The error she made is option c. Jamie did not factor the variable from the second term.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given expression is 15x - 20xy.
We have to factor the expression.
Common factor of both the terms 15x and 20xy is 5x.
Taking the term 5x outside and using the distributive property,
15x - 20xy = 5x (3 - 4y)
But Jamie got it as 5x (3 - 4xy)
So the variable in the second term has not been factored correctly.
Hence the error in the process is that She did not factor the variable from the second term.
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Six pizzas were shared among 8 groups of children. Each child got 3/8 of a pizza. How many children were there in the group?.
There are 24 children in the group.
To divide something into equal groups or to determine how many equal groups there are, use the division procedure. When equal groups are combined to find a total in multiplication, division is the opposite process.
If 6 pizzas were shared among 8 groups of children, each group would receive 6/8 = 3/4 of a pizza.
If each child got 3/8 of a pizza, then in a group of children each group would have 8 * 3/8 = 3 children.
Therefore, in total, there were 8 * 3 = 24 children.
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Preview
-116. Solve the following systems of equations using any method (graphing, elimination, substitution). Check each
solution, if possible.
a. - 2x + 3y = 1
2x+6y= 2
c. 3x - y = 7
y = 3x - 2
b. y = x + 4
x = -3y
d. x + 2y = 1
3x + 5y = 8
The equations are solved using graphing, elimination, substitution methods.
What is system of equation?A system of equations are the set of equations where the solution for these equations are the intersecting point between the equations.
The systems of equations are given below are given below,
(a) -2x + 3y = 1(using elimination method)
2x+6y= 2
eliminating x term we get,
9y = 3
⇒y=3.
(b) y = x + 4 ---(1)(using substitution method)
x = -3y---(2)
Substitute (2) in (1) we get,
y = -3y+4
⇒4y=4 ⇒y=1
(c) 3x - y = 7 (using graphing method)
y = 3x - 2
This system has no intersection point
So this system has no solution.
( The graph is attached below.)
(d) x + 2y = 1-----(1) (using elimination method)
3x + 5y = 8-----(2)
For eliminating x we have to the multiply equation(1) by 3,
we get 3x+6y=3
eliminating 3x we get, y=-5/3 substitute y in (1) we get x=49 /3
Hence, the equations are solved using graphing, elimination, substitution methods.
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A process in which a number is changed, such as by adding, subtracting, dividing, or multiplying.A. operation.B. smart.C. super cool.
Arithmetic operations consists primarily of operations such as addition, subtraction, multiplication, and division. So the option A is correct.
The process of adding things together is known as addition. The '+' sign represents the addition process. It entails combining two or more numbers into a single expression.
The difference between two numbers is calculated using the subtraction operation. The '-' sign represents subtraction. It is nearly identical to addition, but it is the conjugate of the second term.
Multiplication is also referred to as repeated addition. It is indicated by " or '*'. It can also be combined with two or more values to produce a single value.
Division is the inverse of multiplication and is usually denoted by ". It is made up of two terms, dividend and divisor, and the dividend is divided by the divisor to yield a single term value.
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please fill out the steps
The simplified form of a rational equation [x + 1 / (x - 2)] / [x² / (x - 2) + 1] is equivalent to (x - 1) / (x + 2).
How to simplify a rational equation
In this problem we need to determine the simplified form of a rational equation, whose form is:
R(x) = P(x) / Q(x)
Where:
P(x) - Polynomic numerator.Q(x) - Polynomic denominator.
The simplification process can be done by means of algebra properties. First, write the rational equation:
[x + 1 / (x - 2)] / [x² / (x - 2) + 1]
Second, expand the numerator and the denominator:
[(x² - 2 · x + 1) / (x - 2)] / [(x² + x - 2) / (x - 2)]
Third, simplify the fraction by algebra properties:
[(x² - 2 · x + 1) · (x - 2)] / [(x² + x - 2) · (x - 2)]
(x - 1)² / [(x + 2) · (x - 1)]
(x - 1) / (x + 2)
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pls help me my homework is due tmrw and me and my mom are stumped.
Answer:
Step-by-step explanation:
A refrigerator is a cuboid, so W=3ft, L= 2.5ft, and H=6ft,
the volume of the refrigerator =W x L x H=3x2.5x6=45ft^3
The walls and other parts have 20ft^3 volume, so we have to minus them, so
volume left for food =45-20=25ft^3
Answer:
Step-by-step explanation:
Volume of the fridge = 3 × 2.5 × 6 = 45 ft³
then subtract the 20 ft³
45 - 20 = 25 ft³
hi guys can u guys answer this question
Answer:
a= 77, b= 77, c= 103.
Step-by-step explanation:
a= 77 (vertically opposite)
b= a= 77 (corresponding angles)
c= 180-77
= 103 (angles on a straight line)
The answer needs to be a mixed number, please help me with this.
The perimeter of the given triangle in mixed fraction form is 4 1/2 ft.
What is triangle?A triangle is a closed, 2-dimensional shape with three straight sides and three angles. The sum of the interior angles of a triangle is always 180 degrees. There are many types of triangles, including equilateral triangles (all sides and angles are equal), isosceles triangles (two sides and two angles are equal), scalene triangles (no sides or angles are equal), right triangles (one angle is a right angle, or 90), and obtuse triangles (one angle is greater than 90). Triangles are used in many areas of mathematics, science, and engineering.
Here,
The perimeter of the triangle:
=2 1/8+5/6+1 3/4
First, we need to convert all the mixed numbers into improper fractions:
2 1/8 = 17/8
5/6 = 10/16 = 15/24
1 3/4 = 7/4
Now we can add the three fractions:
17/8 + 15/24 + 7/4
To add these fractions, we need to find a common denominator. The smallest number that all three denominators divide into is 24. So we can rewrite the fractions with 24 as the denominator:
17/8 = 51/24
15/24 (already in the correct form)
7/4 = 42/24
Now we can add the numerators:
51/24 + 15/24 + 42/24 = 108/24
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 12:
108/24 = (9 × 12)/(2 × 2 × 2 × 3) = 9/2
=4 1/2 ft
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Calculate the value of each expression. (-8) x 2/3. (-8) x (-2/3). -18/3. 18/(-3). (-18)/(-3)
The values of the given expressions are respectively, -5.33, 5.33, -6, -6, 6
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Here are the calculations for each expression:
1. (-8) x 2/3
= (-8) x 2/3
= -16/3
= -5.33
2. (-8) x (-2/3)
= (-8) x (-2/3)
= 16/3
= 5.33
3. -18/3 = -6
4. 18/(-3) = -6
5. (-18)/(-3) = 18/3
= 6
So, the values of each expression are -5.33..., 5.33..., -6, -6, and 6, respectively.
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The _______ of a probability experiment is the collection of all possible outcomes. a. outcome b. sample space c. event d. unusual event e. experiment
Answer:B.Sample space
Step-by-step explanation:
Which equation represents the graph?(picture below)
1. Y= - 3/2 x + 5
2. Y= - 2/3 x + 3
3. Y= 2/3 x - 3
4. Y= 3/2 x - 5
Help please I’m stuck on a question and I’d greatly appreciate it
The value of the missing part of triangle DFC which is FD would be = 12.
How to calculate the missing part of the triangle?Triangle ACD is congruent to triangle DFC
ED/AD = BC/AC
where;
ED = 9
AD = 15
BC= 12
AC=?
Make AC the subject of formula;
AC= 12×15/9
AC= 180/9
AC = 20
Using the adjacent values of the new and original sides of the triangle to calculate the scale factor.
That is ;
AD is congruent to FC = 15 = 9
But Scale factor = Dimension of the new shape ÷ Dimension of the original shape
Scale factor = 15/9= 1.67
To calculate FD using the scale factor;
1.67= 20/FD
FD= 20/1.67
FD= 12 (approximately)
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By proportion formulas and Pythagorean theorem, the length of side FD is approximately equal to 26.571.
How to determine the lengths of missing sides in a geometric system
Herein we find a geometric system formed by two similar right triangles (ΔABE, ΔACD) and a third distinct right triangle (ΔCDF). Two triangles are similar when both have congruent interior angles and sides that are not congruent though proportional.
Then, the system of similar triangles can be defined by following proportion formula:
AB / AE = AC / AD
x / 6 = (x + 12) / 15
15 · x = 6 · (x + 12)
15 · x = 6 · x + 72
9 · x = 72
x = 8
AB = 8
Now we determine the length of side CD by Pythagorean theorem:
CD = √(AC² - AD²)
CD = √[(x + 12)² + 15²]
CD = √(20² + 15²)
CD = 25
And the side FD is finally found by Pythagorean theorem:
FD = √(CD² + CF²)
FD = √(25² + 9²)
FD = √706
FD ≈ 26.571
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what is 18% of 45 help please
Answer:
8.1
Step-by-step explanation:
100%= 45
1%= 45÷100
= 0.45
18%= 0.45×18
= 8.1
Find the probability that the country is in the south asia region, given that shreya categorized the country's business startup costs as high.
The probability that the country is in the south Asia region is 7/87
The probability is a mathematical concept that tells us how likely an event is to occur.
The probability that a country is in South Asia given that it has high business startup costs is represented as P(A|B). This is calculated as follows:
P(A|B) = P(A and B) / P(B)
Where P(B) is the probability that a country has high business startup costs and can be calculated as:
P(B) = B / Total number of countries
And P(A and B) is the probability that a country is in South Asia and has high business startup costs, which can be calculated as:
P(A and B) = A / Total number of countries
So, substituting the values, total high startup cost is 87 and and, South Asia start up cost is 7, Then, the probability that the country is in the south Asia region is
=> 7/87
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Isaac was comparing the price of pineapple juice at two stores. Isaac can buy 3 bottles
of pineapple juice at Store A for a total cost of $7.32. The graph below represents
what Isaac would pay in dollars and cents, y, for z bottles of pineapple juice at store
B.
How much more is a bottle of pineapple juice at Store A than
at Store B?
The cost of each pineapple juice bottle at Store A is $0.90 more than at Store B.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
The rate of the pineapple juice bottle at store A is given as,
Rate = $7.32 / 3
Rate = $2.44 per bottle
From the graph, the two points are (10, $15.40) and (20, $30.80). Then the rate is given as,
Rate = ($30.80 - $15.40) / (20 - 10)
Rate = $1.54
The difference between the rates is given as,
⇒ $2.44 - $1.54
⇒ $0.90
The cost of each pineapple juice bottle at Store A is $0.90 more than at Store B.
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The complete question is attached below.
The area of a rectangle is 294 in². The ratio of the length to the width is 3:2. Find the length and the width.
Answer:
length = 21 in , width = 14 in
Step-by-step explanation:
the ratio of length : width = 3 : 2 = 3x : 2x ( x is a multiplier )
the area (A) of a rectangle is calculated as
A = length × width
given A = 194 , then
3x × 2x = 194
6x² = 194 ( divide both sides by 6 )
x² = 49 ( take square root of both sides )
x = [tex]\sqrt{49}[/tex] = 7
then
length = 3x = 3 × 7 = 21 in
width = 2x = 2 × 7 = 14 in
|
(3v 8w+19)+ (6w-6)
Answer:
3v + 14w + 13
Step-by-step explanation:
The expression can be simplified as follows:
(3v + 8w + 19) + (6w - 6)
Combining like terms, we have:
(8w + 6w) and (19 - 6)
3v + 14w + 13
So the simplified expression is equal to 3v + 14w + 13.
Find the area of a triangle with a height of 5x7y2 and a base of 4x3y
The area of the triangle is A = 10x¹⁰y³
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Let the area of the triangle be represented as A
Now , the base of the triangle is = 4x³y
Let the height of the triangle be = 5x⁷y²
And , The area of the triangle = ( 1/2 ) x Length x Base
Substituting the values in the equation , we get
Area of Triangle = ( 1/2 ) ( 4x³y ) ( 5x⁷y² )
On simplifying the equation , we get
Area of Triangle A = 10x¹⁰y³
Hence , the area of the triangle is A = 10x¹⁰y³
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Money in a particular savings account increases by about 6% after a year. How much money will be in the account after one year if the initial amount is $100? $50? $200? $125? dollars? If you get stuck, consider using diagrams or a table to organize your work.
106$ money will be in the account after one year if the initial amount is $100.
What is compound interest?The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.
we have
Money in particular savings accounts increases by about 6% after a year.
we know that
The simple interest formula is equal to
A = P(1 +rt)
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is the Number of Time Periods
Part 1) How much money will be in the account after one year if the initial amount is $100
in this problem we have
P = 100
r =6%
t = 1 year
substitute in the formula above
A = 100(1 +0.06)
A = 106$
Part 2) How much money will be in the account after one year if the initial amount is $50
in this problem we have
P = 100
r =6%
t = 1 year
substitute in the formula above
A = 50(1 +0.06)
A = 53$
Part 3) How much money will be in the account after one year if the initial amount is $200
in this problem we have
P = 100
r =6%
t = 1 year
substitute in the formula above
A = 200(1 +0.06)
A = 212$
Part 4) How much money will be in the account after one year if the initial amount is $125
in this problem we have
P = 100
r =6%
t = 1 year
substitute in the formula above
A = 125(1 +0.06)
A = 132.5$
Part 5) How much money will be in the account after one year if the initial amount is $x
in this problem we have
P = 100
r =6%
t = x year
substitute in the formula above
A = 100(1 + 0.06x)
A = 6x +100
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sams monthly gross income is 6000$ if sams federal tax rate is 10.5% and his state tax rate is 4.25%
A)how much money does sam bring home annually
B)How much social security tax does Sam pay monthly
C)How much Medicare tax does Sam pay annually
14. The total cost of three automobile batteries is $340.
The most expensive battery is three times the cost of
the least expensive. The third is $15 more than the leastexpensive. Find the cost of each battery.
The cost of each battery would be Battery 1 = $195, Battery 2 = $80 and Battery 3 = $65.
How to calculate the cost of each battery?Battery 1 (most expensive).= 3(X)
Battery 2 ( third battery) = 15+ X
Battery 3 (least expensive) = X
The total cost of the whole battery = $340
That is;
$340 = 3x + 15+ X + X
340 = 5x + 15
5x = 340 - 15
5x = 325
X = 325/5
X = $65
Therefore the cost of each battery;
Battery 1 = 3× 65 = $195
Battery 2 = 15 + 65 = $80
Battery 3 = $65
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Pythagorean Theorem. I have to turn this in by Friday
Answer:
1. b = [tex]\sqrt{20}[/tex]
2. c = [tex]\sqrt{2[/tex]
3. b = [tex]\sqrt{105}[/tex]
4. c = [tex]\sqrt{113}[/tex]
5. c = [tex]\sqrt{52}[/tex]
6. b = [tex]\sqrt{80}[/tex]
7. b = [tex]\sqrt{130}[/tex]
8. a = [tex]\sqrt{48}[/tex]
9. c = [tex]\sqrt{149[/tex]
10. c = [tex]\sqrt{5}[/tex]
Example:
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]8^{2}[/tex] + [tex]b^{2}[/tex] = [tex]12^{2}[/tex]
64 + [tex]b^{2}[/tex] = 144
64 + [tex]b^{2}[/tex] = 144 - 64
[tex]b^{2}[/tex] = 80
[tex]\sqrt{b}[/tex] = [tex]\sqrt{80}[/tex]
What is 80kmh to mph ?
The conversion factor between kilometers per hour and miles per hour is 1.609344. Therefore, to convert from kmh to mph, we need to divide the speed in kmh by this conversion factor. 80kmh is equivalent to approximately 49.71 mph.
To find the speed in mph, we can use the following formula:
mph = kmh / 1.609344
Plugging in the given speed of 80kmh, we get:
mph = 80kmh / 1.609344
mph = 49.70969538
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the point (3,W) is on the graph of y= 2x +7. What is the value of W
Answer:13
Step-by-step explanation:
y=2x+7
x=3
2*3+7=13?
The solution is, the value of w is 13.
Here, we have,
We are given that the point (3,w) lies on the line y = 2x + 7.
This means that if we substitute x = 3 into the equation y = 2x + 7,
we will get the value of y at x = 3, which is equal to w.
so, we get,
Substituting x = 3 into the equation y = 2x + 7, we have:
y = 2(3) + 7
y = 6 + 7
y = 13
So, after simplification we get, w = 13
Therefore, the value of w is 13.
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What is the area of the mat if it is 184 in please explain.
The dimensions of the original mat are 27 inches by 21 inches.
What is Rectangle :A closed figure bounded by four sides in which opposite sides are equal is known as rectangle.
The area of rectangle is calculated by the given formula,
A = length x breadth
Length and width of the rectangle can be found from the following expression after solving for x. The expression is given by :
outside area - inside area = 184 square inches
{(2·x - 3)·(x + 8)} - {(2·x - 7)·(x + 4)} = 184 (On substitute length and width expressions. Each area is the product of length and width.)
⇒{( 2·x² + 16·x - 3x - 24)} - {(2·x² + 8x -7x -28) }= 184
⇒(2·x² + 13x - 24) - ( 2·x² + x -28) = 184
⇒ 12·x + 4 = 184 .................(On simplifying the expression)
⇒ 12·x = 180
⇒ x = 15
Then the original length of the mat is given by substituting value of x in outside length expression :
2·x - 3 = 2·15 - 3 = 30 - 3 = 27 inches
and the original width of the mat is given by :
x + 6 = 15 + 6 = 21 inches
Hence, the overall dimensions of the original mat are 27 inches by 21 inches.
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an object has a mass of 8.1kg what is its weight
The weight of the object is 79.461 newtons.
How to determine the weightThe standard value for the acceleration due to gravity is approximately 9.81 m/s^2 near the Earth's surface.
To find the weight of an object with a mass of 8.1 kg, we can use the formula:
Weight = mass x acceleration due to gravity
So, the weight of the object is:
Weight = 8.1 kg x 9.81 m/s^2
Weight = 79.461 N (newtons)
Hence, the weight is 79.461 newtons.
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Find the coordinates of the centroid of the triangle with the vertices s(2, 5), t(6, 5), and r(10, 0).
The centroid of this triangle is located at the point (6, 3).
The centroid of a triangle is the point where the three medians of a triangle intersect. Medians are the line segments that connect each vertex of the triangle to the midpoint of the opposite side.
The centroid is the "center of mass" or the "balance point" of the triangle. In other words, if the triangle were made of a solid material and suspended by a string attached to the centroid, it would balance.
To find the coordinates of the centroid of a triangle, we will use the following formula:
G = (x1 + x2 + x3)/3, (y1 + y2 + y3)/3
Where G is the centroid, and (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the triangle's vertices.
So for the triangle with the vertices s(2, 5), t(6, 5), and r(10, 0), we have:
G = (2 + 6 + 10)/3, (5 + 5 + 0)/3
G = (18/3, 10/3)
G = (6, 3.333...), which we can round to (6, 3)
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Morning Donuts has a variety of donuts for sale.
maple donuts
cake donuts
14
15
cream-filled donuts
9
chocolate frosted donuts 11
What is the probability that a randomly selected donut will be a maple donut?
Write your answer as a fraction or whole number.
P(maple donut)
=
Answer:
here are a total of 14 + 15 + 9 + 11 = 49 donuts.
The probability of selecting a maple donut is the number of maple donuts divided by the total number of donuts:
P(maple donut) = 14/49
So the probability of selecting a maple donut is 14/49, which can also be written as a fraction in simplest form: 2/7.
What is Van t Hoff law explain?
Van 't Hoff's law, also known as the law of osmotic pressure, states that the magnitude of the osmotic pressure is directly proportional to the concentration of solute particles in a solution at a given temperature.
Van 't Hoff's law is an important concept in chemistry and thermodynamics. It explains the relationship between osmotic pressure and the concentration of solute particles in a solution. According to the law, the osmotic pressure of a solution is directly proportional to the number of solute particles in the solution, regardless of the type of solute. This means that if the concentration of solute particles in a solution increases, the osmotic pressure also increases, and vice versa. This law has numerous applications, particularly in the field of biology, where it is used to explain the movement of water and nutrients in and out of cells. For example, when a plant cell is placed in a hypertonic solution, water moves out of the cell, causing it to shrink. On the other hand, when a plant cell is placed in a hypotonic solution, water moves into the cell, causing it to expand. Understanding Van 't Hoff's law is therefore critical in many fields of science, particularly in biology, chemistry, and chemical engineering.
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a line segment is a part of a line that is bounded by two distinct end points and contains every point on the line between its endpoints. True/False?
The statement "a line segment is a part of a line that is bounded by two distinct end points and contains every point on the line between its endpoints." is True because a line segment is defined as a part of a line that is bounded by two distinct end points and contains all the points on the line between those endpoints.
A line segment is a part of a line that has two endpoints and connects them. It is the shortest distance between two points and has a definite length, but no width or height. A line segment can be part of a straight line or a curved line.
A line segment is a section of a line that is defined by two distinct end points and includes every point on the line between them. It is the basic building block of geometry and can be used to measure distances, angles, and shapes.
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What is 71 degree F in C?
71 degrees Fahrenheit is equal to approximately 21.7 degrees Celsius using the conversion method formula.
To convert Fahrenheit to Celsius, you can use the following formula:
Celsius = (Fahrenheit - 32) x 5/9
Plugging in 71 degrees Fahrenheit, we get:
Celsius = (71 - 32) x 5/9
Celsius = 39 x 5/9
Celsius = 195/9
Celsius ≈ 21.7
Therefore, 71 degrees Fahrenheit is approximately 21.7 degrees Celsius.
The Celsius scale is also known as the centigrade scale, because it is divided into 100 degrees between the freezing and boiling points of water at standard atmospheric pressure.
On the Fahrenheit scale, there are 180 degrees between the freezing and boiling points of water. Therefore, each degree on the Fahrenheit scale is equivalent to 5/9 of a degree on the Celsius scale.
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