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Answer:

y = 3/2x - 3

Step-by-step explanation:

first find slope (m):

m = (-3/2 -(-15/2)) / (1 - (-3)) = (12/2) / 4 = 6/4 = 3/2

plug the point (1, -3/2) into the point-slope form (y-y1) = m(x-x1):

y - (-3/2) = 3/2(x-1)

y + 3/2 = 3/2x -3/2

now put it in slope-intercept form y = mx + b:

y = 3/2x -6/2

y = 3/2x - 3

Therefore , the solution of the given problem of slope comes out to be  

M = 1/2.

What determines a line's steepness is its slope. Gradient overflow is a mathematical expression for the gradient. The slant is the proportion of both the vertical difference (rise) over the distance between two locations to the lateral change (run) over the same distance. Hill form of an equation is used to express a straight line's equation, which is written as y = mx + b. A point on the line where the slope is m, b equals a, and the y-intercept is placed is (0, b). An illustration would be the slope and y-intercept of the formula y = 3x - 7 (0, 7). At the location of the y-intercept, the line has a slope of m, b, and c.

Here,

Given : (0,-3) and (-2,-4)

Thus,

To calculate the slope ,

We use formula:

=> M = y2 -y1 /x2-x1

=> M = -4 -(-3) / -2 - 0

=> M = -1 /-2

=> M = 1/2

Therefore , the solution of the given problem of slope comes out to be  

M = 1/2.

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The probability that 3 or more copies will be demanded in a particular day is 0.64.

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The probability for 3 or more copies to be demanded is the sum of all the probability distributions for 3 or more copies demanded per day.

This can be written in an equational form -

P(x) = 0.14 + 0.12 + 0.10 + 0.08 + 0.07 + 0.06 + 0.04 +0.03

P(x) = 0.64

Therefore, the probability is 0.64.

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Answer:

The surface area of a sphere is given by the formula:

surface area = 4 * pi * r^2

Where r is the radius of the sphere.

Using this formula, the surface area of an orange with a radius of 3.5 cm is:

surface area = 4 * pi * (3.5 cm)^2

= 4 * pi * 12.25 cm^2

= 49.0307 cm^2

The volume of a sphere is given by the formula:

volume = (4/3) * pi * r^3

Where r is the radius of the sphere.

Using this formula, the volume of an orange with a radius of 3.5 cm is:

volume = (4/3) * pi * (3.5 cm)^3

= (4/3) * pi * 42.875 cm^3

= 113.097 cm^3

Step-by-step explanation:

Given ,

To Find : The Surface Area and the volume of a spherical orange

In order to find the surface area of a spherical orange we use the formula,

[tex]SA = 4\pi r^{2}[/tex]

[tex]SA = 4X\frac{22}{7} X 3.5X3.5[/tex]

[tex]SA =[/tex] [tex]154cm^{2}[/tex]

And now to find the volume of a sphere

[tex]V = \frac{4}{3} \pi r^{3}[/tex]

[tex]V = \frac{4}{3} X \frac{22}{7} X (3.5)^{2}[/tex]

[tex]V[/tex] [tex]= 179.59cm^{2}[/tex]

Hence, the surface area is 154[tex]cm^{2}[/tex]and the volume of a sphere is [tex]179.59cm^{2}[/tex]

The value of r is 105 in this equation.

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

In the quadratic formula, √r =[tex]\sqrt{b^{2}-4ac }[/tex]

Where a = 1, b = -9, and c = -6.

So √r = √(-9)² - 4(1)(-6)

√r = √81 -4(-6)

√r = √81 + 24

√r = √105

Hence, the value of r is 105 in this equation.

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Answer:

y=-2/3x+4

Step-by-step explanation:

slope intercept form = y=mx+b

y=-2/3x+4

Fuel consumption is 53.957 miles per gallon for a car moving at  a speed of 60 miles per hour using least square Regression .

A statistical word for models that evaluate the connections between variables is regression. A single dependent variable Y and one or more independent variables X are studied using a linear regression model.

A technique for employing a goodness-of-fit criterion to fit a curve—not necessarily a straight line—through a collection of points. Regression that is most frequently used is linear regression. Recursion is occasionally used interchangeably with the word regression.

Y = mX + b, where X is the predictor (independent) variable, m is the estimated slope, and b is the expected intercept, is the formula for simple linear regression.

Calculation of Fuel Consumption in 60 miles per hour.

given the least square regression line is

y = 55.3286 - 0.02286x

so, y = 55.3286 - 0.02286 * 60 = 53.957 miles per gallon.

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Answer: m= 0 ; b= 16

(5,16) (-10,16)

Step-by-step explanation:

y=16 so dont need to find y cause it already there so (5,16) (-10,16)

m=y^2- y^1 / x^2-x^1

16-16 / -10-5 = 0/-15 = 0. So m= 0

b is y-intercept and we have y=16 so b=16

The correct factorization are as follows:

(a) x² + x = x(x + 1)

(b) 3x-9x² = 3x(1 - 3x)

(c) 7x³ - 35x = 7x(x^2 - 5)

(d) 4x³ + 24x² = 4x^2(x + 6)

What do you mean by "factorization"?

The most crucial step in factorization is to identify the terms points of commonality. Divide each term by the common factor between them, then multiply the result by the entire expression to maintain the value.

One of the key techniques for reducing an algebraic or quadratic equation to a simple form is factorization. Thus, one should be familiar with factorisation formulas in order to simplify the complex problem.

Additionally, you can always multiply your response to see if you end up with the same result as your starting point.

Step by step solution:

(a): x² + x, [Here both terms have 'x' in common]

=x( (x²/x) + (x/x) )

= x(x+1)

(b): 3x - 9x², [Here both terms have '3x' in common]

=3x( (3x/3x) - (9x²/3x) )

= 3x(1-3x)

(c): 7x³ - 35x, [here both terms have '7x' in common]

=7x( (7x³/7x) - (35x/7x) )

= 7x(x²-5)

(d): 4x³+ 24x² [here both terms have 4x² in common]

=4x²( (4x³/4x²) + (24x²/4x²) )

= 4x²(x+6)

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The given equation t = s/5 represents a proportional relationship and the value of the constant of proportionality is 1/5.

The constant of proportionality is the constant value of the ratio of two proportional values. A proportionality relation exists between two changing quantities when either their ratio or product gives a constant.

Proportional relationships are written in the form y = kx

where k is the constant of proportionality.

The given equation below which is given in the question:

t = s/5

The above equation represents a proportional relationship.

According to the given question, k = 1/5 so the answer is 1/5.

Thus, the value of the constant of proportionality is 1/5.

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Answer:

The least common denominator is 8, you need to multiply the 3 by 2.

Answer:

8

Step-by-step explanation:

Using multiplication we know that the product of 3 * - 4 is -12.

One of the four fundamental arithmetic operations, along with addition, subtraction, and division, is multiplication.

A product is the output of a multiplication operation.

The addition method, lengthy multiplication, grid method, and drawing lines are four different ways to multiply.

So, we have:

3 * -4

Here, we know that 3 is a positive number and -4 is a negative number.

And so the product will be a negative number.

Now, calculate the product as follows:

3 * -4

-12

Therefore, using multiplication we know that the product of 3 * - 4 is -12.

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3 quarts is equal to approximately 285 centilitres.

To Calculate this we have:

3 quarts is equal to 3 x 0.95 liters = 2.85 liters.

1 litre is equal to 100 centilitres, so 2.85 litres is equal to 2.85 x 100 = 285 centilitres.

Therefore, 3 quarts is equal to approximately 285 centilitres.

In detail, a quart is a unit of measurement in the Customary System Units and is defined as a quarter of a gallon. 1 quart is equal to 0.95 litres. To find out how many centilitres are in 3 quarts, we need to multiply the number of quarts (3) by the conversion factor (0.95 litres per quart). This gives us 2.85 litres. Since 1 litre is equal to 100 centilitres, we can multiply 2.85 litres by 100 to get 285 centilitres. Therefore, 3 quarts is equal to approximately 285 centilitres.

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If the population grows by 15 people. The original number of people was 50, hence the new share of each person was Rs. (which is refused).

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Let no. of persons = x

Each person get

= 6500/x

If there 15 persons were added more

= 6500/(x + 15)

(6500/x) - 6500/(x + 15) = 30

[tex]\Rightarrow 6500\left[\frac{(\mathrm{x}+15)-(\mathrm{x})}{\mathrm{x}(\mathrm{x}+15)}\right]=30[/tex]

[tex]\Rightarrow 6500\left[\frac{x+15-x}{x^2+15 x}\right]=30[/tex]

[tex]& \Rightarrow 1625\left[\frac{15}{x^2+15 x}\right]=3 \\[/tex]

Then,

[tex]& \Rightarrow \frac{24375}{x^2+15 x}=3 \\[/tex]

Simplifying the above equation,

[tex]& \Rightarrow 3 x^2+45 x=24375 \\[/tex]

[tex]& \Rightarrow 3 x^2+45 x-24375=0 \\[/tex]

[tex]& \Rightarrow x^2+15 n-3250=0 \\[/tex]

[tex]& \Rightarrow x^2+(65 n-50 n)-3250=0 \\[/tex]

Then we get,

[tex]& \Rightarrow x^2+65 n-50 n-3250=0 \\[/tex]

[tex]& \Rightarrow x+65)-50(x+65)=0[/tex]

[tex]\Rightarrow(\mathrm{x}-50)(\mathrm{x}+64)=0[/tex]

x = 50, x = -65

Since the number of people cannot be zero,

the number of people is 50.

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The quantities which are proportional to 12/4 are 36/12 and 3/1 .

What is proportional ?

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.

The relationship between two quantities is constant for all values when they are proportional, which indicates that as one quantity rises, the other rises as well. An illustration would be the ratio of a circle's circumference to its diameter, which is equal to pi.

12/4 ⇒ 3/1

          = 24/9

          = 8/3

The quantity 12/4 is not proportional to 48/18

        = 18/6

        = 3/1

The quantity 12/4 is proportional to 36/12

       = 7/3

The quantity 12/4 is not proportional to 35/15

       = 12/8

       = 6/4

       = 3/2

The quantity 12/4 is not proportional to 24/16

The quantity 12/4 is proportional to 3/1

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By drawing a number line and then marking it as 0 and 1, and by dividing the distance in 3 equal parts we can graph 1/3 on the number line, where each part will be equal to the 1/3.

A number line is a diagram of a graded straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present.

For drawing 1/3 on a number line, we will follow the following steps:

We will first draw a line and mark 0 and 1 on it.

In between 0 and 1, we will divide the total distance into 3 equal parts, where one part will represent (1/3)th portion.

Hence. by marking there we can locate 1/3 on the number line.

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The correct question may be like:

How do you plot 1/3 on a graph.

No, 16x2 40x 25 is not a perfect square trinomial.

Perfect squares are numbers that are the result of multiplying a number by itself. Examples of perfect squares include 4, 9, 16, 25, 36, and 49. Perfect squares are also known as "square numbers" or "whole numbers." Perfect squares are not just limited to whole numbers; some decimals and fractions can also be perfect squares.

A perfect square trinomial is an expression of the form a2 + 2ab + b2, where a and b are constants. 16x2 40x 25 does not fit this form, and is therefore not a perfect square trinomial.

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Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the laset day of the billing cycle instead of on the first day.

Two or more expressions with an Equal sign is called as Equation.

The billing cycle for the month = 28 days

Current beginning balance = x

Annual percentage rate (APR) = 24%

Monthly percentage rate (MPR) = 2% (24% ÷ 12)

Purchase on the last day = $1,400

Total finance charge for the month = $51

Finance charge for the last-day purchase = $1 ($1,400 x 2% x 1/28)

Finance charge for the beginning balance = $50 ($51 - $1)

The current beginning balance, x = $2,500 ($50 ÷ 2%)

Equation for current beginning balance, x = 51 - 1 ÷ 0.02

Total finance charge for the last-day purchase = $28 ($1,400 x 2%)

Savings in finance charge by purchasing on the last day = $27 ($28 - $1)

Hence, Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the laset day of the billing cycle instead of on the first day.

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The factors of the expression x² 4x 3 are (x + 3)(x − 3).

Factor is a number that can be multiplied to produce another number. Factors are used to find the greatest common factor (GCF) and least common multiple (LCM) of two or more numbers. Factors are also used in equations to find solutions and in algebra to solve polynomials. Factors are also important in computing, since they are used to identify prime numbers and prime factorisation.

This is determined by using the factoring technique called factoring by grouping.

First, the expression is written in two groups: x2 and 4x 3. Then, each group must be factored. For the first group, the factors are x and x, since any number multiplied by itself results in the number itself. For the second group, the factors are 4 and 3, since 4 multiplied by 3 equals 12.

Next, the two factors of each group must be multiplied together. The product of x and 4 is 4x, and the product of x and 3 is 3x. The product of 4 and 3 is 12.

Finally, the two groups of factors are combined to form the final expression: (x + 3)(x − 3).

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Answer: B,D

Step-by-step explanation:

The equation is 4x + 17 = 7. Then the value of the variable 'x' will be negative 2.5.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The triangles are congruent triangles. Then the ratio of the corresponding sides will be equal to one. Then the equation is given as,

4x + 17 = 7

Simplify the equation, then we have

4x + 17 = 7

4x = 7 - 17

4x = - 10

x = - 10/4

x = - 2.5

The equation is 4x + 17 = 7. Then the value of the variable 'x' will be negative 2.5.

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The length AB of the roof is 3.20 m.

What is the Pythagorean theorem.

The Pythagorean theorem is one that can be used to determine the value of the unknown side of a right triangle when given two of its sides.

The theorem states that;

/Hyp/^2 = /Adj/^2 + /Opp/^2

Considering the given picture of the shed, draw a perpendicular to B from a point C on parallel line A. So that the length of AB can be referred to as the hypotenuse of triangle ABC.

Now applying the Pythagorean theorem, we have;

/Hyp/^2 = /Adj/^2 + /Opp/^2

/AB/^2 = /2/^2 + /2.5/^2

            = 4 + 6.25

/AB/^2 = 10.25

AB = (10.25)^ 1/2

AB = 3.20

Thus, the length of AB of the roof is 3.20 m.

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Answer:340 cm long

Step-by-step explanation: multiply 7 x 10 then 70 x 12

The provided schematic must be followed in order to answer these diamond problems. You must multiply the values on the left (x) and right (y) cells in order to find the value that belongs in the top cell.

we have,

For Diamond Problems a

x+y=1.2

xy=.32

so value of x= .8 and y = .4.

for Diamond Problems b

x= 11

x+y=25.

so y= 14 and xy=11*14=154.

for Diamond Problems c

x=-7

y=-9

so x+y=-16 and xy= 63.

for Diamond Problems d

x+y=31

xy=234

x=13 and y=18

Because puzzles engage both the left and right sides of your brain, solving them aids in the development of your problem-solving abilities. Solving puzzles with others is a terrific method to improve your communication and cooperation skills in addition to your problem-solving and critical thinking abilities.

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You now have the total length for the remaining 2 sides. This number divided by 2 is the width.

When given an area of A and a length of h, its width w is equal to A/h.

Its width is w = P/2h if you have the perimeter P and length h.

If you know the length h and the diagonal d, you can calculate the width using the formula w = (d2h2).

The height, area, diagonal, or perimeter of your rectangle are the two measurements that the width of a rectangle calculator uses to calculate the width of your rectangle. We'll also demonstrate various formulas for calculating the width of a rectangle based on the information at hand. The width of a rectangle can be determined in a variety of ways, depending on the information at hand. 

A=w×h

P=(w+h)×2

d = w 2 +h 2

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We refer to the enlargement or reduction of one of two figures as a similarity transformation. For example: When one of two figures can be produced from the other and the ratio of their corresponding sides is equal, we say that the two figures are comparable. Similar figures come in a variety of sizes and shapes.

Either a geometric similarity or a matrix transformation that produces a likeness are referred to as "similarity transformations" in this context. Space items are changed into comparable things by similarity transformations. Fractals and iterated function systems are based on essential principles such as similarity transformations and the idea of self-similarity.

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On solving the provided question, we can say that random samples  range from 5 to 20. Matt's research design could best be classified as a(n): students at Northeastern High School

selected at random (purely random, unpredictable). Every member of the population being polled ought to have an equal probability of getting chosen. She randomly selected 25 names from a pool of 250 employees as an example of a simple random sample. Since there are 250 of her employees in total, and each one has an equal probability of being chosen, the sample in this instance is random. Using simple random sampling, which is a form of probability sampling, researchers choose individuals at random from a population. There is an equal opportunity for selection for every person in the population.

Scores range from 5 to 20. Matt's research design could best be classified as a(n): students at Northeastern High School

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The solution to the system of linear equations is (-8, -2).

NOTE: The problem that is solved here is, 'What is the solution to this system of linear equations? Y - x = 6, Y + x = -10'

The equations with two variables and the largest exponent order of 1 each have one, zero, or an infinite number of solutions, and are referred to as linear equations.

A linear equation with two variables has the conventional form ax + by + c = 0, where x and y are the variables.

Additionally, the answers can be expressed as ordered pairs, like as (x, y). The system of linear equations in two variables is graphically represented by two straight lines, which may intersect, be parallel, or be coincident.

y - x = 6 ----> y = x + 6

y + x = -10 -----> y = - x - 10

As both the equations in terms of y, we get

x + 6 = - x - 10

By further calculation

x + x = - 10 - 6

2x = - 16

Dividing both sides by 2

x = -8

Substituting the value of x in either of the equations

y - x = 6

y - (-8) = 6

So we get

y + 8 = 6

y = 6 - 8

y = - 2

Therefore, the solution to the system of linear equations is (-8, -2).

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So, 600 full cup would be able to be filled from the cooler. This can be solved using the concept of volume of cylinder.

The three-dimensional form of a cylinder is made up of two parallel circular bases connected by a curving surface. The right cylinder is created when the centers of the circular bases cross each other. The measure of space within a cylinder is measured by its volume. Find it by dividing the base area by the height. V = πr²h is the formula for the volume of a cylinder with base radius "r" and height "h."

Given that,

diameter of cylinder = 30 inch

diameter of cup = 3 inch

height of cylinder = 24 inch

height of cup = 4 inch

Calculate the volume of the cylinder:

Volume = πr²h

putting the values we get:

Volume = (3.14)(30/2)²(24)

Volume = (3.14)(15)²(24)

Volume = (3.14)(225)(24)

Volume = 16959 in³

Calculate the volume of the cup:

Volume = (3.14)(3/2)²(4)

Volume = (3.14)(1.5)²(4)

Volume = (3.14)(2.25)(4)

Result

Volume = 28.26 in³

Divide the volume of the cylinder by the volume of the cup, we get:

Number of full cups =  16959 in³ /  28.26 in³

Number of full cups = 600

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