equation in point slope from of slope of 0.25 and point of (5,-2)

The required [tex]f(x) = x/10[/tex] is a valid probability distribution function for a discrete random variable X which can take on the values 0, 1, 2, 3, or 4.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

For a function f(x) to be a valid probability distribution function (pdf) for a discrete random variable X, it must satisfy the following conditions:

Non-negativity: [tex]f(x) = x/k[/tex] is non-negative for all x when k > 0.

Normalization: We need to find the value of k such that the sum of the probabilities for x = 0, 1, 2, 3, 4 is equal to 1.

[tex]f(x) = x/k[/tex] for x = 0, 1, 2, 3, 4.

The sum of the probabilities is given by:

[tex](0/k) + (1/k) + (2/k) + (3/k) + (4/k) = 1[/tex]
[tex]10/k = 1[/tex]

So, k = 10.

Thus,[tex]f(x) = x/10[/tex] is a valid probability distribution function for a discrete random variable X which can take on the values 0, 1, 2, 3, or 4.

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Answer:

18 Rials

Step-by-step explanation:

54 divided by 3= 18

The end behaviour of the polynomial function p(x) = -9x⁹ + 6x⁶ - 3x³ + 1 is

A polynomial function is a function in which the lowest power of the unknown is 2.

Since the graph p hs the polynomial function p(x) = -9x⁹ + 6x⁶ - 3x³ + 1.

To determine its values as x → ∞, we see that the -9x⁹ term is the dominant term in the polynomial function.

So, p(x) ≅  -9x⁹

So, substituting x = ∞ into the equation, we have that

p(x) ≅  -9x⁹

p(∞) ≅  -9(∞)⁹

p(∞) ≅  -9(∞)

p(∞) ≅  -∞

So, as  x → ∞, P(x) → ∞

Also, to determine its values as x → -∞, we see that the -9x⁹ term is the dominant term in the polynomial function.

So, p(x) ≅  -9x⁹

So, substituting x = -∞ into the equation, we have that

p(x) ≅  -9x⁹

p(∞) ≅  -9(-∞)⁹

p(∞) ≅  -9(-∞)

p(∞) ≅  9∞

p(∞) ≅  ∞

So, as  x → -∞, P(x) → ∞

So, the end behaviour is

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In order to determine the exact nature of the distribution, Professor X would need to analyze the data in more detail, for example, by creating a histogram or other visual representation of the grades, and conducting statistical tests to determine the nature of the distribution.

If Professor X finds that the grades on the first exam for their statistics class either did really well or really poorly, it suggests that the distribution of grades is bi-modal, meaning there are two distinct peaks in the distribution. This means that some students did very well on the exam and scored high grades, while others did very poorly and scored low grades, with very few students scoring grades in between these two groups.

A bi-modal distribution is not a common occurrence in a typical exam setting, as most exams tend to have a normal or bell-shaped distribution with a single peak, where the majority of students score around the average or mean grade. The bi-modal distribution found by Professor X could be due to a variety of factors, such as students having widely differing levels of prior knowledge, or students' varying levels of preparation for the exam.

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The comparison of m∠B to m∠E is that both angles are congruent

From the question, we have the following parameters that can be used in our computation:

A dilation with a scale factor of 2 maps ΔABC to ΔDEF

When a shape is dilated to form another, the corresponsing sides change while the corresponding angles remain the same

Using the above as a guide, we have the following:

Angle B cprresponds to angle E

Hence, the are equal angles

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Answer:

(-3.1)^8

Step-by-step explanation:

(-3.1)^4•(-3.1)^4

Because they have the same base is -3.1, we can add the ^4 with ^4 and get

(-3.1)^8

So, the answer is (-3.1)^8

All four data  which is  number of questions answered correctly in a multiple-choice quiz and numbers of tickets sold for a football game and heights of members of a baseball team and population of towns within a state are continuous data.

Countable data is referred to as continuous data. The values in this data are not constant and can take on an endless number of different forms. You can also divide these measures up into smaller, independent components. Examples of continuous data include the following: A person's height or weight

in a) number of questions answered correctly in a multiple-choice quiz can be count

b.) numbers of tickets sold for a football game can be count and c.) heights of members of a baseball team can be measure and d.) population of towns within a state can be count .

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Factor of the expression are,

⇒ (x - 1) (x - 12) (x - 10)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation is,

⇒ x³ - 23x² + 142x - 120 = 0

Now, Put x = 1;

⇒ x³ - 23x² + 142x - 120 = 0

⇒ 1 - 23 + 142 - 120 = 0

⇒ 0 = 0

Thus, One factor of the equation is,

⇒ (x - 1)

Now, After divide we get;

⇒ (x³ - 23x² + 142x - 120 ) ÷ (x - 1)

⇒ x² - 22x + 120

⇒ x² - (12 + 10)x + 120

⇒ x² - 12x - 10x + 120

⇒ x (x - 12) - 10 (x - 12)

⇒ (x - 12) (x - 10)

Thus, Factor of the expression are,

⇒ (x - 1) (x - 12) (x - 10)

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Answer:

r = -5

Step-by-step explanation:

To find the value of 'r', use the slope formula.

(4, 2)    ; x₁ = 4  and y₁ = 2

(5 , r ) ;  x₂ = 5  and y₂= r

            [tex]\boxed{slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]

         [tex]\dfrac{r -2}{5 - 4 }= -7\\\\\dfrac{r -2}{1}=-7[/tex]

          r - 2 = -7

              r = -7 + 2

             r = -5

Here we get 1.3 is the growth factor, 0.3 is the growth rate, and 1 is the initial population of amoebas.

Since Madison's population of 1,000 amoebas begins by doubling every hour for a certain number of hours, h.

In other words, the total number of amoebas after one hour is

3*1000=[tex]3^{1}[/tex]*1000.

Total number of amoebas after two hours is equal to 3*3000=[tex]3^{2}[/tex]*1000. The total number of amoebas after three hours is 3*9000=[tex]3^{3}[/tex]*1000.

In a similar manner, the total number of amoebas,

f(h) = [tex](1+0.3)^{h}[/tex]

where the starting amoeba population is 1000. 3 is the population growth factor, and f(h) is the amoeba population after h hours.

Since Tyler begins with a colony of a single amoeba that grows by 30% per hour for a certain length of hours.

In other words, after one hour, there were =[tex](1+0.3)^{1}[/tex]

After two hours, there were a total of =[tex](1+0.3)^{2}[/tex]

After three hours, there were a total of =[tex](1+0.3)^{3}[/tex]

In a similar manner, the total number of amoebas,

f(h) =[tex](1+0.3)^{h}[/tex]

where 1.3 is the growth factor, 1 is the initial population of amoebas and 0.3 is the growth rate.

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Answer:

10413000 visitors

Step-by-step explanation:

117% = 1.17

8900000 times 1.17 = 10413000 visitors

So, there were 10413000 visitors in 2007.

The oak tree is 35.5 feet tall.

A mathematical expression known as an algebraic expression can include variables, numbers, and operations (such as addition, subtraction, multiplication, and division). If the values of the variables are known, it indicates a value that can be calculated. Although an algebraic expression lacks an equal sign and cannot be solved like an equation, algebraic methods can be used to simplify or manipulate it. For example, the expression 2x + 3y is an algebraic expression, where x and y are variables.

a) To solve this problem, we can draw a diagram to represent the situation:

In this diagram, "A" represents Benjamin's position, "B" represents the mirror, and "C" represents the top of the oak tree. Let's call the height of the oak tree "h".

b) We can use Angle-Angle Similarity to solve for h. In this case, we have two similar right triangles: ABC and ABD. We can write an equation to relate their sides:

(AB)/(BC) = (AD)/(CD)

c) Plugging in the known values:

(5)/(40) = (5.75)/(h + 5.75)

Expanding and solving for h:

h = (40 * 5.75)/5 - 5.75

h = 35.5 feet

So, the oak tree is 35.5 feet tall.

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Answer:

150.72 cubic inches

Step-by-step explanation:

The volume of a cylinder can be calculated using the formula:

V = π * r^2 * h

where V is the volume, π (pi) is approximately equal to 3.14, r is the radius, and h is the height.

For the cylinder with a radius of 4 inches and a height of 3 inches, the volume can be calculated as follows:

V = π * r^2 * h = π * 4^2 * 3 = 3.14 * 16 * 3 = 3.14 * 48 = 150.72 cubic inches.

So the volume of the cylinder is approximately 150.72 cubic inches.

The volume of the prism formed of two rectangles is 528 cm³

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

Volume of the prism is the amount of space that it occupied. From the prism shown:

Volume of prism = area of L shaped base * height

Area of L shaped base = (2 cm * 6 cm) + (8 cm * 15 cm) = 132 cm²

Volume of prism = 132 cm² * 4 cm = 528 cm³

The volume of the prism is 528 cm³

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The correlation coefficient that represents the strongest downward trend in a data set is -0.83.

The correlation coefficient measures the strength and direction of the relationship between two variables, with values ranging from -1 to 1. A negative correlation coefficient indicates a downward trend, meaning as one variable increases, the other decreases.

The magnitude of the coefficient represents the strength of the relationship, with values close to -1 indicating a strong downward trend and values close to 0 indicating a weak or nonexistent relationship. In this case, among the options provided, the correlation coefficient of -0.83 represents the strongest downward trend.

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Answer:-1/2

Step-by-step explanation:

Take two points and use the formula (y2-y1)/(x2-x1). I used (0,4) and (4,2) as my set of coordinate pts.

The body surface area is 1.7 m²

From the question, we have the following parameters that can be used in our computation:

A = (HW/3600)^(1/2)

Where H is the height in cm and W is the weight in kg.

Substitute the known values in the above equation, so, we have the following representation

A = (160 * 64 / 3600)^(1/2)

Evaluate

A ≈ 1.69 m²

Rounding to the nearest tenth:

A ≈ 1.7 m²

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The linear inequalities in the given graph  is [tex]y\geq \frac{1}{2} -1[/tex] and  y< -1/2x -3.

Linear inequalities:

Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, ‘<’, ‘>’, ‘≤’ or ‘≥’. These quantities may be numerical, algebraic, or a combination of the two.

The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality has the same appearance as a linear equation, but uses a different symbol to link the two expressions.

In the given graph, the area above solid line,

points, (-2 , -2) , (0 , -1)

slope = [tex]\frac{-1-(-2)}{0-(-2)}[/tex]= [tex]\frac{1}{2}[/tex]

so,  [tex]y\geq \frac{1}{2} -1[/tex]

The area below dashed line ,

points, (-2 ,-2) , (0 ,-3)

slope= [tex]\frac{-3-(-2)}{0-(-2)}= \frac{-1}{2}[/tex]

so, y< -1/2x -3.

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Answer:

Step-by-step explanation:

if we divide each side with 2,

(2(y-4))/2>0/2

y-4>0

y>4

Answer:

y  > 4

Step-by-step explanation:

2(y - 4) > 0

Solving the inequality:

Divide each side by 2.

2/2(y - 4) > 0/2

y - 4 > 0

Add 4 to each side.

y - 4+4 > 0+4

y  > 4

Therefore , the solution of the given problem of equation comes out to be the equation of the parabola in standard form is x² - 10x - 12y + 13 = 0

In arithmetic equations, the identical figure (=) is used to denote the equivalence of two assertions. It is demonstrated that mathematical methods, which have acted as manifestations of reality, can be used to assess a variety of numerical factors. The equal sign actually splits the number 12 into two separate pieces, despite the fact that the result is y + 6 = 12.

Here,

The distance between the focus and vertex is the same as the distance between the vertex and directrix, which is |-4 - (-1)| = 3. This distance is also equal to the absolute value of the coefficient "a" in the equation of the parabola.

Therefore, the equation of the parabola in vertex form is:

(x - 5)² = 4p(y + 1)

where "p" is the distance between the vertex and the focus, which is 3. Substituting this value into the equation gives:

(x - 5)² = 4(3)(y + 1)

Simplifying:

(x - 5)² = 12y + 12

Expanding the left side:

x² - 10x + 25 = 12y + 12

Moving all the terms to one side:

x² - 10x - 12y + 13 = 0

So the equation of the parabola in standard form is:

x^2 - 10x - 12y + 13 = 0

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The solution is Option A.

The inequality equation is -2 ≤ x < -11

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the first inequality equation be represented as A

Now , the value of A is

4x + 7  ≤ -37   be equation (1)

Let the second inequality equation be represented as B

5x + 3 > -7   be equation (2)

On simplifying the equation , we get

From equation (1) , Subtracting 7 on both sides of the equation , we get

4x ≤ -44

Divide by 4 on both sides of the equation , we get

x ≤ -11

And , from equation (2) , Subtracting 3 on both sides of the equation ,

5x > -10

Divide by 5 on both sides of the equation , we get

x > -2

Hence , the inequality equation is -2 ≤ x < -11

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Letters which represent negative integers on a number line are present on the left side of zero and you can also identify them with the minus sign they carry.

What is  number lines ?

Integers are arranged at equal intervals along horizontal, straight lines known as number lines. A number line can be used to visualize all the numbers in a succession. Both endpoints of this line continue indefinitely.

                             The number line is a straightforward straight line with divisions indicated at regular intervals, much like a scale. Any point can be selected as "0," and all positive and negative numbers are arranged to the right and left of the "0" respectively.

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The complete question is -

Identify the letter that represents the following number negative integers on a number line .

The number of computer chips produced in 3 months will be 2515.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the function f(x) = 5x + 2,500 models the number of computer chips produced by a manufacturing plant each month during its first year.

The number of chips will be calculated as:-

f(x) = 5x + 2,500

f(3) = 5 x 3 + 2500

f(3) = 15 + 2500

f(3) = 2515

Therefore, the number of chips will be 2515.

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The corresponding side in the smaller triangle is 10 cm.

When two or more objects or figures appear the same or equal due to their shape, this property is known as a similarity.

Given that, the ratio of similitude in two similar triangles is 3:1. the side in the larger triangle measures 30 cm, we are asked to find the measure of the corresponding side in the smaller triangle.

Let the corresponding side in the smaller triangle be x,

Since, the ratio similitude is 3:1, therefore, the ratio of the corresponding sides of both the triangle will be in same ratio,

Therefore,

1 / 3 = x / 30

x = 30 / 3

x = 10

Hence, the corresponding side in the smaller triangle is 10 cm.

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21 feet is the perimeter of the kitchen .

In arithmetic, what is a perimeter?

The perimeter is the space surrounding a shape's edge. Discover how to calculate the perimeter of various forms by multiplying their side lengths. The whole distance that the sides or limits of a rectangle cover is known as its perimeter.

                          The perimeter of a rectangle will be equal to the sum of its four sides because rectangles have four sides.

on a blueprint, a rectangular kitchen has a length = 4 inches

                                                  a width = 3 inches

   So it's width is equal to = 6/4 * 3

                                     = 4.5 feet

   the perimeter of this kitchen is = 2(6 + 4.5 )

                                            = 2 * 10.5 = 21 feet

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The perimeter of the figure composed of a semicircle and rectangle is 59.7 inches

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The perimeter of a figure is the total distance along the boundary of that figure.

From the image attached:

Perimeter of circle = π * radius = 3.14 * 5 = 15.7 inches.

Perimeter of rectangle = 2(length + breadth) = 2(12 + 10) = 44 inches

Perimeter of figure = Perimeter of circle + Perimeter of rectangle = 15.7 + 44 = 59.7 inches

The perimeter of the figure is 59.7 inches

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The measures of the three angles are 60 degrees, 75 degrees and 45 degrees.

A semi-circle has a total angle measure of 180 degrees. The sum of the angles formed by the two arcs must equal the total angle measure of the semi-circle.

Let's call the angle formed by the first arc "angle A" and the angle formed by the second arc "angle B".

From the given information, we know that:

angle A = 60 degrees

angle B = 75 degrees

So, angle A + angle B = 60 degrees + 75 degrees = 135 degrees

Since the total angle measure of the semi-circle is 180 degrees, the measure of the remaining angle is:

180 degrees - 135 degrees = 45 degrees

Therefore, the measures of the three angles are:

angle A = 60 degrees

angle B = 75 degrees

angle C = 45 degrees

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Question: Ned made the design at the right. Use a protractor. Find and write the measure of the 3rd angle with given 60 and 75 degrees.

The volume of cuboid is 180 cubic centimeters.

As we know the formula for the volume of the cuboid is given as:

V = l × w × h

where, V is the volume of the cuboid

l is the length of the cuboid

w is the  width of the cuboid

and h is the height of the cuboid

Here, the dimensions of the cuboid are: 9cm × 4cm × 5cm

Let the length of the cuboid is l = 9 cm,

the width of the cuboid is w = 4 cm

and the height of the cuboid is h = 5 cm

Using above formula of volume of cuboid,

V = l × w × h

substitute values, l = 9, w = 4 and h = 5

⇒ V = 9 × 4 × 5

⇒ V = 180 cm³

Therefore, the volume of cuboid 180 cubic centimeters

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In Adventures of Huckleberry Finn, at first, Huck feels good about writing to Jim's owner.

Adventure is an exciting experience or undertaking that is usually daring, sometimes risky. Adventures can be dangerous activities such as travel, exploration, skydiving, mountain climbing, diving, rafting or other extreme sports.

here, we have,

Adventures are often undertaken for psychological excitement or to achieve a greater goal, such as the pursuit of knowledge that can only be obtained through such activities.

Adventure not only expands your mind, increasing  courage, but also gives you the opportunity to grow and learn. New environments and cultures are full of meaningful lessons that you may not encounter in your everyday life. Adventures expand the way we see and interact with the world.

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