we are all pretty familiar with ""means"" or ""averages""…why do we need more information than that? what is the point of calculating variance?

The function g(x) is given by:

g(x) = (68/π) (1/x²) sin(π/4x²).

We have,

To find the integral of the function g(x) = ∫[0, x] (-34t cos(π/4t²)) dt, we can evaluate the integral using the fundamental theorem of calculus.

The antiderivative of -34t cos(π/4t²) with respect to t can be found by applying the chain rule in reverse.

We set u = π/4t² and find du/dt = -π/2t³.

Rearranging, we have dt = -(2/π) x (1/t³) du.

Substituting back into the integral:

g(x) = ∫[0, x] (-34tcos(π/4t²)) dt

= ∫[0, x] (-34tcos(u)) x -(2/π) x (1/t³) x du

= (68/π) x ∫[0, x] (cos(u)/t²) du.

Now, we can evaluate this integral.

The integral of (cos(u)/t²) with respect to u can be found using basic integration rules:

∫ (cos(u)/t²) du = (1/t²) x ∫ cos(u) du

= (1/t²) x sin(u) + C,

where C is the constant of integration.

Substituting back into the expression for g(x):

g(x) = (68/π)  [(1/t²) sin(u)] evaluated from 0 to x

= (68/π)  [(1/x²)  sin(π/4x²) - (1/0²)  sin(π/4 x 0²)]

= (68/π)  [(1/x²)  sin(π/4x²) - 0]

= (68/π) (1/x²) sin(π/4x²).

Therefore,

The function g(x) is given by:

g(x) = (68/π) (1/x²) sin(π/4x²).

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Answer:

Step-by-step explanation:you such a nerd and I will never help u

Answer:

Step-by-step explanation:

There are 64 combinations possible with 4 numbers without repeating. The solution has been obtained by using permutations.

What is permutation?

A permutation is a grouping of objects in a certain order or sequence. When dealing with permutation, it's crucial to consider both the selection and the arrangement. In a nutshell, permutations heavily rely on ordering. In other terms, an ordered combination is a permutation.

Using permutations, the total number of combinations will be as follows:

⇒4P1 + 4P2 + 4P3 + 4P4

⇒4 + 12 + 24 + 24

⇒64

Hence, there are 64 combinations possible with 4 numbers without repeating.

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All people come very close to being able to float in water. therefore, 0.007 is the volume (in cubic meters) of a 50-kg woman.

Correct answer will be a. 0.007

The volume of a person in water is determined by their body density and the amount of air in their lungs. The volume can be estimated using the principle of buoyancy, which states that a body floating in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body.

In this case, we are given the weight of a 50-kg woman and asked to determine her volume in cubic meters. To do this, we can use the formula for buoyancy: Fb = ρf * V * g, where Fb is the buoyant force, ρf is the density of the fluid (water), V is the volume of the woman, and g is the acceleration due to gravity.

Since the woman is floating, the buoyant force is equal to her weight, so we can set these two equal to each other: ρf * V * g = 50 kg * 9.8 m/s^2. Solving for V, we find that V = 50 kg / (ρf * g) = 50 kg / (1000 kg/m^3 * 9.8 m/s^2) = 0.005 m^3.

Comparing this answer to the options given, we can see that the closest option is 0.007 m^3 (choice a), which is our final answer.

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On [0, 2], A(x) can be represented by the linear equation A(x) = (1/2)x.

This means that for every x in the interval [0, 2], the value of A(x) is equal to one-half times x. For example, when x = 1, A(x) = (1/2)x = (1/2) * 1 = 1/2.

On [0, 2], A(x) can be represented by the linear equation A(x) = (1/2)x.

On (2,4], A(x) can be represented by the linear equation A(x) = ((-1/2)x + 2). This means that for every x in the interval (2,4], the value of A(x) is equal to one-half times x minus 2. For example, when x = 3, A(x) = ((-1/2)x + 2) = (-1/2) * 3 + 2 = 2 - 1.5 = 0.5.

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For ε = 0.1, c = 3, and l = 3.2, we can choose δ = 0.2. This means that for all x, 0 < |x - 3| < 0.2 → |f(x) - 3.2| < 0.1.  the values of ε, c, and δ into the equation to check if it satisfies the given condition.

1. Choose an epsilon (ε) value of 0.1 which is the maximum allowed difference between f(x) and l.

2. Identify the value of c which is 3 in this case.

3. Choose a δ value (δ) such that it is greater than 0 and when combined with c, it satisfies the condition 0 < |x - 3| < 0.2.

4. Substitute the values of ε, c, and δ into the equation to check if it satisfies the given condition.

5. If it does, then the answer is 0.2.

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Answer:

got to combine like terms and I think you got your answer

Step-by-step explanation:

The volume of a pyramid is 10x² /3 -40x/ 3 - 40.

Volume is a three-dimensional measurement that's used to gauge a solid shape's capacity. It implies that the volume of a closed form determines how much space it can occupy in three dimensions.

The area that any three-dimensional solid occupies is known as its volume.

We have,

The area of the rectangular base of a pyramid is given by the polynomial equation, B = x²-4x-12.

Now, Volume of Pyramid

= 1/3 x (base area) x height

= 1/3 x ( x²-4x-12) x 10

= 10x² /3 -40x/ 3 - 40

Thus, the Volume is 10x² /3 -40x/ 3 - 40.

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The line segment is divided into the x-axis in the ratio 4:3.

The line segment joining the points (2, 4) and (-3, -2) is divided by the x-axis at the point where the y-coordinate is 0.

To find this point, we can set y=0 in the equation of the line that connects the two points.

The equation of the line is given by:

y = mx + c

The slope m can be found using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the two points. Substituting the values, we get:

m = (-2 - 4) / (-3 - 2) = -6/ -5 = 6/5

The y-intercept c can be found using one of the points and the slope:

c = y - mx

Substituting the values, we get:

c = 4 - 6/5 * 2 = 4 - 6/5 * 2 = 4 - 3.2 = 0.8

So, the equation of the line is:

y = 6/5 x + 0.8

Setting y = 0, we get:

0 = 6/5 x + 0.8

-0.8 = 6/5 x

x = -0.8 * 5/6 = -4/3

Therefore, The line segment is divided into the x-axis in the ratio 4:3.

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Answer: To find the solution of the system of equations:

y = 3x^2 + 5x + 4

y = 2x + 10

We set the two expressions for y equal to each other:

3x^2 + 5x + 4 = 2x + 10

Subtracting 2x and 10 from both sides:

3x^2 + 5x - 2x + 4 - 10 = 0

3x^2 + 3x - 6 = 0

We can use the quadratic formula to solve for x:

x = (-b ± √(b^2 - 4ac)) / 2a

Where a = 3, b = 3, and c = -6. Plugging these values into the formula:

x = (-3 ± √(3^2 - 4 * 3 * -6)) / 2 * 3

x = (-3 ± √(9 + 72)) / 6

x = (-3 ± √(81)) / 6

x = (-3 ± 9) / 6

x = (-3 + 9) / 6 or (-3 - 9) / 6

x = 6 / 6 or -12 / 6

x = 1 or -2

So the solution of the system of equations is (1, 17) or (-2, 4).

Step-by-step explanation:

The difference quotient of f(8 + h) - f(8) / h = x³ + 3x²h + 3xh³ + h³ - 512 / h.

When you hear the phrase "difference quotient formula," what comes to mind? Difference and quotient resemble the slope formula in appearance. Yes, the difference quotient formula does really provide the slope of a secant line drawn to a curve. What is a secant line? A line that joins any two points on a curve is known as the secant line.

Given that the function is f(x) = x³

The value of f(8 + h) = (x+ h)³ = x³ + 3x²h + 3xh³ + h³

The value of f(8) = (8)³ = 512

Substituting the value of f(8 + h) and f(8) we have:

f(8 + h) - f(8) / h = x³ + 3x²h + 3xh³ + h³ - 512 / h

Hence, the difference quotient of f(8 + h) - f(8) / h = x³ + 3x²h + 3xh³ + h³ - 512 / h.

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By applying the concept of the pyramid, it can be concluded that the height of the larger pyramid is 5 m.

Pyramid is a 3-D shape that has a polygonal base and flat triangular faces, which join at a common point (the apex).

To find the volume of a pyramid, we multiply the area of its base by the height of the pyramid and divide by 3.

We have two similar pyramids. Let Va be the volume of the larger pyramid and Vb be the volume of the smaller pyramid:

Va = 123 m³

Vb = 27 m³

Let Ha be the height of the larger pyramid and Hb be the height of the smaller pyramid:

Hb = 3 m

Since these are similar pyramids, then their volume is proportional to their height.

For smaller pyramid:

Vb = 27 m³

     = 3³ = Hb³

So we can determine Ha as follows:

Ha = ∛Va

     = ∛125

     = 5 m

Thus, the height of the larger pyramid is 5 m.

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If there is a correlation between two variables a and b, it may be because a causes b, or because b causes a, but it cannot be both is a False .

Any statistical association between two random variables or bivariate data, whether causal or not, is referred to in statistics as correlation or dependency. Although "correlation" can mean any kind of association in the broadest sense, in statistics it typically refers to the strength of a pair of variables' linear relationships.

In mathematical modelling, statistical modelling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are examined under the assumption or requirement that they are dependent on the values of other variables due to some law or rule (for example, a mathematical function). In the context of the experiment in question, independent variables are those that are not perceived as dependant on any other factors.

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The value of k that makes the given function continuous would be k=3

What is continuous function ?

A continuous function is one in which the interval specified for the function is continuous. A continuous function that does not satisfy the conclusion of the mean value theorem on a closed interval is the function f(x) = |x| on the interval [-1, 1].

The function f(x) = 5 - 3x - 2 is defined for all real values of x. To make the function continuous, the value of f(0) must be equal to the value of the function at x = 0 from the second piecewise definition:

f(x) = k if x = 0

Setting these two values equal to each other and solving for k, we find:

5 - 3(0) - 2 = k

k = 3

So, the value of k that makes the given function continuous is k = 3. This means that the function is continuous at x = 0 if f(x) = 5 - 3x - 2 for x ≠ 0 and f(0) = 3.

Hence, The value of k that makes the given function continuous would be k=3

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JaCorren's height at the end of the year will be approximately 67.61 inches.

The concept used in this problem is exponential growth. The equation y = 60 * (1 + 0.01)^x models the growth of JaCorren's height over time, where the height (y) increases by 1% each month (x). The exponent (1 + 0.01)^x represents the cumulative effect of the 1% monthly growth over the number of months.

In this equation, 60 is the starting height, 0.01 is the growth rate, and x is the number of months. By increasing the exponent x, we can see how the height (y) changes over time, which represents the exponential growth of JaCorren's height during his growth spurt.

Here's the mathematical equation to model JaCorren's growth spurt over the next year:

y = 60 * (1 + 0.01)^x

Where:

y is the height of JaCorren in inches

x is the number of months

60 is the starting height

0.01 is the growth rate (1% per month)

To find JaCorren's height at the end of the year (x = 12 months), we can substitute x = 12 into the equation:

y = 60 * (1 + 0.01)^12

y = 60 * 1.01^12

y ≈ 67.61 inches

So, JaCorren's height at the end of the year will be approximately 67.61 inches.

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The function that models JaCorren's growth spurt over the next year can be expressed.

y = 60 * (1 + 0.01x)^x

Where x is the number of months, and y is the height of JaCorren in inches. The initial height of JaCorren is 60 inches, and the growth increase is 1% each month, which is represented by 0.01. The function calculates the height of JaCorren after x months by taking into account the monthly growth increase, represented by (1 + 0.01x)^x.

Here is a function in Python that models JaCorren's growth spurt over the next year:

def height_over_time(x):

   y = 60 * (1 + 0.01 * x) ** 12

   return y

This function takes in the number of months x and returns the height y of JaCorren in inches after x months. The formula used is y = 60 * (1 + 0.01 * x) ** 12, which calculates the growth of JaCorren by 1% per month over the next year (12 months).

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The period of the function given by the graph of cosine is 2pi.

A period is the amount of time between two waves, whereas a periodic function is one whose values recur at regular intervals or periods. In other terms, a periodic function is one whose values recur after a specific interval. The period of a function that has the formula f(x+k)=f is known as the basic period of a function (x)

The period of the function is the interval between repetitions of any function. A trigonometric function's period is the length of one whole cycle. As a starting point, we can use x = 0 for any trigonometry graph function.

The given function is a cosine function.

The period of the cosine function is given as:

P = 2pi /B

Here, the value of B = 1

Hence, the period of the function is 2pi.

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The period of the function given by the graph of cosine would be 2π.

A periodic function is one whose values repeat at regular intervals or periods, whereas a period is the amount of time between two waves. In other words, a periodic function is one whose values repeat every predetermined amount of time. The basic period of a function is the duration of a function whose formula is f(x+k)=f (x)

The pause between any function's repetitions is known as the function's period. The duration of one complete cycle is the period of a trigonometric function. For any trigonometry graph function, we can take x = 0 as a starting point.

The given function is a cosine function.

Let the period of the cosine function be P = 2π/B

The value of B = 1

Therefore, the period of the function be 2π.

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The mean/standard error of the sampling distribution of the proportion is 0.0111.

The root-mean square deviation, commonly known as the standard deviation and represented by the symbol, is the square root of the mean of the squares of all the values of a series calculated from the arithmetic mean.

How dispersed the data is is indicated by the standard deviation. It expresses the deviation of each observed value from the mean.

Any distribution will have roughly 95% of its values within two standard deviations of the mean. The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.

When the standard deviation is low, the data cluster around the mean; when it is high, the data are more spread.

The formula to calculate the standard error of the sampling distribution of the sample proportion is:

[tex]$ SE(p) =\sqrt{\frac{p(1-p)}{n} }[/tex]

It is given that a bank believes that 8% of the people who receive loans will not make payments on time. That is,

Population proportion, p =0.08

Sample size, n= 800

Using the formula defined :

[tex]$ SE(p) =\sqrt{\frac{0.08(1-0.08)}{600} }[/tex]

[tex]$ SE(p) =\sqrt{0.000123}[/tex]

SE(p) = 0.0111

Thus,  the mean/standard error of the sampling distribution of the proportion is 0.0111.

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The nucleus of a 125Xe atom (an isotope of the element xenon with mass 125 u) is 6.0 fm in diameter. It has 54 protons and charge q=+54e (1 fm = 1 femtometer = 10-15 meters).

An atom has a charge when it has an unequal number of protons and electrons. Protons have a positive charge, while electrons have a negative charge. When there is an excess of protons, the atom has a positive charge, and when there is an excess of electrons, the atom has a negative charge. These atoms are called ions. The total charge of an atom is calculated by subtracting the number of protons from the number of electrons. The result is the atom's net charge.

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For the given statement is 2/7, numerator = 2, denominator = 7

The line that divides the numbers 4 and 5 is an example of a fraction and is known as the fraction bar. Here, the number above and below the fraction bar represent the numerator and denominator, respectively. A numerator is used to symbolise the denominator, or the number of parts that make up the whole.

Fractions are used to represent the parts of an entire or collection of items. A fraction is made up of two parts. The number at the top of the line is known as the numerator. It shows the number of identically sized pieces that were taken from the full product or collection. The quantity specified below the line serves as the denominator.

Following division, the quotient is converted to whole numbers, the remainder becomes the new numerator, and the denominator remains constant.

As he ate 2 pieces out of 7 pieces,

the fraction would be 2/7

numerator = 2

denominator = 7

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Answer:

Step-by-step explanation:

ill explain How to solve.

A:    

     x+4>15

     15-4=11

      x<11

C:

     6b=>54

     54/6=9

      b=>9

USE A WEBSITE CALLED DESMOS

The function f·g(x) for the functions f(x)=4x-5 and g(x)=2x+8 is 8x²+22x-40.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

7) The given functions are f(x)=2x+3 and g(x)=x²-3x-6.

Here, f·g(x) =f(x)×g(x)

f·g(x) = (2x+3)×(x²-3x-6)

f·g(x) = 2x(x²-3x-6)+3(x²-3x-6)

f·g(x) = 2x³-6x²-12x+3x²-9x-18

f·g(x) = 2x³-3x²-21x-18

8) The given functions are f(x)=4x-5 and g(x)=2x+8

f·g(x) =f(x)×g(x)

f·g(x) = (4x-5)×(2x+8)

f·g(x) = 4x(2x+8)-5(2x+8)

f·g(x) = 8x²+32x-10x-40

f·g(x) = 8x²+22x-40

Therefore, the function f·g(x) for the functions f(x)=4x-5 and g(x)=2x+8 is 8x²+22x-40.

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1. The slope of the secant line in terms of x and h is m(sec) =18x - 6 + 9h.

2. The m(sec) for h= 0.5, 0.1, and 0.01 at x = 1 is 16.5, 12.9 and 12.09 respectively.

3. The equation for the secant line at x = 1 with h = 0.01 is y = 12.09x - 0.09.

The function is g(x) = 9x^2 - 6x + 9

m(sec) = [tex]\frac{g(x+h)-g(h)}{h}[/tex]

m(sec) = [tex]\frac{(9(x+h)^2 - 6(x+h)+9)-(9x^2 - 6x+9))}{h}[/tex]

Simplifying

m(sec) = [tex]\frac{((9x^2+18xh+9h^2) - (6x+6h)+9)-9x^2 + 6x-9)}{h}[/tex]

m(sec) = [tex]\frac{(9x^2+18xh+9h^2 - 6x+6h+9-9x^2 + 6x-9)}{h}[/tex]

m(sec) = [tex]\frac{(18xh+9h^2 +6h)}{h}[/tex]

Taking h common

m(sec) =18x - 6 + 9h

At x = 1

m(sec) =18 - 6 + 9h

m(sec) = 12 + 9h

At h = 0.5

m(0.5) = 12 + 4.5 = 16.5

At h = 0.1

m(0.1) = 12 + .9 = 12.9

At h = 0.01

m(0.01) = 12 + .09 = 12.09

as h = 0 , m(sec) = 12

point-slope form

y - 12 = 12.09(x - 1)

y - 12 = 12.09x - 12.09

Add 12 on both side, we get

y = 12.09x - 0.09

The graph of the part c is given below.

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The polygon above has 7 sides. it is an heptagon.

A polygon is a plane figure enclosed by line segments called sides. A polygon is named according to the number of sides.  For example polygon with 5 sides is called pentagon, the polygon with 6 sides is called hexagon, the polygon with 7 sides is called heptagon and the polygon with 8 sides is called octagon

A polygon with equal sides of angle is called a regular polygon.

Therefore, let's count he sides of the polygon to know the polygon name.

Hence the polygon has 7 sides and it is called an heptagon.

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Answer:

(4x+1) (x+6)

(y-1)(5y+3)

(k-2)(7k+5)

Step-by-step explanation:

The approximate speed of a vehicle that left a skid mark measuring 100 feet is 47.63 miles per hour

Given the formula:

0.75d = s² / 30.25

Where,

d = length of the vehicle’s skid marks in feet = 100 feet

s = speed in miles per hour

Substitute d = 100 feet into the equation

0.75d = s² / 30.25

0.75(100) = s² / 30.25

75 = s² / 30.25

cross product

75 × 30.25 = s²

2,268.75 = s²

find the square root of both sides

s = √2,268.75

s = 47.63 miles per hour

Ultimately, 47.63 miles per hour is the approximate speed of the vehicle.

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Answer:

2 1/2

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Solve the equation using the quadratic formula

[tex]\displaystyle x^2-2x+2=0\\\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(2)}}{2(1)}\\ \\x=\frac{2\pm\sqrt{4-8}}{2}\\ \\x=\frac{2\pm\sqrt{-4}}{2}\\ \\x=\frac{2\pm2i}{2}\\ \\x=1\pm i[/tex]

Discriminant and Solution Analysis

As we determined in the quadratic formula, our discriminant is -4 because [tex]b^2-4ac=(-2)^2-4(1)(2)=-4[/tex], under the radical. Because it is negative, our solutions must be imaginary since the square root of a negative number is not real.

The total number of pieces of cake will be 2664

A linear equation is an algebraic equation with simply a constant and a first-order (linear) component of the form y=mx+b, where m is the slope and b is the y-intercept.

The above is sometimes referred to as a "linear equation with two variables," where y and x are the variables.

Ax+By=C is the typical form for linear equations in two variables.

2x+3y=5, for example, is a simple linear equation.

It is rather simple to get both intercepts when an equation is stated in this way (x and y).

Let c be the total number of pieces of cake.

We know that Mindy ate 333 pieces and Troy ate 1/4 of the total,

So, we can write it as:

333 + (1/4)c = 999

Expanding the second term:

333 + c/4 = 999

Solving for c:

c/4 + 333 = 999

Subtracting 333 from both sides:

c/4 = 666

Multiplying both sides by 4:

c = 2664

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An integer is a whole number that can be positive, negative, or zero and is pronounced as "IN-tuh-jer."

Integers include things like -5, 1, 5, 8, 97, and 3,043.

5.643.1, -1.43, 1 3/4, 3.14,.09, and other non-integer numbers are a few examples.

Formally, the following describes the set of numbers designated Z:

Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}

The four most frequent ones are p, q, r, and s.

An infinite set is the set Z. In spite of the possibility of an unlimited number of items in a set, denumerability refers to the property that each element in the set can be represented by a list that implies its identity. The fact that 356,804,251 and -67,332 are integers whereas 356,804,251.5, -67,332.89, -4/3, and 0.232323... are not can be inferred from the list "..., -3, -2, -1, 0, 1, 2, 3,...."

There are no elements missing from either set when pairing the components of Z with N, the set of natural numbers. Let N = {1, 2, 3, ...}. Following that, the pairing may go like this:

The key criterion for assessing cardinality, or size, in infinite sets is the presence of a one-to-one relationship. Z shares the same cardinality with the sets of natural and rational numbers. Real, fictitious, and complex number sets, however, have cardinality that is more than Z.

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Answer:

a person who fortells an event is called