Logarithm and exponential functions are inverse as log(ex)=x and elogx=x.
Knowing that logarithms were once a tool for multiplication when ships employed celestial navigation may be helpful to the layperson. The product of two numbers' logarithms is equal to the total of their individual logarithms. Numerous log tables were published and utilized mechanically.
In 1958, this was an excellent supplemental math topic. The slide rule converts multiplication to addition of lengths using one axis graphs of an exponential function and a graphic log table as a physical correlate. As a result, the logarithm of a product is equal to the sum of the logarithms of its components.
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Late one night a burglar got into one of the vault in Fort Knox and he tole a big ack of gold coin. On hi way out, he wa topped by one of the guard who aw him tealing the bag. Fortunately for him, the burglar wa able to negotiate a deal with the guard and offered him half the money he had taken, plu an extra $2,000 thrown in. Jut a he wa walking away, thinking he had gotten away he wa topped by a econd guard who took the ame bribe: Half the money with an extra $2000 thrown in. Jut a he wa about to leave , he wa topped by a third guard who let him go only after receiving half of all the burglar had left with $ 2,000 extra thrown in. By the time he left he had mixed emotion. After all he did leave with $9,000 more than he had when he arrived and he wa able to ecape. But he thought of all the money he left behind. How much did he teal in the firt place?
Therefore, the burglar's initial theft was $12,000.
To begin, we may express the data in the problem using algebra.
Let x represent the original sum that the burglary victim took.
The thief was left with x/2 + 2000 after giving the first guard the other half of the money plus $2,000, according to the issue.
He had (x/2 + 2000)/2 + 2000 when he gave the same sum to the second guard.
He also handed the third guard the same amount, leaving him with
((x/2 + 2000)/2 + 2000)/2 + 2000.
However, because we are certain that he left with $9,000 more than when he came, we may state:
((x/2 + 2000)/2 + 2000)/2 + 2000 = x + 9000
We can now determine x:
x = (900022*2 - 6000)/3
x = 36000/3
x = 12000
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What is a sum of 4 and 5?.
The sum of 4 and 5 is 9
We know that the sum or also called a summation, is nothing but the result of arithmetically adding numbers.
In simple way we can say that the sum is a way of putting all things together.
The sum is nothing but the whole number which is obtained when two or more numbers have been added together.
and the numbers that are added are known as the addends.
When we add the numbers a plus symbol '+' is used.
Let us assume that we need to find the sum of numbers p and q then we write it as p + q, where p, q are addends.
Here, we need to find the sum of numbers 4 and 5.
4 + 5 = 9
so, the sum is 9
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A newpaper advertiement offer a $10 000 ued car for nothing down and 36 monthly payment of $450. What i the interet rate ued? How much interet will you have to pay if you purchae thi car?
If you purchase the car with this loan, you will have to pay a total of $5,400 in interest.
To calculate the interest rate used for this loan, we can use the formula:
Interest rate = (Monthly payment x 12) / Principal
Plugging in the given values, we get:
Interest rate = ($450 x 12) / $10,000 = 0.54 or 54%
To calculate the total interest paid on the loan, we can use the formula:
Total interest = Principal x Interest rate
Plugging in the given values, we get:
Total interest = $10,000 x 0.54 = $5,400
So if you purchase the car with this loan, you will have to pay a total of $5,400 in interest.
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How do you find the mean value of a Class 10?.
The mean is dividing the sum of all values in a data set by the number of values.
Average is another word for "mean." For instance, if we say that the average height of the 9th grade class is 150 cm, it signifies that this is the mean of all of the kids' heights. The statistical notion of mean, which is employed in a variety of financial areas and corporate appraisal, has significant financial implications. The three statistical measurements of a data set's central tendency are mean, median, and mode.
The mean, which measures the central tendency of the data, is the average or computed central value of a set of numbers. The statistical metric known as central tendency identifies the complete collection of data or distribution by a single value. It offers a precise description of the entire set of facts. The ratio of the sum of all observations to the total number of observations is another way to define the mean in statistics.
Given a data set, X = {x₁,x₂, . . . ,xₙ}, the mean (or arithmetic mean, or average), denoted X, is the mean of the n values x₁,x₂, . . . ,xₙ.
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Your buine ha decided to tart recycling paper product. In exchange, the recycling company will donate 20 boxe of new paper each year to your buine. You currently order 150 boxe of paper per year, at $50 per box. If you tart recycling with the company, how much money will you ave each year?
You will save as much as $1000 each year if you start recycling with the company.
If your current order of 150 boxes of paper per year costs $50 per box, and in exchange of starting recycling with the company, the recycling company will donate 20 boxes of new paper each year to your business, then you will save as much as $1000 each year.
Determine how much you will save by multiplying the amount of boxes of paper the recycling company will give to your business with the cost of each box of paper.
20 boxes of new paper x $50 per box = $1000
Therefore, the amount you will save if you start recycling with the company will be as much as $1000 each year .
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I need help with this question please and thank you
Answer:
See below
Step-by-step explanation:
Please help, 25 points.
Answer:
Elena's calculator is not broken.
Step-by-step explanation:
0.06 x 0.5
You can also do this by ignoring the decimals and multiplying normally.
6 x 5 = 30
Then you you count the decimal places and start at the end of your product and move the number of decimal places to the left.
0.030 or 0.03
Please look at photo!
The correct option A: The solution cannot include x = 3 and x = (-1/2) as it will make the equation as indeterminate form, whose solution is not possible.
Explain the indeterminate form of the equation?If an undefined statement containing an operations between two quantities evaluates to something like a single number meaning or infinity, it is referred to as having a determinate form. If an undefined expression doesn't quite evaluate to just a single numerical value or infinity but instead involves an operation between two numbers, it is referred to as having an indeterminate form.When establishing the limit of a ratio between two functions, including x/x3, x/x, and x2/x, the ratios go to, ∞, 1, and 0 accordingly when x approaches zero.For the stated equation.
6 / (2x + 1) - 1 / (x - 3) = 0.
When putting x = x = 3 and x = (-1/2), the denominator part will become zero.
This makes the whole equation as indeterminate form,whose solution is not possible.
Thus, the solution cannot include x = 3 and x = (-1/2) as it will make the equation as indeterminate form, whose solution is not possible.
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2(3b+6) =78 : Answer is 11
-2(6c-3) = -72 : Answer is 6.5
Check left Side of both equations
Solve each equation in steps:
2(3b + 6) =78 Given3b + 6 = 39 Divide both sides by 23b = 33 Subtract 6 from both sidesb = 33/3 Divide by 3b = 11 Answer-2(6c - 3) = -72 Given6c - 3 = 36 Divide both sides by - 26c = 39 Add 3 to both sidesc = 39/6 Divide by 6c = 6.5 AnswerAnswer:
b = 11 c = 6.5Step-by-step explanation:
1) 2(3b + 6) = 78, value of b?
→ 2(3b + 6) = 78
→ 6b + 12 = 78
→ 6b = 78 - 12
→ 6b = 66
→ b = 66/6
→ [ b = 11 ]
Hence, the value of b is 11.
2) -2(6c - 3) = -72, value of c?
→ -2(6c - 3) = -72
→ -12c + 6 = -72
→ -12c = -72 - 6
→ -12c = -78
→ c = (-78)/(-12)
→ c = 78/12
→ [ c = 6.5 ]
Hence, the value of c is 6.5.
For what value of a the distance between the points 2 3 and 5 A is equal to 5?.
For a = 1 and a = -7, the distance between the points (2, -3) and (5, a) is equal to 5.
As we know according to the distance formula the distance between points (x₁, y₁) and (x₂, y₂) is given by,
[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}[/tex]
Here we have been given the distance between the points (2, -3) and (5, a)
Let us assume that (x₁, y₁) = (2, -3)
and (x₂, y₂) = (5, a)
Let d represents the distance between points (2, -3) and (5, a)
here d = 5 units
Using above distance formula,
[tex]\Rightarrow d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}\\\\\Rightarrow 5 = \sqrt{(5 - 2)^2 + (a -(- 3))^2}\\\\\Rightarrow 5 = \sqrt{(3)^2 + (a+3)^2}\\\\\Rightarrow 5^2=(3)^2 + (a+3)^2\\\\\Rightarrow 25=9+(a+3)^2\\\\\Rightarrow (a+3)^2=16\\\\\Rightarrow a+3=\pm 4[/tex]
⇒ a + 3 = 4 OR a + 3 = -4
⇒ a = 4 - 3 OR a = -4 - 3
⇒ a = 1 OR a = -7
Therefore, the values of 'a' are 1, -7
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The complete question is
For what value of a the distance between the points (2, -3) and (5, a) is equal to 5?.
Find the Maximum on the interval {3,5} for the line y= 2x+1
The maximum value of the linear equation on the given interval is:
y = 11
How to find the maximum on the given interval?We want to find the maximum of the linear function:
y = 2x + 1
On the interval [3, 5]
Notice that we have a line with a positive slope, thus, this is an increasing line.
Then the maximum is just what we get when we evaluate the function on the maximum value of the interval:
y = 2*5 + 1
y = 10 + 1
y = 11
The maximum value is 11.
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can someone explain how 1x-0.30x=0.7x
i just need an explanation ty
Answer:
See attached
Step-by-step explanation:
You can write 1 as 1.00 then line up the decimals with0.30 and subtract. The answer will be .7 or 0.7. They mean the same thing.
The Tanners are installing a rectangular pool in their back yard. They are also enclosing the yard and pool with a fence and the back of their house. See the figure below. What is the minimum number of feet of fencing needed to enclose the yard?
He need a fence that is 54 feet long.
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.
Area of rectangle is A = a*b
Consider the length to be 40 feet, which is how long one side of the yard is known to be. The yard's size is 280 square feet, as you are already aware. Knowing the yard's width is necessary in order to calculate the perimeter:
A = LW
W= 280/40 = 7 feet
The two 7-foot sides and one 40-foot side are fenced in by him . He,
therefore, He needs a fence that is 54 feet long.
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I need some help on this question
The value of x is 39 and the values of angle m1 and m2 is 63 and 117. We can solve the question using linear pair.
What is linear pair?
When two lines meet at a single point, a pair of linear angles is created. If the angles follow the point where the two lines cross, they are considered to be linear pair. A linear pair's angles add up to 180° in every case. These angles are additionally referred to as. Angles with a shared vertex are those that are adjacent.
Therefore, the linear angles also have a common vertex in this instance.
Additionally, a common arm that symbolizes both angles will be present.
A ladder against a wall that creates linear angles at the ground is an example of a linear pair in real life. One who is straight is represented by linearity.
Using linear pair, we have equation
m1 +m2 = 180
x+24 +3x = 180
4x = 156
x = 39
Then the values of m1 =x +24 = 64
m2 = 3x = 117
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A chocolatier made 16 batches of salted caramel chocolate
bars. Each batch consisted of 42 chocolate bars. The
chocolatier sent an equal number of bars to each of its
6 stores. How many bars did each store receive?
Answer:
112 chocolate bars
Step-by-step explanation:
Given that the chocolatier made 16 batches of salted caramel chocolate bars, each batch consisted of 42 bars and he sent an equal number of bars to each of its 6 stores,
What is asked: To determine how many bars did each store receive.
Method of solving: Using elementary operations as multiplication and division.
Start considering each batch as the following box:
So it suggests that to find the total number of chocolates produced is equal to the product
Before multiplying, now see that the chocolatier is equally dividing them to its 6 stores, which means that he will take this quantity and divide equally into 6 boxes.
Therefore, this process is the same as dividing by 6, therefore
Is the expression that gives the result desired.
Simplifying the fraction and multiplying the terms gives
112 chocolate barsThis is the amount of chocolate bars each store received.
Someone help me pleaseeee
For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.
What is right triangle?A right triangle, right-angled triangle, or more formally an orthogonal triangle—previously known as a rectangled triangle—is a triangle with one angle that is a right angle (i.e., a 90-degree angle), meaning that two of its sides are perpendicular. The foundation of trigonometry is the relationship between the sides and other angles of a right triangle.
The hypotenuse is the side that faces the right angle (side c in the figure). Legs are the sides that are next to the right angle (or catheti, singular: cathetus). Side a can be thought of as the side that is adjacent to angle B and opposite to (or opposite) angle A, whereas side b is the side that is adjacent to angle A and opposite to angle B.
Given a right triangle with base = 8 and an angle = 24°
Using angle sum property of triangle
24 + 90 + angle L = 180
L = 66°
Using Sohcahtoa
Tangent: tan(θ) = Opposite / Adjacent
tan(24°) = LK/8
0.445 = LK/8
LH = 8 × 0.445
LK = 3.56
LM = [tex]\sqrt{MK^2 + LK^2}[/tex]
LM = [tex]\sqrt{8^2 + 3.56^2}[/tex]
LM = 8.75
Thus, For the given right triangle, L = 66°, LK = 3.56, and the hypotenuse, LM = 8.75.
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pendiente y ángulos A(-8,6) B(11,2)
The slope of the line containing the points A(-8,6) and B(11,2) is given as follows:
m = -0.2105.
The angle of the line is given as follows:
θ = -11.89º.
How to obtain the slope and the angle?The two points on the line are given as follows:
A(-8,6) and B(11,2).
Given two points, the slope is obtained by the division of the change in y by the change in x, hence:
m = (2 - 6)/(11 + 8)
m = -0.2105.
The slope represents the tangent of the angle, hence the angle is the arc tangent of the slope, thus:
θ = arctan(-0.2105)
θ = -11.89º.
TranslationThe problem asks for the slope and for the angle of the line containing points A and B.
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Sooo yeah umm..... I need help.
Answer:
[tex]\mathrm{Slope } = \dfrac{2}{3}[/tex]
Step-by-step explanation:
To find the slope take any two convenient x, y value combo.
Find the difference between the two y-values(we call it rise).
Find the difference in the corresponding x-values (we call this the run)
[tex]\dfrac{rise}{run} = slope[/tex]
Take points (3, 1) and (6,3). I could choose any two points but working with positive numbers makes it easier
Rise = 3- 1 = 2
Run = 6 - 3 = 3
[tex]\mathrm{Slope } = \dfrac{2}{3}[/tex]
Just for the heck of it let's take two other points to make sure we haven't goofed
Take points (-1, - 5/3) and (1, -1/3)
rise = -1/3 - (-5/3) = -1/3 + 5/3 = 4/3
run = 1 - (-1) = 2
rise over run = 4/3 ÷ 2 = 4/3 x 1/2 = 2/3
spara
2:
Back to task
Calculate the coordinates of the midpoint of point P and point Q, which are
shown below.
12
11
10
9
8
7
65
Calculator
Bookwork code: J44 not allowed
6
5-
43
3
2-
1
P
Q
#I
0 1 2 3 4 5 6 7 8 9 10 11 12
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In the coordinate plane, if a line is drawn to connect two points (4, 2), and (8, 6), then the coordinates of the midpoint of the line joining these two points are ({4 + 8}/2, {2 + 6}/2) = (12/2, 8/2) = (6, 4).
What is midpoint?Midpoint refers to a point that is in the middle of the line joining two points. The two reference points are the endpoints of a line, and the midpoint is lying in between the two points. The midpoint divides the line joining these two points into two equal halves. Further, if a line is drawn to bisect the line joining these two points, the line passes through the midpoint.
The midpoint formula is used to find the midpoint between two points whose coordinates are known to us. The midpoint formula is also used to find the coordinates of the endpoint if we know the coordinates of the other endpoint and the midpoint. In the coordinate plane, if a line is drawn to connect two points (4, 2), and (8, 6), then the coordinates of the midpoint of the line joining these two points are ({4 + 8}/2, {2 + 6}/2) = (12/2, 8/2) = (6, 4). Let us learn more about the formula of the midpoint, and different methods to find the midpoint of a line.
(3, 8 )
given 2 points (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
(x+x /2 ,y+y/2 )
here (x₁, y₁ ) = P (1, 6 ) and (x₂, y₂ ) = Q (5, 10 ) , then
midpoint = (1+5/2 ,++10/2 ) = ( 6/2 , 16/2 ) = (3, 8 )
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What is the standard form of Y =- 2x 5?.
The standard form of the line is Ax + By + C = 0 or we can say y = mx + c.
Equation of Line Point-slope form: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.Slope-intercept form: y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).Standard form: Ax + By = C, where A and B are the x and y coefficients, respectively, and C is a constant.Intercept form: x/a + y/b = 1, where a and b are the x and y intercepts, respectively.Two-point form: (x - x1)/(x2 - x1) = (y - y1)/(y2 - y1), where (x1, y1) and (x2, y2) are two points on the line.Parametric form: x = x0 + at, y = y0 + bt, where x0, y0 are the coordinates of a point on the line and a, b are the direction ratios and t is a parameter.Normal form: (x - x0)nx + (y - y0)ny = 0, where (x0, y0) is a point on the line and nx, ny are the direction ratios of the line's normal vector.To know more about the equation of a line on brainly : brainly.com/question/21511618
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3. Ura Snob has three times as many dimes as quarters. If he has $2.75, how many quarters
does he have?
Answer:
75x = 300
x = 4
So he has
4 quarters
3x = 3*4 = 12 dimes
4x = 4*4 = 16 nickels
Step-by-step explanation:
Lexie's younger brother helped pick up all the paper clips in
Lexie's room. He was able to collect 8,100 paper clips. If he wants
to distribute the paper clips in 90 boxes, write an equation
showing how many paper clips each box will contain?
This equation divides the total number of paper clips (8100) by the number of boxes (90)
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. It is usually expressed using an equals sign (=), with the expressions on either side of the sign separated by the equation symbol. Equations are used to describe relationships between different variables, or to solve for unknown values. Equations are also used to explain physical phenomena, such as Newton's second law of motion, which states that force equals mass times acceleration (F = ma).
The equation that would be used to determine how many paper clips each box will contain is 8100 ÷ 90 = 90.
This equation divides the total number of paper clips (8100) by the number of boxes (90) in order to determine that each box will contain 90 paper clips.
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You are placing a fountain in a triangular koi pond. You want the
fountain to be the same distance from each edge of the
pond. Where should you place the fountain? Explain
your reasoning. Use a sketch to support your answer.
As the person wanted the fountain to be the same distance from each edge of the pond and the incenter of the triangle is equidistant
How to illustrate the distance?From the information, the person is placing a fountain in a triangular koi pond and want the fountain to be the same distance from each edge of the
pond.
The intersection of all three of the triangle's interior angle bisectors is where a triangle's incenter is located. It can be thought of as the intersection of the triangle's internal angle bisectors. The fountain is equally spaced from each edge of the pond because the person wanted it to be, and the triangle's incenter is also evenly spaced.
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The number of loaves of bread purchased and the total cost of the bread in dollars can be modeled by the equation c = 3.5b. Which table of values matches the equation and includes only viable solutions?
A 2-column table with 4 rows. The first column is labeled loaves (b) with entries negative 2, 0, 2, 4. The second column is labeled cost (c) with entries negative 7, 0, 7, 14.
A 2-column table with 4 rows. The first column is labeled loaves (b) with entries 0, 0.5, 1, 1.5. The second column is labeled cost (c) with entries 0, 1.75, 3.5, 5.25.
A 2-column table with 4 rows. The first column is labeled loaves (b) with entries 0, 3, 6, 9. The second column is labeled cost (c) with entries 0, 10.5, 21, 31.5.
The table for the function c{b} is -
{b} : 1 2 3 4
c{b} : 3.5 7.0 10.5 14
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that the number of loaves of bread purchased and the total cost of the bread in dollars can be modeled by the equation c = 3.5b.
We can write the table for the function c{b} as -
b c{b}
1 3.5
2 7.0
3 10.5
4 14
Therefore, the table for the function c{b} is -
{b} : 1 2 3 4
c{b} : 3.5 7.0 10.5 14
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What does represent? index of refraction index of reflection angle of incidence angle of refraction.
The figure represents the angle of refraction
The angle of refraction is represented by the angle θ2
Light rays that are refracted change their direction as they travel through different media. Light changes direction when it travels from one medium to another.
The refracted beam will bend toward the normal if the incident light is moving from a less dense to a denser material. Here, the angle of refraction (hence, "r") is always smaller than the angle of incidence. (In line with the diagram)
Similar to this, the refracted ray will bend away from the normal if the incident light is moving from a denser medium to a less dense material. In this situation, the angle of incidence is never greater than the angle of refraction, or "r."
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number 6 please help
Answer: x = 26
Step-by-step explanation: All you need to do is to add up given two unknown angles. Then, you can solve the equation for 180 degree. Because in this case, these angles are complementary to 180 degrees.
If you add them up:
[tex]8x - 28 = 180\\x = 26[/tex]
So, the answer is 26.
solve for N.
40 = 5n
Answer:
n=8
Step-by-step explanation:
40=5n
40=5x8
Answer:n=8 I hope this helps mark brainlist if correct
Step-by-step explanation:
40=5n
Swap the sides of the equation
5n=40
Divide both sides of the equation by 8
n=8
Eddie and Ellen use a calculator to work out
Eddie's answer is 1.5
Ellen's answer is 15
One of those answers is correct.
431.1/ 14.3 +3.8²2
Use approximations to find out which answer is correct.
Answer: 14.3 times 1.5 equals 55.
Step-by-step explanation: multiplication can be used to solve the equation
How do you sketch the graph of a function of two variables?.
A two-variable function's graph can be thought of as a surface in three dimensions.
The points (x, y, f(x, y)) where x and y are in the domain make up the graph of z=f(x, y). You can fine-tune the shape of the surface by drawing the curve k=f(x, y) in the plane z=k for different values of k. For instance, we're trying to comprehend the graph of z=f(x, y)=x2+y2. Keep in mind that k=f(x, y) is a circle for k>0 and since 0=x2+y2 implies that x=y=0.
Additionally, it is symmetric in relation to the z axis. We have a parabola for x=k or y=k. As a result, the graph represents the revolution of the parabola z=x2 over the z axis (see Thomas, math).
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What is the formula of the range Mcq?.
The range formula determines the difference between the highest and the lowest values in a given set of numbers.
The range formula is mostly used in statistics where the range is the spread of the numbers or data from the lowest to the highest value and it is commonly used in variability. Let's learn more about the range formula and solve a few examples.
The range formula is highly used in statistics to consider the range given in a particular data set. The formula assists in determining the center of the set by finding the difference between the lowest and the highest number. In distribution, the big range means more variability whereas the less range means low variability. The range formula has the other aspects of statistics such as mean, median, and mode. Therefore, the formula to calculate the range is:
R = Highest Value (H) - Lowest Value (L)
Range Formula
R = H - L
In this context,
R is the range
H is the highest value
L is the lowest value
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Answer:
Step-by-step explanation:
The range formula determines the difference between the highest and the lowest values in a given set of numbers. The range formula is mostly used in statistics where the range is the spread of the numbers or data from the lowest to the highest value and it is commonly used in variability. Let's learn more about the range formula and solve a few examples.
The range formula is highly used in statistics to consider the range given in a particular data set. The formula assists in determining the center of the set by finding the difference between the lowest and the highest number. In distribution, the big range means more variability whereas the less range means low variability. The range formula has the other aspects of statistics such as mean, median, and mode. Therefore, the formula to calculate the range is:
R = Highest Value (H) - Lowest Value (L)
Range Formula
R = H - L
In this context,
R is the range
H is the highest value
L is the lowest value
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