The graphs below have the same shape. What is the equation of the blue graph?

The general solution of the differential equation is [tex]& y=\sqrt{\frac{x}{2+c x^5}}[/tex].

The general solution of the following differential equation is [tex]$\quad 3 x^2 y^{\prime}+6 x y=15 y^3$[/tex].

The differential equations which are represented in terms of (x,y) such as the x-terms and y-terms can be ordered to different sides of the equation (including delta terms). Thus, each variable after separation can be integrated easily to find the solution of the differential equation. The equations can be written as:

solution: [tex]$\quad y^{\prime}=\frac{d y}{d x}$[/tex]

So rewritten question as

[tex]$$\begin{aligned}& 3 x^2 \frac{d y}{d x}+6 x y=15 y^3 \\& \frac{d y}{d x}+\frac{6 x y}{3 x^2}=\frac{15 y^3}{3 x^2} \\& \frac{d y}{d x}+\frac{2 y}{x}=\frac{5}{x^2} y^3\end{aligned}$$[/tex]

compare equation (1) with Bernoulli's Equation

[tex]$$\begin{aligned}& \frac{d y}{d x}+P(x) y=Q(x) y^n \\& P(x)=\frac{2}{x} \quad Q(x)=\frac{5}{x^2} \\& n=3\end{aligned}$$[/tex]

Substitute:

[tex]v & =y^{1-n} \\v & =y^{1-3} \\v & =y^{-2} \\y \quad y & =v^{(-1 / 2)}-(2) \\\frac{d y}{d x} & =-\frac{1}{2}\left(v^{-\frac{1}{2}-1}\right) \frac{d v}{d x}\end{aligned}$$[/tex]

[tex]\frac{d y}{d x}=-\frac{1}{2} v^{-3 / 2} \frac{d v}{d x}[/tex]

substitute value of y and [tex]$\frac{d y}{d x}$[/tex] from 4 (2) and (3) respectively in equation (1)

⇒[tex]& \frac{-1}{2} v^{-3 / 2} \frac{d v}{d x}+\frac{2}{x} \cdot v^{-1 / 2}=\frac{5}{x^2} \cdot v^{-3 / 2}[/tex]

⇒[tex]& \frac{d v}{d x}-\frac{4}{x} v=\frac{-10}{x^2} \\[/tex]

⇒ Integrating factor[tex]=e^{\int-4 / x d x} \\[/tex]

[tex]& =e^{-4 \ln x} \\& =e^{\ln x^{-4}} \\& =x^{-4} \\& =\frac{1}{x^4} \\[/tex]

⇒[tex]\frac{1}{x^4} v=\int \frac{1}{x^4} \times \frac{-10}{x^2} d x \\[/tex]

[tex]& =-10 \int x^{-6} d x \\[/tex]

[tex]& =+10 \frac{x^{-6+1}}{(-6+1)}+C=\frac{+10^2}{+8} x^{-5}+C \\&[/tex]

⇒[tex]\frac{1}{x^4} \cdot v & =\frac{2}{x^5}+c \\[/tex]

⇒[tex]v & =\left(\frac{2}{x^5}+c\right) x^4 \\[/tex]

⇒[tex]v & =\left(\frac{2}{x}+c x^4\right)[/tex]

Now replace v=y-2

⇒[tex]& y^{-2}=\frac{2}{x}+c x^4 \\[/tex]

⇒[tex]& y=\left[\frac{1}{\left(\frac{2}{x}+\left(x^4\right)\right.}\right]^{1 / 2} \\[/tex]

⇒[tex]& y=\sqrt{\frac{x}{2+c x^5}}[/tex]

Therefore, the general solution of the differential equation is [tex]& y=\sqrt{\frac{x}{2+c x^5}}[/tex].

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Answer:

Below

Step-by-step explanation:

Vertical angles are equal so    8x+3 = 9x-2

                                                     x = 5 °

Since they are equal, if they each are 45° they are complementary ( which means they add to 90°)

8x + 3   = 8 ( 5) + 3   = 43 °    <===== so they are NOT complementary !

The value of x is 21.

The question above can be written:

2x-6=36, then simplified the equation

2x=36+6

2x=42

x= 21

Mathematical models are used to simplify problems so that they are easy to understand. Therefore, a mathematical model is a model that represents a problem with a system that reflects relationships between symbols or mathematical relationships.

A mathematical model is a form of human interpretation in translating or formulating existing problems into mathematical forms, so that these problems can be solved using mathematics.

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The probability of getting 1 spade card when we take two cards out randomly of a deck of cards is 1/4.

By dividing the entire number of possible outcomes by the total number of possible events, the probability is determined.

Probability and odds are two distinct ideas.

To calculate chances, divide the likelihood of an event by the likelihood that it won't occur.

Mathematicians investigate probability, which may be broken down into four primary categories: axiomatic, classical, empirical, and subjective.

So, we know that:
There are 13 spades in the deck of 52 cards.

Then use the probability formula which is as follows:

P(E) = Favourable events/Total events

P(E) = 13/52

P(E) = 1/4

Therefore, the probability of getting 1 spade card when we take two cards out randomly of a deck of cards is 1/4.

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The mixture used 13.125 pounds of peanuts and 21.875 pounds of cashews to produce 35 pounds of the mixture.

Let x = the number of pounds of peanuts used in the mixture

Let y = the number of pounds of cashews used in the mixture

We can set up the following equation to solve for x and y:

2.25x + 3.25y = 2.65(x + y)

We can rearrange the equation to solve for x:

2.25x + 3.25y - 2.65x - 2.65y = 0

0.6x - 0.6y = 0

x = 0.6y

Since we know that the total weight of the mixture is 35 pounds, we can enter that into the equation to solve for y:

0.6y + y = 35

1.6y = 35

y = 21.875 pounds of cashews

x = 0.6(21.875) = 13.125 pounds of peanuts

Therefore, the mixture used 13.125 pounds of peanuts and 21.875 pounds of cashews to produce 35 pounds of the mixture.

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Answer:

D

Step-by-step explanation:

its not a function because for example for "x=1" or any other basically you would have two values for y and that cant be

Answer:

484 ft²​

Step-by-step explanation:

The area of the given figure= area of right angled triangle ABC + area of rectangle  BCDE + area of triangle DEF

=1/2 * base*height+ length*height+ 1/2*base*height

here base of triangle is equal to height of triangle ABC

=1/2*8*22+22*16+1/2*22*4

=484 ft²​

Answer:

10.44

Step-by-step explanation:

part(p)=%*whole

so 58% * 18 = 10.44 or .58 * 18 = 10.44

Using  probability, the possible PINs with 5 digits if digits can be repeated are 3125.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. The fundamental ingredient of probability theory is an experiment that can be repeated, at least hypothetically, under essentially identical conditions and that may lead to different outcomes on different trials.

Given that, The PIN has 5 digits, the digits can be repeated.

The number of possible PINs are 5⁵

= 5 * 5 * 5 * 5 * 5

= 3125

the possible PINs with 5 digits if digits can be repeated are 3125.

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Answer:

(−3.6)y − 4

Step-by-step explanation:

2/5 y − 0.2y − 6 + (−2)

= (2/5 y − 0.2y) − (6 + (−2))

= (2/5 y − 0.2y) − 4

= (2/5 y − 4) − 0.2y

= (2/5 y − 0.2y) − 4

= (2/5 − 0.2)y − 4

= (−3.6)y − 4

The Sum of interior angles is, 2160°.

The sum of the exterior angles of a 14-sided polygon is 360°

Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three internal angles. Interior angles are sometimes defined as "angles confined in the interior area of two parallel lines when they are crossed by a transversal."

Given:

A polygon with 14 sides.

The Sum of interior angles = (n - 2) × 180°

= 12 x 180

= 2160°

The sum of the exterior angles of a 14-sided polygon is 360°

Therefore, all the required values are given above.

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The ratio of the area of circle A to the area of circle B is 9:1

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, the ratio of the circumference of circle A to the circumference of circle B is 3:1. What is the ratio of the area of circle A to the area of circle B

The circumference of circle = 2π × radius

We have,

Circumference(A) / Circumference(B) = 3 / 1

Let the radius of A be R and that of B be r,

2πR / 2πr = 3/1

R/r = 3

R = 3r

Now, the area of a circle = π × radius²

Area(A) = πR²

= π(3r)² = 9πr²

Area(B) = πr²

Ratio of the area of circle A to Circle B = 9πr² / πr²

= 9/1

Hence, the ratio of the area of circle A to the area of circle B is 9:1

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The linear function is 8.50x + 5.50 and a $5.50 delivery fee would be included in the price of each hoodie purchased.

Part 1

The linear function rule is used in cases with only one shipping charge.

= 8.50x + 5.50, where x is the number of sweatshirts and y is the total cost in dollars.

Part 2

The linear function rule would be y = 8.50x + 5.50x = 14x, where y is the total cost in dollars and x is the number of sweatshirts if the shipping fee is applied to each sweatshirt. This implies that the $5.50 delivery fee would be included in the price of each hoodie purchased.

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Answer:

y = 20x +22

Step-by-step explanation:

Based on the word problem "I am thinking of a fraction that is equivalent to 2/5 and the numerator is 18 less than the denominator." Eric's fraction is 12/30.

Generally speaking, a fraction comprises two (2) main parts and these include the following:

Next, we would translate the word problem "I am thinking of a fraction that is equivalent to 2/5 and the numerator is 18 less than the denominator." into an algebraic expression as follows;

n/(n + 18) = 2/5

By cross-multiplying, we have:

5n = 2(n + 18)

5n = 2n + 36

5n - 2n = 36

3n = 36

n = 36/3

n = 12.

Now, we can determine the fraction as follows;

n/(n + 18) = 12/(12 + 18)

n/(n + 18) = 12/30.

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Complete Question:

Eric has a riddle: "I am thinking of a fraction that is equivalent to 2/5 and the numerator is 18 less than the denominator." what is his fraction?

Using the graphical methods [online graph calculator], the domain of (fx) = (x-3)/7x is given as All real numbers except 7/2 and 0.

(−∞,0)∪(0,7/2)∪(7/2,∞),

{x∣∣x∣≠0,7/2}

A relation's domain and range are defined as the sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively.

here, we have,

y=(x^2+7x+12)/(2x^2-7x)

by solving, we get, domain as,

(−∞,0)∪(0,7/2)∪(7/2,∞),

{x∣∣x∣≠0,7/2}

Graphs may also be used to determine the domain and range of functions. The domain of a graph consists of all the input values represented on the x-axis since the domain refers to the set of potential input values. The range is the collection of potential output values represented on the y-axis.

Notice as indicated in the graph that the coordinates or ordered pairs plotted DO NOT go through the origin which is zero. Also notice that the curved lines, extend to all real numbers on the grapy to infinity.

Hence stated as a mathematical expression, the domain would be:

a domain of all real numbers except 7/2 and 0

(−∞,0)∪(0,7/2)∪(7/2,∞),

{x∣∣x∣≠0,7/2}

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The correct answer is option 1. The version of the sample variance where you divide by n is biased.

This is because dividing by n will produce a biased downward population variance estimate. We must divide by n-1 rather than n to correct this bias. Mathematically, this can be expressed as:

Population Variance = s2 = ∑ (x - μ)2 / n Sample Variance = s2 = ∑ (x - x(bar))2 / (n-1)

In other words, we must subtract 1 from the sample size in the denominator when calculating the sample variance. This is due to the fact that the sample variance and the sample mean are both unbiased estimators of the population variance, respectively.

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Complete Question:

which of the following statements is true?

group of answer choices

Answer: A. 2.7

Step-by-step explanation:

Answer: 2.7

2 7/10 = 27/10 = 2.7

= Hence, Proved that 2.7 = 2 7/10

The figures below are similar.  By using this, the perimeter of the smaller rectangle P₂ = 3 cm.

When applying a scale factor, similar shapes are enlarged versions of one another. All of the corresponding angles and lengths in related shapes are equal and in the same ratio.

We divide the length of the enlarged shape by the length of the original shape to calculate the length scale factor.

The ratio of perimeter of both shapes is same as the ratio their corresponding side.

Given that one side of shape 1 is 4 cm and its perimeter P₁ is 12 cm.

and the corresponding side of shape 2 is 1 cm.

comparing the sides and perimeter of both shapes we get

4cm/1cm = 12cm/P₂

by cross multiplication we get,

4 * P₂ = 12cm * 1

P₂ = 12cm/4

P₂ = 3cm

So the perimeter of the smaller rectangle P₂ = 3 cm.

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Here you have 31 integrated circuits, each with a probability of 0.04 of being defective is 0.3428

If only one of them is defective, then the electronic product doesnt work.

Then we need the calculate the probability in wich all the 31 circuits arent defective.

the probability for each one to not be defective is 1 - 0.04 = 0.98

And if i want to see the probability for all of them to work fine, then i need to do the product of all the probabilities, this is multiply 0.98 53 times, or:

rounding to the four decimal place, we have: 0.3428

Wich is a kinda small probability for our product to work.

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The value of 8 in the number is 800million

Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one's position.

For example the place place value of 4 in 400 is 4 hundred. Place value starts with unit, tens hundreds, thousands, ten thousands, hundred thousands , million, ten million, 100million e.t.c

The place value of 8 in the number is 8 hundred million. This means 800,000.

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Answer:

The standard form is  [tex]\boxed{3n^4m^2}[/tex] .

The coefficient is [tex]\boxed{3}[/tex]

Step-by-step explanation:

What is Standard Form of Polynomial?

The standard form of a polynomial is a way of writing a polynomial such that the term with the highest power of the variables comes first followed by the other terms in decreasing order of the power of the variable

We are given the expression

[tex]\dfrac{2}{3}m^2n \cdot 4.5 n^3\\\\[/tex]

and we have to convert to standard form

First multiply the constants together to get the coefficient:

[tex]\dfrac{2}{3} \cdot 4.5 = \dfrac{2 \cdot 4.5}{3} = \dfrac{9}{3} = 3[/tex]

There is only one m term which is m²

Multiply the two n terms to get [tex]n \cdot n^3 = n^(1 + 3} = n^4[/tex]

Therefore in standard form we get ( in decreasing order of exponents)
[tex]3n^4m^2[/tex]

The coefficient is 3

The measure angle EBF is (5b-24)°.

Adjacent angles are those angles that are always placed next to each other in such a way that they share a common vertex and a common side but they do not overlap each other.

Give that, m∠ABF =(7b-24)° and m∠ABE =2b°.

From the figure,

m∠ABF =m∠ABE + m∠EBF

(7b-24)°=2b° + m∠EBF

m∠EBF = 7b-24-2b

m∠EBF = (5b-24)°

Therefore, the measure angle EBF is (5b-24)°.

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The correct statement is :David started at 0 instead of 2

A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, plotting a point.

Given here: In a number line the interval (-5,5) is marked and 2 to 5 is 3

The right steps are

Add 3 to 2 to obtain the required number as there are 3 spaces between 2 and 5

Thus 2+3=5 which is the required answer

but David addes 2-3=-1 which is incorrect.

Hence, David started at 0 instead of 2

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The point of intersection is (1.82, 1.45).

The equations of the two lines are:

y = 0.8x and y = -2.5x + 6.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of a line is given by:

y = mx + c

From the graph,

Take two coordinates from each line.

One line:

(0, 0) and (2.5, 2)

m = (2 - 0) / (2.5 - 0)

m = 2/2.5

m = 0.8

(0, 0) = (x, y)

0 = 0.8 x 0 + c

c = 0

So,

y = 0.8x

Another line:

(2, 1) and (1, 3.5)

m = (3.5 - 1) / (1 - 2)

m = 2.5 / -1

m = -2.5

(2, 1) = (x, y)

1 = -2.5 x 2 + c

1 = -5 + c

c = 1 + 5

c = 6

So,

y = -2.5x + 6

Now,

The point of intersection is (1.82, 1.45).

0.8x = -2.5x + 6

0.8x + 2.5x = 6

3.3x = 6

x = 6/3.3

x = 1.82

And,

y = 0.8x

y = 0.8 x 1.82

y = 1.45

Thus,

(1.82, 1.45) is the point of the intersection.

y = 0.8x and y = -2.5x + 6 are the equation of the line.

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According to the z table, there is a 0.3814 percent chance that a standard normal random variable will fall between 0.3 and 3.2.

The probability is calculated by dividing the total number of outcomes by the total number of potential events.

Odds and probability are two different concepts.

Calculating odds involves dividing the probability of an event by the probability that it won't happen.

Probability is the study of random events in mathematics, and it can be classified into four main categories: axiomatic, classical, empirical, and subjective.

So, we must determine the likelihood that a standard normal random variable will occur with a probability between 0.3 and 3.2.

First, a standard normal random variable with a mean and standard deviation is introduced.

We must determine the likelihood that a standard normal random variable will fall within the range of 0.3 and 3.2.

The likelihood therefore should be:

P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)

Using z's typical value:

P(0.3<z<3.2)=0.9993−0.6179

Simplify as follows:

P(0.3<z<3.2)=0.3814

Therefore, according to the z table, there is a 0.3814 percent chance that a standard normal random variable will fall between 0.3 and 3.2.

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Answer:

This is referred to as an expression. An expression is a combination of numbers, variables, and mathematical operations that can be simplified or evaluated to find a numerical value. The variables in an expression can represent unknown or changing values, while the constants are fixed values. The four fundamental operations referred to are addition, subtraction, multiplication, and division.

The 7th term of the geometric sequence is -0.0021 .

What is geometric progression?

If in a sequence of terms, each succeeding term is generated by multiplying each preceding term with a constant value, then the sequence is called a geometric progression. (GP), whereas the constant value is called the common ratio.

For example, 2, 4, 8, 16, 32, 64, … is a GP, where the common ratio is 2.

Given :

first term : -2100

common ratio : -0.1

7th term =-2100 *-0.1^(7 - 1)

                =-2100 * -0.1^6

                =-2100 * 0.000001

                =- 0.0021

Hence , the 7th term of the geometric sequence is -0.0021 .

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The new price of the item after a deduction of 80% from the original price is $14

Percentage discount = 80%

Original price of the item = $70

New price of the item= Original price of the item - (Percentage discount × Original price of the item)

= 70 - (80% × 70)

= 70 - (0.8 × 70)

= 70 - 56

= $14

In conclusion, the item now cost $14 after deducting discount.

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The solution is Option D.

The quotient of the coordinates will be a coefficient in the equation

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 0 , 0 )

Let the second point be Q ( 4 , 7 )

Now , the slope of the line between the points is ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 7 - 0 ) / ( 4 - 0 )

On simplifying the equation , we get

Slope m = 7/4

Therefore , the quotient of the coordinates will be a coefficient in the equation

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 7 = ( 7/4 ) ( x - 4 )

On simplifying the equation , we get

y - 7 = ( 7/4 )x - 7

Adding 7 on both sides of the equation , we get

y = ( 7/4 )x

Hence , the equation of line is y = ( 7/4 )x

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Answer:d

Step-by-step explanation: