# Math - Others Questions

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Math - Others

Basic MathThe line graph shows the goals per game average for a sporting series during the years shown During what year shown was the average number of goals per game the lowest The average number of goals per game was the lowest during the year Ave of Goals per Game Goals per Game Average 3 8 3 2 2 6 2 1977 1985 1993 2001 Year Q Su

Math - Others

Basic MathThe table shows the worldwide box office in billions of dollars for the movie industry during the years shown Year 1997 1999 2001 2003 2005 Box office in billions of dollars 22 9 24 3 26 3 27 9 30 8 c Create a scatter diagram of the paired data Choose the correct scatter diagram below O A OB Box Office 32 Box Office 0 1996 O C 32 07 1996 Year 2006 2006 Box Office 32 Box Office 0 1996 O D 32 0 1996 Year Year 2006 2006

Math - Others

Basic MathThe histogram shows the number of miles that each adult from a survey of 97 adults drives per week How many adults drive 0 49 miles per week adulto who driven 19 miles per week Number of Adults A 30 25 20 15 10 5 0 0 49 50 99 100 149 150 199 200 249 250 299 Number of Miles

Math - Others

Basic MathK The line graph shows the goals per game average for a sporting series during the years shown Find the average number of goals per game in 1983 The average number of goals per game in 1983 was Round to the nearest tenth as needed CELO Ave of Goab per Game Goals per Game Average 3 8 3 4 3 2 6 2 2 1 8 1979 1987 SOU 1995 2003 Year

Math - Others

Basic MathPeople drive on average 14 058 miles per year About how many miles each week is that Note There are 52 weeks in a year People drive about miles each week Type a whole number or decimal rounded to the nearest tenth as needed

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FunctionsDraw a tree diagram for spinning Spinner A one time and then Spinner B two times Use the diagram to find the number of possible outcomes A P B V V V V V V OB Spinner A R R D V V V V V V V Spinner B 3 4 O OU O C Viller 26 86 Villere P N Yeller Gen Villen Val M Vallen Rad Vollere 2 Kw Vilhey Y Villow Kal P Ma Vellow kad O D 2 VVV

Math - Others

Basic MathThe histogram shows the projected ages of householders in the near future How many householders will be under 25 years old Approximately million householders will be under 25 years old Round to the nearest million as needed Millions of Households 222 27 24 21 18 15 12 9 woo Under 25 34 35 44 45 54 55 64 65 74 Age in Years 25 75 and O

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Mathematical ReasoningIdentical twins come from a single egg that split into two embryos and fraternal twins are from separate fertilized eggs Also identical twins must be of the same sex and the sexes are equally likely and sexes of fraternal twins are equally likely Use the data table to complete parts a and b below Identical Twins Fraternal Twins boy boy 8 3 boy girl 0 3 girl boy 0 3 Sexes of Twins girl girl G 8 3 a After having a sonogram a pregnant woman learns that she will have twins What is the probability that she will have identical twins The probability is Type an integer or a simplified fraction

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Mathematical InductionThe data represent the results for a test for a certain disease Assume one individual from the group is randomly selected Find the probability of getting someone who teste negative given that he or she had the disease The probability is approximately The individual actually had the disease Yes C No 142 6 Positive Negative Round to three decimal places as needed H 20 132

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Basic MathIdentical twins come from a single egg that split into two embryos and fraternal twins are from separate fertilized eggs Also identical twins must be of the same sex and the sexes are equally likely and sexes of fraternal twins are equally likely If a pregnant woman is told that she will give birth to fraternal twins what is the probability that she will have one chile of each sex Use the data table below to find the probability Identical Twins Fraternal Twins boy boy 4 8 boy girl 0 9 The probability is Type an integer or a simplified fraction girl boy 0 9 girl girl 4 8 Sexes of Twins

Math - Others

Basic MathThe report Digital Democracy Survey t describes a large national survey In a representative sample of Americans of age 14 to 18 years 45 Indicated that they usually use social media while watching TV Suppose that the sample size was 600 Let p be the population proportion of Americans of age 14 to 18 years who usually use social media while watching TV LAUSE SALT a Is there convincing evidence that less than half of Americans of age 14 to 18 years usually use social media while watching TV Use a significance level of 0 05 State the appropriate null and alternative hypotheses Enter for as needed Ho H Find the test statistic Round your answer to two decimal places Use technology to find the P value Round your answer to four decimal places P value State the conclusion in the problem context Fail to reject Ho We do not have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV Reject Ho We have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV Reject Ho We do not have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV Fail to reject Ho We have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV TICE ANOTHER b Suppose that the sample size had been 100 rather than 600 and that 45 of those in the sample indicated that they usually use social media while watching TV Based on this sample of 100 is there convincing evidence that less than half of Americans of age 14 to 18 years usually use social media while watching TV Use a significance level of 0 05 State the appropriate null and alternative hypotheses Enter for as needed Hi

Math - Others

Mathematical ReasoningAn article about financial literacy in America summarized a national survey of 2 000 U S adults over the age of 18 The sample was selected to be representative of adults in this age group LUSE SALT MY NOTES a of those surveyed 64 reported that they had credit card debt Use this information to construct a 95 confidence interval for the proportion of all adults in this age group who have credit card debt Enter your answer using interval notation Round your numerical values to three decimal places Interpret the interval We are 95 confident that the true proportion of all adults in the United States who have credit card debt is directly in the middle of this confidence interval We are 95 confident that the true proportion of all adults in the United States who have credit card debt is within this confidence interval There is a 95 chance that the mean number of all adults in the United States who have credit card debt is directly in the middle of this confidence interval There is a 95 chance that the true proportion of all adults in the United States who have credit card debt is directly in the middle of this confidence interval We are 95 confident that the mean number of all adults in the United States who have credit card debt is within this confidence interval b of those surveyed 25 reported that they always pay their bills on time Use this information to construct a 90 confidence interval for the proportion of all adults in this age group who always pay their bills on time Enter your answer using interval notation Round your numerical values to three decimal places Interpret the interval There is a 90 chance that the mean number of all adults in the United States who always pay their bills on time is directly in the middle of this confidence interval We are 90 confident that the mean number of all adults in the United States who always pay their bills on time is within this confidence interval We are 90 confident that the true proportion of all adults in the United States who always pay their bills on time is directly in the middle of this confidence interval We are 90 confident that the true proportion of all adults in the United States who always pay their bills on time is within this confidence interval There is a 90 chance that the true proportion of all adults in the United States who always pay their bills on time is directly in the middle of this confidence interval c Give two reasons why the confidence interval from part b is narrower than the confidence interval from part a The confidence interval in part b is narrower because p of 0 25 is farther from 0 5 than p of 0 64 Another reason is that the confidence level in part b is smaller than in part a

Math - Others

Mathematical Reasoning4 According to a data intelligence company that specializes in the short term rental market 76 of listings by a website specializing in renting properties are for entire homes or apartments as opposed to shared spaces Do the listings in a particular city have the same distribution of housing types Using publicly available data suppose you take a random sample of 100 listings in this particular city Of those 80 were for entire homes or apartments Is there sufficient evidence to conclude that the percentage of listings in this particular city that are for entire homes or apartments is different from 76 Using the five step process for hypothesis testing HMC3 and a significance level of a 0 05 test the appropriate hypotheses LUSE SALT State the appropriate null and alternative hypotheses Let p be the population proportion of listings that are for entire homes or apartments Enter for as needed Ho H Find the test statistic Round your answer to two decimal places Use technology to find the P value Round your answer to four decimal places P value MY NOTES State the conclusion in the problem Reject H We do not have sufficient evidence to conclude that the percentage of listings in this particular city that are for entire homes or apartments is different from 76 Reject Ho We have sufficient evidence to conclude that the percentage of listings in this particular city that are for entire homes or apartments is different from 76 Fail to reject Ho We do not have sufficient evidence to conclude that the percentage of listings in this particular city that are for entire homes or apartments is different from 76 Fail to reject Ho We have sufficient evidence to conclude that the percentage of listings in this particular city that are for entire homes or apartments is different from 76

Math - Others

Basic Math1 0 2 Points DETAILS PREVIOUS ANSWERS PECKSTAT3 10 1 002 MY NOTES PRACTICE ANOTH CareerBuilder com conducted a survey to learn about the proportion of employers who perform background checks when evaluating a candidate for employment Suppose you are interested in determining if the resulting data provide strong evidence in support of the claim that more than six sevenths of employers perform background checks To answer this question what null and alternative hypotheses should you test Let p be the population proportion of all employers who perform background checks Hint See Example 10 2 Enter for as needed Ho

Math - Others

Mathematical ReasoningA report describes a survey of 500 licensed drivers Each driver in the sample was asked if they would prefer to keep complete control of the car while driving to use a partially self driving car that allowed partial driver control or to turn full control over to a driverless car Suppose that it is reasonable to regard this sample as a random sample of licensed drivers in the United States and that you want to use the data from this survey to decide if there is evidence that fewer than half of all licensed drivers in the United States prefer to keep complete control of the car while driving USE SALT a Describe the shape center and variability of the sampling distribution of p for random samples of size 500 if the null hypothesis Ho P 0 50 is true Round your standard deviation to four decimal places The shape of the sampling distribution is approximately normal The sampling distribution is centered at The standard deviation of the sampling distribution is b Would you be surprised to observe a sample proportion as small as p 0 49 for a sample of size 500 If the null hypothesis Ho P 0 50 were true Explain why or why not Consider the event surprising if the probability that the event occurs when Ho P 0 5 is true is less than 0 05 Round your answer to four decimal places We would not 8 be surprised to observe a sample proportion of p 0 49 for a sample of size 500 if the null hypothesis Ho p 0 5 is true The probability of a sample proportion this which is greater than the signficance level of 0 05 small or smaller is c Would you be surprised to observe a sample proportion as small as p 0 46 for a sample of size 500 if the null hypothesis Ho P 0 50 were true Explain why or why not Consider the event surprising if the probability that the event occurs when Ho P 0 5 is true is less than 0 05 Round your answer to four decimal places We would B be surprised to observe a sample proportion of p 0 46 for a sample of size 500 if the null hypothesis Ho P 0 5 is true The probability of a sample proportion this small or smaller is which is less than the signficance level of 0 05 d The actual sample proportion observed in the study was p 0 44 Based on this sample proportion is there convincing evidence that fewer than 50 of licensed drivers prefer to keep complete control of the car when driving or is the sample proportion consistent with what you would expect to see when the null hypothesis is true Support your answer with a probability calculation Round your answer to four decimal places Consider the that fewer than 50 of licensed drivers prefer to keep complete control of the car when driving convincing if the probability that the event occurs when Ho p 0 5 is true is less than 0 05 which is less than Since the probability of a sample proportion this small or smaller is fewer than 50 of licensed drivers prefer to keep complete control of the car when driving B the signficance level of 0 05 there is B convincing evidence that

Math - Others

Trigonometric equationsantities Prove the given identity sin xsec x cos xcsc x sec xcsc x Choose the correct proof below OA sin xsec x cos xcsc x sin X cos x sin x cos x cos2x sinx cos sin x cos x sec Xcsc X OC sin xsec x cos xcsc x 1 sin x cos x sin x cos x cos x sin 2x cos2x x sin x cos x 1 sec Xcsc X sin x Question 7 of 10 This quiz 20 point s poss This question 2 point s pr OB sin xsec x cos xcsc x sin X cos X 2 sin x cos x sin x cos x 1 sin x cos x sec Xcsc X OD sin xsec x cos xcsc x sin x 2 sin x cos sin xcos X 1 cos x cos X cos2 sin x cos X sec xcsc x 1 sin x

Math - Others

Basic MathVerify the identity csct 1 cott B Choose the sequence of steps below that verifies the identity OA O C O D cott csct 1 csct 1 csct 1 csct 1 cott cott csct 1 csct 1 cott csct 1 cott csct 1 cott csct 1 cott csct 1 cott csct 1 csct 1 csct 1 sc t 1 csct 1 cott csct 1 csc t 1 cott csct 1 CSC csc t 1 cott csct 1 csct 1 csct 1 csc t 1 cott csct 1 cott csct 1 cott cot t cott csct 1 csct 1 cot t cott csct 1 cot t cott csct 1 cott cott csct 1 cott csct 1 cott csct 1 cott csct 1

Math - Others

Basic Mathcies Prove the given identity sin xsec x cos x csc x sec xcsc x Choose the correct proof below A sin xsec x cos xcsc x 1 sin x cOS X sin x cos x 2 x cos X 2 sin sin x cos x 1 sec x csc x OC sin xsec x cos xcsc x sin x 1 cos x COS X sin x cos x 2 sin x cos sin x cos x 1 sec x csc X X sin x Question 7 of 10 OB sin xsec x cos xcsc x 1 sin x cOS X sin x cos 2 sin x cos x 1 sin x cos x sec x csc X This quiz 20 poin This question 2 OD sin xsec x cos xcsc x 1 sin x COS X X cos X sin x cos x sin x cos x 1 sin x cos x sec x csc X 1 sin

Math - Others

Binomial theoremSimplify the given expression The result will be one of sin x cos x tan x cotx secx or csc x tan x cot x CSC X tan x cot x CSC X

Math - Others

Basic MathK Prove the given identity cos 8 cot 8 csc 8 sin 8 Choose the correct proof below OA cos 8 cot 8 csc 8 cos 8 OC cos 8 cot 8 csc 8 cos 8 cos 8 sin 8 OD cos 8 cot 8 csc 8 cos 8 sin 8 sec8 OB cos 8 cot 8 csc 8 cos 8 cos 8 sin 8 cos 8 sin 8 cos 8 sin 8 1 sin 8 1 sin 8 1 sin 8 Question 4 of 10 cos 8 1 sin 8 cos 8 1 sin 8 sin 8 cos2 8 1 cos 8 1 sin 8 sin 8 sin 8 sin 8 sin 8 sin 8 sin 8 sin 8 sin 8 sin 8 sin 8 sin 8 sin 8

Math - Others

Basic MathEstablish the identity cos x sin x 1 2 sin x Using the identity sin x cos x 1 make the appropriate substitution Which of the followin O A 1 cos sin 1 2 sin x OB 1 sin sin 1 2 sin O C 1 sin sin 1 2 sin x 1 2 sin 1 2 sin a 2 1 2 sin 2 1 2 sin a 1 2 sin 1 2 sin x OD 1 cos sin 1 2 sin x 2 1 2 sin 1 2 sin x

Math - Others

Mathematical InductionA radioactive material decays according to the function A t Age 0 0244t where Ao is the initial amount present and A is the amount present at time t in years Assume that a scientist of the radioactive material a What is the decay rate of the radioactive material b Graph the function using a graphing utility c How much radioactive material is left after 30 years d When will only 300 grams of the radioactive material be left e What is the half life of the radioactive material a The decay rate of the radioactive material is 2 44 Type an integer or a decimal b Graph the function Choose the correct graph below The graphing window is 0 800 100 by 0 1 0 25 A B c There will be about 192 4 gram s of the radioactive material left after 30 years Do not round until the final answer Then round to the nearest tenth as needed d In about year s only 300 grams of the radioactive material will be left Do not round until the final answer Then round to the nearest tenth as needed O C Points 3 of 5 d D Q

Math - Others

Basic Mathtities Prove the given identity cot x sec xcsc x tan x Choose the correct proof below OA cot x sec xcsc X 1 1 sin x cos x sin x sin x cos x 2 1 cos X COS X sin x cos x sin 2 tan x OC cot x sec xcsc x cOS X 1 1 sin x sin x X cos x 2 1 cos X tan x sin x cos x sin x sin x cos x Question 2 of 10 OB cot x sec xcsc x cOS X sin x sin x cos x This quiz This ques 2 cos X 1 tan x sin x cos x sin x OD cot x sec xcsc x cos x sin x 1 cos x sin x cos x Sin sin x cos x tan x

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Basic MathVerify the following identity 1 tan 0 2 cos 20 1 tan 0 Which of the following four statements establishes the identity 2 1 tan 0 1 tan 0 2 1 tan 0 O A cos 20 2 sin 0 cos 0 OB cos 20 cos 0 sin 0 OC cos 20 cos 0 sin 0 O D cos 20 2 sin 0 cos 0 2 csc 0 2 1 tan 0 2 sec 0 2 1 tan 0 csc 0 2 1 tan 0 sec 0 2 1 tan 0 1 tan 2 2 1 tan 0 1 tan 0 2 1 tan 0 2 1 tan 0 2 0

Math - Others

Trigonometric equations112 In a recent sample of 84 used car sales costs the sample mean was 6 425 with a standard deviation of 3 156 Assume the underlying distribution is approximately normal a Which distribution should you use for this problem Explain your choice b Define the random variable X in words c Construct a 95 percent confidence interval for the population mean cost of a used car i State the confidence interval ii Sketch the graph iii Calculate the error bound al moons for this study

Math - Others

FunctionsA 0 700 m rigid tank contains refrigerant 134a initially at 200 kPa and 40 percent quality Heat is transferred now to the refrigerant from a source at 35 C until the pressure rises to 400 kPa Problem 07 047 a Entropy change of R134a heated in a rigid tank Determine the entropy change of the refrigerant Use the tables for R 134a The entropy change of the refrigerant is kJ K

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Basic MathFive lbm of R 134a is expanded isentropically in a closed system from 100 psia and 100 F to 10 psia Determine the total heat transfer and the work production for this process Use the tables for R 134a The total heat transfer is Btu The work production for this process is Btu

Math - Others

Inverse Trigonometric functions3 5 Book Print erences Check my work Prepare a flexible budget performance report for July at activity level of 7 260 units Show variances between budgeted and actual amounts Note Indicate the effect of each variance by selecting favorable unfavorable or no variance For Month Ended July 31 Sales Variable costs Direct materials Direct labor Indirect materials Sales commissions Total Variable Costs Contribution margin Fixed costs Depreciation Machinery Supervisory salary Insurance Depreciation Office equipment Administrative salaries Total Fixed Costs Income NINA COMPANY Flexible Budget Performance Report Flexible Budget 7 260 units 24 43 27 9 103 0 Actual Results 7 260 units 0 Variances 2 624 000 Favorable or Unfavorable 20 E marks

Math - Others

Basic MathProblem 07 027E Isothermal heat rejection process of Carnot cycle During the isothermal heat rejection process of a Carnot cycle the working fluid experiences an entropy change of 0 760 Btu R The temperature of the heat sink is 95 F Sink 95 F Heat 95 F Carnot heat engine roblem 07 027E a Heat transfer to working fluid in a heat rejection process he amount of heat transfor is etermine the amount of heat transfer

Math - Others

Basic MathA radioactive material decays according to the function A t Age 0 0244t where Ao is the initial amount present and A is the amount present at time t in years Assume that a scientist has a sample of 400 g of the radioactive material a What is the decay rate of the radioactive material b Graph the function using a graphing utility c How much radioactive material is left after 30 years d When will only 300 grams of the radioactive material be left e What is the half life of the radioactive material a The decay rate of the radioactive material is 2 44 Type an integer or a decimal b Graph the function Choose the correct graph below The graphing window is 0 800 100 by 0 1 0 25 A Q B O c There will be about gram s of the radioactive material left after 30 years Do not round until the final answer Then round to the nearest tenth as needed O C 20 Q OD Sa Q

Math - Others

Inverse Trigonometric functionsA sample of bacteria is decaying according to a half life model If the sample begins with 900 bacteria and after 10 minutes there are 360 bacteria after how many minutes will there be 40 bacteria remaining When solving this problem round the value of k to four decimal places and round your final answer to the nearest whole number

Math - Others

Linear AlgebraAfter the 25 years have passed I plan on retiring and will now use the money that has built up as my retirement pay I will make monthly withdrawals every month for 20 years 5 How much money can I withdraw each month from this same account 3 5 compounded monthly for the next 20 years Show all work

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Basic MathA plane has an airspeed of 127 km h It is flying on a bearing of 85 while there is a 27 km h wind out of the northeast bearing 225 What are the ground speed and the bearing of the plane The ground speed is km h Round to the nearest tenth as needed

Math - Others

Basic MathLet A 3 6 8 Which of the following relations on A are antisymmetric Select all that apply A 3 3 6 8 8 3 8 8 B 3 6 3 8 6 8 8 3 OC 3 6 3 8 6 8 8 6 OD 3 3 6 6 8 8

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Basic MathFind the adjacency matrix for the relation r 3 9 6 5 8 5 6 9 from the set A 3 6 8 to the set B 3 5 9

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Linear AlgebraWhich of the following relations on P are symmetric Select all that apply Be able to explain your answers DA i e the relation of divides OB OC OD DE 2

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Basic MathLet A 3 4 8 Which of the following relations on A are symmetric Select all that appl DA 3 8 4 8 8 3 8 4 8 8 B 3 3 3 4 4 3 4 8 8 8 OC 3 3 4 4 OD 3 4 3 8 4 3 4 8 8 3

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Basic MathThe link below gives the Hasse diagram for a poset with partial ordering Click this link to view the Hasse diagram Which of the statements below are true Select all that apply DA bza OB a a OC c f OD d b DE b d OEde e a b C

Math - Others

Basic Math4 1 4 relation r relation 3 2 3 4 relation relation r 3 2 3 4 attempts remaining The link below gives the digraphs for four different relations r1 12 13 14 on the set A 1 2 3 4 Click this link to view the digraphs Which of these relations are antisymmetric Select all that apply Be able to explain your answers OA TA OB rs DC n OD 12

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Basic MathProblem 07 021 Heat transferred between two reservoirs Heat is transferred at a rate of 2 kW from a hot reservoir at 900 K to a cold reservoir at 300 K Calculate the rate at which the entropy of the two reservoirs changes Round the final answer to three decimal places The rate at which the entropy of the two reservoirs changes is Is the second law satisfied Click to select Click to select Yes No kW K

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Basic Math11 az a 160 B 7 Use decimal notation Give your answers to three decimal places Include the degree symbol in your answers where nee

Math - Others

Basic MathMacmillan Learning Solve the given triangle Use degree measure B A 55 A 5 Use decimal notation Give your answers to three decimal places Include the degree symbol in your answers where n C A

Math - Others

Basic MathMacmillan Learning Find the area of the triangle in the figure 5 area 3 Macmillan Learning Crauder et al Preparation for Calculus le 2022 Give an exact answer Use symbolic notation and fractions where needed

Math - Others

Functions4 1 relation r 4 relation N 3 2 3 4 1 4 relation r relation r 2 2 3 4 attempts remaining The link below gives the digraphs for four different relations r 72 73 74 on the set A 1 2 3 4 Click this link to view the digraphs Which of these relations are reflexive Select all that apply Be able to explain your answ nswers A Ti B 73 OC T2 OD T4 Submit answer

Math - Others

Basic Mathoblem 1 Use the Law of Sines of the Law of Cosines when it applies Solve each triangle and assume standard labeling a b 3 4 c 2 8 A 82 b A 30 a 20 B 45 c A 30 a 5 b 5 2 d a 19 b 2 c 3 e a 40 2 A 135 B 30 f A 63 C 55 a 8 3

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Basic Mathne opens an account at the local bank by depositing 50 of his birthday money He continues to deposit 50 each month for 5 years If the account 3 25 interest compounded monthly how much is in the account after 5 years 0 10000 Word Limit

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Basic MathLet A 3 6 8 Which of the following relations on A are antisymmetric Select all that apply OA 3 3 6 8 8 3 8 8 B 3 6 3 8 6 8 8 3 OC 3 6 3 8 6 8 8 6 P 3 3 6 6 88