Answer:
Step-by-step explanation:
noun
verb
preposition
adjective
interjection
adverb
i can compute the derivative of an implicitly-defined function and find the slope of the tangent line to an implicit curve
Finding the equation of the tangent line by using implicit differentiation is essentially the same as doing it by using ordinary differentiation. Keep in mind that we use normal differentiation to complete the following procedures to determine the equation of the tangent line:
Take the given function's derivative.To get the slope of the tangent line, evaluate the derivative at the specified position.Simplify by entering the provided point and the slope of the tangent line into the [tex](y-y_{1} ) = m(x-x_{1} )[/tex] formula for the equation of a line.The equation for the tangent line to the given function at the given position is the outcome. The methods we just stated apply when we have a function that isn't explicitly defined for yy and obtaining the derivative needs implicit differentiation; however, in Step 1, we utilize implicit differentiation rather than standard differentiation.
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Does the point (4, 7) satisfy the equation y = x + 3?
Review the graph of f(x).
On a coordinate plane, a curve goes through (negative 4, 1), (0, 0) and then curves up and approaches x = 2 in quadrant 1. Another curves approaches x = 2 in quadrant 4.
Which function g(x) has the same end behavior as f(x)?
g (x) = StartFraction 3 Over x EndFraction
g (x) = StartFraction x Over 3 EndFraction
g (x) = negative StartFraction 3 Over x EndFraction
g (x) = negative StartFraction x Over 3 EndFraction
The function g(x) that has the same end behavior as function f(x) is given as follows:
g(x) = -x/3.
How to obtain the end behavior of a function?The end behavior of a function is given by the limits of the function as x goes to infinity.
On the graph, these limits are found looking at the behavior at the left tail and at the right tail of the graph, as follows:
Left tail: x -> ∞.Right tail: x -> -∞.Then the function with the same end behavior as f(x) graphed is given as follows:
g(x) = -x/3.
At the left tail, we have that:
g(-∞) = -(-∞)/3 = ∞/3 = ∞.
At the right tail, we have that:
g(∞) = -(∞)/3 = -∞/3 = -∞.
Hence the fourth function is the correct option among those given.
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If f(x) = 8 - 3|x + 21, find f(-6)
Answer:
18.33
Step-by-step explanation:
f=-6
-6(x)=8-3(x-21)
-6x=8-3x-63
-6x+3x=8-63
-3x=-55
-3x/-3=-55/-3
x=18.33
hope it helps
Enter the ordered pair for the vertices for Rx-axis(QRST).
The ordered pair after Rx-axis will be equal to Q' (1, -3), R' (3, 3), S' (0, 2), T' (-2, -1).
What is a graph?In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.
Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.
The initial coordinates of given quadrilateral are,
Q = (1, 3)
R = (3, -3).
S = (0, -2).
T = (-2, 1)
The deflection rule along the x-axis is,
(x, y) ⇒ (x, -y)
Now, the coordinates are,
Q' = (1, -3)
R' = (3, 3)
S' = (0, 2)
T' = (-2, -1)
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3. Which of the following is the solution to lx + 12| = 3x.
A. x = 3
C. x = 6
b. x = -6
d. x = - 3
demonstrate 3 way how Alonso and his children went into a grocery store and he bought $14 worth of apples and bananas. Each apple costs $1.75 and each Banana costs $0.70. He bought a total of 11 apples and bananas altogether. By following the steps below, determine the number of apples, ∞, and the number of bananas, y, that Alonso bought.
The number of apples(x) and bananas (y) that Alonso bought at the grocery store is x = 6 and y = 5.
Calculating Unknown quantity:To find an unknown quantity we use Linear equations. Here we use variables like a, b, c... x, y, z, etc. to represent the unknown number.
By using different variables we need to make equations according to the condition given problem and solve the equation for the value of variables.
Here we have
Alonso bought $ 14 worth of apples and bananas
The cost of each Apple = $ 1.75
The cost of each banana = $ 0.70
Let's assume that Alonso bought 'x' apples and 'y' bananas
Given that the total of Apples and Bananas = 11
=> x + y = 11 ----- (1)
The cost f x apples = 1.75 × x = 1.75x
The cost of y bananas = 0.70 × y = 0.70y
Given the total worth, 1.75x + 0.70y = 14 ---- (2)
=> x + 0.4y = 8 ------ (2)
Now solve (1) and (2) for x and y values
Do (1) - (2)
=> x + y - x - 0.4y = 11 - 8
=> 0.6y = 3
Multiply with 10 on both sides
=> 6y = 30
Divide by 6 into both sides
=> y = 5
Now substitute y = 5 in (1)
=> x + 5 = 11
=> x = 6
Therefore,
The number of apples(x) and bananas (y) that Alonso bought at the grocery store is x = 6 and y = 5.
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x^2+4x-9=x+1 i have no idea what the answer would be
Answer:
x = 2
Step-by-step explanation:
Simplify both sides of the equation.
[tex]x(2)+4x-9=x+1\\2x+4x+-9=x+1\\(2x+4x)+(-9)=x+1[/tex] (combine like terms)
[tex]6x+-9=x+1\\6x-9=x+1\\[/tex]
subtract x from both sides.
[tex]6x-9-x=x+1-x\\5x-9=1[/tex]
add 9 to both sides.
[tex]5x-9+9=1+9\\5x=10[/tex]
divide both sides by 5
[tex]\frac{5x}{5} =\frac{10}{5} \\x=2[/tex]
Graph the inequality in a coordinate plane y ≤ 5
the inequality model will be y ≤ 5 in the shaded region, attached below.
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
coordinate plane y ≤ 5
So it states that the region should be less than equal to 5.
Hence, the inequality model will be y ≤ 5 in the shaded region.
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Can someone please explain step by step on how I stole this problem?
-1 - ( -0.25 )
The final answer of the problem is -0.75.
What is the order of operations?
The order of operations is also known as the hierarchy of operations. The order of operations tells us the order in which we should perform mathematical operations in order to get the correct result. The order of operations is usually represented by the acronym PEMDAS:
P: Parentheses first
E: Exponents (ie Powers and Square Roots, etc.)
MD: Multiplication and Division (left-to-right)
AS: Addition and Subtraction (left-to-right)
We have,
-1 - (-0.25)
Using the order of operations, we can solve this problem as follows:
Parentheses: The first step is to perform any calculations inside parentheses. In this case, there are no parentheses, so we can move on to the next step.
Exponents: There are no exponents in this problem, so we can move on to the next step.
Multiplication and Division: There is no multiplication or division in this problem, so we can move on to the next step.
Addition and Subtraction: Finally, we can perform addition and subtraction in the problem. We start from left to right, so we start with the first operation: -1 - (-0.25). To subtract a negative number, we can use the rule that subtracting a negative number is the same as adding a positive number.
Therefore, we have -1 + 0.25.
The final step is to simplify the expression by performing the addition: -1 + 0.25 = -0.75.
Therefore, the final result of the problem is -0.75.
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Identify the angular displacement, the angular velocity, and the angular acceleration
of the second hand on a clock over the time interval in which it moves
from the number 12 to the number 6. Provide answers in both degree- and
radian-
based units
Answer:
Angular Displacement: 180° or π radians
Angular Velocity: 3°/sec or 0.0524 radians/sec
Angular Acceleration: 0°/sec^2 or 0 radians/sec^2
Step-by-step explanation:
What is the equation of this line?
y=4 x+6
y=6 x+4
y=12 x+2
v=4 x-6
Answer:
y = 4x - 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, - 2) and (x₂, y₂ ) = (2, 2) ← 2 points on the line
m = [tex]\frac{2-(-2)}{2-1}[/tex] = [tex]\frac{2+2}{1}[/tex] = [tex]\frac{4}{1}[/tex] = 4
the line crosses the y- axis at (0, - 6 ) ⇒ c = - 6
y = 4x - 6 ← equation of line
What is the rate of change of the linear function whose graph includes the points (5, 2) and (10, 0)?
21.) Evaluate when
a=-2, b=-4, c=1 for b²-4 a c
Answer:
24
Step-by-step explanation:
Put all the values in given equation and compute.
An online shopping club has 13,000 members when it charges $7 per month for membership. For each $1 monthly increase in membership fee, the club loses approximately 500 of its existing members. Write and simplify a function R to represent the monthly revenue received by the club when x represents the price increase.
The purpose of the function to represent the club's earnings is R(x) is (13,000 - 500x) (7+x)
What is the the purpose of the function?The purpose of the function to represent the club's earnings is
R(x) = (13,000 - 500x) (7+x)
Total members in the Online shopping Club = 13,000
Monthly membership fee equals $7
Increase in the Monthly Membership Fee = $1
The group loses around = 500 members for every $1 increase in monthly dues.
To Locate:
The formula to calculate the club's income when x represents a price rise
Solution:
Each month, there is a $1 rise, which causes the number of members to drop by 500.
The reduction is one dollar for a month.
500*1
For two months, a two dollar increase will result in a loss of
500* 2 =1,000 members.
then for x months
Members have decreased by 500 * x = 500x.
Additionally, the membership fee will increase by 8 + x
Monthly revenue = number of members * monthly freeMonthly revenue = (13,000 - 500x) (7+x)R(x) = (13,000 - 500x) (7+x)To learn more about Monthly revenue refer to:
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Use Figure 1 to evaluate the trigonometric function.
A right triangle with side a of length 13 opposite of angle A, and side b of length 6 opposite of angle B.
The expression of the trigonometric ratios are;
sin θ = 6/√205
cos θ = 13/√205
tan θ = 6/13
How to use trigonometric ratios?
The primary trigonometric ratios for a right angle triangle are expressed as;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the attached triangle, we can find the hypotenuse using Pythagoras theorem;
Hypotenuse = √(opposite² + adjacent²)
Thus;
Hypotenuse = √(13² + 6²)
Hypotenuse = √205
We are given;
Opposite = 6
Adjacent = 13
Thus;
sin θ = 6/√205
cos θ = 13/√205
tan θ = 6/13
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PLEASE HELP ME!!!!
Question Help Challenge Last month, Stephen's neighbors paid him to take care of their fish when they went on vacation. He spent $3 of his earnings on an afternoon snack and $17 on a new book. Afterward, he had at most $9 left. How can you best describe how much Stephen's neighbors paid him?
Answer:
stephen was paid at least $20.00001, and at most $29.
explanation:
we know he had at least $20 to spend, since that's what he spent.
we're given the information that he has at most $9 left. that means originally, he was paid no more than $29.
since kind of given, he has something left, he does have more than $20. which is why I wrote the ".00001" part. but that's a little weird, and it would be acceptable to write stephen was paid at least $20 and at most $29
The sampling distribution of the sample mean is formed from random samples of size 16 taken from a population with mean μ = 64 and standard deviation σ = 10. What are the mean and standard deviation of the sampling distribution of ?
mean = 64, standard deviation = 0.625
mean = 8, standard deviation = 2.5
mean = 64, standard deviation = 2.5
The mean and standard deviation of the sampling distribution include the following: C. mean = 64, standard deviation = 2.5.
What is the Central Limit Theorem?In Mathematics and statistics, the Central Limit Theorem states that the sampling distribution of means would always be normally distributed, as long as the sample size is large enough.
This ultimately implies that, the sampling distribution of means would always be normally distributed as the sample size gets larger in accordance with the Central Limit Theorem.
Mathematically, the standard deviation of a sampling distribution can be calculated by using this mathematical expression:
Standard deviation, σy = σ/√n
Where:
σ represents the standard deviation.n represents the sample size or number of items.Substituting the given parameters into the formula, we have;
Standard deviation, σy = 10/√16
Standard deviation, σy = 10/4
Standard deviation, σy = 2.5.
In conclusion, the mean of an original population is expected to be equal to the mean of the sampling distribution of means i.e 64.
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The sum of two forces, one having a magnitude of 9 N acting due east and other having a magnitude of 4 N acting due north is _ _ _ _ _.
The sum of two forces, one having a magnitude of 9 N acting due east and other having a magnitude of 4 N acting due north is 9.85 N.
One of the forces is of magnitude 9 N acting due east
The second force is of magnitude 4 N acting due north
Therefore, the sum of the two forces (say F1 and F2) will be the resultant of the two forces,
that is: sqrt ( (F1) ^ 2 + (F2) ^ 2)
= sqrt ( (9) ^ 2 + (4) ^ 2) = sqrt (97) = 9.8488 N ≈ 9.85 N
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Are the two expressions equivalent when x=3 ? 8x + 40 , 5 (2x + 8)
The two expressions are not equivalent when x = 3
What is expression ?
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math.
A mathematical expression is as straightforward as 12 + 2. We might alter the (+) to create many mathematical equations, like 12 - 2, 12*2, and 12/2. Operations include multiplication, division, addition, and subtraction. A mathematical expression can make use of a great number of additional procedures.
when x = 3
8x + 40
8 * 3 + 40
= 24 + 40
= 64
when x = 3
5 (2x + 8)
10x + 40
10 * 3 + 40
= 30 + 40
= 70
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A random sampling of people are asked whether they like comedies or dramatic movies, and whether they prefer to watch them in the theater or at home. The results are in the table.Create a relative frequency table that shows the percentage of comedy lovers that prefer each location and the percentage of drama lovers that prefer each location.
As per the random sampling, the marginal relative frequency for action movies is 44%.
The term sampling refers the process of selecting the group that you will actually collect data from in your research.
Here we have given that a relative frequency table that shows the percentage of comedy lovers that prefer each location and the percentage of drama lovers that prefer each location.
And we need to find the marginal relative frequency of action movies.
While we looking into the given question, we have identified that the joint relative frequency for 8th graders who like comedy movies is 16%. And the half of the 7th graders prefer action movies.
Based on these facts the resulting frequency is 44%.
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Suppose that the daily number of miles driven per school bus driver in the United States is normally distributed with a mean of 300 mi and standard deviation equal to 26 mi. A local school bus budget committee believes the daily number of miles driven per bus driver in their community is different from 300 mi, but they are not sure if it is greater than or less than the national average.
To test their hypothesis, the committee chooses a random sample of 40 school bus drivers and records how many miles each of them drives per day during a typical week. On average, the bus drivers from the sample drive 309 mi per day. To test the hypothesis that the average number of miles driven by local bus drivers is different from the national average, the budget committee calculates the z-statistic to be 2.19 standard deviations above the population mean.
Use the standard normal z-distribution table to calculate the P-value that represents the probability of mistakenly rejecting the claim that the daily number of miles driven by local bus drivers is not statistically different from the national average. Give your answer as a decimal rounded to four places.
P-value:
The p-value for the z-distribution table is 0.4854.
What is z-distribution?
A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution. By transforming the values of any normal distribution into z scores, it is possible to standardise it. Z scores provide the number of standard deviations from the mean that each value falls within.
Given that the z statistic to be 2.19 standard deviation above the population mean.
2.19 can be written as 2.1 + 0.09
Z₂.₁₉ = Z₂.₁₊₀.₀₉ = 0.4854
Therefore p-value is 0.4854.
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Use the data{1,1,1,3,3,5,7,7,9,11,13,14} to create a histogram with 5 bins.
The information needs to be divided into class intervals in order to make a histogram. Following that, make a tally to display the frequency (or relative frequency) of the data within each interval.
How do you make a histogram with data?A frequency histogram or a relative frequency histogram can be used to depict data if there are several data points and we want to examine how they are distributed.A histogram resembles a bar chart in appearance, but it displays numerical data. The data must be divided into class intervals in order to make a histogram. Then make a tally to display the frequency (or relative frequency) of the data within each interval. The frequency in a given class divided by the overall number of observations is the relative frequency. The bars are the same width as the class interval and the same height as the frequency (or relative frequency).Histogram Illustration
Jessica has been self-weighing every Saturday for the past 30 weeks. She was weighed in pounds, as shown in the table below.135 137 136 137 138 139
140 139 137 140 142 146
148 145 139 140 142 143
144 143 141 139 137 138
139 136 133 134 132 132
Her weight should be a histogram.
Answer
Usually, we want histograms to have intervals between 5 and 20. With a class of width 2, which will offer us 9 intervals given that the data ranges from 132 to 148, it is practical to have.131.5-133.5
133.5-135.5
135.5-137.5
137.5-139.5
139.5-141.5
141.5-143.5
143.5-145.5
145.5-147.5
147.5-149.5
To eliminate any doubt about whether the end point belongs to the interval to its left or to its right, we chose the end points to be.5, which is why. The endpoint convention specification is a substitute. The left end point, for instance, is included by Minitab but the right end point is not.To Learn more About histogram refer to:
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In a hardware store you must first go to server 1 to get your goods and then go to a server 2 to pay for them. Suppose that the times for the two activities are exponentially distributed with means six and three minutes. Compute the average amount of time it takes Bob to get his goods and pay if when he comes in there is one customer named Al with server 1 and no one at server 2.
The average amount of time it takes Bob to get his goods and pay if when he comes in there is one customer named Al with server 1 and no one at server 2 will be 16 minutes.
Let us assume that, T = the total amount of time Bob spends in the hardware store.
Let us assume that, T1 = the amount of time Bob spends waiting in line for Al to get his goods from server 1
Let us assume that, T2 = the amount of time it takes for Bob to get his goods from server 1
Let us assume that, T3 = the amount of time Bob spends waiting in line for Al to pay server 2 for his goods
Let us assume that, T4 = the amount of time it takes for Bob to pay server 2 for his goods
So, the value of total time T will be
T = T1 + T2 + T3 + T4 and E[T] = E[T1] + E[T2] + E[T3] + E[T4]
Now, E[T1] = 6 min. because of the memoryless property of the exponential distribution
E[T2] = 6 min.
To find E[T3], the condition on the availability of server 2 after Bob is done with server 1
So, the value of E[T3] will be
E[T3] = E[T3 | Server 2 is free] P(Server 2 is free) + E[T3 | Server 2 is not free] P(Server 2 is not free)
= 0 + 3 . P(Bob is done with server 1 before AI is done with server 2)
[tex]$$=3 \cdot \frac{1 / 6}{1 / 6+1 / 3}$$[/tex]= 3(1/3) = 1 min. and E[T4] = 3 min.
So, E[T] = E[T1] + E[T2] + E[T3] + E[T4]
or, E[T] = 6+6+1+3= 16 minutes
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A bi-weekly visit to your favorite restaurant. Say on average you spend $25 each visit.
A bi-weekly visit to your favorite restaurant. Say on average you spend $25 each visit.
You will spend an average of $50 a week at this restaurant.
the function witht he greater rate of change is blank. its rate of change is blank. the function with the smaller y-intercept is function blank. its y-intercept is at y value of blank.
Function 2 is the one with the fastest rate of change. It changes at a rate of six. Function 1 is the function with the smaller y-intercept. At a y value of 4, its y-intercept is located.
What is the difference between the rate of change and the y-intercept of a linear function?This is a question about linear functions. The function with the greater rate of change is the steeper line. Its rate of change (slope) is the same as the ratio of the rise over run.The function with the smaller y-intercept is the line with the smaller y-value when x=0. Its y-intercept is at the y value of the point where the line crosses the y-axis.This theory is the Slope-Intercept Form of a Linear Equation.Function 2 is the one with the fastest rate of change. It changes at a rate of six. Function 1 is the function with the smaller y-intercept.At a y value of 4, its y-intercept is located.To learn more about Slope-Intercept Form of a Linear Equation refer to:
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Data is collected from the US Geologic Survey about the flow rate of the Poudre river. After some study, and unit conversions, a scientist makes a first model of the historical flow rate data as F(t) = 1.5 + 1.2 cos(2 t) in billions of cubic feet per year, while t is measured in fractions of a year since May 1, 2000. Use the Fundamental Theorem of Calculus to find the net amount of water from t = 0) to t = using this flow rate F"(t).First, F(t) = +C The model predicts the net amount of water discharged from the Poudre is F112 -Filo 0.75 What does the model predict the net discharge will be from t = 0 to t = 12 Net discharge = 1.5 Billions of ft 3
The model predicts that the net discharge will be -0.8 + 1.2 cos(24) billions of cubic feet from t = 0 to t = 12.
The net amount of water discharged from the Poudre river from t = 0 to t = 12 can be found using the Fundamental Theorem of Calculus, which states that the net change in a function over an interval is equal to the function evaluated at the endpoints of the interval minus the function evaluated at the beginning of the interval.
In this case, the net discharge from t = 0 to t = 12 can be calculated as follows:
Net discharge = F(12) - F(0)
= (1.5 + 1.2 cos(212)) - (1.5 + 1.2 cos(20))
= 1.5 + 1.2 cos(24) - 1.5 - 1.2
= -0.8 + 1.2 cos(24)
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SOLVE FOR N
-np-5=4(c-2)
The solution of the algebraic equation is n = (3-4c)/p
How to solve for N?
An algebraic equation or expression is any equation that contains unknown values, usually represented with alphabets or letter
Given: -np-5=4(c-2)
-np-5 = 4(c-2)
Expand the bracket:
-np-5 = 4c-8
Collect like terms:
-np = 4c-8+5
-np = 4c-3
Divide both sides by -p:
n = -(4c-3)/p
n = (-4c+3)/p = (3-4c)/p
Thus, the solution is n = (3-4c)/p
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Awnser if this is a function or not yes or no please.
Answer: NO
Step-by-step explanation:
This is not a function, since there are multiple outputs for ONE input.
Answer:
no
Step-by-step explanation:
to be a function, the x's can only have one partner. Here, 7 has two partners (7 goes to 20 and also to 18) and the 11 has two partners also. This relation is not a function.
Construct a finite-state machine that models an old fashioned soda machine that accepts nickels, dimes, and quarters. The soda machine accepts change until 35 cents has been put in. It gives change back for any amount greater than 35 cents. Then the customer can push buttons to receive either a cola, a root beer, or a ginger ale.
To create a finite-state machine that models an old fashioned soda machine which can perform the stated work we can follow the given steps.
The machine accepts nickels (5 cents), dimes (10 cents) and quarters (25 cents).
Let the states be s , s1 ,s2 ,s3 ,s4 etc.
If we add a nickel to the machine, then the the input is 5 to the current state s , we move them to state s+1 ans so on , and similarly for dime and quarter.
On taking x a the input button for soda pop , we can create the required finite-state machine that models an old fashioned soda machine that accepts nickels, dimes, and quarters.
A finite-state machine (FSM), sometimes known as a finite automaton or simply a state machine, is a mathematical model of computation.
It is an abstract machine that can only be in one of a finite set of states at any one moment. In response to some inputs, the FSM can transition from one state to another; this transition is referred to as a transition. An FSM is defined by a set of states, an initial state, and the inputs that cause each transition.
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