Math - Others Questions

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Complete the following truth table pVq r pqr 0000 0 0 1 0 1 0 0 11 100 101 1 2 3 4 5 1 10 6

Complete the following truth table p p q Pq 000 01 A

Complete the following truth table p q r Pqr 000 001 0 1 0 0 11 100 101 1 10

Complete the following truth table p q v q Pq 0 0 01 10 11 G 94 S FI

Which of the following statements are true Select all that apply DA 9 2 if and only if 7 14 21 OB 7 14 21 and 9 2 OC 9 2 or 7 14 21 OD 7 14 21 if and only if 9 2 OE 7 14 21 if and only if 9 2

Complete the following truth table bd 00 01 10 d v b A

Consider the following statement If Jane has taken chemistry then Jane has taken biology a Which of the following statements is the converse of the given statement OA If Jane has not taken chemistry then Jane has not taken biology OB If Jane has taken biology then Jane has taken chemistry OC If Jane has taken chemistry then Jane has not taken biology OD If Jane has not taken biology then Jane has not taken chemistry OE None of the above b Which of the following statements is the contrapositive of the given statement OA If Jane has not taken biology then Jane has not taken chemistry OB If Jane has not taken biology then Jane has taken chemistry OC If Jane has not taken chemistry then Jane has not taken biology OD If Jane has taken biology then Jane has taken chemistry OF None of the above

Let p q be the following propositions p 7 17 q 1 8 Match each proposition with its symbolic representation 1 If 717 then 1 8 2 1 8 if and only if 7 17 3 7 17 or 1 8 4 7 17 and 18 5 If 18 then 1 8 A qp B p q C p Aq D q q E p F p q G p V q q

A student is taking a standardized test consisting of several multiple choice questions One point is awarded for each correct answer Questions left blank neither receive nor lose points There are 1 four options for each question and the student is penalized point for each wrong answer Is it in the student s best interest to guess Explain Determine if it is in the best interest of the student to guess and explain your answer using the expected value Choose the correct answer below Round to two decimal places as needed OA The student will have no loss or gain by guessing because the expected value is B Yes the student should guess because the expected value is OC No the student should not guess because the expected value is COLLE

Assume that the probability of a 25 year old male living to age 26 based on mortality tables is 0 992 If a 15 000 dollar one year term life insurance policy on a 25 year old male costs 100 dollars what is its expected value What is the expected value The expected value is dollars CLIES

A player can bet on a line by placing a chip at location A in the figure to the right By placing the chip at A the player is betting on 1 2 3 0 and 00 This bet pays 3 5 to 1 which means that if a player wins the player wins 3 5 dollars as well as keeping his or her bet When the player loses he or she loses 1 Recall that there are 38 numbers on a roulette wheel Determine the expected value of betting on the roulette wheel The expected value of betting on the roulette wheel is EX C 0 1 4 10

Assume that you have 12 000 to invest in bonds Use the table to the right which shows the probabilities for gain or loss for these investments over the next year What would be the expected gain or loss in dollars if you invested in bonds There would be an expected Type an integer or a decimal of dollars gain B Bonds Probability Change 0 6 Gain 7 0 2 0 2 No Change Lose 1

Assume that it costs 2 to play a state s daily number The player chooses a three digit number between 000 and 999 inclusive and if the number is selected that day then the player wins 500 this means the player s profit is 500 2 498 If the player buys 20 chances on 20 different numbers what is the expected value for the player There is an expected Type an integer or a c of gain loss

A certain game consists of rolling a single fair die If a four or five comes up you win 10 dollars otherwise you lose 5 dollars Find the expected winnings for this game Is this a fair game The expected value for this game is dollars

A lottery costs 1 dollar to play Bella must pick four digits in order from 0 to 9 and duplicates are allowed If she wins the prize is 7 000 dollars First calculate the expected value of the lott Determine whether the lottery is a fair game If the game is not fair determine a price for playing the game that would make it fair What problem solving technique should be used OA The analogies principle OB The three way principle C Relate a new problem to an older one OD Be systematic COD Select the correct choice below and if necessary fill in the answer box to complete your choice The expected value of the lottery is dollars Round to the nearest cent as needed

A buyer is planning to purchase a franchise to sell decorations for the home The table to the right shows average weekly profits rounded to the nearest hundred for a number of the current franchises If the buyer were to purchase a franchise what would the expected weekly profit be The expected weekly profit is dollars Round to the nearest cent as needed Weekly Profit 100 dollars 200 dollars 300 dollars 400 dollars 500 dollars 600 dollars Number Who Earned This 4 11 13 14 8 4

A company estimates that it has a 50 chance of being successful in bidding on a 50 000 contract If it costs 6 300 in consultant fees to prepare the bid what is the expected gain or loss for the company if it decides to bid on this contract There is an expected Type an integer or a c for the company of gain loss

To the right are the probabilities and values associated with five outcomes of an experiment Calculate the expected value for the experiment The expected value for this experiment is Round to the nearest tenth as needed C Outcome A B C D E Probability 0 1 0 2 0 1 0 2 0 4 Value 3 8 1 3 9

K A game has two four sided dice having the numbers 3 6 9 and 2 on their faces Outcomes in the sample space are pairs such as 3 6 and 2 2 a How many elements are in the sample space b Express the event the total showing is even as a set c What is the probability that the total showing is even d What is the probability that the total showing is greater than 6 A The Analogies Principle OB The Draw Pictures Principle C The Be Systematic Principle OD The Choose Good Names for Unknown Strategies Principle a How many elements are in the sample space 16 b Express the event the total showing is even as a set 3 3 3 9 6 6 6 2 9 3 9 9 2 6 2 2 Type an ordered pair Use a comma to separate answers as needed c What is the probability that the total showing is even 1 2 Type an integer or a simplified fraction d What is the probability that the total showing is greater than 6

Use a calculator to evaluate the amortization formula P 1 1 1 n m for the values of the variables P r and t respectively Assume n 12 Round your answer to the nearest cent 14 000 5 5 yr Enter a number

Consider the monthly payment for the following loan new car financing of 3 3 on a 30 month 12 550 loan Identify the following for the given loan where P is the amount of the loan in dollars r is the annual interest rate as a decimal n is the number of payments p year and it is the time in years P r n t Find the monthly payment for the loan Round your answer to the nearest cent

An insurance policy offers you the option of being paid 750 per month for 20 years or a lump sum of 100 000 Assume that the current rate of return is 4 5 compounded monthly and you expect to live for 20 years Identify the following for the annuity monthly payment option where m is the periodic payment in dollars r is the annual interest rate as a decimal n is the number of payments per year and t is the time in years m r n t Determine the present value of the annuity Round your answer to the nearest cent Which has more value O the annuity O the lump sum payment

Use a calculator to evaluate the present value of an annuity formula nt 1 P m 1 r for the values of the variables m r and t respectively Assume n 12 Round your answer to the nearest ce 50 5 9 yr

Self employed persons can make contributions for their retirement into a special tax deferred account called a Keogh account Suppose you are able to contribute 15 000 into this account at the end of each year How much will you have at the end of 20 years if the account pays 3 annual interest Round your answer to the nearest cent

A game has two four sided dice having the numbers 3 6 9 and 2 on their faces Outcomes in the sample space are pairs such a 3 6 and 2 2 a How many elements are in the sample space b Express the event the total showing is even as a set c What is the probability that the total showing is even d What is the probability that the total showing is greater than 6 Identify the problem solving method that should be used Choose the correct answer below OA The Analogies Principle OB The Draw Pictures Principle C The Be Systematic Principle D The Choose Good Names for Unknown Strategies Principle a How many elements are in the sample space 16 b Express the event the total showing is even as a set 3 3 3 9 6 6 6 2 9 3 9 9 2 6 2 2 Type an ordered pair Use a comma to separate answers as needed c What is the probability that the total showing is even Type an integer or a simplified fraction

Find the amount of periodic payment necessary for the deposit to a sinking fund Round your answer to the nearest cent Amount Needed A 9 000 Frequency n annually Rate r 0 5 Time t 8 yr

You want to retire at age 65 You decide to make a deposit to yourself at the end of each year into an account paying 4 compounded annually Assume you a now 25 and can spare 1 900 per year Identify the following from the given information Let m represent the periodic payment in dollars r the annual interest rate as a decimal n the number of payments per year and t the time in years until retirement m r n t How much will you have when you retire at age 65 Round your answer to the nearest cent

Use a calculator to evaluate an ordinary annuity formula nt A A m 1 r n for m r and t respectively Assume monthly payments Round your answer to the nearest ce 50 5 3 yr

The graph given below summarizes statistics regarding distracted drivers below the age of 40 who were involved in fatal crashes Assume that we are selecting a driver at random from the 3 145 tallied If a driver in this group is under 20 what is the probability that the accident was related to cell phone use The probability is Round to three decimal places as needed Fatal Traffic Accidents Involving Distracted Driving Number 1500 1200 900 600 300 0 Age under 20 538 188 Fatal Traffic Accidents Involving Distracted Driving Age between 20 29 1191 Non Cell Phone Distraction GELER 387 Cell Phone Distraction Age between 30 39 650 191 X

Assume that a person is working for a company that has a mandatory drug testing policy It is estimated that 1 of the employees use a certain drug and the company is giving a test that is 97 accurate in identifying users of this drug Calculate the positive predictive value for the drug test The positive predictive value is Type an integer or decimal rounded to three decimal places as needed

Assume that 2 cards are drawn from a standard 52 card deck Find the following probabilities a Assume the cards are drawn without replacement Find the probability of drawing a ten followed by not drawing a ten b Assume the cards are drawn with replacement Find the probability of drawing a ten followed by not drawing a ten a The probability of drawing a ten followed by not drawing a ten without replacement is Simplify your answer www

K The residents of a small town and the surrounding area are divided over the proposed construction of a sprint car racetrack in the town as shown in the table on the right If a newspaper reporter randomly selects a person to interview from these people a what is the probability that the person supports the racetrack b what are the odds in favor of the person supporting the racetrack 8 9 a The probability is Type an integer or a simplified fraction b What are the odds in favor of the person supporting the racetrack OA 8 to 1 OB 1 to 8 OC 8 to 9 OD 1 to 9 Live in Town Live in Surrounding Area Support Opp Racetrack Racet 38 3 049 4 975 61

A person wants to purchase a DVD drive for his laptop computer Assume that 81 of the drives are made outside the United States Of the U S made drives 2 are defective and of the foreign made drives 7 are defective Determine the probability that the drive purchased is U S made and is not defective The probability is Type an integer or decimal rounded to four decimal places as needed

The editors of Auto Web have evaluated several E uropean and J apanese crossovers and given them either a H igh or A verage safety rating The probability tree to the right summarizes the results of the study If a car from the study is selected randomly find the probability P A P A TUR 0 40 E 0 55 H 0 60 J 0 45 A 0 75 H 0 25 A

Imagine a subject is taking part in a study to test a new cold medicine The probability that the subject is taking drug A is 10 that it is drug B is 40 and that it is drug C is 50 From past clinical trials the probabilities that these drugs will improve the subject s condition are A 40 B 30 and C 60 What is the probability that the subject will improve given that he is taking dru B The probability is Type an integer or a decimal

Find the probability P SIN associated with the tree diagram What problem solving method should be used A Draw pictures B Be systematic C Relate a New Problem to an Older One OD The Three Way Principle What is P SIN P SIN Type an integer or decimal rounded to one decimal place as needed 0 3 M 0 4 N 0 3 Q 0 5 0 5 0 4 0 6 R S 0 3 R 0 7 R S S

Assume that a softball player has 0 20 probability of getting a hit in each at bat Assume that the player bats four times What is the probability that she gets a hit only in her first at bat The probability is Round to four decimal places as needed SCCCB

A container contains 40 green tokens 10 blue tokens and 2 red tokens Two tokens are randomly selected without replacement Compute P FIE E you select a blue token first F the second token is blue P FIE Simplify your answer Type an integer or a fraction

The Political Action Club has surveyed 270 students on your campus regarding the relationship between their political affiliation and their preference in the 2016 presidential election The results are given in the following table Republican 23 87 110 Totals 151 119 270 Democrat Independent 22 Preferred Candidate A Preferred Candidate B 106 17 123 15 Totals 37 If a student is selected randomly from those surveyed find the probability that the student is an Independent given that the student preferred candidate B The probability is Type an integer or decimal rounded to three decimal places as needed RECERR

According to U S government statistics mononucleosis mono is four times more common among college students than the rest of the population Blood tests for the disease are not 100 accurate Assume that the following table of data was obtained regarding students who came to a certain school s health center complaining of tiredness a sore throat and slight fever Has Mono 45 12 57 Doesn t Have Mono 26 10 36 Totals 71 22 93 Positive Blood Test Negative Blood Test Totals If a student is selected from this group find the probability a student doesn t have mono given that the test is negative The probability is Type an integer or decimal rounded to three decimal places as needed

The given urn contains green G blue B and red R balls Assume that two balls are being drawn without replacement from the urn to the right What is the probability that neither ball is red B B B B The probability is Tyne an integer or decimal rounded to three decimal places as needed B B B

You are to randomly pick one disk from a bag that contains the disks shown below Find P face blue the probability of picking a disk with a face given that the disk is blue Blue Yellow Blue Pink Pink Yellow Yellow Blue Pink Yellow Find P face blue P facelblue Simplify your answer

K When an object is dropped on a certain earth like planet the distance it falls in t seconds assuming that air resistance is negligible is given by s t 19t where s t is in feet Suppose that a medic s reflex hammer is dropped from a hovering helicopter Find a how far the hammer falls in 2 sec b how fast the hammer is traveling 2 sec after being dropped and c the hammer s acceleration after it has been falling for 2 sec a The hammer falls 76 feet in 2 seconds Simplify your answer b The hammer is traveling ft sec 2 seconds after being dropped Simplify your answer c The hammer s acceleration is ft sec sec after it has been falling for 2 sec Simplify your answer

Let g x 2 x 4 a Find the domain of Let f x b c 1 g x 8 x g x The function f x can be written as f x a x b a b e Z Find a and b e Hence or otherwise sketch f x d Find f x stating any domain restrictions Find the domain of g x

Let g x 2 x 4 a Find the domain of Let f x b 1 g x 8 x g x The function f x can be written as f x a x b a bez Find a and b

K Raggs Ltd a clothing firm determines that in order to sell x suits the price per suit must be p 180 0 75x It also determines that the total cost of producing x suits is given by C x a Find the total revenue R x b Find the total profit P x c How many suits must the company produce and sell in order to maximize profit d What is the maximum profit e What price per suit must be charged in order to maximize profit a R x b P x c d The maximum profit is e The price per unit must be suits

Is this problem one where we should take the percent of the other number shown in the problem Joy bought a 90 skirt on sale for 15 off What was the discount yes no

class we conside optimizing can Square MSE practice ther are other choices of loss functions as well For this problem we will consider linear regression using Mean Absolute Error MAE as our loss function Specifically the MAE loss is given as JMAE 0 Solution a 4 points Derive the partial derivative JMAE 0 30 otherwise Solution OJMAE 0 20 Hint For this question you don t need to worry about J 0 You can use the sign function 1 2 y s t sign y n 76 n 0 x i y i i 1 VOJMAE 0 1 20 n 81 30 n sign 0 x y x sign 0x y 0 x i y i 1 1 0Tx y b 2 points Write the vectorized solution for the gradient of the loss function i e VeJMAE 0 Solution n sign Tx y i x c 4 points Given the following dataset of 8 points what is the value of of JMAE 0 and JMSE 0 at 0 1 0 1 0 1 0 How about their gradients VJMAE 0 and VoJMSE 0 1 i 1 2 5 3 24 0 1 1 0 1 2 2 2 1 12 3 1 6 3 JMAR A 3 375 IMSE A 10 3125 6 7 8 1 0 5 2 3 0 6 8 7

For each of the statements below state True T or False F or pick the correct option Explain your answer in 1 2 sentences For every part below 1 point for correct assertion and 1 point for correct explanation a T F Ridge regression does not have a closed form solution b T F If we have m values for a hyperparameter of a classifier and we use k fold cross validation for hyperparameter tuning then we train the classifier mk times from scratch c T F Consider a linear function basis o x 1 log x x2r3 where x R There exists a closed form solution for minimizing the mean squared error for the hypothesis he x eTo x If True state the solution Otherwise give a justification d Which of the following is a major drawback of linear regression A It assumes a linear relationship between the independent and dependent variables B It can handle only numerical data C It is not suitable for high dimensional data D It is prone to overfitting E None of the above e Which of the following is a common method for preventing overfitting in machine learning A Increasing the complexity of the model B Decreasing the size of the training data set C Regularization D Using a simpler evaluation metric