Irreflexive closure is the creation of a new binary relation by adding irreflexivity property, meaning no element is related to itself.
What is binary ?
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" and "1".
An irreflexive closure is a mathematical concept that refers to the creation of a new binary relation from a given binary relation by adding the property of irreflexivity. A binary relation is irreflexive if it does not relate any element to itself. The irreflexive closure of a binary relation is the smallest irreflexive relation that contains it.
In other words, the irreflexive closure of a binary relation is a modified version of the original relation where no element is related to itself. The process of finding the irreflexive closure involves removing all self-referential relationships and adding new relationships to preserve the original relationships between elements.
Irreflexive closure is the creation of a new binary relation by adding irreflexivity property, meaning no element is related to itself.
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U.9 Arcs and chords P63
OH OE. What is the length of CD?
C
CD =
75°
E
D
285°
H
F
28
G
The length of arc CD is 92.69
From the given circles we know that:
Circle E = Circle H
GF = CD = 28
∠CED = 75°
Arc CD?
We can imagine an imaginary radius line here are:
GH = FH = CE = DE
However we have no idea the length of the radius line of both circles.
We will use Law of Cosines to find the length of the radius line by taking GHF as a, isosceles triangle:
GF² = GH² + FH² - 2 GH FH cos H
28² = 2GH² - 2GH² cos 75°
28² = 2GH² (1 - cos 75)...(i)
Remember that:
Cos (A+B) = cos A cos B - sin A sin B
cos 75° = cos (30 + 45)°
cos 75° = cos 30 cos 45 - sin 30 sin 45
cos 75° = (√3/2)(√2/2) - (1/2)(√2/2)
cos 75° = √6/4 - √2/4
cos 75° = 1/4 (√6 - √2)
cos 75° = 0.921 ... (ii)
We subtitute equation (ii) into equation (i)
784 = 2GH² (1 - 0.921)
2GH² = 784 / (0.079)
GH = 70.78 = ED = EC
The length of arc CD is:
Arc CD = 75°/360° 2πr
Arc CD = 75°/360° 2π.ED
Arc CD = 92.69
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a mint produces 100,000 coins. upon weighing some of them with a precise scale, officials find that the coins vary slightly in weight, with an independent uncertainty of 1%. about how many coins must be randomly sampled and weighed in order to determine the total weight of the coins to within 0.1% uncertainty? assume there are no sources of systematic uncertainty.
To determine the total weight of the coins to within 0.1% uncertainty, we need to weigh 100 coins.
We can use the formula for the standard deviation of the mean to determine the number of coins needed to be weighed. The formula is given by -
σ mean = σ/√N
Where σ is the standard deviation of the coins and N is the number of coins weighed.
We are given that the standard deviation of the coins is 1%, we have,
σ mean = 1%/√N
We want to determine the number of coins N such that σ mean = 0.1%. So, 0.1% = 1%/√N
Dividing both sides by 0.1% we get,
√N = 1%/0.1% = 10
Taking the square of both sides,
N = [tex]10^2[/tex] = 100
Therefore, to determine the total weight of the coins to within 0.1% uncertainty, we need to weigh 100 coins.
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Directions; find the area and perimeter of each figure. Assume all lines that appear are parallel. Round to the nearest tenth if necessary.
The area and perimeter of the given parallelogram are
30√30 cm² and 56 cm respectively.
Define area and perimeter.Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.Perimeter is the length of the boundary of the 2 - D figure.Given is a parallelogram as shown in the image attached.
{ 1 } -From the Pythagoras theorem, we can write that -
h² = 13² - 7²
h² = 169 - 49
h² = 120
h = √120
h = 2√30 .... Eq { 1 }
Now, we can write the parallelogram as -
A = b x h
A = 15 x 2√30
A = 30√30 cm²
{ 2 } -We can write the perimeter as -
P = 15 x 2 + 13 x 2
P = 30 + 26
P = 56 cm
Therefore, the area and perimeter of the given parallelogram are
30√30 cm² and 56 cm respectively.
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The two polygons shown are similar. Determine the value of y and z.
The required values of x = 8 units and z = 15 units for the given polygon.
What is a polygon?A polygon is a two-dimensional flat form with straight, completely closed sides. Straight, not curved, sides are required. Polygons, on the other hand, can have any number of sides.
The two polygons shown are similar.
As we know that two similar polygons with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.
So QP/WX = PS/WZ
⇒ x/12 = 6/9
⇒ x = 72/9
⇒ x = 8 units
Now, RS/YZ = PS/WZ
⇒ 10/z = 6/9
⇒ z = 90/6
⇒ z = 15 units
Thus, the required values of x = 8 units and z = 15 units.
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In the scale drawing below, 1 cm represents 2 m. a) What is the width, in metres, of the building in real life? b) The real building is 8.2 m tall. What is the height of the drawing of the building, in centimetres? 0 cm HH 1 8 HABHARAA. 2 HHE 88 3 4 5 6 7 8 וייייייייויי 9 10
Answer:
a) 11m
b)4.1cm
Step-by-step explanation:
if 1 cm = 2m
hence,
5.5cm = (5.5 x 2) = 11m
if 2m = 1cm
hence,
8.2 = (8.2 ÷ 2) = 4.1cm
What are the most common graphs for numerical data (interval or ratio data)?
The histogram, time series, box plot, stem and leaf, and frequency polygon.
What kind of graph do you use to represent numerical data?Dot plots, stem and leaf graphs, histograms, box plots, ogive graphs, and scatter plots are all used to graph numerical data. The dot plot: Stem and leaf: The stem represents the first digit of the number in these graphs, while the leaf/leaves indicate the second digit (s). A histogram or a polygon graph should be used for scores that fall on an interval or ratio scale. A bar is centered above each score (or interval) in a histogram, with the height corresponding to the frequency of that score or interval and the width according to the true boundaries of that score or period.
Scatterplot. Scatter plots are effective for displaying accurate, dense data visualizations, relationships, and groupings between variables.
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what is the probability that a normal random variable will take a value that is less than 1.05 standard deviations above its mean? in other words, what is p(z < 1.05)?
The probability that a standard normal random variable will take a value less than 1.05 is approximately 0.8528.
Probability is a mathematical concept that quantifies the likelihood or chance of an event occurring. It is a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
To find the probability that a standard normal random variable is less than a certain value, use a standard normal table or use a calculator with a cumulative distribution function (CDF) for the standard normal distribution.
Look up that value in the standard normal table and find the corresponding cumulative probability.
Hence, p(z < 1.05) = 0.8528.
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There were x dogs at the park and 1/5 of the dogs were on a leash. How many dogs were not on a leash? Write an expression using both subtraction and multiplication to express how many dogs were not on a leash.
Answer:
Let y be the total number of dogs
dogs on leash = y/5
dogs not on leash = y-y/5
= 4y/5
The expression to represent how many dogs were not on a leash is 4x / 5, using both subtraction and multiplication.
What is Expression?An expression is combination of variables, numbers and operators.
If 1/5 of the dogs were on a leash, then the remaining 4/5 of the dogs were not on a leash.
To find the number of dogs that were not on a leash, we can multiply the total number of dogs (x) by 4/5:
Number of dogs not on a leash = x * 4/5
We can also express this using subtraction:
Number of dogs not on a leash = x - (x * 1/5)
Simplifying the expression on the right side:
Number of dogs not on a leash = x - x/5
Combining like terms:
Number of dogs not on a leash = (5x - x) / 5
= 4x / 5
Therefore, the expression to represent how many dogs were not on a leash is 4x / 5, using both subtraction and multiplication.
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Kathryn leaves her home and travels at an average speed of 45 mi./hr. until she reaches her grandmother's home 180 mi. away. How long does it take her to reach her grandmother's house?
using newman projections to sight along the c1-c2 bond, draw the lowest and highest energy conformations of 1-chloropropane.
The lowest energy and highest energy conformations of 1-chloropropane is as follow
Cl-CH2-CH2-CH3.
For better visualize different conformations of a given molecule,
A drawing convention is convenient to use called the Newman projection.
In a Newman projection,
we look lengthwise down a specific bond of interest – the carbon-carbon bond in ethane.
We depicted the front atom as a dot, and the ‘back’ atom as a larger circle.
the C-C bond in this way, the angle formed between a C-H bond on the front carbon and a C-H bond on the back carbon
carbon is referred to as a dihedral angle.
1-chloropropane. molecular formula is C3H7Cl
The lowest energy and highest energy conformations of 1-chloropropane is as follow
Cl-CH2-CH2-CH3.
Cl would be the largest substituent for Carbon 1, and CH3 would be the largest substituent for Carbon 2,
so I would put them opposite from each other on the projection.
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Given that vC(0) = 2 cos(155°) V, what is the instantaneous voltage across a 2-μμF capacitor when the current through it is i = 8 sin(106t + 25°) A? Please report your answer so the magnitude is positive and all angles are in the range of negative 180 degrees to positive 180 degrees. (The final answer should also be in sine, not cosine form, similar to the i given above).
The instantaneous voltage across a capacitor is |2cos(155°)| sin(106t + 25° - angle(2 cos(155°))).
The instantaneous voltage across a capacitor is given by the equation:
vC(t) = vC(0) + 1/C * ∫i(t)dt
Since i(t) = 8 sin(106t + 25°), we can find the integral using the formula for the integral of a sine function:
∫i(t)dt = -8/106 cos(106t + 25°)
So,
vC(t) = 2 cos(155°) - 8/106 ∫ cos(106t + 25°)dt
vC(t) = 2 cos(155°) - 8/106 sin(106t + 25°)
The magnitude of vC(t) is positive, and the angle should be in the range of -180° to 180°. The final answer is in sine form, so we can write:
vC(t) = |2 cos(155°)| sin(106t + 25° - angle(2 cos(155°)))
where angle(2 cos(155°)) is the angle of 2 cos(155°).
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Sammi borrowed 11 DVDs from her local library for a total of 1,200 minutes. All of the DVDs were either animated or a superhero movie. Each of the animated DVDs lasted for about 90 minutes. Each superhero movies lasted about 120 minutes. How many of each type of movie did Sammi borrow?
In your handwritten work do the following:
Clearly define your variables used
Write a system of linear equations representing the scenario
Solve the system of equations algebraically either by substitution or elimination
Check your solution algebraically and describe what your solution means in context
In the textbox below:
Write your solution and describe why you chose the method you did (substitution or elimination) instead of choosing the other option. After solving, do you feel you chose the most efficient or easiest method?
Answer:
Let x be the number of animated DVDs Sammi borrowed and y be the number of superhero DVDs she borrowed.
The total number of minutes of all DVDs is 1,200, so we have:
90x + 120y = 1,200
And the total number of DVDs borrowed is 11, so we have:
x + y = 11
To solve this system of linear equations, we can use substitution method. Solving for y in the second equation, we get:
y = 11 - x
Substituting this expression for y into the first equation, we have:
90x + 120(11 - x) = 1,200
Expanding the right side, we get:
90x + 1320 - 120x = 1,200
Combining like terms, we get:
-30x = -120
Solving for x, we get:
x = 4
Since x is the number of animated DVDs, Sammi borrowed 4 animated DVDs. Substituting this value of x back into the expression for y, we have:
y = 11 - x = 11 - 4 = 7
So Sammi borrowed 7 superhero DVDs.
The solution means that Sammi borrowed 4 animated DVDs and 7 superhero DVDs, which lasted for a total of 1,200 minutes. This method was relatively simple and efficient, as it only involved solving for one variable and then using substitution.
How to find the domain and range in interval notation on a graph?
The collection of all feasible inputs and outputs for a function, respectively, is its domain and range.
What is the domain and range of a function in interval notation?A function's domain is its collection of inputs. The collection of outputs for a function is known as range. For example, when specifying domain and range, interval notation is used to describe groups of numbers. There are two types of intervals: open and closed.
The collection of possible input values is referred to as the domain, and the domain of a graph is made up of all the input values displayed on the x-axis. The collection of potential output values that make up the range is represented by the y-axis.
By using values enclosed in brackets to define a group of numbers, interval notation can be used to express the domain and range. In interval notation, we use a square bracket to denote that the endpoint is included in the set and a parenthesis to denote that the endpoint is either excluded from the set or that the interval is unbounded.
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an athlete leaves one end of a pool of length at and arrives at the other end at time . she swims back and arrives at the starting position at time . if she is swimming initially in the positive direction, determine her average velocities symbolically in (a) the first half of the swim, (b) the second half of the swim, and (c) the round trip. (d) what is her average speed for the round trip?
(a) The average velocity for the first half of the swim: v1 = L / t1.
(b) The average velocity for the second half of the swim: v2 = L / t2.
(c) The average velocity for the round trip is given by: v = 2L / (t1 + t2).
(d) The average speed for the round trip is the magnitude of the average velocity: s = |v| = 2L / (t1 + t2).
Let's assume the length of the pool is L and
The time for the athlete to swim to the other end is t1,
And the time for her to swim back is t2.
(a) The average velocity for the first half of the swim (from one end to the other end) is given by:
the distance travelled divided by the time taken:
=> v1 = L / t1.
(b) The average velocity for the second half of the swim (from the other end back to the starting position) is given by
v2 = L / t2.
(c) The average velocity for the round trip is given by:
the total distance traveled divided by the total time taken:
=> v = 2L / (t1 + t2).
(d) The average speed for the round trip is the magnitude of the average velocity:
s = |v| = 2L / (t1 + t2).
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ECONOMICS - what is in the change in the quantity deanded when the price of oil increases from 20 to 5 per barrel
The change in demand is $15 per barrel.
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 price of oil increases from 20 to 5 per barrel.
A change in quantity demanded refers to a change in the specific quantity of a product that buyers are willing and able to buy. This change in quantity demanded is caused by a change in the price.So we can write the change in demand as -
$20 per barrel - $5 per barrel
$15 per barrel
Therefore, the change in demand is $15 per barrel.
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Entre ana y maria tienen 65 lápices. Si Ana tiene el doble que maría más 10 lápices, ¿cuántos lápices tiene cada una?
The number of pencils that each person has is given as follows:
Ana: 47 pencils.Maria: 18 pencils.How to obtain the number of pencils that each person has?The number of pencils that each person has is obtained by a system of equations, for which the variables are given as follows:
Variable x: number of pencils that Ana has.Variable y: number of pencils that Maria has.They have a total of 65 pencils, hence:
x + y = 65.
Ana has double Maria's amount plus 10 pencils, hence:
x = 2y + 10.
Replacing x = 2y + 10 on the first equation, Maria's amount is obtained as follows:
2y + 10 + y = 65
3y = 55
y = 55/3
y = 18.
Hence Ana's amount is given as follows:
x = 65 - 18 - 47.
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Keiko the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other
(not both). On Monday there were 5 clients who did Plan A and 3 who did Plan B. On Tuesday there were 2 clients who did Plan A and
12 who did Plan B. Keiko trained her Monday clients for a total of 7 hours and her Tuesday clients for a total of 19 hours. How long
does each of the workout plans last?
tom invested $3460 into a bank for 6 years. His money was compounded annually at a 8.5% interest rate. What is his total amount of money now?
Answer:
$5644.88
Step-by-step explanation:
Formula for Compound interest: P(1 + r/n)^nt
P: initial amount
r: Interest rate
n: number of times compounded pet t
t: time period (usually in years)
3460(1 + 0.085/1)^6 = 5644.8775806
What is the least common denominator of 1/4,1/2, and 3/4
The least common denominator of the fractions 1/4,1/2, and 3/4 is 4.
What is the least common denominator?
The smallest number that can serve as a common denominator for a group of fractions is known as the least common denominator. The smallest number that may be used as the denominator to produce a group of comparable fractions that all have the same denominator is known as the lowest common denominator.
All integers and mixed numbers (mixed fractions) must first be converted into fractions before attempting to identify the least common denominator. Next, determine the denominators' lowest common multiple (LCM). This value corresponds to the lowest common denominator (LCD). Then, using the same LCD denominator, you can write each phrase as an equivalent fraction.
Given 1/4, 1/2, 3/4
We are asked to find the least common denominator.
LCD of the given fractions is the LCM of the denominators 4,2,4.
LCM = 4
Therefore the least common denominator of the given fractions is 4.
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The area of a rectangular field i given a (2x^2 5x -3) m^2. Find the dimenion of the field
The dimensions of the rectangular field are L = 2x - 1 m and W = x + 3 m.
Let's call the length of the field L and the width of the field W. Then we have:
Area = Length * Width
(2x² + 5x - 3) m² = L * W
To find the dimensions, we need to factor the expression for the area.
Area = 2x² + 5x - 3
Area = 2x² + 6x - x - 3
Area = 2x(x + 3) - (x + 3)
Area = (2x - 1)(x + 3)
We can now see that the expression for the area is the same as (2x^2 + 5x - 3), so:
Area = (2x - 1)(x + 3) m²
Therefore, the dimensions of the rectangular field are L = 2x - 1 m and W = x + 3 m.
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A line intersects the points (4,3) and (6,9) m = 3 write an equation in point-slope form using the point (4,3)
Answer:
y = 3x + 9
Step-by-step explanation:
Point-slope form: y - y₁ = m(x - x₁)
y - 3 = 3(x - 4)
y - 3 = 3x - 12
y = 3x + 9
What percentage of the work force between the ages of 25 and 65 has achieved post-secondary educational credentials in Canada?
a. 25.5 percent b. 38.3 percent c. 64.1 percent d. 73.9 percent
Option D is correct. 73.9 percent of the workforce between the ages of 25 and 65 has achieved post-secondary educational credentials in Canada.
According to the most recent data from Statistics Canada, approximately 73.9 percent of the workforce between the ages of 25 and 65 has achieved post-secondary educational credentials in Canada. This data shows a significant increase in the number of Canadians who have pursued higher education in recent years, reflecting a trend towards increased investment in education and training as a means of achieving higher levels of skills and knowledge.
This high percentage of workers with post-secondary credentials is a positive indicator of the strength of Canada's economy, as it demonstrates a well-educated and highly skilled workforce. This, in turn, attracts investment and contributes to the growth of industries, creating new job opportunities and fostering economic prosperity.
Furthermore, the attainment of post-secondary education is associated with higher earnings and improved job prospects, both of which contribute to greater overall financial security and stability. As such, the high percentage of the workforce with post-secondary credentials in Canada is a testament to the country's commitment to education and the pursuit of economic and personal success.
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Sebastian bought 3 envelopes with 6 figures each. How many figures did he buy in all?
If the world were a village of 100 people, how many of the people would not have electricity
1 billion people in the world don't have electricity
Answer:
13 people wouldn't have electricity
Step-by-step explanation:
Ratio of people with electricity to people without electricity is 8,000,000,000 : 1,000,000,000 or 8:1
8:1 = 100:x We need to find x. To do this, divide 100 by 8.
100/8 = 12.5
Then multiply the other side of the ratio (1) by that number.
12.5 · 1 = 12.5
Out of 100 people in a village 12.5 of them don't have electricity. (You can't have half of a person so you round it to 13.)
orter made a scale drawing of a campsite. The scale of the drawing was 8 inches = 6 feet. What is the scale factor of the drawing?
Simplify your answer and write it as a fraction.
The drawing's scale factor, if The scale of the drawing was 9 inches = 6 feet, is 3/4.
What is the scale factor?
To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilized. It is employed to change the size of an object.
Given,
orter made a scale drawing of a campsite. The scale of the drawing was 8 inches = 6 feet.
The scale of the drawing was 8 inches = 6 feet,
The original value = 6 feet,
The value on paper = 8 inches,
Calculate the scale factor as shown below,
Scale factor = The original value / The value on paper
Scale factor = 6 / 8
Scale factor = 3 / 4
Therefore, The drawing's scale factor, if The scale of the drawing was 9 inches = 6 feet, is 3/4.
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To convert a temperature from degrees Fahrenheit to degrees Celsius, you can use the formula (°F 32)0.56 °C. Write 4 °C in degrees Fahrenheit.
Answer:
Step-by-step explanation:
(F - 32)0.56 = 4
F - 32 = 4/0.56
F = 39.1⁰ F
Holly P. has invested her latest paycheque of $500 in two accounts. One earns 5% interest a year the other 7.5% interest a year. After 3 years she has made $100.50 in interest. How much did she invest into each account?
Answer:
Let's assume Holly invested x dollars in the first account that earns 5% interest and (500-x) dollars in the second account that earns 7.5% interest.
The interest made from the first account after 3 years is x * 0.05 * 3 = 0.15x
The interest made from the second account after 3 years is (500-x) * 0.075 * 3 = 0.225(500-x)
The total interest made is 0.15x + 0.225(500-x) = 100.50
Expanding and solving for x, we get:
0.15x + 112.5 - 0.225x = 100.50
-0.075x = -12
x = 160
So, Holly invested $160 in the first account and $340 in the second account.
6. (9, -4); slope = -2/3
The point be (9, -4) and slope = -2/3 the slope of the equation of line be y = -2x/3 +2
What is meant by slope of the line?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. While there has been no net change in the x coordinate, there has been no net change in the y coordinate.
The slope is m and the y-intercept is b in the slope-intercept version of the equation (y=mx+b). We can also change some equations to be written in slope-intercept form.
Let the equation be y - (-4) = (-2/3)(x - 9)
y + 4 = -2 x/3 + 6
simplifying the equation, we get
y = -2x/3 + 6 - 4
Therefore, the slope of the equation be y = -2x/3 +2
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What is the point of . (9, -4); slope = -2/3
The scale on a map shows that 10 kilometers is represented by 4 centimeters. Which proportion can be used to find the actual distance, x, represented by 20 centimeters on the map?
StartFraction 10 over 4 EndFraction = StartFraction x over 20 EndFraction
StartFraction 10 over 4 EndFraction = StartFraction 20 over x EndFraction
StartFraction 10 over 20 EndFraction = StartFraction 4 over x EndFraction
StartFraction 10 over 20 EndFraction = StartFraction x over 4 EndFraction
The proportion that can be used to find the actual distance is given as [tex]\frac{10}{4} = \frac{x}{20}[/tex], and the correct option is A.
What is scaling?By scaling, we may create a drawing of an item that corresponds to the object's true size. In geometry, scaling refers to either growing or reducing figures in order to preserve their fundamental shape. Similar figures are those that have been scaled.
Given that the scale on a map shows that 10 kilometers is represented by 4 centimeters.
We are to find the proportion can be used to find the actual distance, x, represented by 20 centimeters on the map.
We have
4 centimeters on the map = 10 kilometers.
So, 1 centimeter on the map
[tex]1 cm = \frac{10}{4}[/tex]
Also, 20 centimeters on the map = x kilometers.
So, 1 centimeter on the map
[tex]1cm = \frac{x}{20}[/tex]
Equating the two expressions:
[tex]\frac{10}{4} = \frac{x}{20}[/tex]
Therefore, the proportion that can be used to find the actual distance is given as [tex]\frac{10}{4} = \frac{x}{20}[/tex], and the correct option is A.
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How can the least common multiples of 8 and 12 be calculated?
Find the multiples of 8 and 12 (multiples of 8 = 8, 16, 24, 32; multiples of 12 = 12, 24, 36, 48) and select the lowest multiple that is precisely divisible by 8 and 12, which is 24.
Using the listing approach, what is the LCM of 8 and 12?The LCM of 8 and 12 is 24 regardless of the technique chosen. To obtain this number, the listing technique will display the first three multiples of 8 and the first two multiples of 24. The prime factor technique compares the two numbers’ prime factors and multiplies them together, omitting repeated factors.
The first approach to compute the least common multiple: This is the method we used previously; in other words, we write the initial multiples of each integer, record the common multiples, and pick the least common multiple.
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