The caramel topping demand curve will not change:
The cost of caramel topping is falling; there will be an increase in demand for caramel topping:
Butterscotch topping costs more money;
There will be less demand for caramel topping:
Ice cream now costs more money.
Description of the curveThe quantity of caramel topping demanded would increase if the price of the topping dropped. Consequently, the demand curve for caramel topping would go lower.
Ice cream and caramel toppings are complementary products.
Products that are consumed together are said to be complementary.
The amount of ice cream demanded would drop if the price went up. There would be a drop in the number of caramel toppings needed as a result of the fall in demand.
a decline in the popularity of caramel toppings. With less demand, the demand curve for caramel toppings would move inward.
Butterscotch and caramel ice cream toppings serve as stand-ins.
Products that can be used in place of one another are known as substitute goods.
The quantity demanded for butterscotch topping would decline if the price of butterscotch topping rose, making it more expensive overall. Customers might switch to caramel topping. As a result, demand for caramel topping would rise and the demand curve would move outward.
Demand curve: what is it?
The demand curve is a graphical representation of how the cost of an item or service relates to how much is demanded over a given period of time.
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in 2012, the average donation to a certain charity was $235 with a standard deviation of $47. in 2013, the average donation was $360 with a standard deviation of $54. in which year did the donations show a more dispersed distribution? the coefficient of variation for 2012 is %, while the coefficient of variation for 2013 is %. therefore, the donations in ---select--- show a more dispersed distribution.
The coefficient of variation for 2012 is 20 %. While the coefficient of variation for 2013 is 15%.Therefor the donations in 2012 shows more dispersed distribution.
Here
for 2012 x=245, s = 49
for 2013 X = 480 ,s=72
CV for 2012 is
CV =S /x* 100% =(49 / 245)*100
CV = 20 %.
of cv for 2013 is
CV= (S /x)*100= (72 /480)*100
CV = 15%
The coefficient of variation for 2012 is 20 %. While the coefficient of variation for 2013 is 15%.Therefor the donations in 2012 shows more dispersed distribution.
The coefficient of variation (CV) is a statistical measurement used to compare the amount of variation in a set of data to the mean of the data. It expresses the variation as a percentage of the mean. The formula for CV is the standard deviation divided by the mean, multiplied by 100. CV is used to determine whether the data has a large or small amount of variation relative to its mean. A low CV indicates that the data is relatively consistent, while a high CV means that the data is more spread out. The CV is useful for comparing data sets with different units of measurement or data sets with different means. CV is commonly used in fields such as finance, economics, and quality control.
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Which row of the table reveals the x-intercept of function f?
The row of the table that reveals the x-intercept of the function f is given as follows:
Second row.
What are the intercepts of a function?A function has two intercepts, which are listed as follows:
x-intercept.y-intercept.The definition of each type of intercept is given as follows:
x-intercept: values of x when y = 0.y-intercept: value of y when x = 0.From the second row of the table, we have that when x = -4, f(x) = 0, hence the x-intercept of the function is of x = -4.
The y-intercept is of y = -16, as from the fourth row, when x = 0, y assumes a value of 16.
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a square tile, a regular hexagon tile, and a regular -sided polygon tile share a common vertex. there are no gaps or overlaps between the tiles. what is
The value of n is 4, and the regular n-sided polygon becomes a square.
When a square tile, a regular hexagon tile, and an equilateral triangle tile share a common vertex, the total interior angle between them is 360°.
We can represent the interior angle between the sides of the regular n-sided polygon as 360°/n.
In the given problem, the square tile has an interior angle = 90°
The regular hexagon tile has an interior angle = 120°
The equilateral triangle tile has an interior angle = 60°.
The sum of all these interior angles = 270°.
Now equal the sum of interior angles = 360°
360° - 270° = 90° to the total interior angle.
This can be obtained by considering n=4 for the regular n-sided polygon, as the interior angle between sides of a regular 4-sided polygon is 360°/4 = 90°.
Therefore, the value of n is 4, and the regular n-sided polygon becomes a square.
Did you mean, A square tile, a regular hexagon tile, an equilateral triangle tile, and a regular n-sided polygon tile share a common vertex? There are no gaps or overlaps between the tiles. What is n?
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1/2 (4x + 6) = 12
What is the value of Y
Answer:
9/2
Step-by-step explanation:
1 Simplify the expression
2 Subtract 6 from both sides
3 Simplify the expression
4 Divide both sides by the same factor
5 Simplify the expression
Answer:
1/2*4x +1/2*6=12
2x+3=12
2x=12-3
2x=9
x=9/2
Please I need Help!!!
The matrix of the caps size is
13 36 27
10 15 0
The matrix that shows the total value of each cap size in each location is
247 684 513
190 285 0
How to determine the matrixFrom the question, we have the following parameters that can be used in our computation:
13 small baseball caps, 36 medium baseball caps, and 27 large baseball caps on the store shelves. 10 small baseball caps and 15 medium baseball caps in the stockroom.When represented as a matrix, we have
13 36 27
10 15 0
The matrix for the total valueIn (a), we have
13 36 27
10 15 0
Multiply the individual elements by 19
So, we have
247 684 513
190 285 0
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4
Jackson ate 5 of a chocolate cake at his brother's birthday party. If the chocolate cake contained 681 calories, how many calories did
he eat?
A. 667
B. 544 4/5
C. 136 1/5
D. 851 1/4
The number of calories in each cake will be 136¹/₅. The correct option is C.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Jackson ate 5 of a chocolate cake at his brother's birthday party. If the chocolate cake contained 681 calories.
The number of calories in each cake will be calculated as:-
Amount of calories = 681 / 5
Amount of calories = 136.2
Amount of calories = 136¹/₅
Therefore, there will be 1361/5 calories in each cake. The right answer is C.
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To express as a trinomial
we can express a trinomial as,
2x² + 5x + 6.
Where 2, 5, and 6 are non-zero real numbers.
2x², 5x, and 6 are the three terms.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
A trinomial is an expression that contains three on-zero terms separated by + or -.
Example:
ax² + bx + c
Where a, b, and c are non-zero real numbers.
Thus,
Trinomials can be 2x² + 5x + 3.
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a person must be at least 7 years old to join baseball club the inequality is
A person must be at least 7 years old to join the baseball club the inequality is x ≥ 7 where x is the age of the person
What is an inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given is a condition, a person must be at least 7 years old to join a baseball club, we need to represent the age in terms of an inequality,
If we say, a person who wants to join the baseball club is x years old,
Then, the condition for x is given by inequality,
x ≥ 7
Hence, a person must be at least 7 years old to join the baseball club the inequality is x ≥ 7 where x is the age of the person,
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it took Mr. Black 2 hours to drive to his friends house. on the way back the traffic was heavy and Mr. Black drove 20 mph slower. The trip back took 1 hour longer. What was Mr. Blacks speed to his friend's house?
The speed that Mr. Blacks used to drive to the friend's house would be = 13.3 mph.
How to calculate speed of Mr. Blacks?The number of hours used by Mr Black to the friend's house = 2 hours
The speed that was used by Mr Black while returning from the friends house = 20 mph.
The number of hours it took to return = 1+2 = 3hrs
Then, if 20 mph = 3hrs
X. mph = 2 hrs
Make X the subject of formula;
X = 20×2/3
= 40/3
= 13.3 mph
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I NEED HELP ON THIS ASAP! WILL GIVE BRAINLIEST IF IT LETS ME
An equation that represents this situation is 5s + 10a = 3000.
By using the x- and y-intercepts, a graph of the function modeling the total number of tickets sold is shown in the image attached below.
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would a assign variable to the number of student tickets sold and the adult tickets sold respectively, and then translate the word problem into a linear equation as follows:
Let the variable s represent the number of student tickets sold.Let the variable a represent the number of adult tickets sold.Since student are paying $5 while adults are paying $10 for a ticket and the athletic association need to raise $3000 by selling tickets, a linear equation that models the situation is given by:
5s + 10a = 3000
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Complete Question:
The Marshall High School Athletic Association sells tickets for the weekly football games. Students pay $5 and adults pay $10 for a ticket. The athletic association needs to raise $3000 selling tickets to send the team to an out-of-town tournament.
1. Write an equation that represents this situation.
2. Use x- and y-intercepts to graph the function modeling the total number of tickets sold on each coordinate plane.
Use the vectors u = 3, 3 and v = −5, 1 to find the indicated quantity.
The indicated quantity is a zero vector for the given vectors.
What is a vector?A vector is a quantity that has both magnitude and direction (numerical size). The inverse of a scalar, which is a quantity with just magnitude and no direction.
The vectors are given in the question, as follows:
u = <3,3>
v = <-5,1>
The vectors u = (3, 3) and v = (-5, 1) represent points in the x-y plane.
Let
u+v = <-2,4>
Now
(u+v).0 = <-2.0,4.0> = <0,0>
(u+v).0 = 0
Thus, the result is a zero vector.
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in experimental research, which group does not receive the independent variable and is used to determine whether the independent variable actually influenced change in the dependent variable?
In experimental research, a control group does not receive the independent variable and is used to determine whether the independent variable influenced change in the dependent variable.
A test sample or the group that undergoes an experimental method is referred to as an experimental group. This group is exposed to modifications in the test's independent variable. The independent variable's values and its effects on the dependent variable are noted. Multiple experimental groups may be present at once during an experiment.
A control group is a subset of the experiment that is kept apart from the other groups so that the independent variable under test cannot affect the outcomes. Isolating the effects of the independent variable on the experiment can help rule out other possible explanations for the findings of the experiment.
control groups can be of two types:
Positive control groups are control groups when the circumstances ensure a favorable outcome. Positive control groups are useful for demonstrating that the experiment is running according to plan.Negative control groups are control groups where the circumstances result in a bad result. Negative control groups aid in identifying potential external factors, such as pollutants, that may be present but were not previously accounted for.to know more about 'control group' try:
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a metal cylinder is measured to have a length of 5.0 cm and a diameter of 1.26 cm. compute the volume of the cylinder in cm3. use pi
The volume of the cylinder is 6.18 [tex]cm^3[/tex].
The volume of a cylinder—which corresponds to how much material can be transported inside of it or immersed in it—determines its density. The volume of a cylinder is calculated using the formula [tex]r^2h[/tex], where r is the radius of the circular base and h is the height of the cylinder. The material might be any substance that can regularly fill the cylinder with liquid or another substance.
Use the following formula to determine a cylinder's volume:
V = π[tex]r^2h[/tex]
where r is the radius of the cylinder (diameter / 2), h is the height of the cylinder, and π is approximately equal to 3.14.
First, find the radius:
r =[tex]\frac{ 1.26}{ 2}[/tex]
r = 0.63 cm
Next, find the volume:
V = π[tex]r^2h[/tex]
V = π[tex](0.63)^2(5.0)[/tex]
V= π * 0.3969 * 5.0
V= 3.14 * 0.3969 * 5.0
V = 6.18 [tex]cm^3[/tex] (rounded to 2 decimal places).
So, the volume of the cylinder is 6.18 [tex]cm^3[/tex].
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(pic will be provided.) Construct the two-way frequency table. 6th Graders 7th Graders 8th Graders Total Very Unhappy Unhappy 9 6 7 11 How do You Feel About a Longer School Year? Very Happy Neutral Happy 11 36 5 35 24 58 14 18 Total 47 60 191.
Based on the information in the graph, we can infer that the missing numbers are: 9, 4, 19, 30, 84, 16, 8, 22, and 40.
How to complete the table?To complete the table correctly we must identify the columns or rows with more data. These will be the easiest to complete. First of all, we must fill in those that already have a number in the total box because we can add the available numbers and later subtract them from the total to identify the missing number.
We can also find the numbers in the total cells by adding all the numbers in a column or row to find this result. Finally, the boxes that are being completed serve as clues to complete the others.
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In the 2021 football season, the Riverside Red Dragon's manager gathered the points scored by the team during the regular season games. The following data set shows the values collected by the manager.
{13, 0, 20, 27, 27, 31, 13, 30, 30, 26, 20, 27, 30, 11, 30, 4}
Which of the following stem-and-leaf plots correctly graphs the data set?
2021 Riverside Red Dragon Football Season Points
1 1 3 3
2 0 0 6 7 7 7
3 0 0 0 0 0 1
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
0 0 4
1 1 3
2 0 6 7
3 0 1
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
0 0 4
1 1 3 3
2 0 0 6 7 7 7
3 0 0 0 0 1
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
1 1 3
2 0 6 7
3 0 1
Key 1|1 = 11
The required stem-and-leaf plot shown below that the majority of the scores fall in the 20s and 30s, with some scores in the teens and low 20s.
What is stem-and-leaf plots?A stem-and-leaf plot is a type of data display that helps to show the distribution of a set of numerical data.
here,
For the given data set:
Stem Leaf
0 4
1 1, 3, 3
2 0, 0, 0, 6, 7
3 0, 0, 0, 7
The stem-and-leaf plot shows that the majority of the scores fall in the 20s and 30s, with some scores in the teens and low 20s. The plot makes it easier to see the distribution of the data, rather than just looking at the raw values.
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Donnie is new to a town that does not have a doggie day care facility. Upon researching the situation, Donnie decides to open a doggie day care facility. Which
marketing option for this new business should be a point of emphasis?
Location
Features
Price
Service
Answer: In this situation, location should be a point of emphasis for marketing the new doggie day care business. As a new business in a town without a doggie day care facility, it is important for potential customers to be aware of the new facility's location. This will help people find the business and consider using it for their dog care needs. Additionally, the location of the business will likely impact its accessibility and convenience for customers, so it's important to make sure people know where it is. Once people are aware of the location, they can then consider other factors such as features, price, and service when deciding whether to use the business.
Step-by-step explanation:
Grant wants to earn enough money to buy a skateboard that costs $56. He earns $8 per hour babysitting and $10 per hour for yard work. If x represents the number of hours babysitting and y represents the number of hours doing yard work, which inequality represents the situation?
The required inequality is 8x + 10y ≥ 56 which represents given the situation.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
Let x represent the number of hours babysitting and y represent the number of hours doing yard work,
The inequality that represents the situation is:
8x + 10y ≥ 56
This means that the total amount earned from babysitting (8x) plus the total amount earned from yard work (10y) must be greater than or equal to the cost of the skateboard ($56).
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a quadrilateral with 90 degree angles is shown. the lengths of the left and right sides are 10 and 2 y 4. the lengths of the top and bottom sides are 18 and 10 2 x. what is the value of y? 3 4 5 6
The value of y of a quadrilateral is 3.
A rectangle is a quadrilateral with four right angles, meaning that all of its angles measure 90 degrees. Given the information provided, the lengths of the left and right sides of the rectangle are equal to 10 and 2y + 4, respectively.
We also have the lengths of the top and bottom sides equal to 18 and 10 + 2x, respectively. However, we don't need to use the information about x as it does not affect the calculation for y.
To find the value of y, we can use the fact that the length and width of a rectangle must be equal. Therefore, we can set the length equal to the width:
10 = 2y + 4
Now that we have an equation, we can solve for y by subtracting 4 from both sides:
2y + 4 - 4 = 10 - 4
2y = 6
Finally, to find y, we can divide both sides of the equation by 2:
2y / 2 = 6 / 2
y = 3
Therefore, the value of y is 3.
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Elisabeth reads 15 of her book in 112 hours. elisabeth continues to read at this pace. how long does it take elisabeth to read 34 of the book? enter your answer as a mixed number in simplest form by filling in the boxes. $$ h
The mixed numbers of hours it takes Elisabeth to read 3/4 of the book is; 5³/₅ hours
What are mixed numbers?A mixed number can be used to represent both a whole number and a lawful fraction. It frequently represents a number that lies either between two whole numbers. Look at the figure; it depicts a fraction that is greater than 1 but less than 2. Therefore, it is a mixed number.
According to the information provided:We are informed that she reads 15 of her novels in 112 hours.
As a result, reading a book takes 112–15 hours.
As a result, the number of hours needed to finish reading the first third of the book is 3/4 * 112/15 = 28/5.
53 and 5 hours per book when expressed as a mixed number.
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Elisabeth needs 253 hours and 64/100 of an hour to read 34 books, which is stated as a mixed number in the simplest form as 253 3/5 hours.
How long will it take Elisabeth to read 34 of the book?In order to calculate the amount of time it takes Elisabeth to read 34 books, we need to calculate the amount of time it takes her to read 1 book first.
Since she reads 15 books in 112 hours, we can divide 112 by 15 to find the amount of time it takes her to read 1 book.
112 / 15 = 7.46
This means that it takes Elisabeth 7.46 hours to read 1 book.
Now we can multiply 7.46 by 34 to find the amount of time it takes her to read 34 books.
7.46 x 34 = 253.64
This means it takes Elisabeth 253.64 hours to read 34 books. Since this is a mixed number, we can convert it to its simplest form by subtracting the whole number from the decimal number and expressing it as a fraction.
253.64 - 253 = 0.64
Therefore, it takes Elisabeth 253 hours and 64/100 of an hour to read 34 books, which can be expressed as a mixed number in simplest form as 253 3/5 hours.
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solve for: 5(x+4)=6x-5
Answer:
Step-by-step explanation:
5 (x + 4) = 6x - 5
5x + 20 = 6x - 5
5x + 20 - 20 = 6x - 5 - 20
5x = 6x -25
x= 25
Answer:
x=25
Step-by-step explanation:
[tex]5(x+4)=6x-5\\5x+20=6x-5\\5x+20-20=6x-5-20\\5x=6x-25\\5x-6x=6x-25-6x\\-x=-25\\\frac{-x}{-x} =\frac{-25}{-x} \\x=25[/tex]
What are the equations of the asymptotes of the graph of f(x)=4x+1+11?
The equations of the asymptotes of the graph of f(x) = 4/(x + 1) + 11 are;
horizontal asymptote: y = 11
vertical asymptote: x = - 1
How to find the Asymptotes of the graph?In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity.
In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity.
The function we are given is expressed as;
f(x) = 4/(x + 1) + 11
From the attached graph of the function f(x) = 4/(x+1) + 11, it is clear that function will have two asymptotes which are;
horizontal asymptote: y = 11
vertical asymptote: x = - 1
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Find the distance. In units, between P and Q Express the answer as a square root
P(-4,2)
Q(2,4)
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{-4}~,~\stackrel{y_1}{2})\qquad Q(\stackrel{x_2}{2}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{(~~2 - (-4)~~)^2 + (~~4 - 2~~)^2} \implies PQ=\sqrt{(2 +4)^2 + (4 -2)^2} \\\\\\ PQ=\sqrt{( 6 )^2 + ( 2 )^2} \implies PQ=\sqrt{ 36 + 4 } \implies PQ=\sqrt{ 40 }[/tex]
Can someone help me with this math problem, ASAP? The math problem is in the picture, THANKS!
The base function before the transformation is f ( x ) = x³
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the base function be represented as f ( x )
Now , the equation will be
The transformed function is represented as p ( x )
The value of p ( x ) = ( x + 2 )³
So , we can see that the function p ( x ) has been shifted horizontally by a factor of 2 units to the left
So , the base function would be f ( x ) = ( x )³
On simplifying the equation , we get
The base function is f ( x ) = x³
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The point where the graphs of two equations intersect has y-coordinate 2. One equation is y=3x+5. Find the other equation if its graph has a slope of 1.
y = x + 2 is the other equation if its graph has a slope of 1.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
If the y-coordinate of the intersection point of the two equations is 2, and one of the equations is y = 3x + 5,
The other equation must be of the form y = mx + b, where m is the slope of the line and b is the y-intercept.
m=1 is the slope of the other equation.
y = mx + b
2 = 1x + b
b = 2 - 1x
b = 2 - x
So the other equation is y = x + 2.
Hence, y = x + 2 is the other equation if its graph has a slope of 1.
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Round 17 nearest ten
Answer:
20.....
Step-by-step explanation:
Answer:
17.0
Step-by-step explanation:
17 is a whole number, so when rounding to the nearest tenth, it would still be 17.
Name three solution for a variable and a number
Therefore , the solution of the given problem of equation comes out to be
there Are Countless Solutions.
What is an equation?The equivalent indicator (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors using mathematical techniques, which have served as manifestations of reality. For example, the equal sign divides the number 12 or even the solution y + 6 = 12 in two different halves. How many characters already appear on either side of this symbol can be calculated. Conflicting symbol meanings occur frequently.
Here,
Each set of linear equations can have one of three different sorts of solutions.
Unique Solution are them.
No Answer.
There Are Countless Solutions.
Therefore , the solution of the given problem of equation comes out to be
there Are Countless Solutions.
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pls, help me I really don't understand this stuff.
Answer:
X = -2
Step-by-step explanation:
To find slope, it's
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
You're given two points
First one being (-9, -4) and second one being (x, 7). Both are these are in (x,y) form.
Let's plug it in.
[tex] \frac{11}{7} = \frac{7 - ( - 4)}{x - ( - 9)} [/tex]
^ Solving that, we get...
[tex] \frac{11}{7} = \frac{11}{x + 9} [/tex]
And that's because 7 minus a negative 4 means 7 + 4. Two negatives make a positive.
Now the top is good. 11 = 11.
The bottom says 7 = x + 9
If we were to subtract 9 from both sides... 7-9= -2, so
-2 = x
Hope this helps
20/-12 help please the answer are A -0.__67 B 0.67 C 1.67 D 1._6 asap which is it
Answer:C.
Step-by-step explanation:
plot scatter plot and compute the strength of as- sociation between variables. are these variables are associated? x
The given statement that the scatter plot is used to visualize the association (or lack of association) between two quantitative variables is true.
A scatter plot is a graphical representation of the relationship between two quantitative variables. The data points are plotted on a coordinate plane, and the pattern or association between the two variables is visualized.
This can help identify the presence or absence of a relationship, the strength of the relationship, and the direction of the relationship (positive or negative). The scatter plot can also be used to identify any outliers or outliers in the data.
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--The given question is incorrect; the correct question is
"A scatter plot is used to visualize the association (or lack of association) between two quantitative variables.
True
False"--
How is the formula for converting radians to degrees determined?
Answer:
See below
Step-by-step explanation:
Converting from radians to degrees
[tex]r=\frac{\pi}{180}d^\circ[/tex]
Converting from degrees to radians
[tex]d^\circ=\frac{180}{\pi}r[/tex]
Because [tex]2\pi[/tex] radians is equivalent to [tex]360^\circ[/tex], the measure of a full circle, then 1 radian would be [tex]\frac{360^\circ}{2\pi}=\frac{180^\circ}{\pi}[/tex] degrees. Similarly, 1 degree would be [tex]\frac{2\pi}{360^\circ}=\frac{\pi}{180^\circ}[/tex] radians. This is where the formulas come from!