Almost done:))))))))

y(x)  = [tex]\frac{1}{3-x^2}[/tex] is the solution of the given differential equation.

A differential equation is an equation that relates a function and its derivatives; it describes how a quantity changes with respect to another. and its solution is a function that satisfies the equation for all values of the independent variable

y'=2x[tex]y^2[/tex]

where y' is dy/dx

so dy/dx = 2x[tex]y^2[/tex]

=> dy/ [tex]y^2[/tex] =2xdx

integrating on both side we get:

-1/y = [tex]x^2[/tex] +c   --- (i)

where c is a constant

given that y(1) =2

putting the value of y = 1/2 and x=1 in equation (i) we get

so  -2 = 1+c

=>  c= -3

y(x) = 1/(3-[tex]x^2[/tex])  is the required solution of the differential equation.

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Marco practiced 1.13 hours more on Tuesday than on Monday.

In mathematics, a fraction is used to denote a portion or component of the total. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, while the denominator is the number at the bottom. 

Given that,

Marco practiced for only 7/10 hours on Monday (less than the expected  [tex]1\frac{1}{4}[/tex]hours)

He practiced for [tex]1\frac{5}{6}[/tex] hours on Tuesdays.

He is supposed to practice [tex]1\frac{1}{4}[/tex] hours each day.

Finding the difference between the hours he practiced each day:

[tex]1\frac{5}{6} - 7/10 = 11/6-7/10= (110-42)/60 = 68/60 = 1.13 hours[/tex]

Thus,  Marco practiced 1.13 hours more on Tuesday than on Monday.

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The probability that a randomly selected muffin will be a banana nut muffin is; P(banana nut muffin) = 0.5

From the table in the question, we are given;

Number of blackberry muffins = 10

Number of banana nut muffins = 25

Number of Chocolate chip muffins = 1

Number of blueberry muffins = 11

Number of pumpkin spice muffins = 3

Total number of muffins = 10 + 25 + 1 + 11 + 3

= 50

Probability = number of successful outcomes/Total number of outcomes

Thus;

P(banana nut muffin) = 25/50

= 0.5

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the area of a triangle with base 16 cm and height 8 cm is 64 cm^2

What is triangle?

" Triangle is defined as the two dimensional geometric shape with three vertices, three sides, and three interior angles enclosed in it."

Standard formula A= 1/2 bh

Area of the triangle =1/2 bh

According to the question,

Given,

Given formula of the area of the triangle

b represents the base of a triangle=16

h represents the height of a triangle

Area of the triangle =?

Height of the triangle =8

Substitute the value in the given formula we get,

=1/2*8*16

= 64

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Answer:

My idea is to look all at the left side of the graph, and whatever number without the decimal is lowest, label first, and do the same for the right side, for instance, if the lowest is 161, then label from lowest to highest across the x-axis, if it is something like 7 as the lowest on the right side of the graph, lowest to highest up the y-axis

Step-by-step explanation:

a. The simple interest for 4 years would be $960.

b. The amount at the end of the 4 years would be $2160.$

A man deposited $1200 in his bank account. A simple interest of 20% per annum was paid on his deposit.

a. For calculating simple interest for the 4 years

We have been given data as:

Principal (P) = $1200

Rate of Interest (R) = 20%

Time (T) = 4 years

⇒ Simple interest  = P × R × T

Substitute the value of P, R, and T in the above formula,

The simple interest for 4 years would be:

⇒ 1200 x 20% x 4 = 960

b. For calculating the amount at the end of the 4 years

The amount at the end of the 4 years would be:

1200 + 960 = 2160

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The value of x-y from the given condition is 14.

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.

The given ratio is x:y=5:3.

So, x/y =5/3

3x=5y

To the equation x+y=56, multiply 5 on both side, we get

5x+5y=280

5x+3x=280

8x=280

x=35

Substitute x=35 in equation x+y=56, we get

35+y=56

y=21

Now. x-y is

35-21=14

Therefore, the value of x-y from the given condition is 14.

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Complete transformations and then enter the final coordinates of the figure will be: A(2,2) B(1,-2) C (4,-4)

If a point (x, y) is translated by 4 units horizontally right and 1 unit upwards, coordinates of the image point will be,

(x, y) → (x + 4. y + 1)

Therefore, vertices of the image triangle ABC will be,

A(2, 2) → A'(2+4, 2+1)

         → A'(6, 3)

B(5, -1) → B'(5+4, -1+1)

         → B'(9, 0)

C(1, -2) → C'(1+4, -2+1)

Then reflected across y-axis.

Rule for the reflection across y-axis will be,

(x, y) → (-x, y)

A'(6, 3) → A"(-6, 3)

B'(9, 0) → B"(-9, 0)

C'(5, -1) → C"(-5, -1)           → C'(5, -1)

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The domain of a relation or function are the input values. In this image the domain is represented by the begining of the arrows (the values on the x column).

What is a one one function?

In Maths, an injective function or injection or one-one function is a function that comprises individuality that never maps discrete elements of its domain to the equivalent element of its codomain. We can say, every element of the codomain is the image of only one element of its domain.

The range are the output values. In this case they are the ends of the arrows (the values on the y column

• Domain: {5, 10, 15, 20}

• Range: {-3, -1, 1, 3}

• Description: ,this is an injective function, because it is a one to one relation

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The 5 coordinate systems are Cartesian Coordinate System, Polar Coordinate System, Cylindrical Coordinate System, Spherical Coordinate System, Elliptic Coordinate System.

1. Cartesian Coordinate System: This system uses two perpendicular axes (X and Y) to determine the location of a point. The point's coordinates are the distances from the origin point (0, 0). The axes divide the plane into four quadrants and the coordinates can be positive or negative. The axes are also referred to as the x-axis and y-axis.

2. Polar Coordinate System: This system uses an angle and a distance from a fixed origin point to specify a point. The angle is measured in radians and the distance is measured from the origin. The coordinates of the point are usually written as (r, θ).

3. Cylindrical Coordinate System: This system combines the two-dimensional polar system and the one-dimensional Cartesian system. It uses three coordinates, (r, θ, z) to determine a point's location in three-dimensional space. The r coordinate is the distance from the origin, θ is the angle measured from the z-axis, and z is the height.

4. Spherical Coordinate System: This system uses three coordinates, (r, θ, φ), to determine a point's location in three-dimensional space. The r coordinate is the distance from the origin, θ is the angle measured from the z-axis, and φ is the angle measured from the x-axis.

5. Elliptic Coordinate System: This system uses two coordinates, (a, b), to specify a point on an ellipse. The a coordinate is the distance from one of the ellipse's foci, and the b coordinate is the distance from the other. This system is useful for describing orbits, such as those of planets.

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The correct answer is A. 5 + 9 = 9 + 5 is an example of the commutative property of addition.

The commutative property of addition states that the order of the numbers being added does not affect the sum. In other words, for any two numbers a and b, a + b = b + a. In this example, 5 + 9 = 9 + 5, which shows that the order of the numbers being added does not change the sum.

B. (9 + 2) + 8 = 9+ (2 + 8) is an example of the associative property of addition.

C. 4+ 7 = 3 +4 is not an example of commutative property as its not true 4+7 != 3+4

D. 6 x 1 = 6 is an example of identity property of multiplication.

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Answer:

-------------------------------------

Solve the following equation:

The linear correlation coefficient unknown population is denoted by the statistic r and correlation strength is denoted by the parameter p, respectively.

As a result, correlations are generally portrayed by the two integers r and p. A number of +1 denotes a fully linearly positive correlation, while a number of -1 denotes a fully linearly negative connection. The correlation coefficient has a range of -1 to +1. The linear correlation becomes weaker as r approaches closer to zero.

The sample correlation coefficient evaluates the scatter plot points and a linear regression line constructed from those points (r). The correlation coefficient, denoted as r, ranges in value from -1 to 1. A p-value is a measure of statistical significance.

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The value of x is given as follows:

x = 13.7.

The value of x is obtained using similar triangles, which share these two following features:

The proportional side lengths are given as follows:

Hence the proportional relationship of these lengths is given as follows:

x/16 = 6/7.

Meaning that the value of x is obtained as follows:

7x = 16 x 6

x = 16 x 6/7

x = 13.7.

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On solving the provided question, we can say that the solution of the System of Equation  3000 + 500x = 1000*

A finite collection of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

A system of equations consists of two or more equations and looks for common answers. "A collection of equations fulfilled by the same set of variables is called a system of linear equations."

The point provides a singular solution to the system of equations if the two lines cross at the same location. There are an endless number of solutions in the situation when the two lines meet, and there is none in the case where the two lines are parallel.

The equation for Appleville is

3000 + 500x,       in x years after the year 2000

The equation for Bananaville is

1000*   , in x years after the year 2000

The solution of the equations

3000 + 500x = 1000*

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The measure of angle A rounded to the nearest whole number is 25°.

Hence, option C is the correct answer.

Given that?

First, we determine the length of side c using the law of cosines.

c = √( a² + b² - 2ab( cosC ) )

We substitute in our values

c = √( 20² + 13² - 2×20×13( cos 139° ) )

c = √( 400 + 169 - 520( cos 139° ) )

c = √( 569 + 392.44898 )

c = √961.44898

c = 31 cm

Next, we find Angle A, using the law of cosines.

A = cos⁻¹[ ( b² + c² - a² ) / 2cb ]

We substitute in our values

A = cos⁻¹[ ( 13² + 31² - 20² ) / ( 2 × 31 × 13 )  ]

A = cos⁻¹[ ( 169 + 961 - 400) / 806]

A = cos⁻¹[ 730 / 806]

A = cos⁻¹[ 0.9057 ]

A = 25°

The measure of angle A rounded to the nearest whole number is 25°.

Hence, option C is the correct answer.

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No, 6 is not considered as a prime number, it is a composite number.

As given in the question,

Given number is equal to :

6

Prime numbers are those numbers which has only two factors one and the number itself.

Example of prime numbers are :

2, 3, 5, 7, 11, 13,... so on.

Here six has more than two factors .

Factors of 6 are equal to :

1, 2, 3, 6

There are four factors of six.

When a number has more than two factors then it is considered as composite number.

Example of composite factors are :

4, 6, 8, 9, 10, ... so on.

6 is a composite number.

Therefore, 6 is not a prime number it is a composite number.

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Answer:c

Step-by-step explanation:

c

The students were interested in the proportion of rental apartments in these suburbs that were leased as furnished apartments and whether this varied with the number of bedrooms in these apartments 500x + 900y + 1500z = 750,000

formal test, using a = 0.05,of whether the proportions of furnished apartments varies across number of bedrooms, that is, whether the furnishing status of an apartment independent of the number of bedrooms in the apartment You may use R to carry out these calculations, but please state the following information from this test: i. the table of expected frequencies ii. the observed value of the test statistic iii. the relevant degrees of freedom for the distribution of the test statistic iv

500x + 900y + 1500z = 750,000 - - - (1)

x + y + z = 1000 - - - - (11)

x = 200 + y + z - - - - (111)

x + 2y + 3z = 1550 - - - (1V)

I bedroom = x

2 bedroom = y

3 bedroom = z

All the condition s gjvbbs'

500x + 900y + 1500z = 750,000 - - - (1)

x + y + z = 1000 - - - - (11)

x = 200 + y + z - - - - (111)

x + 2y + 3z = 1550 - - - (1V)

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Answer:

w is greater than or equal to 15

Step-by-step explanation:

15(5)=75

The angle of elevation that the instruments have to record to be at the correct height is given as 79°

We have 2x + 70 = 180

We have to find the value of x

2x = 110

x = 55

y/sin x = 225/sin70

This is the use of sine rule

From here we would have

y = 225(sinx/sin70)

Remember x = 55

y =  225(sin55/sin70)

y = 196.1378

tanθ = 1000/y

tan θ = 1000/196.1378

tanθ = 5.098

θ = tan⁻¹5.098

= 78.90°

Hence the conclusion is that the angle of elevation has to be 78.9 degrees for it to be at the correct height.

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They spoke of a bicycle that is 1-foot long. the revolutions the tire will make when it is ridden one mile is 1681.52 revolutions.

Generally, The circumference of a tire is equal to the diameter times pi

C = d * pi.

Since the spoke of the bicycle is 1 foot long, the diameter of the tire is also 1 foot.

Therefore, the circumference of the tire is 1 * pi = approximately 3.14 feet.

To find out how many revolutions the tire will make when it is ridden one mile, you need to divide the distance traveled (1 mile) by the circumference of the tire.

One mile is equal to 5280 feet, so to find out how many times the tire will revolve, you would divide

5280/ 3.14

=1681.52 revolutions.

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The equation that models the situation is 33 / 4 = h + 13 / 4.

Jamal measured the height of a flower growing in his garden at the beginning of the month. The flower was 3 1 / 4 inches tall . The flower grew h inches during the month.

At the end of the month it was 4 1 / 8 inches tall.

Hence, the equation to model the situation can be represented as follows:

Let's convert the mixed fractions to improper fractions.

3 1 / 4  inches = 13 / 4 inches

4 1 / 8 inches = 33 / 4 inches

Hence, the equation is as follows:

33 / 4 = h + 13 / 4

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if we plug in different values for the input, we get corresponding values of output. There is always a pattern in the way input values x and the output values y are related which is given by the function rule.

What are the Slope and intercepts ?

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction of function

The slope expresses how quickly the dependent variable changes when the independent variable changes. The Greek capital letter D or D is frequently used by mathematicians and economics to represent change. Slope contrasts the change in the vertical axis, y, with the change in the horizontal axis, x.

On the x-axis, negative numbers are below the origin, and on the y-axis, they are to the left of the origin. If the x-value is negative, begin at the origin and go to the left; if the y-coordinate is negative, move downward.

Line graphs, also known as XY graphs, are used to visually represent data (the outcomes of an experiment) in order to demonstrate the link between various factors, such as the severity of the disease and time.

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The given polynomial function has 1 relative minimum and 1 relative maximum.

The given function is

f(x) = 2x³ - 2x² + 1

derivating the above function,

f'(x) = 6x² - 4x

At slope = 0, f'(x) = 0 (for maximum and minimum values)

⇒ 6x² - 4x = 0

⇒ 2x(3x - 2) = 0

2x = 0 or 3x - 2 = 0

∴ x = 0 or x = 2/3

Then the y-coordinates are calculated by substituting these x values in the given function,

when x = 0;

f(0) = 2(0)³ - 2(0)² + 1 = 1

So, the point is (0, 1)

when x = 2/3;

f(2/3) = 2(2/3)³ - 2(2/3)² + 1 = 19/27

So, the point is (2/3, 19/27)

Since y = 1 is the largest value, the point (0, 1) is the relative maximum for the given function.

So, y = 19/27 is the smallest value, the point (2/3, 19/27) is the relative minimum for the given function.

Thus, option A is correct.

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The six types of algebraic expressions are:

Monomial: An expression with only one term, such as 5x or 2[tex]y^3[/tex].

Binomial: An expression with two terms, such as 3x + 4y or 7a - 5b.

Trinomial: An expression with three terms, such as 2[tex]x^2[/tex] + 4x - 6 or 5[tex]a^2[/tex] + 3ab - 2[tex]b^2[/tex].

Polynomial: An expression with more than one term, such as 2[tex]x^3[/tex] + 4[tex]x^2[/tex] - 6x + 8 or 5[tex]a^4[/tex] - 3[tex]a^2[/tex]b + 2[tex]b^3[/tex].

Rational expression: An expression that is the ratio of two polynomials, such as (2x+3)/(x-4) or (5[tex]a^2[/tex]-3b)/(a-2b).

Radical expression: An expression that contains a square root, cube root, or any other root of a number or a variable, such as √x or 3√(2y+5)

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Answer:

Photo 1:

             Question 4:

                   If the angles are the same (two 45° and one 90°) the vertical  side is equal to side C. the Pythagorean theorem states that A²+B²=C².

if Side C is equivalent to 4, both sides of the right angle are 4 (Because they are equivalent to each other.) so 4²+4²= 4 x [tex]\sqrt{2}[/tex] (5.8) so D=5.8, C=4

D is roughly 1.45 C

Step-by-step explanation:

There is a total of 420 Oranges were sold on Friday.

What is a fraction?

A fraction is a mathematical expression that represents a ratio of two numbers. It is written as a ratio of two integers, with the numerator (top number) representing the number of parts being considered and the denominator (bottom number) representing the total number of parts in the whole. The fraction can be written with a slash (/) or a horizontal line.

let the original number of orange be x

total orange sold = 2x/7 + 3x/8 + x/5 = 241x/280

Oranges left = x - 241x/280 = 39x/280

now, 39x/280 = 156

x = 1120 were there.

According to question

number of oranges sold on Friday = 3/8 * 1120

= 420 Oranges were sold on Friday.

Hence, there is a total of 420 Oranges were sold on Friday.

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Using the equation we know that the required value of x is (B) 30 cm.

Basically, an equation is when you have two expressions with the same value on either side of an "equal to" sign.

For example, 3x + 5 = 15.

There are lots of different types of equations, like linear, quadratic, and cubic, among others.

So, looking at the diagram, the equation is true.

x/75 = 12/30

Solve as follows:

30x = 12 * 75

30x = 900

30x/30 = 900/30

x = 30

Therefore, using the equation we know that the required value of x is (B) 30 cm.

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Correct question:

What is the value of x?

(A) X= 4.8 cm

(B) X= 30 cm

(C) X= 93 cm

(D) X= 187.5 cm