0.980199 = 9802

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The value of -0.6675 for the correlation coefficient of X and Y indicates that there is a negative correlation between the two variables.

The correlation coefficient, denoted as p, is a measure of the linear relationship between two random variables X and Y. It is defined as the ratio of the covariance of X and Y to the product of their standard deviations:

p = cov(X,Y) / (stdDev(X) × stdDev(Y))

To compute the correlation coefficient, we need to first calculate the covariance and the standard deviations of X and Y.

Since the marginals pdfs of X and Y are the same, we know that the expected value (mean) of X is equal to the expected value of Y, which is denoted as Mu x = Mu y = A.

The expected value of XY is given as E(XY) = 2/5.

The covariance of X and Y is defined as E((X-Mu x )(Y-Mu y )), which simplifies to E(XY) - Mu x × Mu y

Substituting the given values, we have:

cov(X,Y) = E(XY) - Mu x × Mu y = 2/5 - A²

To calculate the standard deviation of X and Y, we need to calculate the variance first. The variance of X is defined as E(X²) - (Mu x )²,

which can be easily calculated by replacing x with y in fx(x) and applying the same formula.

The standard deviation is the square root of the variance, so we have:

stdDev(X) = √(variance(X)) = √(E(X²) - (Mu x )²)

stdDev(Y) = √(variance(Y)) = √(E(Y²) - (Mu y )²) = √(E(X²) - (Mu x )²)

Now we can substitute these values into the formula for p:

p = cov(X,Y) / (stdDev(X) × stdDev(Y)) = (2/5 - A²) / (√(E(X²) - (Mu x )²) × √(E(X²) - (Mu x )²)).

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Doing moves to keep an equation balanced is a powerful part of solving equations, but thinking about what the structure of an equation tells us about the solutions is just as iimportant

Sometimes it’s possible to look at the structure of an equation and tell if it has infinitely many solutions or no solutions. For example, look at

2(12x + 18) + 6 = 18x + 6(x + 7)

Using the distributive property on the left and right sides, we get

24x + 36 + 6 = 18x + 6x + 42

From here, collecting like terms gives us

24x + 42 = 24x + 42

Since the left and right sides of the equation are the same, we know that this equation is true for any value of x without doing any more moves!

Similarly, we can sometimes use structure to tell if an equation has no solutions. For example, look at

6(6x + 5) = 12(3x + 2) + 12

If we think about each move as we go, we can stop when we realize there is no solution

1/6 · 6(6x + 5) = 1/6 · (12(3x + 2) + 12) Multiply each side by 1/6

6x + 5 = 2(3x + 2) + 2 Distribute 1/6 on the right side.

6x + 5 = 6x + 4 + 2 Distribute 2 on the right side.

The last move makes it clear that the constant terms on each side, 5 and 4 + 2, are not the same. Since adding 5 to an amount is always less than adding 4 + 2 to that same amount, we know there are no solutions.

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Answer:

parallel

Step-by-step explanation:

solve for the second equation so y is by itself

y=-2x+3

their slopes are the same so they're parallel

The measure of angle S in ΔRST to the nearest degree is 44°.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know sine rule of a triangle ABC is, a/sinA = b/sinB = c/sinC.

Given, In ΔRST, m < R = 100°, r = 20, and t = 12.

Therefore,

r/sinR = t/sinT.

20/sin100° = 12/sinT.

20.30 = 12/sinT.

sinT = 12/20.3.

sinT = 0.59.

T = sin⁻¹(0.59).

T = 36°.

We know the sum of all the interior angles in a triangle is 180°.

Therefore, m∠R + m∠T + m∠S = 180°.

100° + 36° + m∠S = 180°.

m∠S = 180° - 136°.

m∠S = 44°.

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The expression, 5 ÷ 3, in standard form, would be 1. 67 x 10⁰.

For the purposes of representing large or small numbers in mathematics, a standard form of a number is essentially mentioned. To represent such numbers in standard form, we employ exponents.

It would be easier to understand the correct definition of standard form if you used decimal numbers and adhered to specific restrictions. As is well known, fractions are expressed more simply as decimal numbers.

Basically, in standard form, we try to ensure that only one digits is to the left of the decimal point and then to the right are the rest of the digits in the number. The position of the number is then reflected as a power of 10.

First, solve 5 ÷ 3 :

= 5 / 3

= 1. 667

The result already has only one number to the left of the decimal so the power of 10 would be 0:

= 1. 667 x 10⁰

This is because every number to the power 0, is 1 and so 1.667 x 10⁰ would be the same as 1. 667 x 1 which is correct.

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On solving the provided question, we can say that by percentage, 19.7% 0f female = 19.7/100 * 54 = 10.638

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

by percentage,

male = 2139

female  = 54

19.7% 0f female = 19.7/100 * 54 = 10.638

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The equation that represents the line that has a slope of 1/3 and an x-intercept of 5 is y - 0 = 1/3(x - 5). The correct option is b. y - 0 = 1/3(x - 5)

From the question, we ae to write the equation of a line that has the given slope and x-intercept.

From the equation for the point-slope form of a line,

y - y₁ = m(x - x₁)

Where m is the slope

and (x₁, y₁) is a point on the line

From the given information,

m = 1/3

and

The x-intercept is 5, that is, (5, 0)

Thus,

The equation of the line is

y - 0 = 1/3(x - 5)

Hence, the equation is y - 0 = 1/3(x - 5)

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Answer: 3

Step-by-step explanation: Whenever we have midsegment, the length of it is half of the base which is 30 so 5x =15.

The function shown in the graph is f(x)=3x-2.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

From the given graph let us take two points.

(0, -2) and (2,4)

m=6/2=3

Now let us find y intercept.

4=3(2)+b

4=6+b

-2=b

Hence, the function shown in the graph is f(x)=3x-2.

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The numeric values of each function at x = 3 are given as follows:

f(3) = 50.

g(3) = 10.

The division is given as follows: f(3)/g(3) = 5.

The space of f(x)/g(x) is given as all genuine values with the exception of x = - 7, as the function g(x), which is the denominator of the division, expects a worth of 0 at x = - 7.

To track down the numeric worth of a function or of articulation, we supplant each example of the variable in the function or in the articulation with the worth at which we need to track down the numeric worth.

Subsequently, the numeric values are found to supplant the solitary example of x by 3 in each function, as follows:

f(3) = 5(3) + 35 = 15 + 35 = 50.

g(3) = 3 + 7 = 10.

Subsequently, the division is given as follows:

(f/g)(3) = f(3)/g(3) = 50/10 = 5.

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For p = (3, 5), the value of - 3p is (- 9, - 15).

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

The values are,

⇒ p= (3, 5) and q = (-2, 10)

Now, We can find the value of - 3p as;

⇒ - 3 p

Substitute p = (3, 5) we get;

⇒ - 3 × (3, 5)

⇒ (3×- 3, - 3×5)

⇒ (- 9, - 15)

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Answer:

Step-by-step explanation:

In order to properly fit the website for Faria mobile devices such as tablets and smartphones, the company will need to make sure that the website is optimized for different screen sizes. The original website was designed for a screen dimension of 16" x 9", but mobile devices have varying screen sizes. The company can use the dimensions listed in the table to ensure that the website looks and functions properly on the five mobile devices they are researching.