We may use the instructions provided to build a finite-state machine that simulates a vintage soda machine and can carry out the specified work.
Nickels (5 cents), dimes (10 cents), and quarters are all accepted by the machine (25 cents).
The states should be s, s1, s2, s3, s4, etc.
If we add a nickel to the machine, we move from state s to state s+1 and so on, and the process is the same for a dime and a quarter.
We can build the necessary finite-state machine to simulate an antique soda machine that takes nickels, dimes, and quarters by using x as the input button for soda pop.
A mathematical model of computation is called a finite-state machine (FSM), often known as a finite automaton or just a state machine.
It is an abstract machine that has a limited number of states that it can only be in at any given time. The FSM can change from one state to another in response to some inputs; this change is known as a transition. A set of states, an initial state, and the inputs that trigger each transition comprise an FSM.
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A linear relationship is given in the table below. Determine the slope of the relationship.
-1 / -3/ 2/3/4/7/8/15/10/19
The slope of the linear relationship will be 2.
What is Equation of line?The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
A linear relationship is given in the table.
Now,
Let two point on the table are (- 1, - 3) and (2, 3).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - (-3)) / (2 - (-1))
m = 6 / 3
m = 2
Thus, The slope of the linear relationship = 2.
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Please Help
Have a close look at the diagram below. What is the probability of selecting the following marbles in order: red - blue - blue - blue ? Show your work and explain your thinking.
The probability of selecting the following marbles in order: red - blue - blue - blue will be 3 / 40.
How to calculate the probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1. In this case, 0 denotes the impossibility of the event and 1 represents certainty.
From the diagram Illustrated, it should be noted that that there are 2 blue balls and 3 red balls. The total number of balls will be 5.
The probability of selecting the following marbles in order: red - blue - blue - blue will be:
= 3/5 × 2/4 × 1/4 × 0/3
= 6 / 80
= 3 / 40
The probability is 3 / 40.
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Frosty the Snowman thought he could last in a greenhouse for 2 hours before melting. Unfortunately, it only took him 1 12
hours to melt.
Percent error is a way to describe error, expressed as a percentage of the actual amount. What is the percentage error in this situation?
The percentage error in this situation will be 33%.
How to calculate the percentage?It's important to note that Percent error is a way to describe error, expressed as a percentage of the actual amount.
Since Frosty the Snowman thought he could last in a greenhouse for 2 hours before melting but it only took him 1 1/2 hours to melt. The percentage error in this situation will be:
= (2 - 1 1/2) / 1 1/2 × 100
= 1/2 ÷ 1 1/2 × 100
= 1/3 × 100
= 33.33%
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4. The diagram shows a right triangle and the lengths of two of its sides in inches.
11.9
d
¡0m
7.9 in.
Which measurement is closest to the value of din inches?
Answer:
Step-by-step explanation:
Read the following prompt and type your response in the space provided.
Kim's teacher has marked this problem as one to recheck, but Kim cannot determine what she has done incorrectly. Identify Kim's error and write a correct solution.
Six less than 2 times a number is 50. What is the number?
2x – 6 = 50 (line 1)
2x – 6 – 6 = 50 – 6 (line 2)
2x = 44 (line 3)
2x ÷ 2 = 44 ÷ 2 (line 4)
x = 22 (line 5)
A random sample of n measurements was selected from a population with unknown mean and standard deviation o = 20 for each of the situations in parts a through d. Calculate a 95% confidence interval for ju for each of these situations. a. n=70, X = 27 b. n = 150, x= 115 c. n= 80. x = 18 d. n = 80, x=5.33
The 95% confidence interval for this situation is (0.95, 9.71).
What is the Standard deviation?
The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.
The formula for Confidence Interval for Population Mean When Population Standard deviation is known
[tex]\bar{x} \pm Z_{a/2} * \frac{\sigma}{\sqrt{n} }[/tex]
α for 95% confidence level = (100-95)/100 =0.05
[tex]Z_{\alpha/2}[/tex] = 0.05/2=0.025
[tex]Z_{\alpha/2}[/tex] = Z0.025 = 1.96
σ = 20
95% Confidence Interval for Population Mean When Population Standard deviation is known
[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]
a.
n=70 ; [tex]\overline{x}=27[/tex]
[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]
27 ± 1.96 × (20/√70)
= 27 + 1.96 x 2.3905
= 27 + 4.6853 = (22.31.31.69)
(22.31, 31.69)
b.
n=150 ; [tex]\overline{x}=115[/tex]
[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]
= 115 + 1.96 x
= 115 +1.96 x 1.633 = 115 + 3.2007 = (111.8, 118.2)
(111.8, 118.2)
c.
n=80 , [tex]\overline{x}=18[/tex]
[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]
= 18 + 1.96 x 2.2361 = 18 + 4.3827 = (13.62.22.38) V8018+
(13.62, 22.38)
d.
n=80, [tex]\overline{x}=5.33[/tex]
[tex]\bar{x} \pm 1.96* \frac{20}{\sqrt{n} }[/tex]
= 5.33 1.96 x 2.2361 = 5.33 4.3827 = (0.95, 9.71)
(0.95, 9.71)
e.
No. Since Sample sizes are large [tex](n\small \geq30)[/tex] and randomly selected from the target population, the condition guarantees that the sampling distribution of [tex]\overline{x}[/tex] is approximately normal.
Hence, the 95% confidence interval for this situation is (0.95, 9.71).
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The equation the quantity x plus 28 end quantity over 5 equals 3 times x models the workload of a class project, where x is the number of hours each student must contribute. How many hours does each student work on the project?
2 hours
5 hours
7 hours
12 hours
The number of hours that each student work on the project is 2 hours.
How many hours will be illustrated?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this situation, the equation the quantity x plus 28 end quantity over 5 equals 3 times x models the workload of a class project, where x is the number of hours each student must contribute.
This will be:
(x + 28) /5 = 3x
Cross multiply
x + 28 = 15x
Collect like terms
15x - x = 28
14x = 28
Divide
x = 28 / 14
x = 2
The number of hours is 2 hours.
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Answer: that answer is right ^
Step-by-step explanation:
sylvia went on a trip. The number of shirts she packed was 2 fewer than twice the number of pants she packed. The total number of pairs of pants and shirts was 16
Answer:
She packed 6 pairs of pants and 10 shirts.
Step-by-step explanation:
Say the number of pants is x. Then, the number of pants is 2x-2. Now you have the equation:
x+ (2x-2)=16
Solving this equation gives x=6.
Therefore, she packed 6 pairs of pants and 10 shirts.
The given point is reflected across the line indicated. Find the coordinates of the image.
R across y = -2
If the given point R is reflected across the line y = -2, the image is
(Type an ordered pair.)
noise levels at 3 volcanoes were measured in decibels yielding the following data:142,113,135construct the 90% confidence interval for the mean noise level at such locations. assume the population is approximately normal.step 1 of 4 : calculate the sample mean for the given sample data. round your answer to one decimal place.
The t critical value and confidence interval must be determined.
What is confidence interval?A confidence interval (CI) is a range of estimates for an unknown parameter in frequentist statistics.
The 95% confidence level is the most popular, however other levels, such 90% or 99%, are occasionally used when computing confidence intervals.
The percentage of related CIs over the long run that include the parameter's actual value is represented by the confidence level.
For instance, 95% of all intervals calculated at the 95% confidence level should include the parameter's actual value.
The sample size, sample variability, and confidence level are all variables that have an impact on the width of the CI.
Assuming all other factors remain constant, a larger sample results in a narrower confidence interval, while a sample with more variability results in a wider confidence interval.
According to our question-
At a confidence level of 90%, we have α = 1 - 0.90 = 0.1
α/2 = 0.1/2 = 0.05.
Degree of freedom = 4-1 = 3
When we look this up in the t critical value table,
t critical = 2.353
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Test of Independence 6. Are the factors that contribute to a person's wellbeing, (ie: Friendship and social life, job or primary activity, and health and physical condition), Independent of a person's marital status. See the chart. Marital married Widowed/divorced totals 42 132 49 Factors contribution to a 50 33 110 person's wellbeing. 21 25 58 100 300 a. a. b. b. C. C. d. d. e. e. status single Friendship 41 and social life Job or 27 primary activity Health and physical condition totals 80 120 State the null and alternative hypothesis State the observed values State the expected values Give the p-value Give a conclusion for the hypothesis test. 12
The conclusion of the hypothesis test is 0.342112
What is meant by hypothesis?
In statistics, hypothesis means an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.
Here we have given that the factors that contribute to a person's wellbeing, That is Friendship and social life, job or primary activity, and health and physical condition), Independent of a person's marital status.
And we need to find the null and alternative hypothesis and the conclusion of the hypothesis test.
As per the given table of data we have to calculated the p value in order to find the null and alternative hypothesis,
For that we gathered the value of the following,
Number of samples = 9
Then the mean value of data = 83.63
And the standard deviation of the data = 80.475
Then the p - value is calculated as,
p-value ≈ 0.342112
This decision is made at significance level α = 0.05.
Therefore, the result is not statistically significant: there is not enough evidence to reject the null hypothesis.
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(100 points plus brainliest) A proportional relationship between the number of pounds of potatoes (x) and the price in dollars (y) is graphed, and the ordered pair (4, 3) is on the graphed line
what is the price of 1 pound of potatoes? SHOW YOUR WORK
Answer: $0.75
Step-by-step explanation:
-We know that the line must also contain the point (0,0), as 0 pounds of potatoes would cost $0. Thus we can find the slope of the line and write an equation:
slope = Δy/Δx = (3-0)/(4-0) = 3/4
y = (3/4)x
(The y-int (aka b) is 0 since the line passes through (0,0))
Plugging in 1 yields $0.75
Answer:
$0.75 per pound-------------------------------------------------------
Proportional relationship equation:
y = kx, where k-constant of proportionalityGiven point (4, 3).
Use its coordinates to find the value of k:
3 = 4kk = 3/4k = 0.75This is representing the price of 1 pound of potatoes.
Calculate the difference and enter below. 3-9
Answer: -6
Step-by-step explanation: Since 9 is being subtracted from 3, we know that it will be a negative number. So, 9-3 = 6, and a greater number subtracted from a smaller number is a negative number. So, that results in this being -6. I hoped this helped.
[tex]3-9[/tex]
[tex]3+(-9)[/tex]
[tex]=\fbox{-6}[/tex]
[tex]3+(-9)[/tex] on a number line:
pls do this qwick
What is the product of (−23)(18)(−4)?
−1,656
−322
74
1,656
Answer:
1656
Step-by-step explanation:
Answer: 1656
Step-by-step explanation:
just trust me, that's the answer! I did the same question.
Math geometry,
GIVEN
The SSS congruence theorem is used to prove that triangles MAH and THA are congruent to each other. See proof below.
How to Apply the SSS Congruence Theorem?"SSS" stands for side-side-side congruence theorem, which says that given the criteria that two triangles both have three corresponding sides that are equal or congruent to each other, both triangles are congruent.
The proof below shows how we can apply the SSS to prove that triangles MAH and THA are congruent to each other.
Statement Reason
1. MA ≅ TH 1. Given
2. MH ≅ AT 2. Given
3. AH ≅ HA 3. Reflexive property of congruence
4. ΔMAH ≅ ΔTHA 4. SSS congruence theorem
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Compare the key features of f(x)=2x-3 and the
linear function g shown below.
23. What do the slopes and the y intercepts
indicate about the linear functions f and g?
Answer:
f slopes was [tex]\frac{3}{2}[/tex] ,the y intercepts was -3
g slopes was [tex]-\frac{1}{3}[/tex],the y intercepts was -2
Step-by-step explanation:
g slopes :
functions g has point (0,-2) and (3,-3)
the slopes =[tex]\frac{-2-(-3) }{0-3} =-\frac{1}{3}[/tex]
URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Question 7
The first blank as required to be filled in the task content should be filled with; two.
The second blank as required to be filled in the task content should be filled with; 134.1 in³.
What is the volume of the cone?According to the information given; the diameter of the beachball is; 8 inches. Therefore, it's radius is half that; 4 inches.
On this note, the volume of the beachball which is spherical in shape given by the formula;
Volume of a sphere = (4/3)πr³ where;
Radius, r = 4;
Therefore, volume of beachball is;
4/3 π (4)³ = 256π / 3.
Also, the volume of the cone which is given by the formula;
Volume of a cone = (1/3) π r² h
where; Radius, r = 4 and Height, h = 8.
Therefore, volume of the cone is;
(1/3) π (4²) × 8 = 128π / 3.
On this note, by dividing the volume of beachball by that of cone; we have that;
( 256π / 3 ) / ( 128π / 3 ) = 2.
On this note, the cone will fit into the beachball about 2 times.
Also, the volume of the cone given that; π = 22 / 7 can be evaluated as;
( 128 × 22 ) / ( 7 × 3 )
= 134.1 in³.
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An evergreen nursery usually sells certain shrub after 6 years of growth and shaping: The growth rate during those 6 years is approximated by dh/dt = 1.2t + 2, where t is the time in years and h is the height in centimeters. The seedlings are 15 centimeters tall when planted (t = 0). (a) Find the height after years h(t) (b) How tall are the shrubs when they are sold? cm
(a) After t years, the height is 18t² + 3t + 10
(b) The shrubs are847 cm tall when they are sold.
Given growth rate
dh/dt = 1.8t + 3
dh = (18t + 3)dt
Integrating this, we have
h = 18t² + 3t + C
When t = 0, h = 10cm
Then
10 = C
So
(a) h = 18t² + 3t + 10
(b) Because they are sold after every 9 years, then at t = 9
h = 18(9)² + 3(9) + 10
= 810 + 27 + 10
= 847 cm
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Hey WRLD... 999
Match each polynomial with its factorization. Type the number of the corresponding polynomial on the line of it’s factorization on the right.
1.
x2 – 2x – 48
_____ (x + 2)(9 – x)
2.
-3x2 + 14x - 8
____ (2 – 3x)(x – 4)
3.
X2 – 10x – 25
_____ (x + 6) (x – 8)
4.
-x2+7x+18
____ 3(x – 7) (x + 7)
5.
X4 – 16
_____ (x – 5)2
6.
3x2 – 147
_____ ( x – 2)( x + 2)( x2 + 4)
Each equation is expressed and mentioned in its factorized form are given above.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given are the polynomials along with their factorized forms.
The polynomials along with their correct factorized forms are as follows -
x² - 2x - 48 → (x + 6) (x – 8)-3x² + 14x - 8 → (2 – 3x)(x – 4)x² – 10x + 25 → (x - 5)²- x² + 7x + 18 → (x + 2)(9 – x)x⁴ - 16 → (x – 2)(x + 2)(x² + 4)3x² – 147 → 3(x – 7) (x + 7)Therefore, each equation is expressed and mentioned in its factorized form are given above.
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Simplify (-3x^4) (-4x^2)
Step-by-step explanation:
(-3x⁴)(-4x²)
as multiplication is commutative (that means the sequence of the factors is irrelevant), we get
-3×-4×x⁴×x²
we can combine everything of the same type (constants or variable names).
-3×-4 = 12
remember, -×- = +
x⁴×x² = x⁶
remember, when multiplying terms with the same base variable, we can simply add the exponents.
why ? because an exponent is a short way of saying that the base variable has to be multiplied by itself that many times.
e.g.
a³ = a×a×a
a⁷ = a×a×a×a×a×a×a
a³×a⁷ = a×a×a × a×a×a×a×a×a×a = a¹⁰
that's why.
so, the complete simplified expression is
12x⁶
when max and evie were counting their items of candy after trik or treating. the total humber of items was at least 90 and at most 115. If Evie had 42 items of candy, which of the following inequalities represents all possible number of items, m, that Max could have had?
Answer:
48 ≤ m ≤ 73
Step-by-step explanation:
Evie has 42, Max has x.
Total candy = x + 42
90 ≤ x+42 ≤ 115
48 ≤ m ≤ 73
Max can have 48 or more, but no more than 73
What number is 0.1 less than 15.2?
Answer:
15.1
Step-by-step explanation:
Please help will mark Brainly
Answer:
Below
Step-by-step explanation:
The solution set is the point(s) where the two plotted graphs intersect:
Claim: all natural numbers are either even or odd. Proof: By induction. Base case:0 is even, since 0 = 2.0. Now suppose that n - 1 is either even or odd, and we must show that n is either even or odd. Case 1: If n - 1 is even, then n - 1 = 2k for some k, so n = 2k + 1, showing n must be odd. Case 2: If n - 1 is odd, thenn - 1 = 2k +1 for some k, so n = 2k + 2 = 2(k+1), showing n must be even. Is this proof correct?
• Yes • No
No. The proof is wrong.
Here we are asked to prove all Natural numbers are either even or odd.
Natural numbers start from 1 to infinity.
Hence to prove by mathematical induction, we need to take the base case to be n = 1.
here, 1 = 2X0 + 1, therefore 1 is odd
Then we need to assume that for any integer m < n, m is either even or odd.
Now n > 1
Therefore,
n -1 > 0
Hence n - 1 will be a natural number.
Hence by our earlier assumption where any number smaller than is either even or odd
n - 1 has to be either even or odd.
case 1
here n - 1 is odd
if n - 1 is odd then
n-1 + 1 is a sum of two odd numbers, hence n is even
Case 2- If n - 1 is even
then, n-1 + 1 is a sum of an even and n odd number hence n is odd
Therefore n will either be even or odd.
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Here are the shopping times (in minutes) for each of fifteen shoppers at a local grocery store. Shopping times (in minutes) 29 35 27 26 24 20 37 34 24 33 24 36 32 18 31 (b) Construct a histogram for the data. (a) Complete the grouped frequency distribution for the data. (Note that the class width is 5.) Frequency Shopping times (in minutes) Frequency 18 to 22 23 to 27 OOOO 28 to 32 33 to 37 18 to 22 23 to 27 28 to 32 Shopping times in minutes) 33 to 37 X 5 ? xo?
Frequency is the number of occurrences of a repeating event.
What do you mean by frequency?The frequency of an occurrence or a value is the number of times it happens. A frequency table is a list of objects with the frequency of each item shown in the table.
The information that is gathered is called data. The quantity of occurrences of an event or value is referred to as its frequency. A frequency table is a table that lists items and displays how frequently each item happens.
The number of times a specific data value occurs is the frequency of that data. We use f to symbolise the frequency of a data value.
As an illustration, the grade A is said to occur frequently if five students received an A in science.
Here we have the events:
shopping time between occurrences frequency
18 to 22: 20, 18 2
23 to 27: 27, 24, 26, 24, 24 5
28 to 32 29, 31 2
33 to 37 37, 34, 35, 33, 36, 32 6
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A local university offers a review course for those who are planning to take the GRE exam. Thirty
percent of the people who took the exam had attended the university's GRE review course. The results
of the test showed that 60% of those who attended the review passed the exam, while among those who
did not attend the course, only 20% passed the exam. An individual has passed the exam. Knowing this,
what is the probability that he attended the review course?
The probability that an individual attended the course given he passed
is 37.5%.
What is conditional probability?Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
We know the probability of A given B is P(A/B) = P(A∩B)/P(B).
Let, The number of students be 100.
Given, Thirty percent of the people who took the exam had attended the university's GRE review course which is 30 and hence 70 people did not attend the review course.
60% of those who attended the review passed the exam,
= (60/100)×30.
= 18 people.
20% who passed the exam did not attend the review course.
= (20/100)×70.
= 14.
So, The no. of people who passed is (18 + 14)/100 = 32/100 = 0.32.
The probability that a student passed and taken the course is (18/30)×(14/70) = 0.12.
Therefore, Given that he passed, the likelihood that someone took the course is = (0.12/0.32) = 0.375 Or 37.5%.
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how do you prove 6^7-6^6+6^5 is divisible by 31
Step-by-step explanation:
I don't know if this is valid but
We can think of this problem like
(6^7-6^6+6^5)/31 = x
Where x is a whole number so 6^7-6^6+6^5 is divisible by 31
Multiply each side with 31 :
6^7-6^6+6^5 = 31x
We can turn 6^7 into 6^5 x 6^2
We can also turn 6^6 into 6^5 x 6
So the equation turns into this :
(6^5 x 6^2) - (6^5 x 6) + (6^5 x 1) = 31x
We can factor out the 6^5 out of the left side of the equation, which turns into :
(6^5) x (6^2 - 6 + 1) = 31x
Which is also :
(6^5) x (31) = 31x
Divide each side with 31
6^5 = x
X is obviously a whole number
give an example of a continuous map with x and y connect that is one to one and honto but is not a homemorphism g
Let X be the integers with the topology created by declaring a set to be open if either it is a subset of N or it is the entire set Z. Then, we define a map f: X --> X such that f(x) = x- 1 is an example of continuous map is one to one and honto but is not a homemorphism .
What is a bijective function?A function f: A --> B is said to be bijective or bijection if it satisfies both injective (one-to-one function) and surjective (over-function) properties. Let X be the integers with the topology created by declaring a set to be open if either it is a subset of N or it is the entire set Z. Then, we define a map
f : X--> X such that f(x) = x- 1 ; x∈X (domain)
Now, we show that it is bijective, so
One to One : let x₁ and x₂ belongs to X such that f(x₁) = f(x₂) we have to show x₁= x₂
f(x₁) = f(x₂) => x₁ - 1 = x₂ - 1
=> x₁ = x₂ -1 + 1
=> x₁ = x₂
So, f(x) is one to one.
Onto : let y be a element of X ( co-domain) We can show that there exists x∈A such that f(x)=y. Choose x= f⁻¹(y) and so f(f⁻¹(y))=y. So for all y∈B, there exists an x∈A such that f(x)=y. Therefore, it is onto. Thus, f(x) is one to one and onto and continus( due to polynomial nature) i.e it is a continuous bijection from X to itself, but it is not a
homeomorphism, since the image of N is not open.
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Indicate whether a binomial distribution is a reasonable probability model for the random variable X. give your reasons in each case.
joey buys a virginia lottery ticket every week. x is the number of times in a year that he wins a prize.
The given statement is a reasonable probability model because it fulfills the 4 conditions of binomial distribution.
How to identify binomial distribution model?The conditions for binomial distribution are;
1: The number of observations n must be fixed.
2: Each observation must be independent.
3: Each observation must represent one of two outcomes ("success" or "failure").
4: The probability of "success" p must be the same for each outcome.
Now, we are given the statement;
Joey buys a Virginia lottery ticket every week. x is the number of times in a year that he wins a prize.
From that statement, we can tell that the number of observations is fixed at 52 weeks since a year is made up of 52 weeks.
Secondly, we can say that there could be success by winning a price or failure by not winning the price.
Each weekly observation is independent.
The probability is the same for each outcome.
Thus, we conclude that since it fulfills all the four conditions then it is a binomial model.
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Write the
slope-intercept form of the equation of
the line that passes through the point (1, 2) and
has the slope of 6.