A and be are both negative integers with a>b. Classify these are true or false. A) b

Answer:1024 grid squares

Step-by-step explanation:

Let's call the side length of the original piece of graph paper "x".

Since, side length of the cut out square is then (x-2) because the cut out square has to have an integer number of grid squares, and each side of the square would take up 2 grid squares on the graph paper.

The number of grid squares in the cut out square is then (x-2)^2.

The number of grid squares left on the graph paper is 124, so we have:

x^2 - (x-2)^2 = 124

Expanding the right side:

x^2 - x^2 + 4x - 4 = 124

Simplifying:

4x = 128

therefore:

x = 32

therefore original graph paper contains 32 grids i.e 32^2 = 1024

Answer:

  any of {128, 133, 140, 160, 224, 320, 380, 700, 1024}

  1024 if the original grid was square

Step-by-step explanation:

You want to know how many grid squares are on a piece of graph paper if a square number of grid squares can be cut from it to leave 124 grid squares.

If the graph is square to begin with, a square of x² can be removed from its size (x+a)² to leave 124 squares. That is ...

  (x +a)² -x² = 124

  (a)(2x+a) = 124

The factor pairs of 124 are ...

  124 = 1·124 = 2·62 = 4·31

Of these, only 2 and 62 differ by an even number, so we have a=2 and x=30.

The graph paper could be 32 units square originally, having 1024 grid squares.

There is nothing in the problem statement that requires the original graph paper be square. If it is not necessarily square, there are 13 possible shapes it could be. Those have 9 different possibilities for numbers of grid squares.

The graph paper could have originally had this number of grid squares:

__

Additional comment

You may notice that removing a 24×24 square from a graph that is 25×28 leaves no border on one side.

These values were found using a search script.

<95141404393>

The approaches to building a multiple linear regression model is option (C) Backward elimination

Here the multiple linear regression model involves taking all of the possible independent variables, and then systematically eliminating insignificant ones until only significant ones remain

We know the independent variable is the variable that does not depends on any other variables

Here the given elimination methods is eliminating insignificant ones until only significant ones remain

In the backward elimination method starts with explanatory variables in the regression model then starts to eliminates the least significant ones will eliminates one by one

Therefore, the suitable approach is backward elimination method

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When the water cooler is completely full, there are approximately 143.52 gallons of water in it.

To calculate the number of gallons of water in the water cooler when it is completely full, we can use the formula for the volume of a cylinder, which is:

Volume = π * (radius)^2 * height

where radius is half of the diameter, and π is the constant pi.

In this case, the diameter of the water cooler is 3.5 feet, so the radius is 1.75 feet. The height of the water cooler is 2 feet. Plugging these values into the formula, we get:

Volume = 3.14 * (1.75)^2 * 2 = 19.18 cubic feet

To convert this volume to gallons, we can multiply it by the conversion factor of 7.48 gallons per cubic foot:

Volume in gallons = 19.18 * 7.48 = 143.52 gallons

In summary, to calculate the number of gallons of water in a cylindrical water cooler, we can use the formula for the volume of a cylinder and then convert the resulting volume from cubic feet to gallons using a conversion factor.

In this case, we needed to use the diameter and height of the water cooler, along with the constant pi and the conversion factor of gallons per cubic foot, to calculate the number of gallons of water in the water cooler when it is completely full.

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a) The equation of  perpendicular line is y=2x+1

b) The equation of  parallel  line is y = -2x+6

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

a) An equation perpendicular to y= (-1/2)x+4 through the point (-2, -3):

m= -1/2

Slope of perpendicular line is -1/m  = -1/( -1/2) = 2

(x,y) = (-2, -3)

Slope intercept form:

y=mx+b

Substitute x,y and m values to find b

-3= 2(-2) + b

=> -3 = -4 + b

=> b= -3+4 = 1

So the equation of  perpendicular line is y=2x+1

b)  An equation through the point  (1,4)  parallel to  y = -2x + 1

Parallel lines will have same slope , m= -2

(x,y) =  (1,4)

Slope intercept form:

y=mx+b

Substitute x,y and m values to find b

4=-2(1)+b

=> 4 = -2 + b

=> b=4+2 = 6

So the equation of  parallel  line is y = -2x+6

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The distance travelled by Rahul, if he takes 6 rounds of a square field of side = 120m is 2880 meters.

We are given that Rahul takes 6 rounds of a square field of side length 120m. To find the total distance he travels, we need to calculate the perimeter of the square field and multiply it by the number of rounds.

The perimeter of a square is the sum of the lengths of its four sides. Since the side length of the square field is 120m, the perimeter is:

4 * 120m = 480m

This is the distance Rahul covers in one round around the square field.

To find the total distance he covers in 6 rounds, we multiply the distance covered in one round by the number of rounds:

480m * 6 = 2880m

So, Rahul covers a total distance of 2880 meters.

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Why is it crucial to ensure that each sample has at least 10 successes and failures when building a confidence interval for the difference between two population proportions. This will allow us to select a sample distribution for p1-p2 that is roughly normal.

A distributor is a business that takes part in the value chain's distribution step. Making a good or service available to the consumer or business user who wants it is the process of distribution. This might be done by the producer or service provider directly or through indirect channels like distributors or intermediaries. Distribution is one of the four elements of the marketing mix, along with the other three being the product, pricing, and promotion. The broad strategic goal and objective of a corporation should guide distribution decisions. The main task of strategic planning is to develop a thorough distribution plan. At the strategic level, there are three basic distribution tactics: mass, selective, and exclusive distribution.

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The function for the Pakistani Rupee (y) in terms of UAE Dirhams (x) can be represented as, y = 71.59 x.

A function is defined as a relation from a set A to a set B for which an element in set A maps to one and only one image in set B.

Usually the set A consists of the independent variable and set B consists of dependent variable.

We have to find a function relating the conversion of Pakistani rupees and UAE dirhams.

Let y denotes Pakistani Rupees and x denotes the UAE dirhams.

We know that,

1 UAE dirham = 71.59 Pakistani Rupees

So,

2 dirhams = 2 × 71.59 = 143.18 rupees

In this way,

x dirhams = 71.59 x rupees

So, we can write this as,

y = 71.59 x

Hence the required function is y = 71.59 x.

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The factors of the cubic function f(x) = 64x³ + 27 are (4x + 3) and (16x² − 12x + 9). The correct answer would be options (A), and (D).

Factorization, also known as factoring, is the breakdown of one element into a product of other objects, or factors, which when multiplied together generate the original.

The cubic function is given in the question, as follows:

f(x) = 64x³ + 27

The above expression can be rewritten as:

f(x) = (4x)³ + (3)³

Compare the sum of cubic formula a³ + b³ = (a + b)(a² - ab + b²) and we get

f(x) = (4x + 3)(16x² − 12x + 9)

Thus, the factors of the cubic function are (4x + 3) and (16x² − 12x + 9).

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The length of the diagonal of an isosceles trapezoid is 2.83 cm

An isosceles trapezoid is a quadrilateral with two parallel sides and two non-parallel sides of different lengths.

In this case, the non-parallel sides are the bases, which are 3cm and 7cm long. The height is the perpendicular distance between the two bases and is given as 4cm. To find the length of the diagonals, we can use the Pythagorean theorem, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse (the longest side).

In an isosceles trapezoid, the diagonals are equal in length and bisect each other. Let's call the length of the diagonal d. We can draw a right triangle with one leg being half of the trapezoid's height (2cm), the other leg being half of the difference between the two bases (2cm), and the hypotenuse being the length of the diagonal d. Using the Pythagorean theorem, we get:

(2cm)² + (2cm)² = d²

4cm² + 4cm² = d²

8cm² = d²

d = √(8cm²)

d = 2√(2)cm

d = 2.83cm

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The value of x is 80 degrees.

The correct answer is an option (A)

Consider the following figure.

Let us assume that the upper triangle be ABC and the lower triangle be NMC.

We can observe that both the triangles are isosceles triangles, because in both the triangles two sides are congruent.

Consider triangle ABC.

As the triangle is isosceles triangle, from the definition of  isosceles triangle ∠A = ∠B

So, ∠A = 65°

We know that the sum of all the angles of triangle is 180°

⇒ ∠A + ∠B + ∠C = 180°

⇒ ∠C = 180° - (65° + 65°)

⇒ ∠C = 180° - 130°

⇒ ∠C = 50°

We can observe that ∠ACB and ∠MCN are opposite angles.

So,  ∠MCN = 50°

Also, triangle MNC is also an isosceles triangle.

so, ∠C = ∠N

⇒∠N = 50°

We know that the sum of all the angles of triangle is 180°

⇒ ∠M + ∠N + ∠C = 180°

⇒ ∠M = 180° - (50° + 50°)

⇒ ∠M = 180° - 100°

⇒ ∠M = 80°

Therefore,  x = 80°

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Answer:

x = 2/3

0r 0.6(6)

both are positive

Step-by-step explanation:

3x - 5 = -3 is the answer positive or negative?

3x - 5 = -3

3x = -3 + 5

3x = 2

x = 2/3

0r 0.6(6)

The mentioned characteristics of quadrilateral are the properties of the Rhombus. So option C is correct.

Given that,

A quadrilateral  TUVW,

UV || WT,  

TU || VW

TV = UW  (Diagonals )

TV ⊥ UW (Diagonals are perpendicular)

Hence, the given characteristics are of the rhombus.

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Answer: [tex]36/\pi[/tex] or approximately 11.4592

Step-by-step explanation:

The distance around a circle equals its circumference.

The circumference equation is: C = 2[tex]\pi[/tex] * r where r = radius.

Now, we know that the distance around the circle is 36 so C = 36

Using the equation, we have 36= 2[tex]\pi[/tex]*r

Now, we solve for r by dividing by 2[tex]\pi[/tex] to both sides.

r = [tex]36/2\pi[/tex] which equals [tex]18/\pi[/tex] which is approximately 5.7296

Now, since radius is half of the diameter, we need to multiply this by 2.

This finally gives us the answer of diameter = [tex]36/\pi[/tex] which is approximately 11.4592

Sullivan received half as many candy as Carter did, or half as many candies as Sullivan received.

" Amount is defined as the representation of total quantity of given object."

According to the question,

Number of candies Sullivan got = s

Number of candies Carter got = 2s

Compare the given amount of data we get,

Number of candies Carter got = 2(Number of candies Sullivan got )

This shows Carter got twice number of candies comparison to Sullivan.

or

Number of candies Sullivan got = 1/2 (Number of candies Carter got)

Sullivan got half number of candies compare to Carter.

Hence, we conclude Carter got twice number of candies in comparison to Sullivan or Sullivan got half number of candies compare to Carter.

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Answer:

Tony and his cousin will each have 42 points in 3 turns.

Step-by-step explanation:

10 x 3 = 30

30 + 12 = 42

14 x 3 = 42

The function that best models the number of game systems sold  is

y = 30.5(0.7)ˣ

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Consider the equation :

y = 30.5(0.7)ˣ

Plug in x=0,

y= 30.5(0.7)⁰ = 30.5 *1 = 30.5

The point is (0,30.5)

Similarly, when we plug in x=1 and x=2, we get y=21.35 and y=14.95 respectively

The other 2 points in (x, y) form are (1,21.35) and (2, 14.95)

These points are matching with the points on the graph

So, the function that best models the number of game systems sold  is

y = 30.5(0.7)ˣ

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The length of the side is 10 units.

To solve word problems, we try to assign variables to the quantities involved and use the given information to interpret the situation as a mathematical equation. Mathematical equations can then be solved using various techniques, so we get a solution which is then reinterpreted into the situation.

Now, According to the question:

Let the length of the side is 'L'

The area of a square is numerically 60 more than the perimeter.

Then, P = perimeter = 4L

A = area = [tex]L^2[/tex]

A = P + 60 ⇒

[tex]L^2[/tex] = 4L + 60

[tex]L^2[/tex] - 4L - 60 = 0

(L - 10)(L + 6) = 0

L = 10 or -6

L must be positive,

Since s can't be negative, L = 10 units.

Hence, The length of the side is 10 units.

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Answer: B D I J M

Step-by-step explanation: you just gotta see if any of the two answers work an if they don’t it’s nethier!

Bill should use the "Print It"company.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

To determine which company Bill should use, you need to calculate the total cost of each option and compare them.

For "Print It," the total cost would be :

= 30 x $21.50

Apply the multiplication operation, and we get

= $645.00

For "Top Print," the total cost would be :

= $70.00 + (30 x $18.00)

= $690.00

Since the cost of "Print It" is lower than "Top Print," Bill should use "Print It" as it would be a more cost-effective option for him.

Thus, he should use the "Print It"company.

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The equation of the circle graphed above is equal to (x - 1)² + (y - 6)² = 9.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²

Where:

By critically observing the graph of this circle, we have the following parameters:

Radius, r = 3 units.

Center, (h, k) = (1, 6).

Substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - 1)² + (y - 6)² = 3²

(x - 1)² + (y - 6)² = 9.

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Answer: 37 points

Step-by-step explanation:

The probability that a randomly chosen child has a height of less than 68.15 inches is 0.9162, the probability that a randomly chosen child has a height of more than 54.4 inches is 0.6255.

Simply put, probability is the liability that commodity will do. When we do not know how an event will turn out, we can bandy the liability or liability of several issues. Statistics is the study of events that follow a probability distribution.

a) We need to find p(x<68.15)

Standardize x to z, we have, z = (68.15-μ)/σ

=(68.15-57)/8.1

=1.38

Reading from standard normal tables,

p(z<1.38) =0.9162.

Therefore, the probability that a randomly chosen child has a height of less than 68.15 inches is 0.9162.

b) We need to find p(x>54.4)

Standardize x to z, we have, z = (54.4-μ)/σ

=(54.4-57)/8.1

=-0.32

Reading from standard normal tables,

p(z>-0.32) = 0.6255

Therefore, the probability that a randomly chosen child has a height of more than 54.4 inches is 0.6255.

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The equation of the total bill with x number of refills is y = 5 + x and the refills if the bill is $9 is 4.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

Let us consider the number of times we refill = x.

For every refill the cost will be = 1(x) = x.

Then, a basket of fries for $5, and each refill basket of fries is only $1 is:

y = 5 + x

The equation of the total bill with x number of refills is y = 5 + x.

The graph of the equation is obtained by substituting different values of x.

For x = 1:

y = 5 + 1 = 6

Similarly, x = 2:

y = 5 + 2 = 7

If the bill is $9 then,

y = 5 + x

9 = 5 + x

9 - 5 = x

x = 4

Hence, the equation of the total bill with x number of refills is y = 5 + x and the refills if the bill is $9 is 4.

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Answer:

Below

Step-by-step explanation:

Second choice      at x = 0     it is = 6

  and as the exponent (x) gets more negative it gets larger meaning it has a coefficient of < 1     ( it is 3/4)

Answer:

4 : 2 = 10 : 5.

Step-by-step explanation:

Let's put this in a fraction way. 4/2 = 2, and 10/5 = 2. Likewise, we can keep going and putting things that equal to 2. (e.g. 42 : 21)

There were total 4 people at table A and each of them pay €18.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Table A's bill of €72 is split equally.

and, Table B has two more people than Table A and its bill of €108 is also split equally.

let number of people at table A be x and at table B be (x+2).

So, the number of people

x/ 72 = (x+2)/108

108x = 72x + 144

108x - 72x = 144

36x= 144

x=4

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Answer:

5.6lbs

Step-by-step explanation:

multiply 180 by .08

8%=14.4

14.4-180=165.6

165.6-160= 5.6

Answer: 188in^2

Step-by-step explanation:

You can break the figure into 3 smaller shapes

15 x 5

10 x 5

and 9 x 7

The areas of these smaller shapes are 75, 59 and 63

adding these areas together would get you 188 in squared.

Some of the similarities between sales tax and hotel tax include the following:

B) Both must be paid in advance when you make a hotel reservation.

C) Both are based on a percentage of the original cost.

Taxation can be defined as the involuntary fees that are levied on individuals or business firms by the government of a particular country, so as to generate revenues that can be used to fund public projects, institutions and activities.

The types of tax.

In Economics, there are different types of tax that are levied on individuals or business firms by the government and these include the following:

Hotel tax

Sales tax

Property tax

Income tax

we can reasonably infer and logically deduce that both sales tax and hotel tax must be paid in advance when making a hotel reservation in the United States of America.

Hence, Some of the similarities between sales tax and hotel tax include the following:

B) Both must be paid in advance when you make a hotel reservation.

C) Both are based on a percentage of the original cost.

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The complete question is given below:

What are some similarities between sales tax and hotel tax? Select all that apply. Multiple select question. cross out A) Both are an additional amount one must pay. cross out B) Both must be paid in advance when you make a hotel reservation. cross out C) Both are based on a percentage of the original cost. cross out D) Both the sales tax and the hotel tax are equal when you stay in a hotel. cross out E) Both represent a guest fee that hotels charge their customers.