Central Park in New York City is rectangular with a length of 2.5 miles and a width of 0.5 mile. During an afternoon, its population density is about 15 people per acre. Find the number of people in the park that afternoon. One acre is equal to 1640 square mile.

Answer: Hypotenuse

Step-by-step explanation:

The Hypotenuse is known as the longest side of a triangle.

Therefore , the solution of the given problem of function comes out to be x(3x²- 15 ) + 8 / 12x² , Domain : x ∈ R : x≠ 0 and

Domain :[ -∞,0 ] U [ 0,∞].

According to a function's rule, every x value in the domain has one and only one range of y values. Definition. A one-to-one function exists when there is just one and only one value of x such that f(x) = y.

Here,

Part A:

=> 4/6x² - 5x²/4x

=> 8 - 15x + 3x³/12x²

=>  3x³- 15x +8 / 12x²

=> x(3x²- 15 ) + 8 / 12x²

Part B:

Domain : x ∈ R : x≠ 0

Part c:

The function domain at x= 0 Domain :[ -∞,0 ] U [ 0,∞]

Therefore , the solution of the given problem of equation comes out to be x(3x²- 15 ) + 8 / 12x² , Domain : x ∈ R : x≠ 0 and Domain :[ -∞,0 ] U [ 0,∞].

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]2y=6-2x\implies 2y=-2x+6\implies y=\cfrac{-2x+6}{2} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ -1 \implies \cfrac{-1}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-1} \implies 1}}[/tex]

so we're really looking for the equation of a line whose slope is 1 and it passes through (6 , -7)

[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{ 1}(x-\stackrel{x_1}{6}) \implies y +7= 1 (x -6) \\\\\\ y+7=x-6\implies {\Large \begin{array}{llll} y=x-13 \end{array}}[/tex]

The difference between the polynomials 9x² + 8x and 2x² + 3x is 7x² + 5x.

A polynomial is formed mathematically by combining one or more algebraic terms (monomials). The roots of "polynomial" are poly- (many) and -nomial (terms). A polynomial can have exponents (powers), constants (numbers), and variables (letters), but not negative exponents or variable division.

Polynomials are typically expressed in standard form. Furthermore, because there are no similar terms among the exponents, they are arranged in descending order (largest to smallest).

To find the difference between

(9x² + 8x) - (2x² + 3x)

We do calculation

= 9x² + 8x - 2x² - 3x

= 9x² - 2x² + 8x - 3x

= 7x² + 5x

Thus, the difference between the polynomials is 7x² + 5x.

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Therefore Because of this, the square root is 2 is "irrational" (cannot be written as a fraction) since, if it were, the result would be absurd.

A mathematical concept known as a square root is indeed a factor of a number that, when multiplied on its own, equal the original value. For instance, 3 and -3 are the cube roots of 9. Starting in the second millennium BC, the Babylonians created effective methods for approximating square roots.

Here,

In this case, The square root of 2 is "irrational" (cannot be expressed in a fraction) because, if It Could,

You Would Have the Nonsensical Situation That The Fraction Would Have Even Integer value

At Both The Top And Bottom And Could Therefore Always Be Simplified.

.

Therefore Because of this, the square root is 2 is "irrational" (cannot be written as a fraction) since, if it were, the result would be absurd.

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By using the ASA Congruence Theorem, Delta PQR is congruent to Delta TSR.

We can prove this by using the fact that triangle PQR and triangle TSR are both right triangles and that R is the midpoint of overline PT and overline PQ is congruent to overline TS. Since R is the midpoint of overline PT, it follows that overline PR is congruent to overline TR (by the midpoint theorem).

Since PQR is a right triangle, and R is the right angle, it follows that angle PQR is congruent to angle TSR (by the definition of a right angle). Since overline PQ is congruent to overline TS, it follows that angle PQS is congruent to angle TSR (by the definition of congruence). Together, these congruences imply that triangle PQR is congruent to triangle TSR by the ASA congruence theorem.

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Answer:

I'm not sure what equation is needed here. Could you share the table?

Either way, you can take the number of students there are and multiply that to the number of chaperones needed per group of 12- basically see how many groups of 12 you can fit in the overall group of students

The slope is $125 and the slope tells the annual due payment of $125.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take two points from the graph as (2, 400) and (4, 650)

Then, the slope of line is

slope, m = ( 650- 400) / ( 4- 2)

slope, m = 250 /2

slope , m = 125

Hence, the slope is 125.

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The general solution of the given differential equation is y(x) = C₁e^-x + 4xe^-x. The largest interval over which the general solution is defined is (-∞, ∞). There are no transient terms in the general solution.

The differential equation given can be rearranged into the form dy/dx + (x + 2)/(x + 1)y = 8xe^-x, which is a linear first order differential equation. Using the integrating factor method, an integrating factor of e^(x + 1) can be used to obtain the general solution y(x) = C₁e^-x + 4xe^-x.

The integration constant C₁ can be determined by supplying the appropriate initial conditions. As the equation is a linear first order differential equation, the general solution is valid over the entire domain of x, which is (-∞, ∞). As the equation does not involve any terms that provide a particular value for y at any point in the domain, there are no transient terms in the general solution.

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Answer:

Gianna has $760 to spend and she has already spent $356.46 on a new bicycle, $10.01 on 2 bicycle reflectors, and $20.72 on a pair of bike gloves.

The total amount spent on these items is $356.46 + $10.01 + $20.72 = $387.19.

Gianna has $760 - $387.19 = $<<760-387.19=372.81>>372.81 left to spend on biking outfits.

She wants to buy biking outfits that cost $45.35 each.

We can write an inequality to represent the number of outfits Gianna can purchase while staying within her budget as follows:

45.35o <= 372.81

This inequality can be solved by dividing both sides by 45.35:

o <= 8.24

Therefore, Gianna can purchase 8 biking outfits while staying within her budget.

Step-by-step explanation:

The amount of cherries bought by the Harrison is 62.5 pounds.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.

The amount of cherries bought by the Harrison should be more than the cherries bought by the Liam which is 5/8. Thus, The amount of cherries bought by the Harrison is more than the 5/8 or 62.5 pounds of cherries percent.

The cherries bought by the Liam is 5/8 pounds

The cherries bought by the Harrison is more than the Liam.

As in the problem the number of cherries bought Harrison (let) should be more than the cherries bought by the Liam (let ). Therefore,

H > L

As we know that the number of cherries bought by the Liam is 5/8 pounds. Keep the value of  in the above equation, we get,

H > 5/8

This equation can be rewritten in the percentile form as,

h > (5/8) * 100 %

h > (5/2) * 25 %

h > 62.5 %

Hence, The amount of cherries bought by the Harrison is more than 5/8 pounds or 62.5 pounds of cherries percent.

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The solution for the given equation would be [tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex].

What is an equation?

An equation is a statement that two expressions are equal to each other. It is a mathematical sentence that asserts the equality of two expressions. An equation can be written in the form of:

expression_1 = expression_2

The given equation is √2x – 1- x = −8.

[tex]2x=x^2-14x+49[/tex]

[tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex]

Hence, the solution for the given equation would be [tex]x=8+\sqrt{15},\:x=8-\sqrt{15}[/tex].

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There is a chance (probability) of about 94.84% that the pregnancy last at least 240 days and P (X ≥ 240) = 0.9484 and the  the value of c such that P(X ≥ c) = 0.20 is 279.44

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur,

Given that Mean (μ) = 266

and Standard deviation(σ) = 16

The z-score is the value decreased by the mean divided by the standard deviation:

z = (x−μ)/σ = (240−266)/16

≈−1.63

Determine the corresponding probability using the normal probability table in the appendix:

P (X ≥ 240)

= 1 - P (X < 240)

= 1 - P(Z < -1.63)

= 1 - 0.0516

=0.9484

(a) There is a chance of about 94.84% that the pregnancy last at least 240 days

(b) P (X ≥ 240) = 0.9484

(C) Given that 20% is greater than z, then we know that 80% or 0.80 is smaller than z.

The area of 0.7995 is closest to 0.8, and it is located in the row 0.8 and column .04

thus, the z-value is z=0.84.

x = μ+zσ = 266+0.84*(16 )

=279.44

The  the value of c such that P(X ≥ c) = 0.20 is 279.44

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There is a chance (probability) of about 94.84% that the pregnancy last at least 240 days and P (X ≥ 240) = 0.9484 and the  the value of c such that P(X ≥ c) = 0.20 is 279.44

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur,

Given that Mean (μ) = 266

and Standard deviation(σ) = 16

The z-score is the value decreased by the mean divided by the standard deviation:

z = (x−μ)/σ = (240−266)/16

≈−1.63

Determine the corresponding probability using the normal probability table in the appendix:

P (X ≥ 240)

= 1 - P (X < 240)

= 1 - P(Z < -1.63)

= 1 - 0.0516

=0.9484

(a) There is a chance of about 94.84% that the pregnancy last at least 240 days

(b) P (X ≥ 240) = 0.9484

(C) Given that 20% is greater than z, then we know that 80% or 0.80 is smaller than z.

The area of 0.7995 is closest to 0.8, and it is located in the row 0.8 and column .04

thus, the z-value is z=0.84.

x = μ+zσ = 266+0.84*(16 )

=279.44

The  the value of c such that P(X ≥ c) = 0.20 is 279.44

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The inequality that represents negative one third is greater than or equal to the product of negative two fifths and a number is: B. negative one third is greater than or equal to negative two fifths y where y is greater than or equal to five sixths.

In Mathematics, an inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values, numbers, and variables in an algebraic equation, especially based on any of the following inequality symbols:

Note: Let the variable y represent the unknown number.

Next, we would translate the word problem "negative one third is greater than or equal to the product of negative two fifths and a number" into an algebraic inequality as follows;

-1/3 ≥ -2/5 × y

-1/3 ≥ -2y/5

Multiplying both sides of the algebraic inequality by -5/2, we have:

-1/3 × -5/2 ≥ -2y/5 × -5/2

5/6 ≤ y

y ≥ 5/6.

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Answer:

Step-by-step explanation:

We label points A=(x1,y1)=(1,1) A = (x1, y1) = (1,1) and A′=(x2,y2)=(3,3) A ′ = (x 2, y 2) = (3,3) to identify the centre of dilation. The centre of dilation's coordinates are then determined using the formula. (xo,yo) ( xo,yo) ( xo,yo )

When the scale factor exceeds 1, the dilation becomes an enlargement. If it falls within the range of 0 and 1, the dilation is a contraction. The point from which the image is dilated is known as the centre of dilation (or point of dilation).

The equation for the circle must be converted into standard form, (x h), in order to be able to determine the centre and radius.[tex](x-h)^2+(y-k)^2=r^2[/tex], where r is the radius and h and k are the coordinates for the centre.

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If George is trying to fence the garden with less fences possible between the two options given in the question, the first option of measurements i.e 20 feet long and 15 feet wide would take less fencing.

It is the entire distance encircled on all sides by the rectangle.One of the key equations for the rectangle might be regarded to be its perimeter.

The formula for calculating the perimeter of a rectangle is :

P = 2*l + 2 *b where , l and b are the length and breadth of the rectangle.

For the first option, where the garden is 20 feet long and 15 feet wide, the perimeter would be 20+20+15+15 = 70 feet.

For the second option, where the garden is 30 feet long and 10 feet wide, the perimeter would be 30+30+10+10 = 80 feet.

Therefore, the first option where the garden is 20 feet long and 15 feet wide would use less fencing, 70ft in this case, as the perimeter is lower than the other option which is 80 ft.

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Answer:

1 bucket

Step-by-step explanation:

3/4 buckets = 3/4 hours

multiply both sides by 4/3 to get one hour

(4/3) * (3/4) buckets = (4/3) * (3/4) hours

1 bucket = 1 hour

Answer:

Step-by-step explanation:

x² = 17² - 8²

x² = 289 - 64

x² = 225

x = √225

x = 15in

8 + 15 + 8 + 15 =

46in

Answer:

girl I have the same question

Answer:

Without being able to see the graph, it is not possible for me to accurately compare the two functions. Is it possible for you to provide more information about the functions or the graph?

Answer:

Step-by-step explanation:

graph please

The sum of all the positive two-digit integers where one of the digits is three times the other is 630.

To arrive at this result, the numbers can be broken down into two groups. The first group consists of numbers with 3 as the first digit, and the second group consists of numbers with 3 as the second digit.

For the first group, the sum is calculated by multiplying the 3 by all the numbers from 1 to 9. This gives a sum of 3+6+9+12+15+18+21+24+27 = 135.

For the second group, the sum is calculated by multiplying the 3 by all the numbers from 1 to 9 and then reversing the digits. This gives a sum of 30+60+90+12+51+81+21+42+72 = 495.

The total sum of all the positive two-digit integers where one of the digits is three times the other is 135+495 = 630.

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a) The minimum number of dogs that could have a mass of more than 27 kg is 4.

b) The maximum number of dogs that could have a mass of more than 27 kg is 17.

What is interval?

In mathematics, an interval is expressed in numerical terms. All the numbers between two specific integers are referred to as an interval. All actual values between those two are included in this range. Any form of number one may imagine is a real number.

The given table shows information about the masses of some dogs.

a) As, the minimum number of dogs is needed to be found, then -

Assume all dogs present in the interval 20 to 40 have a mass of more than 27 kg so the minimum value out of 13 and 4 is 4.

b) As, the maximum number of dogs is needed to be found, then -

Assume all dogs present in the interval 20 to 40 have a mass of more than 27 kg so the maximum of the values present in the interval 20 to 40 is 13 + 4 = 17.

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The directions of XYZ in graph are left and right, top and bottom and outward from the screen respectively.

The term graph is known as a pictorial representation or a diagram that represents data or values in an organized manner.

Here we have to find the directions of XYZ on the graph.

Here we have know that X-Y-Z matrix is a three-dimensional structure whereby the x-axis and y-axis denote the first two dimensions and the z-axis is the third dimension.

And then in a graphic image, then the x denotes width, y denotes height and the z represents depth.

The directions of the x axis is in the plane of the screen and is positive toward the right and negative toward the left. Where as the directions of the y axis is in the plane of the screen and is positive toward the top and negative toward the bottom.

Finally the directions of the z axis is perpendicular to the screen or keyboard, and is positive extending outward from the screen.

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On solving the provided question we can say that  by linear equation number of, Red Balls = 6x 18; Blue Balls = 3;  Yellow Balls = 6

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

A bag contains 27 balls

• The ratio of red to blue to yellow balls is 6:1:2

To Find : The number of red,blue and yellow balls present in the bag

Let us take the variable as 'x' to represent the number of balls in the bag

When we Put the values in a equation,

6X+X+2x = 27

9x = 27

x = 3

Hence the number of,

Red Balls = 6x 18

Blue Balls = 3

Yellow Balls = 6

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The unit price of one gallon of paint is going to be $35.96.

We can use the unitary method to solve this problem. The unitary method is a technique used for solving a problem by first finding the value of a single unit, and finding the necessary value by multiplying the single unit value.

In this question, it is given that 1/4 gallon of paint costs $8.99 so for 1 gallon we will have to multiply both the paint amount and the money which buys it to 4 which will conclude that 1 gallon costs $8.99 × 4 is equal to $35.96. So, 1 gallon of paint will cost $35.96.

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The polynomial 4 2x3 is a degree 3 polynomial, also known as a cubic polynomial.

Polynomial is an expression consisting of variables, constants, and coefficients. It is an algebraic expression that can contain exponents, fractions, multiplication, addition, and subtraction. Polynomials are used to model many real-world situations, such as the volume of a cylinder or the area of a triangle. The degree of the polynomial is determined by the highest exponent of the variables in the expression. Polynomials can be divided, factored, and manipulated using the rules of algebra.

It consists of three terms and its general form is

ax³ m + bx² + cx + d, where a, b, c, and d are constants

and x is the variable. In this case,

a = 4, b = 2, c = 0 and d = 0,

so the polynomial is 4x³ + 2x².

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