How do you graph inverse operations?.

Answers

Answer 1

The inverse operations can be graphed by determining the inverse of the function by swapping the x and y variables,

Not all functions have inverses, and in order for a function to have an inverse, it must be a one-to-one function that is, there must not be repeated output for many inputs which indicates that not all functions have inverses. The various steps to graph inverse functions can be noted as -

By switching the x and y variables, first determine the function's inverse, and then solve for y. The inverse function, for instance, will be x = f-1 if the original function is y = f(x) (y).By switching the original function's x and y values, plot the inverse function's points. For instance, if the original function is y = 2x + 1, the inverse function would be x = (y-1)/2, and instead of plotting the point (0,1), you would plot (1,0), (2,-1) and so on (-1,2)Over the line y = x, reflect the original function's graph. You will then be shown the inverse function's graph.Lastly, it is required to correctly identify the axes and the points.

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Related Questions

The store is selling lemons at $0.60 each. Each lemon yields about 2 tablespoons of juice. How much will it cost to buy enough lemons to make four 9-inch lemon pies, each requiring half a cup of lemon juice?

Answers

Answer:

$9.60

Step-by-step explanation:

This is a tricky question because it uses different units.

Let's first convert everything to one unit to make things simpler

1 cup = 16 tablespoons

1/2 cup = 8 tablespoons

Each lemon yields 2 tablespoons of juice

Each lemon pie requires 1/2 cup of juice = 8 tablespoons of juice

4 lemon pies will require 4 x  8 = 32 tablespoons of juice

To get 32 tablespoons at 2 tablespoons per lemon we will require 32/2 = 16 lemons

16 lemons at $0.60 per lemon will cost 16 x 0.60 = $9.60 ANS

Scale factor = 2/5
15inches high; 35 inches length
What is the dimensions?

Answers

The new dimensions are height is 6 inches and length is 14 inches.

What is scale factor?

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, scale factor = 2/5, 15 inches high and 35 inches length.

Here, height is

2/5 = New height/15

New dimension =30/5

= 6 inches

Length of a shape is

2/5 =New length/35

= 70/5

= 14 inches

Therefore, the new dimensions are height is 6 inches and length is 14 inches.

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xiv 2. Complete the table. Make drawings if needed. a. b. C. d. e. Rectangle Length: 4 cm Width: 2 cm Length: 3 cm Width: 2 cm Length: 5 cm Width: 4 cm Length: 6 cm Width: 3 cm Length: 7 cm Width: 6 cm 0 1 2 3 Perimeter Area Enlarge by: 2 times Length: Width: 3 times Length: Width: 4 times Length: Width: 2 times Length: Width: 3 times Length: Width: 4 5 6 7 8 9 Perimeter Are 10 11 12​

Answers

Answer:

bsbsnhs

Step-by-step explanation:

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Please help. I need a response in 48 mins (will give 30 pts)

Answers

Answer: 8/17

Step-by-step explanation:

sinA = opp.side/hypotenuse

 = BC/AB

 = 8/1

The vertices of ΔABC are A(−5,4)​, B(−2,3)​, and C(−3,2). If ΔABC is reflected across the line y=−1 to produce the image Δ​A'B'C', find the coordinates of the vertex C​'.

Answers

The coordinates of the vertex C​' will be (-5, -4). And the graph is given below.

What is a transformation of a point?

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

The reflection does not change the shape and size of the geometry. But flipped the image.

The vertices of ΔABC are A(−5,4)​, B(−2,3)​, and C(−3,2). If ΔABC is reflected across the line y = −1 to produce the image Δ​A'B'C'.

Then the coordinate of the triangle Δ​A'B'C' will be given as,

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

A' = (-5, -4 - 2) = (-5, -6)

B' = (-2, -3 - 2) = (-5, -5)

C' = (-3, -2 - 2) = (-5, -4)

The coordinates of the vertex C​' will be (-5, -4). And the graph is given below.

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Can you find the sin of a right angle?.

Answers

Sine of a right-angled triangle is 1 i.e., sin 90°=1

One of the three fundamental functions in trigonometry, along with cosine and tan functions, is the sine function. The ratio of the opposite side of a right triangle to its hypotenuse is known as the sine x or sine theta.

Let the base of the triangle be ‘x’ and the perpendicular be ‘y’ and θ  be the angle

Sine acts as the ratio of the lengths of the opposing side and the hypotenuse side for any right-angled triangle measured from any angle.

sin θ =y/1

When the angle measurement hits the positive y-axis, it will have reached 90°, starting with the first quadrant. Since it now contacts the circle's rim, the value of y changes to 1. Consequently, y's value is changed to 1.

sin θ =y/1=1/1

Therefore, sin 90°=1/1

or, sin 90°=1

Hence, proved.

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A farmhouse shelters 11 animals. Some are goats and some are ducks. Altogether there are 34 legs. How many of each animal are there?(with work)

Answers

Answer: 6 Goats and 5 Ducks

Hope this helps :)

Step-by-step explanation:

6 goats (4 legs) = 24 legs

5 ducks (2 legs) = 10 legs

6 * 4 = 24

5 * 2 = 10

24 + 10 = 34

6 + 5 = 11

Answer:

6 goats and 5 ducks

Step-by-step explanation:

Given: g+d=11

Goats have 4 legs. Ducks have 2 legs. For total of 34 legs.

Use the word problem to create equation: 4g+2d=34

We can solve for either, we'll solve for g(goat) first:

4g+2d=34

2d=34-4g

d=17-2g

Plug what we found for d into other equation:

g+d=11

g+(17-2g)=11

-g+17=11

-g=-6

g=6

Plug what we found for g into equation to solve for d(duck):

g+d=11

6+d=11

d=5

mark as brainliest if this helps :)

please help me. i have no idea what to do

Answers

Answer:

F

Step-by-step explanation:

(x + 2)² + (y - 3)² = 37

intersection points with the x-axis means that their y-values are 0 !

that is the whole trick, as I am sure you experienced already with lines and y-intersects (x = 0) and x-intersects (y =0).

so, we need to solve for x, when y = 0 :

(x + 2)² + (-3)² = 37

x² + 4x + 4 + 9 = 37

x² + 4x - 24 = 0

the solution to a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (-4 ± sqrt(4² - 4×1×-24))/(2×1) =

= (-4 ± sqrt(16 + 96))/2 = (-4 ± sqrt(112))/2 =

= (-4 ± sqrt(16×7))/2 = (-4 ± 4×sqrt(7))/2 =

= -2 ± 2×sqrt(7)

x1 = -2 + 2×sqrt(7)

x2 = -2 - 2×sqrt(7)

so, F is the right answer.

Why do we use log log?.

Answers

Data is displayed in two dimensions using log-log graphs, where both axes have logarithmic scales.

A straight line is depicted on a log-log graph when one variable varies as a constant power of the other. We can determine that X and Y do not have a power law connection if the data points do not form a straight line.

The linear function is equivalently written as log Y = log k + n log X. The statement by John Tukey that "the best thing about being a statistician is that you get to play in everyone's backyard" is amply illustrated by this example.

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What is the general form of linear equation class 10?.

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The general form of linear equation is expressed in the form of ax+b=0 where a and b are the integers and X is the variable and has the only one solution and the general form of a linear equation in two variables is ax + by + c = 0, where a and b cannot be zero simultaneously.

An equation is a statement that two mathematical expressions having one or more variables are equal And the equations in which the powers of all the variables involved are one are called linear equations. The degree of a linear equation is always one.

Define Linear Equation in One Variable

A linear equation with one variable is one with a single variable of order 1 or less. Where x is the variable, it has the form a x +b = 0.

There is just one solution to this equation. Examples include:

3x = 1

22x-1=0

4x+9=-11

A simple equation is deemed to be a linear equation of two variables when it is given the form ax+by+c=0, according to the Linear Equations in Two Variables CLass 10 textbook. A, B, and C in this scenario should all be constants or real integers, such 2, 3, 4, etc. The a and b coefficients of x and y in this situation shouldn't be equal to zero. Given that a, b, and c are real values, the two unknown variables in this case would be x and y. An illustration of a two-variable linear equation is 4x+5y+3=12.

therefore , the general form of linear equation in one variable and intwo variable are ax+b=0 and ax+by+c=0

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7. Determine if each sequence represents a function. Explain why
or why not. If it is a function, identify its domain and range.
Create a mapping to verify your answer.
a. 2, 4, 6, 8, 10, ...
b. 1, 0, 1, 0, 1, ...
c. 0, 5, 10, 15, 20, ...

Answers

Only a and c represent function

How is a sequence defined?

In mathematics, a sequence is a list of items that is in order (or events). It has members and is similar to a set (also called elements, or terms). The number of ordered elements determines the length of the sequence (potentially infinite).

a. The sequence 2, 4, 6, 8, 10, ... represents a function. The domain of the function is the set of natural numbers, and the range is the set of even natural numbers. We can create a mapping by using the rule "multiply by 2" to match each input value of the domain with its corresponding output value in the range. For example, 2 maps to 4, 4 maps to 8, 6 maps to 12, and so on.

b. The sequence 1, 0, 1, 0, 1, ... does not represent a function. The reason is that for any given input value, the output value is not unique. For example, the input value of 1 maps to both 1 and 0, which means that the function is not well-defined.

c. The sequence 0, 5, 10, 15, 20, ... represents a function. The domain of the function is the set of natural numbers, and the range is the set of multiples of 5. We can create a mapping by using the rule "multiply by 5" to match each input value of the domain with its corresponding output value in the range. For example, 0 maps to 0, 1 maps to 5, 2 maps to 10, and so on.

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The ratio 800g : 1kg can be written in the form 1:n.
Find the value of n.

Please help

Answers

The value of n is 1/8. A ratio in math displays how many times one number is contained in another.

What is a ratio?

A ratio in math displays how many times one number is contained in another. The ratio of oranges to lemons, for instance, is eight to six if there are eight oranges and six lemons in a bowl of fruit. In a similar way, the ratio of oranges to all other fruits is 8:14, while the ratio of lemons to oranges is 6:8.

The ratio shows how many times one value is contained in another value.

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

800g : 1kg = 1 : n

This can be written as,

800g/1kg = 1/n

Cross multiply.

n = 1kg/800g

[ 1 kg = 1000g ]

n = 1000g/8000g

n = 1/8

Thus,

The value of n is 1/8.

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Evaluate the expression when a = -5, b = 7, c = -2, and d = 3.2. a-2-b+ (4.7 -d) - c​

Answers

The value of the expression is -10.5 .

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given expression is ,

a-2-b+(4.7-d)-c

Now put a=-5, b=7 , c=-2 and d=3.2 then

=> -5-2-7+(4.7-3.2)-(-2)

=> -14+(1.5)+2

=> -14+3.5

=> -10.5

Hence the value of the expression is -10.5 .

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help me solve this quick please
the questions are
1-reflection about the x-axis
2-reflection about the y axis
3- vertical shift upwards by 10
4-vertical shift downward by 10
5-horizontal shift to the right by 10

Answers

Answer:

1- Reflection about the x-axis: The equation for this transformation would be: f(x) = -(-5^x + 10) = 5^x - 10. This flips the graph of the original function over the x-axis.

2- Reflection about the y axis: The equation for this transformation would be: f(x) = -(5^x + 10) = -5^x -10. This flips the graph of the original function over the y-axis.

3- Vertical shift upwards by 10: The equation for this transformation would be: f(x) = 5^x +10 + 10 = 5^x + 20. This shifts the graph of the original function upward by 10 units on the y-axis.

4- Vertical shift downward by 10: The equation for this transformation would be: f(x) = 5^x + 10 - 10 = 5^x. This shifts the graph of the original function downward by 10 units on the y-axis.

5- Horizontal shift to the right by 10: The equation for this transformation would be: f(x) = 5^(x-10) + 10. This shifts the graph of the original function to the right by 10 units on the x-axis.

Answer:1- Reflection about the x-axis: The equation for this transformation would be: f(x) = -(-5^x + 10) = 5^x - 10. This flips the graph of the original function over the x-axis.

2- Reflection about the y axis: The equation for this transformation would be: f(x) = -(5^x + 10) = -5^x -10. This flips the graph of the original function over the y-axis.

3- Vertical shift upwards by 10: The equation for this transformation would be: f(x) = 5^x +10 + 10 = 5^x + 20. This shifts the graph of the original function upward by 10 units on the y-axis.

4- Vertical shift downward by 10: The equation for this transformation would be: f(x) = 5^x + 10 - 10 = 5^x. This shifts the graph of the original function downward by 10 units on the y-axis.

5- Horizontal shift to the right by 10: The equation for this transformation would be: f(x) = 5^(x-10) + 10. This shifts the graph of the original function to the right by 10 units on the x-axis.

Step-by-step explanation:

A city double it ize every 24 year. If the population i currently 145,000, what will the population be in 48 year?

Answers

The population in 48 year becomes 580,000.

what is Doubling ?

Doubling or Double numbers or doubles simply represent twice the given amount or number.

To double means to add an amount equal to what you already have. An example: If you have one bottle of coke, and you get one more bottle, you have two bottles of coke. Two is the double of one, because, which means you have doubled the amount of coke you had.

As given, if the current population is = 145,000

and after 24 year, it will double its size = 145,000×2 = 290,000

and then in the next 24 years i.e. (48 years later) = 290,000×2 = 580,000

Therefore, the population in 48 year becomes 580,000.

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i have an axis of symmetry of x= -1 what am i?

Answers

The parabola has an axis of symmetry at x= -1.

Step-by-step explanation:

What is the length of the side opposite?.

Answers

A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question.

The side opposite the right angle is always the hypotenuse of a right triangle. In a right triangle, it is the longest side. The opposing and neighboring sides are the other two sides. The labels on these sides relate to an angle.

One side is opposite the other at a specific angle. The non-hypotenuse side that lies next to a particular angle is known as the neighboring side. The terms hypotenuse, opposite, and adjacent are used to define the trigonometric functions sine, cosine, and tangent.

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Help pleaseee!! I need it done before Monday

Answers

In point-slope form, the equation of the line through the indicated points is y - 2 = -4/3. ( x - 4 ).

What is the formula for the line passing through the specified points?

Y - Y1 = m is the line's equation in point slope form (x – x1).As a result, the equation for a line passing through the origin and having a slope of m is given by y - 0 = m(x = 0), which equals y = mx. Given the information in the query;

A Point (4, 2)

x₁ = 4

y₁ = 2

B Point (1, 6)

x₂ = 1

y₂ = 6

We start by figuring out the line's slope.

Slope m is equal to (y2 - y1)/(x2 - x1)

Slope: m = (6 - 2) ( 1 - 4 )

(4)/ Slope m ( -3)

Slope m=-4/3

Then, simplify the point slope formula y - y1 = m(x - x1) using the slope -4/3 and point (4,2).

y - y₁ = m(x - x₁)

y - 2 = -4/3( x - 4 ) ( x - 4 )

As a result, y - 2 is the equation of the line in point-slope form that passes through the indicated places.

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The atomic radius of metal x is 135 picometers (pm) and a crystal of metal x has a unit cell that is face-centered cubic. Calculate the density of metal x (atomic weight = 42. 3 g/mol).

Answers

We have that the Density of metal X  is mathematically given as

∅ = 5048.33 Kg/[tex]m^{3}[/tex]

Density is a word we use to describe how much space an object or substance takes up (its volume) in relation to the amount of matter in that object or substance (its mass). Another way to put it is that density is the amount of mass per unit of volume. If an object is heavy and compact, it has a high density.

Density of metal,

Generally the equation for the side of fcc  is mathematically given as

fcc = 2 × [tex]\sqrt{2}[/tex] × radius of metal

fcc = 2 × 1.414 × 135

fcc = 381.78 ×  [tex]10^{-12}[/tex] m.

where, volume of 1 unit cell of fcc

fccV = ( 381.78 ×  [tex]10^{-12}[/tex] ) ^3

fccV = 55,646,713.615752 ×  [tex]10^{-36}[/tex] [tex]m^{3}[/tex]

And

weight of 1 atom

Wa = molecular weight / avagadro number

Wa = 42.3/(6.023 × [tex]10^{23}[/tex])

Wa = 7.023 × [tex]10^{-23}[/tex] gm/atom

Therefore, density is

∅ = (28.0923 ×  [tex]10^{-26}[/tex]) / (55,646,713.615752 ×  [tex]10^{-36}[/tex] )

∅ = 5048.33 Kg/[tex]m^{3}[/tex]

Therefore, we have that the Density of metal X  is mathematically given as  ∅ = 5048.33 Kg/[tex]m^{3}[/tex]

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Write an expreion to repreent the um of three time the quare of a number and -7. In your expreion, what i the value of the contant?

Answers

The given expression is expressed in an algebraic expression as:  3x^2 - 7 and the value of the number is √7/3

What is an equation?

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

In mathematics, when we express "square" we mean an exponent equal to two. So the expression “the square of a number ” is represented by:

x^2

When we express “three times” we mean a multiplication by three. So the expression "three time the square of a number"  is represented by:

3x^2

When we express “sum” we mean an addition. So the expression "the um of three time the square of a number and -7"  is represented by:

3x^2 + ( - 7)

The complete expression "the um of three time the square of a number and -7" in an algebraic expression represented by: 3x^2 - 7 = 0

Finding the value of the constant we get:

3x^2 - 7 = 0

3x^2 = 7

x^2 = 7/3

x = √(7/3)

x = 1.53

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Correctly written question:

Write an expression to represent the sum of three time the square of a number and -7. In your expression, what is the value of the constant?

PLSSS HELP IF YOU TURLY KNOW THISSS

Answers

The answer  for algebraic expression is Option B 3(-3)

What is Algebraic expression?

A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is called an algebraic expression. In general, something is considered equal if two of them are the same. Similar to this, analogous expressions in mathematics are those that hold true even when they appear to be different. However, both forms provide the same outcome when the values are entered into the formula.

Given

9-12+(-2)+3(-3)

Subtract: 9 - 12 = -3

Add: the result of step No. 1 + (-2) = -3 + (-2) = -5

Multiple: 3 * (-3) = -9

Add: the result of step No. 2 + the result of step No. 3 = -5 + (-9) = -14

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Terry hared an apartment with three other people each peron paid an equal hare of the rent together they pay $1,095 per month how much doe Terry pay per month?

Answers

If everyone paid equal share of amount of rent, then Terry paid $365 per month.

A property is considered to be rented out if it is occupied by someone other than the owner and the tenant consistently pays the owner a set rent. A person is renting when they desire to pay a landlord to live on that landlord's property. The term "letting" refers to the process of someone transferring ownership of their property in return for cash.

The total amount per month for the rent is given as $1095.

Since there are three persons including Terry, The rent is divided equally among all three people.

So, the toal amount should be divided by three to get individual amount

= 1095 / 3

= $365

Hence Terry paid $365 per month as the apartment rent.

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A man is x years old and his son is y years old. what is their average age ​

Answers

Answer:(x+y)/2

Step-by-step explanation:

t's call the man's age as "x" and the son's age as "y". To find the average age of the two, we add their ages and divide by 2:

Average age = (x + y) / 2

So, the average age of the man and his son is equal to the sum of their ages divided by 2.

PLEASE HELP I WILL MARK BRAINIEST

Answers

Answer:

y = 8

Step-by-step explanation:

The angle represented by (8x - 31)° = angle represented by (6x + 3)° since they are alternate interior angles

8x - 31 = 6x + 3

=> 8x-6x = 3 + 31

2x = 34

x = 17

Angles (8x - 31) and (5y + 35) are adjacent linear angles - they lie on the same straight line. their sum must equal 180

8x - 31 + 5y + 35 = 180

Plugging x = 17

8(17) -31 + 5y + 35 = 180

5y + 140 = 180

5y = 180 - 10 = 40

y = 40/5 = 8

A rectangle has an area of 209 square yards and a height of 19 yards. What is the length of the base?

Answers

The length of the base of the rectangle is B = 11 yards  

What is the Area of a Rectangle?

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be represented as A

Now , the value of A is

Let the base of the rectangle be represented as B

Area of rectangle A = 209 yards²

The length of the rectangle L = 19 yards

And , Area of Rectangle = Length x Width

Substituting the values in the equation , we get

Area of Rectangle = 19 x B

209 = 19 B

Divide by 19 on both sides of the equation , we get

B = 209 / 19

B = 11 yards

Hence , the length of the base of rectangle is 11 yards

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What is the image of (-5, -1) after a reflection over the y-axis?

Answers

Answer:

5, -1

Step-by-step explanation:

Hope it helps! =D

How do you find the points of intersection when given a quadratic function and a line?.

Answers

When given a quadratic function and a line, the points of intersection can be found by solving for x using the Quadratic Formula.

The Quadratic Formula states that:

x² + ax+ b = 0

where the constants are a, b, and c. We utilise this equation to solve for x in order to determine the places of intersection. In order to accomplish this, we must be aware of both the line's slope and the quadratic function's y-intercept.

The slope of the line can be found by dividing the y-intercept by the distance between the points of intersection (x1 and x2), and then multiplying that number by the slope of the line (y/x).

The y-intercept can be found by simply plugging in x1 into the equation above. Once we have these two pieces of information, we can solve for x using algebraic equations.

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(1 point) A data set consists of the data given below plus one more data point. When the additional point is included in the data set the sample mean of the resulting data set is 27.917. What is the value of the additional data point?

Note: the additional data point is an integer. If the mean contains decimals, it may be a rounded value.

21, 24, 19, 36, 52, 15, 40, 47, 19, 20, 30

Answers

The value of the additional data point is equal to 12.0

What is a sample mean?

In Mathematics, a sample mean is sometimes referred to as an arithmetic average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

How to calculate the sample mean for the set of data points?

Mathematically, the sample mean for this set of data points can be calculated by using the following formula:

Mean = [F(x)]/n

Note: Let the variable x represent the additional data point.

For the total data points, we have;

F(x) = 21 + 24 + 19 + 36 + 52 + 15 + 40 + 47 + 19 + 20 + 30 + x

F(x) = 323 + x.

Now, we can determine the additional data point as follows;

27.917 = 323 + x/12

323 + x = 335.004

x = 335.004 - 323

x = 12.004 ≈ 12.0

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How do you find Z score with mean and standard deviation in R?.

Answers

A z-score can be calculated using the formula z = (x-)/, where x is the raw score, the mean of the population, and the standard deviation of the population.

The z-score is simply the raw score minus the mean of the population divided by the standard deviation of the population, as the formula demonstrates.

How can I use R to convert data to z-scores?

Typically, z-scores, or standardized scores, are calculated by dividing the mean of all data points by the standard deviation of all data points, then subtracting the mean from each individual data point. Again, using scale(), this can be done in one call.

On a TI 84, how can the mean and standard deviation be used to calculate the z-score?

Press EDIT after pressing Stat. Press Enter after highlighting L2 and entering the formula (L1-10) / 5.558. In column L2, the z-score for each individual value will be displayed automatically: Note: Press 2 and then 1 to enter "L1" into the formula.

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32% of the field i red. If the field i 600 quare feet, how many quare feet of the field i red?

Answers

So, 32% of the field is red, which is equivalent to 192 square feet.

To find out how many square feet of the field is red, we need to use the percentage of the field that is red in the calculation. We know that 32% of the field is red, and the total size of the field is 600 square feet.

To calculate the number of square feet of the field that is red, we can use the following formula:

(32/100) * 600 square feet = 192 square feet

This calculation shows us that 32/100 of the field is red. To express this fraction in decimal we divide 32 by 100, which equals 0.32. To find the area of the field that is red, we then multiply 0.32 by 600 square feet.

So, the field has 192 square feet of the field is red.

Another way to think about it is: 32% is equal to 0.32, so we can multiply 600 square feet by 0.32, which also gives us 192 square feet.

Therefore, 32% of the field is red, which is equivalent to 192 square feet.

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