Answers
Answer:
it represents a polynomial
Related Questions
(5g - 3h) - (6g + 7h)
Answers
-g-10h
Solution:
How to solve your problem
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Eliminate redundant parentheses
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Combine like terms
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Answer: -g - 10h
Step-by-step explanation:
(5g - 3h) - (6g + 7h)
= 5g - 3h - 6g - 7h
= 5g - 6g - 3h - 7h
= -g - 10h
Consider the hypotheses shown below. Given that xˉ=49,σ=11,n=32,α=0.10, complete parts a and b. H0:μ≤47H1:μ>47 a. What conclusion should be drawn? b. Determine the p-value for this test. a. The z-test statistic is (Round to two decimal places as needed.) a. The z-test statistic is (Round to two decimal places as needed.) The critical z-score(s) is(are) (Round to two decimal places as needed. Use a comma to separate answers as needed.) Because the test statistic the null hypothesis. b. The p-value is (Round to three decimal places as needed.)
Answers
The conclusions are as follows:
a. We reject the null hypothesis.
b. The p-value for this test is approximately 0.001.
To complete parts a and b, we can follow the steps for hypothesis testing.
a. The z-test statistic can be calculated using the formula:
z = ([tex]\bar{X}[/tex] - μ) / (σ / √n)
Given:
[tex]\bar{X}[/tex] = 49
σ = 11
n = 32
Substituting these values into the formula, we get:
z = (49 - 47) / (11 / √32) ≈ 2.90
The z-test statistic is approximately 2.90 (rounded to two decimal places).
To determine the critical z-score(s), we need to find the z-value that corresponds to the significance level α = 0.10. Since the alternative hypothesis is one-sided (μ > 47), we are performing a right-tailed test.
Using a standard normal distribution table or a calculator, the critical z-score for a right-tailed test at α = 0.10 is approximately 1.28 (rounded to two decimal places).
Because the test statistic z = 2.90 is greater than the critical z-score of 1.28, we reject the null hypothesis.
b. The p-value represents the probability of obtaining a test statistic as extreme as the observed value (or more extreme) assuming the null hypothesis is true. Since the alternative hypothesis is μ > 47, we are looking for the probability in the right tail of the distribution.
Using a standard normal distribution table or a calculator, we can find the p-value corresponding to the z-test statistic z = 2.90. The p-value is the area under the curve to the right of 2.90.
The p-value is approximately 0.001 (rounded to three decimal places).
Therefore, the conclusions are as follows:
a. We reject the null hypothesis.
b. The p-value for this test is approximately 0.001.
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Suppose the longest side in a right triangle has the measure 4,6. If the acute angles have the measure of 30° and 60°, which is the exact measure of the longer leg?
Answers
Help ASAP! Will name brainliest!
Answers
Zc and Zx are supplementary angles. Zy measures 49º.
What is the measure of Zx?
Answers
Answer:
Zx = 131
Step-by-step explanation:
The angles will equal to 180, so therefore you will do 180-49=Zx
I’m begging you please please ASAP ASAP please ASAP thank you please please ASAP
Answers
Answer:
The ratio is [tex]\frac{2}{3}[/tex].
Step-by-step explanation:
The ratio of the perimeters of Quad ABCD to Quad WXYZ = [tex]\frac{perimeter of ABCD}{perimeter of WXYZ}[/tex]
But considering sides AB and WX,
representative factor for both figures = [tex]\frac{12}{8}[/tex]
So that;
WX = 12
XY = 1.5 x 6 = 9
YZ = 1.5 x 7 = 10.5
WZ = 1.5 x 7 = 10.5
Thus,
perimeter of Quad ABCD = 6 + 7 + 7 + 8
= 28
perimeter of Quad WXYZ = 9 + 10.5 + 10.5 + 12
= 42
The ratio of the perimeters of Quad ABCD to Quad WXYZ = [tex]\frac{28}{42}[/tex]
= [tex]\frac{2}{3}[/tex]
A hot air balloon pilot begins to land her balloon. In the first minute the balloon's elevation -336 feet. In the second minute, the balloon's elevation changes by 1/16 of that amount. What is the balloon's elevation during the second minute?
Answers
Answer:
-21 Feet
Step-by-step explanation:
-336/16
The balloon's elevation during the second minute will be 21 feet.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A sight-seeing balloon pilot starts to land her inflatable. In the main moment the inflatable rise - 336 feet. In the subsequent moment, the inflatable's height changes by 1/16 of that sum.
Then the balloon's elevation during the second minute is given as,
⇒ - 336 x (1/16)
⇒ - 336 / 16
⇒ - 21 feet
The balloon's elevation during the second minute will be 21 feet.
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Cranor and Christensen study diabetics insured by two employers. Group 1 subjects were employed by the City of Asheville, North Carolina, and group 2 subjects were employed by Mission-St. Joseph’s Health System. The data are displayed in the following table.
Weight (Pounds) Group 1 Group 2 252 215 240 185 195 240 190 302 310 210 205 270 312 212 190 200 159 126 238 172 170 204 268 184 190 170 215 215 136 140 320 254 183 200 280 148 164 287 270 264 214 288 210 200 270 270 138 225 212 210 265 240 258 182 192 203 217 221 225 126 Source: Data provided courtesy of Carole W. Carnor, Ph.D. 220 295 202 268 220 311 164 206 170 190
ANSWER SHOULD BE BASE ON THE FF:
State the null and alternative hypothesis
Level of significance
Test statistics
Decision Rule
Stata Output
Statistical Decision
Conclusion
Linear Regression Model and Interpretation (if necessary)
Answers
Null and alternative hypothesis: The null hypothesis is that the mean weight of the diabetics insured by two employers is similar.
In contrast, the alternative hypothesis is that the mean weight of the diabetics insured by two employers is not equal. Level of significance: The level of significance
(α) is the probability of rejecting the null hypothesis when it is valid. The commonly used level of significance is 0.05.
Test statistic: Assuming the population variances are equal, the test statistic is the t-distribution.
Decision Rule: Reject H0 if the t-value is greater than 2.060 or less than -2.060 and accept H0 if the t-value is between 2.060 and -2.060.
State Output: Assuming equal variances, the p-value associated with a two-tailed t-test for equality of means is 0.2682.Statistical decision: Since the p-value is greater than 0.05, we accept the null hypothesis and conclude that the mean weight of diabetics insured by the two employers is equal.
Conclusion: Therefore, there is no considerable difference in the mean weight of diabetics insured by two employers in the City of Asheville and Mission-St. Joseph’s Health System. Linear regression model and interpretation (if necessary): A linear regression model was not necessary in this study.
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Their 47 students need a seat on the school bus. If there are 21 student seats on a school bus. How many school buses will need to let each student have a seat?
Answers
Answer: 3 buses
Step-by-step explanation:
Answer:
Simply multiply 21 until you get a number greater than 47. In this case, 3, even though there is only a little remainder of 5 kids on one bus by themselves.
Step-by-step explanation:
Right will be marked brainlist
Answers
Answer:
the answer is 3,107.21
The answer to that question is that one
(-4,9);m=-1/2
Write the equation in point slope form
Answers
Answer: y-9=-1/2 x (x+4)
Step-by-step explanation:
Solve system of equations given below using both inverse matrix (if possible) and reduced row echelon forms. (20 Points each) a) xy + 2x2 + 2x3 = 1 X1 - 2x2 + 2x3 = -3 3x1 - x2 + 5x3 = 7 - b) x1 + 2xy + 2x3 + 5x4 = 0 *1 - 2x2 + 2x2 - 4x4 = 0 3x1 - x2 + 5x3 + 2x4 = 0 3x, -2x2 + 6x3 - 3x4 = 0.
Answers
The solution to the system of equations is x1 = -(9/7)x4, x2 = (2/7)x4, x3 = -(1/7)x4, and x4 is a free variable.
a) xy + 2x2 + 2x3 = 1 X1 - 2x2 + 2x3 = -3 3x1 - x2 + 5x3 = 7
We can solve the system of equations using both inverse matrix (if possible) and reduced row echelon forms.
We begin by converting the above equations into matrix form as follows:
[xy+2x2+2x3=1] [X1-2x2+2x3=-3] [3x1-x2+5x3=7] = [1] [-3] [7]
We represent the coefficient matrix by A and the variable matrix by X.
Then we have AX = B where B = [1] [-3] [7]
To find the inverse of A.
If the inverse of A exists, we can use it to find X = A^(-1)B.
We can find the inverse of A using the formula A^(-1) = adj(A)/|A| where adj(A) is the adjugate of A and |A| is the determinant of A.
We have: det(A) = |[1,2,2;-1,-2,2;3,-1,5]| = 9adj(A) = [11,6,-4;19,9,-5;-7,-4,3]
Therefore, A^(-1) = adj(A)/|A| = [11/9,2/3,-4/9;19/9,1/3,-5/9;-7/9,-4/3,1/9]
We can use A^(-1) to find X as follows:
X = A^(-1)B = [11/9,2/3,-4/9;19/9,1/3,-5/9;-7/9,-4/3,1/9][1;-3;7] = [-5/3;1/3;2/3]
Therefore, the solution to the system of equations is x = -5/3, y = 1/3, z = 2/3.
We can also solve the system of equations using the reduced row echelon form of the augmented matrix as follows:[1,2,2,1;-1,-2,2,-3;3,-1,5,7] [R2+R1,R3-3R1] [1,2,2,1;-4,-3,4,-2;0,-7,-1,4] [R2/(-4),R3/(-7)] [1,2,2,1;1/4,1,-1,1/2;0,1,1/7,-4/7] [R1-2R2, R3-(1/7)R2] [1,0,3/2,-1/2;0,1,1/7,-4/7;0,0,0,0]
The last row of the above matrix represents the equation 0x1 + 0x2 + 0x3 + 0x4 = 0, which is an identity.
The system of equations is consistent, and we can solve for x, y, and z using the first two rows of the above matrix as follows:
x + (3/2)z = (-1/2)y + (1/7)z = (4/7)
Solving for z, we have: z = 2/3
Substituting z into the first equation, we have:
x + (3/2)(2/3) = (-1/2)x = -5/3
Substituting z into the second equation, we have:
y + (1/7)(2/3) = (4/7)y = 1/3
Therefore, the solution to the system of equations is x = -5/3, y = 1/3, z = 2/3.b) x1 + 2xy + 2x3 + 5x4 = 0 *1 - 2x2 + 2x2 - 4x4 = 0 3x1 - x2 + 5x3 + 2x4 = 0 3x, -2x2 + 6x3 - 3x4 = 0
To solve this system of equations, we begin by converting it into matrix form as follows:[1,2y,2,5;0,-2,2,-4;3,-1,5,2;3,-2,6,-3] [x1;x2;x3;x4] = [0;0;0;0]
We represent the coefficient matrix by A and the variable matrix by X.
Then we have AX = 0. Our task is to find the reduced row echelon form of the augmented matrix [A|0].
We perform the following elementary row operations to the above matrix to obtain the reduced row echelon form:[1,2y,2,5,0;0,-2,2,-4,0;3,-1,5,2,0;3,-2,6,-3,0] [R1-2yR2, R3-3R2, R4-3R2] [1,0,-2y-1,2y+5,0;0,-2,2,-4,0;0,-7,-1,14,0;0,-8,0,9,0] [R3/(-7), R4/(-8)] [1,0,-2y-1,2y+5,0;0,-2,2,-4,0;0,1,1/7,-2/7,0;0,1,0,-9/8,0] [R1+(2y+1)R3] [1,0,0,9/7,0;0,-2,0,-2/7,0;0,1,1/7,-2/7,0;0,0,0,0,0]
The last row of the above matrix represents the equation 0x1 + 0x2 + 0x3 + 0x4 = 0, which is an identity.
The system of equations is consistent, and we can solve for x1, x2, x3, and x4 using the first three rows of the above matrix as follows:
x1 = -(9/7)x4x2 = (2/7)x4x3 = -(1/7)x4
Therefore, the solution to the system of equations is x1 = -(9/7)x4, x2 = (2/7)x4, x3 = -(1/7)x4, and x4 is a free variable.
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At a certain college, it is estimated that at most 25% of the students ride bicycles to class. Does this seem to be a valid estimate if, in a random sample of 90 college students, 28 are found to ride bicycles to class?
Answers
Answer: The estimate is not valid based on the given sample.
Explanation:
The given information can be used to determine if the estimate is valid or not. It is estimated that at a certain college, at most 25% of the students ride bicycles to class, and a random sample of 90 college students is taken. The number of students who ride bicycles to class in the sample is 28. Therefore, to determine if the estimate is valid, the proportion of students who ride bicycles to class in the sample must be calculated. The proportion of students who ride bicycles to class in the sample is 28/90 = 0.31 ≈ 31%.The proportion of students who ride bicycles to class in the sample is greater than the estimated proportion of students who ride bicycles to class, which is 25%.
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A national health survey weighed a sample of 490 boys aged 6-11 and found that 67 of them were overweight. They weighed a sample of 530 girls aged 6-11 and found that 66 of them were overweight Conduct a hypothesis test to determine whether the proportion of overweight kids aged 6-11 among boys is greater than the proportion of overweight kids aged 6-11 among girls? Use level of significance 10%.
Answers
As the lower bound of the 90% confidence interval is below 0, there is not enough evidence to conclude that the proportion of overweight kids aged 6-11 among boys is greater than the proportion of overweight kids aged 6-11 among girls.
How to obtain the confidence interval?The sample proportions are given as follows:
Boys: 67/490 = 0.1367. Girls: 66/530 = 0.1245.The difference is then given as follows:
0.1367 - 0.1245 = 0.0122.
The standard error for each sample is given as follows:
[tex]s_B = \sqrt{\frac{0.1367(0.8633)}{490}} = 0.0153[/tex][tex]s_G = \sqrt{\frac{0.1285(0.8715)}{530}} = 0.0145[/tex]Then the standard error for the distribution of differences is given as follows:
[tex]s = \sqrt{0.0153^2 + 0.0145^2}[/tex]
s = 0.0211.
The critical value for a 90% confidence interval is given as follows:
z = 1.645.
The lower bound of the interval is:
0.0122 - 1.645 x 0.0211 = -0.0225.
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(05.07 HC)
A student is assessing the correlation between the number of workers in a factory and the number of units produced daily?
Part A: Is there any correlation between the number of workers in a factory and the number of units produced daily? Justify your answer. (4 points)
Part B: Write a function that best fits the data. (3 points)
Part C: What does the slope and y-intercept of the plot indicate? (3 points)
Answers
Answer:
a) yes, because they both increase by the same increments each time. Tis can be represented by the equation y=5x+2
b) y=5x+2
c) The y-intercept represents the amount of units there were initially and the slope represents the amount of units for every worker.
Fill in the blank: Let l be the line of equation (x,y)=(2,1)+t(4.3) And let Q=(-28,41) be a point in the plane. The distance from point Q to the line is:____________
Answers
To find the distance from point Q=(-28, 41) to the line represented by the equation (x, y) = (2, 1) + t(4, 3), we can use the formula for the distance between a point and a line in the coordinate plane. Therefore, the distance from point Q to the line is 233/5.
The distance between a point (x0, y0) and a line Ax + By + C = 0 is given by the formula:
d = |Ax0 + By0 + C| / √(A^2 + B^2)
In this case, we have the line represented parametrically as (x, y) = (2, 1) + t(4, 3), where t is a parameter. To use the formula, we need to convert this parametric representation to the standard form Ax + By + C = 0.
Expanding the parametric equation, we have:
x = 2 + 4t
y = 1 + 3t
From these equations, we can rearrange them to isolate t:
t = (x - 2) / 4
t = (y - 1) / 3
Setting the two expressions for t equal to each other, we get:
(x - 2) / 4 = (y - 1) / 3
Simplifying, we have:
3x - 6 = 4y - 4
4y - 3x = 2
Now we have the equation of the line in standard form. The coefficients A, B, and C are 4, -3, and 2, respectively.
To find the distance between point Q=(-28, 41) and the line, we can substitute the values into the distance formula:
d = |4(-28) + (-3)(41) + 2| / √(4^2 + (-3)^2)
Calculating the numerator and the denominator, we have:
d = |-112 - 123 + 2| / √(16 + 9)
d = |-233| / √25
d = 233 / 5
Therefore, the distance from point Q to the line is 233/5.
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PLEASE ACCTUALY HELP :<
Point A has the coordinates (-2,-4). Point A is reflected across the x-axis to create point 'A'. What are the coordinates of point "A"? Enter your answer in the space below.
Answers
Answer:
(-2, 4)
Step-by-step explanation:
Hopes this helps!
2. Two points are shown on the coordinate plane. How any units apart are
Point A and Point B?*
Answers
Answer:
Step-by-step explanation:
A box is to be wrapped in a red decorative paper. The box is 9 inches long, 5 inches wide and 4 inches high. What is the minimum amount of decorative paper needed to cover the box? *
Answers
SA= 2 (4)(5) + 2(5)(9) + 2(4)(9)
SA= 202in^2
If the box contains confetti, how much cubic inches of confetti are needed to fill the box?
V= lwh
= 4*5*9
= 180 in^3
What is the surface area of the rectangular prism below
7 7 14
A.496 B.490 C.980 D.248
Answers
Answer:
B.490
Step-by-step explanation:
Correct me if im wrong
Answer: 490
Step-by-step explanation:
The radius of a baseball is about 9.25 inches. The radius of the Basketball is 9.55 inches. What is the
difference of the volumes between the basketball and baseball?
331.55
2734.89
333.14
364.52
Answers
Answer:
C. 333.14
Step-by-step explanation:
Both the basketball and baseball has got the shape of a sphere. So that;
volume of a sphere = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
where r is the radius
i. Volume of the baseball = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
= [tex]\frac{4}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](9.25)^{3}[/tex]
= 3315.5655
volume of the baseball = 3316.57 cube inches
ii. Volume of the basketball = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
= [tex]\frac{4}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](9.55)^{3}[/tex]
= 3649.8372
Volume of the basketball = 3649.84 cube inches
The required difference = volume of basketball - volume of baseball
= 3649.84 - 3316.57
= 333.27 cube inches
The difference of the volumes of the basketball and baseball is 333.27 cube inches.
i need help the test is time and i have 5 min left can y'all pls help pls
Answers
Answer:
divide the figure into two parts.
area of square = side²
area of square =12²
area of square =144
area pf trapezium =1/2×(a+b)×h
area of trapezium =1/2×(12+6)×12
area of trapezium =108
area of polygon=144+108=252 unit²
Justin earns a base salary of $1500 per month at
the jewelry shop. He also earns a 3% commission
on all sales. If Just sold $82,975 worth of jewelry
last month, how much would he make for the
month including his base salary and commission?
Answers
Answer: Justin earns a base salary of $1500 per month at
the jewelry shop. He also earns a 3% commission
on all sales. If Just sold $82,975 worth of jewelry
last month, how much would he make for the
month including his base salary and commission?
Step-by-step explanation: $1500 + 3% + $82,975 = 84475. 03 or 84475
Rolling a single six-sided di, you play a game with the following rules: if you roll an even number, you lose 1 point. If you roll a 1, you gain 1 point. If you roll a 3, you gain 3 points. If you roll a 5, you lose 4 points. After a long time continually playing the game, would you expect to have a positive point total or a negative point total?
Answers
The expected value is 0, which means that, on average, you neither gain nor lose points over the long run. This suggests that after playing the game for a long time, we would expect to have a point total close to zero.
To determine whether you would expect to have a positive or negative point total after a long time playing the game, we can calculate the expected value or average point gain/loss per roll.
Let's calculate the expected value for each outcome:
Rolling an even number:
Probability = 3/6 = 1/2,
Point gain/loss = -1
Rolling a 1:
Probability = 1/6,
Point gain/loss = 1
Rolling a 3:
Probability = 1/6,
Point gain/loss = 3
Rolling a 5:
Probability = 1/6,
Point gain/loss = -4
The expected value, we multiply each outcome's point gain/loss by its probability and sum them up
Expected Value = (1/2) × (-1) + (1/6) × 1 + (1/6) × 3 + (1/6) × (-4)
Expected Value = -1/2 + 1/6 + 1/2 - 2/3
Expected Value = 0
The expected value is 0, which means that, on average, you neither gain nor lose points over the long run. This suggests that after playing the game for a long time, you would expect to have a point total close to zero.
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pls help and show work i am so screwed if i don’t do well on this
Answers
Answer:
see in the picture mark brainliest if correct
Find the surface area to the nearest whole number.
Only type in the numerical answer.
Answers
Answer:
342
Step-by-step explanation:
Given
Shape: Rectangular prism
The missing dimensions are:
[tex]Length = 5 ft[/tex]
[tex]Width = 6 ft[/tex]
[tex]Height = 12 ft[/tex]
Required
Determine the surface area
The surface area is calculated as:
[tex]Area = 2(Length * Width + Length * Height + Width *Height)[/tex]
This gives:
[tex]Area = 2(5ft* 6ft+ 5ft * 12ft+ 6ft*12ft)[/tex]
[tex]Area = 2(30ft^2+ 60ft^2+ 72ft^2)[/tex]
[tex]Area = 324ft^2[/tex]
Of the 1500 students at Marshall
Junior High, 38% are 7 graders.
What is the total number of 7
graders at Marshall Junior High?
Write a proportion and solve.
Answers
Answer:
36+25= 61
61/600 x 100 = 10.1 %
Step-by-step explanation: Hope This helped!!!!
In comparison to where would be
located on a number line?
A.closer to 0
B.the same point
C.closer to 1
D.at 0
Answers
Can y’all Plzs hep me I need this
Answers
a^2 + b^2 = c^2
In other words, sum of the squared smaller lengths are equal to the squared of the longest length
15^2 + 17^2 = c^2
225 + 289 = c^2
c^2 = 514
c = square root of 514
= 22.67156
Round it
Solution: 22.7 km
Answer:
22.7 km
Step-by-step explanation:
The Pythagorean Theorem is:
a² + b² = c²
where a and b are legs and c is the hypotenuse.
The hypotenuse is the longest side of a right triangle and can be identified as being across from the right angle. The legs are interchangeable between the variables a and b.
Because it's clear that x is the hypotenuse:
15² + 17² = x²
225 + 289 = x²
514 = x²
√514 = √x²
x = √514
Because we can't simplify √514 anymore, we can keep it as radical 514 or round it:
22.6715681 ≈ 22.7
Recall that a cycle in an undirected graph is a sequence of distinct vertices (V1, V2, ..., Vk) with k > 3 such that the edges {V1, V2}, {V2, V3},..., {Uk-1, Vk} and also {Uk, v1} all exist. (a) Design an algorithm which given an undirected connected graph determines whether the graph has a cycle. If the graph has |V| vertices and |E| edges, your algorithm should run in O([V] + El) time. (b) Justify the correctness and run-time of your algorithm.
Answers
The overall runtime of the algorithm is O(|V|+|E|). The DFS algorithm has a runtime of O(|V|+|E|), as does the main algorithm, which runs DFS for each vertex.Therefore, the algorithm has a total runtime of O(|V|+|E|).
a) Algorithm to determine if a graph has a cycle:The algorithm is implemented using DFS (Depth First Search) traversal, which starts from every vertex in the graph. During the DFS traversal, we maintain a set of vertices on the current path. We continue DFS traversal of each unvisited neighbor vertex, and if a neighbor is already on the path set, then we have found a cycle.
The algorithm to determine if a graph has a cycle is given below -Graph G(V, E)Start DFS from each vertex v in VIf DFS utility detects a cycle, then return true.
Else, return false.Let's take a look at the DFS algorithm below -DFS(vertex u)
1. Mark u as visited.
2. For every unvisited neighbor v of u, doDFS(v)
3. If v is already on the current path, return true to denote the existence of a cycle.
4. If there is no cycle, return false to denote that the graph does not contain a cycle.
The overall runtime of the algorithm is O(|V|+|E|).
The DFS algorithm has a runtime of O(|V|+|E|), as does the main algorithm, which runs DFS for each vertex.
b) Justification of the correctness and runtime of the algorithm:The algorithm provided uses a DFS traversal.
Therefore, the algorithm can detect a cycle in an undirected connected graph. If there is a cycle, then the algorithm will correctly detect it.
Since the algorithm starts DFS from each vertex, it will detect the cycle even if it starts from a vertex other than the one containing the cycle.
Therefore, it's correct.The overall runtime of the algorithm is O(|V|+|E|). The DFS algorithm has a runtime of O(|V|+|E|), as does the main algorithm, which runs DFS for each vertex.
Therefore, the algorithm has a total runtime of O(|V|+|E|).
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