Math - Others Questions

1 point Consider the relation R whose digraph is given below Co 8 t without

13 This graph shows the number of cars n in the school parking lot as a function of time t Number of Cars in the School Parking Lot Number of cars 60 40 20 0 n 08 00 Time 16 00 a Identify the independent and dependent variables Justify your choices b Why are the points on the graph not connected c Estimate the domain and range of the graph Are there any restrictions on the domain and range Explain

4 3 5 6 Graph the solution to the system y 2 x 4 y x 7 Show Your Work

1 point Consider the relation Rwhose digraph is given below 4 00 8 3 List the equivalence classes of R Separate your answers using commas In sets containing more than one element write them from smallest to largest without sp

1 point a Consider the relation R on the set A X Y Z defined by R X Y X Z Y X Y Z Z X Z Y This relation is not reflexive What element s would we need to add to R in order for it to be reflexive b Consider the relation R on the set A X Y Z defined by R X X X Y X Z Y Y Y Z Z X This relation is not symmetric What element s would we need to add to R in order for it to be symmetric c Consider the relation R on the set A X Y Z defined by R X Y Y X Z Z This relation is not transitive What element s would we need to add to R in order for it to be transitive

1 point Consider the relations R R2 R3 R R5 on A 1 2 3 4 defined by R 1 2 2 1 R 2 2 2 3 2 4 3 2 3 3 3 4 R3 1 1 1 2 2 1 2 2 3 3 4 4 R4 1 2 2 3 3 4 R5 1 1 2 2 3 3 4 4 Determine which of the following statements are true Select all that apply A R is not symmetric B R is reflexive C R is symmetric D R4 is transitive E R is reflexive F R5 is transitive G R5 is not reflexive H R3 is reflexive I R is transitive J R3 is not transitive K R4 is symmetric L None of the above

livia was recently promoted to manager at the coffee shop where she has been working She will now be earning 1 000 each month and has decided to eate a budget to control her spending and save for her first apartment Use the Budget Template to fill in Olivia s budget information Although the amount she spends on gas groceries and utilities changes each month assume her budgeted and actual amounts are the same When you have completed her budget answer the two questions at the bottom of the template Budget Template Expenses Gas Car payment Car insurance Phone bill Nails Health insurance Clothing Groceries Utilities Streaming service 40 average per month 250 per month 100 per month 60 average per month 30 per month 50 per month 50 per month 50 average per month 45 average per month 50 per month

1 point Consider the relation R on the set whose digraph is given below 1 3 5 Is R an equivalence relation OA Yes B No 4 C R is not symmetric D R is not transitive E None of the above 2 because select all that apply A R is reflexive symmetric and transitive B R is not reflexive

1 point Determine whether each of the relations whose digraphs are given below are reflexive symmetric transitive or none of the above Select all that apply a A Reflexive OB Symmetric C Transitive b 0000 c 0000 d A D None of the above 200 A A Reflexive B Symmetric C Transitive D None of the above A D A Reflexive B Symmetric C Transitive D None of the above A D A Reflexive OB Symmetric 20 C Transitive D None of the above A D A Reflexive OB Symmetric C Transitive Co B E C B E B B C B

point Let denote the set of all integers Determine whether each of the relations on Z given below are reflexive symmetric transitive or none of the above Select all that apply a xy 1 OA Reflexive B Symmetric C Transitive D None of the above b x y 0 OA Reflexive B Symmetric C Transitive D None of the above c x 2y A Reflexive B Symmetric C Transitive D None of the above d x y is an integer A Reflexive B Symmetric C Transitive D None of the above

1 point Consider the relations R R2 R3 R4 R5 on A 1 2 3 4 defined by R 1 2 2 1 R 2 2 2 3 2 4 3 2 3 3 3 4 R3 1 1 1 2 2 1 2 2 3 3 4 4 R4 1 2 2 3 3 4 R5 1 1 2 2 3 3 4 4 Determine which of the following statements are true Select all that apply A R is not symmetric B R is reflexive C R is symmetric D R4 is transitive E R is reflexive F R5 is transitive G R5 is not reflexive H R3 is reflexive I R is transitive J R3 is not transitive K R4 is symmetric L None of the above

The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition He wants to first determine the percentage of adults who have heard of the brand How many adults must he survey in order to be 90 confident that his estimate is within six percentage points of the true population percentage Complete parts a through c below a Assume that nothing is known about the percentage of adults who have heard of the brand n Round up to the nearest integer

Refer to the accompanying data display that results from a sample 13 046 22 15 of airport data speeds in Mbps Complete parts a through c below x 17 598 Sx 16 01712719 n 50 distribution table Click the icon to view a t df a What is the number of degrees of freedom that should be used for finding the critical value to 2 IT TInterval number

1 point a Consider the relation R on the set A X Y Z defined by R X Y X Z Y X Y Z Z X Z Y This relation is not reflexive What element s would we need to add to R in order for it to be reflexive b Consider the relation R on the set A X Y Z defined by R X X X Y X Z Y Y Y Z Z X This relation is not symmetric What element s would we need to add to R in order for it to be symmetric c Consider the relation R on the set A X Y Z defined by R X Y Y X Z Z This relation is not transitive What element s would we need to add to R in order for it to be transitive

1 point Let A denote the set of all people Determine whether each of the relations on A given below are reflexive symmetric transitive or none of the above Select all that apply a a is older than b A Reflexive B Symmetric C Transitive D None of the above b a and b have a common child A Reflexive B Symmetric C Transitive D None of the above c a and b were born on the same day A Reflexive B Symmetric C Transitive D None of the above d a has the same first name as b A Reflexive B Symmetric C Transitive D None of the above

Time from start of journey h b How much gas was ir the tank at the stai the journey Was the tank full at this time Explain 0 An oven is turned on at a room temperature of 20 C and it takes 10 min to reach a temperature of 190 C A tray of cookies is placed in the oven to bake for 10 min The oven is then turned off and returns to room temperature after 15 min Sketch a graph of temperature as a function of time Label each section of the graph and explain what it represents

5 To raise a flag Sepideh pulls the rope steadily with both hands for a short time then moves both hands up the rope and pulls again She does this until the flag has been raised Which graph best represents the height of the flag Give reasons for your choice Graph A Graph B Height m Height m Time s Graph C Time s Height m Height m Time s Graph D Time s

14 The two graphs below have the same shape but different vertical axes Copy each graph and include numbers and units on both axes Write and justify a possible situation that it represents a Distance Graph A Time b Speed Graph B Time 18 t t e

13 A student drew a graph to represent this situation Jonah is watching television After 3 min his mom enters the room to ask him a question He turns the volume down a bit answers his mom then turns the volume back up Two minutes later Jonah s dad turns on the dishwasher so Jonah gradually turns up the volume After a further 3 min a commercial comes on so Jonah presses the mute button Describe any errors in the student s graph Volume of a Television Volume scale 80 60 40 20 0 to Time min 8 10

13 Which of the following is equivalent to An B 0 0 O An B O AUB O An B

14 Given two sets A and B which one of the following is equivalent to AUB OA B 0 0 O An B OB A

12 Given the following Venn diagram where each area is labeled by three binary digits which one of the following represents the area 111 000 O AUB C O ANB nC O AUB C A 100 101 110 111 001 010 011 C B U

3 Let S 0 0 Which of these statements are true OCS S S 1 ES

15 Let A and B be two subsets of the universal set U Which of the following is equivalent to An BUA O An B 0 0 O AUB O None of these answers

3 Let S be a set and n be an integer If P S 2 then S is

10 Which one of the following statements is false O 2 EAUB implies that if 2 E A then 2 B 1 2 C A implies that 1 A and 2 A 2 C A B and 1 C B implies that 1 2 CAU B 1 2 CAN B implies that 1 2 CA and 1 2 CB

7 Given a set A of 0 elements what is the number of elements in P A

6 Let S be a set Which of one of the following is always correct O a E Simplies a P S O a ES and b E Simplies a b P S a ES and b E S implies a b P S OaESand b E Simplies a b S

11 If the universal set U a c b d e f g h i j k l m n o p and A is a set of vowels in the word home then A is O a b c d f g h i j k l m n p O c b d f g h j k l m n p O e o None of these answers

5 Given the set S 1 2 4 8 16 1024 which one of the following sets represents S using the rule of inclusion 2n ne Z and 0 n 10 O 2n ne Z and 0 n 11 O n ne Z and 0 n 10 2n ne Z and 0 n 10

4 The members of the set S n n is the square of an integer and 0 n 40 is O 0 1 2 3 4 5 6 O 1 4 9 16 25 36 O 1 2 3 4 5 6 0 1 4 9 16 25 36

2 Which of the following is a subset of b c d O b c d O 1 2 3 O a b c O a

1 Let S 1 2 3 1 2 3 What is the cardinality of S

Homework 15 Distribution Date 10 30 2023 Due Date 11 02 2023 1 An exploratory drill hole was made in a stiff saturated clay The sand underlying the clay was observed to be under artesian pressure Water in the drill hole rose to a height of 18 ft above the top of the sand layer If an open excavation is to be made in the clay how deep can the excavation proceed before the bottom heaves 25 ft 4 18 ft 16 ft Saturated clay Exploratory drill hole Sand G 2 7 Moisture content w 40 NOTE Show all the calculation steps

Tan ml oldu u aral kta f fonksiyonu f x log x 1 oldu una g re f fonksiyonunun tersini bu

Use the savings plan formula to answer the following question At age 45 you start saving for retirement If your investment plan pays an APR of 6 and you want to have 1 3 million when you retire in 20 years how much should you deposit mor You should invest each month Do not round until the final answer Then round to two decimal places as needed COLO

Two friends take a 2000 mile cross country trip together but they drive their own cars Car A has a 14 gallon gas tank and averages 40 miles per gallon while car B has a 22 gallon gas tank an averages 20 miles per gallon Assume both drivers pay an average of 2 35 per gallon of gas a What is the cost of one full tank of gas for car A For car B b How many tanks of gas do cars A and B each use for the trip c About how much do the drivers of cars A and B each pay for gas for the trip a The cost for car A is 32 90 per tank and the cost for car B is 51 70 per tank Round to the nearest cent as needed b Car A uses 3 57 tanks and car B uses 4 55 tanks for the trip Round to two decimal places as needed c The driver of car A pays 117 45 for the trip and the driver of car B pays 235 24 Round to the nearest cent as needed

A new sidewalk will be 6 feet wide 220 feet long and filled to a depth of 6 inches 0 5 foot with concrete How many cubic yards of concrete are needed The new sidewalk needs 24 4 cubic yards of concrete Round to one decimal place as needed C

The impact of the recession of 2009 has seen an ensuing slow recovery which has lasted well into 2013 Since the slowing of the recession Americans have seen a small increase in disposable income averaging less than one percent a month in 2013 Despite the small gains in income Americans are looking to place more discretionary money into savings plans and investments than into vacations and luxury items Source Bureau of Economic Analysis U S Department of Commerce 2013 Retrieved from http www bea gov newsreleases national pi pinewsrelease htm CODE If an individual saves 5 700 and elects to place the total dollar amount into a savings account earning 2 75 APR compounded monthly how much will the original deposit grow to in 12 years The initial deposit plus interest equals Round to the nearest dollar as needed

Find the present value of the given amounts F with the indicated annual rate of return r the number of years t and the indicated compounding Round your answers to the nearest cer F 6300 r 8 7 t 13 a compounded annually X b compounded quarterly X c compounded monthly TEAFM2 F 2 016 d compounded daily MY NOTES ASK YOUR TEACHER PRACTI

EAFM2 F 2 032 ank advertises a nominal rate of 6 41 compounded semiannually A second bank advertises a nominal rate of 6 37 compounded daily What are the effective yields Round your ans two decimal places first bank 0 07 second bank 6 54 X X In which bank would you deposit your money O first bank Osecond bank Oddill MY NOTES ASK YOUR TEACHER PRACTICE A

Part 1 of 2 15 10 5 0 Normal curve with u 2 0 4 u 2 o 2 2 a 4 Part 2 of 2 b 15 10 and standard deviation 0 5 10 15 05 X 10 15 C

typical glass of wine contains about 19 grams of alcohol Consider a 105 pound woman with approximately 4 liters 4000 milliliters of blood who drinks two glasses of wine Complete parts a nd b below a If all the alcohol were immediately absorbed into her bloodstream what would her blood alcohol content be 9 100 mL Round to two decimal places as needed Note that a blood alcohol content BAC of 0 08g 100mL is the legal driving limit in the U S A BAC at or above 0 4g 100mL usually leads to coma or death Explain why it is fortunate that in reality the alcohol is not absorbed immediately Choose the correct answer below OA It is fortunate that alcohol is not absorbed immediately because this blood alcohol content is above the legal limit for driving and is a dangerous level of intoxication OB It is fortunate that alcohol is not absorbed immediately because although this blood alcohol content is below the legal limit it will impair brain function OC It is fortunate that alcohol is not absorbed immediately because this is a lethal concentration of alcohol and is far beyond the legal limit OD It is fortunate because any amount of alcohol consumption can impair brain function b Again assume all the alcohol is absorbed immediately but now assume her body eliminates the alcohol through metabolism at a rate of 11 grams per hour What is her blood alcohol content 3 hours after drinking the wine 100 mL Round to two decimal places as needed Is it safe for her to drive at this time Explain plophol content is lower than it was three hours ago

In Arizona where there are 320 sunny days per year it requires 321 acres of land to generate 300 MW of average annual power If there are only 159 sunny days per year in Pennsylvania how many acres of land would it require to generate the same average annual power Please round to the nearest acre Note assume that a cloudy day delivers 0 watts acre of solar power This is not true but it simplifies the problem for us

For the following situation find the average monthly expense that you would use in budgeting for the given expense Note Annual means once a year and semiannual means twice a year You own your own home and pay 1600 annually in homeowners insurance 2500 semiannually in property tax and 850 monthly in mortgage house loan payments In addition just to be safe you decide to set aside 1760 per year for unexpected expenses for example water heater replacement sewer clean out or roof repair The average monthly expense that you would use in budgeting is

G A report on the trends in college pricing in a certain year included the information in the accompanying relative frequency distributions for public and private nonprofit four year college students Tuition and Fees 3 000 to 6 000 6 000 to 9 000 9 000 to 12 000 12 000 to 15 000 Proportion of Students Relative Frequency Private Nonprofit Four Year College Students Public Four Year College Students 0 04 0 40 0 26 0 13 0 04 0 04 0 02 0 02 0 02 0 02 15 000 to 18 000 18 000 to 21 000 21 000 to 24 000 24 000 to 27 000 27 000 to 30 000 30 000 to 33 000 33 000 to 36 000 36 000 to 39 000 39 000 to 42 000 42 000 to 45 000 45 000 to 48 000 a Construct a relative frequency histogram for tuition and fees for students at public four year colleges Wr center and variability 0 01 0 00 Chapter 0 00 0 00 0 00 0 02 0 06 0 02 0 02 0 03 0 03 0 04 0 07 0 09 0 09 0 09 0 08 0 07 0 07 0 22 G a few sentences describing the distribution of tuition and fees commenting on shape The center is in the range Select B Values are spread from a low range of

For the following situation find the average monthly expense that you would use in budgeting for the given expense Note Annual means once a year and semiannual means twice a Lan pays a semiannual premium of 450 for automobile insurance a monthly premium of 165 for health insurance and an annual premium of 400 for life insurance The average monthly expense is Round to the nearest cent as needed

municipal manager wants to put the system back to work as a small hydroelectric system to help supply the borough s electricity Does this idea make sense How much power could this system produce The height difference between the mill race and the tailrace is ten feet 3 meters and the stream can supply on average 100 cubic feet of water per second 2 8 m 3 sec The planned turbine would be 72 efficient under those conditions Power watts density of water height flow rate acceleration of gravity coefficient of efficiency NOTE the coefficient of gravity is 9 81 for this problem Don t round your answers Question 2 20 pts

Calculate the amount of money you ll have at the end of the indicated time perioc You invest 3000 in an account that pays simple interest of 6 for 30 years The amount of money you ll have at the end of 30 years is

professionals refer to science technology engineering and mathematics as the STEM disciplines A research group reported that 26 of freshmen entering college in a recent year planned to major in a STEM discipline A random sample of 90 freshmen is selected Round the answer to at least four decimal places Part 1 of 6 Is it appropriate to use the normal approximation to find the probability that less than 29 of the freshmen in the sample are planning to major in a STEM discipline It is andn 1 p 66 6 Part 1 6 appropriate to use the normal curve since np 23 4 A Part 2 of 6 10 10 Find the probability that less than 29 of the freshmen in the sample are planning to major in a STEM discipline The probability that less than 29 of the freshmen in the sample are planning to major in a STEM discipline is