Sets and Relations Questions and Answers

Scores on the Graduate Record Examination GRE follow a normal distribution Bonnie s score is 1 standard deviation above the mean About what percent of scores are higher than Bonnie s a 50 b 16 c 5 d 2 5 e can t tell from the information given O A OB O C OD DE

Use the following Venn diagram to find the cardinality of the indicated set 17 n B A A 8 15 13 16 G 12 B 5 3

7 On the day their son Peter was born Madeline and Ben invested 1500 for his education at 6 7 interest compounded quarterly Today is Peter s birthday He is 19 years old and wants to go to college a Circle the four important pieces of information in the question b Use a TMV Solver to determine the value of the investment today Fill in the box on the right c How much interest did the investment earn d How much interest would the investment have earned in a savings account that paid 0 7 interest per year compounded yearly N 1 PV PMT FV P Y C Y PMT END BEG

Find all matrices that commute with 11

ind a sine or cosine function for the given graph Leave your answers in exact form i e no decimal approximations If necessary type pi for T a b f x 15 14 13 11 10 7 f x 4 3 3 2 1 C

Income Tastes and preferences What does the question mark refer to O Consumer awareness O Consumer choice Availability of the products

28 A n is a valuation of property by an authorized person O a broker price opinion b comparison approach c market value O d appraisal

Without using a calculator determine which of the following numbers is closest to sin 126 0 2 0 8 0 0 8 or 0 2 sin 126 is closest to Type an integer or a decimal

in Problems 51 62 the function f is one to one a Find its inverse function and check your answer b Find the domain and the range off and f Graph f and yz on the same coordinate axes 51 f x 3 52 f x 42 53 f x 4x 2 54 f z 1 3z 55 f 2 2 1 56 f 2 z 1 57 f 2 44 58 f 2 9 59 f x 4 60 f z 61 f 2 52 f 2 in Problems 63 80 the function is one to one jal Find its inverse function and check your answer b Find the domain and the more of tang f Z 20 20

6 What is the value of x in the equation 1

A bond with a face value of 1 000 matures in 20 years pays interest semi annually and has a yield to maturity of 9 percent What is the current market price of the bond if the coupon rate is 12

Two wooden members of uniform rectangular cross section are joined by the simple glued scarf splice shown Knowing that P 11 kN determine the normal and shearing stresses in the glued splice 150 mm P 75 mm 450

10 Mary gives her nephew a document that provides evidence of ownership of her property What was given to the nephew O a the mortgage b the title c the pledge d the deed

12 Students from a business school were surveyed to find if they prefer to work for a firm start their own business or study further after graduation The pie chart below shows the results of the survey Work for a firm 1 Which of these bar graphs best represents the result of the survey Number of 5 Number of Students business the Work for afirm Work for Startown Study a firm business further Survey Choices Start own Study business further Survey Choices Work for Start c 21 DUS TH Survey Choices Study further 4

Progressive Regressive Proportionate What does the green round indicate Tax structure O Tax types Tax principles

For the statement Some birds do not fly complete the following steps a Write a logical form b Form negation of the statement from a so that there is no negation symbol to the left of the quantifie c Express negation found in b in simple English Show your work on paper then take a picture of it and then attach your file here

e Venn diagrams to determine ether the following statements are equal for all sets A B and C AUB n BUC BU ANC the statements equal for all sets A B and C Yes No T COOLED 1 C IV

Wenn diagram shown to list the set 8 nC in roster form 10 11 13 16 14 18 ancy Use ascending order Use a comma to sepas

Construct a Venn diagram illustrating the following sets U Store 1 Store 2 Store 3 Store 13 Store 14 A Store 2 Store 4 Store 5 Store 8 Store 9 B Store 2 Store 6 Store 9 Store 11 Store 14 C Store 2 Store 5 Store 7 Store 12 Store 13 Choose the correct Venn diagram below OA D U 5 C C 7 12 13 6 11 14 B 6 11 14 3 10 7 12 13 10 Q S OB OE UC UC 6 9 7 12 13 13 10 6 11 14 2 B n 1 3 10 B 6 11 14 7 12 13 C C OC OF U C C 2 8 7 12 13 7 12 13 6

set con How many subsets does it have How many proper subsets does it have The set has The set has subsets Simplify your answer proper subsets Simplify your answer

subsets give pineapple apple mango Choose the answer that lists all of the subsets of pineapple apple mango OA pineapple apple mango pineapple apple pineapple mango apple mango OB pineapple apple mango pineapple apple pineapple mango apple mango OC pineapple apple mango pineapple apple pineapple mango apple mango pineapple apple mango OD pineapple apple mango pineapple apple pineapple mango apple mango pineapple apple mango

E x XEN and 21 x 64 Choose the correct answer below O A E 21 22 23 24 64 OB E 21 22 23 24 63 OC E 22 23 24 25 63 D E 21 22 23 24 OE E 22 23 24 25 OF E 22 23 24 25 64 O G G

A fair coin is tossed 5 times 4 How many possible distinct sequences are there where 2 heads in a row are to For the toolbar press ALT F10

Let A B X be sets Write a proof by contradiction that shows that if A B then X B X A For the toolbar press ALT F10 PC or ALT FN F10 Mac 10pt 13

Section 1 Knowledge Understanding Directions For each of the questions in this section write your answers in the spaces provided

4 to O Problem 4 28 pts A 100 mm long rectangular bar with a 10 mm x10 mm cross section shown here is made of brass The bar is deformed elastically in tension with a force of 30 000 N With the information provided in the table for brass answer the following questions Stress Ft Ao Modulus of Elasticity 10 psi 14 6 GPa 97 a Calculate the stress generated by the load in MPa 8 pts 100mm x10 m 0 1 m W 30000N 0 1m Shear Modulus 10 psi 5 4 GPa 37 Poisson s Ratio 0 34 300 000 Na m pa Gf 0 3MPa b What type of stress is generated under the load normal stress or shear stress 5 pts Normal Shess c Calculate the strain generated by the load 5 pts E 10mm 100mm 0 1 d Calculate the total length of the bar under the load in mm 5 pts 0 1 AL 0 1 L loo Li 0 1 100 100 1 mm Wo e Calculate the width of the bar under the load in mm 5 pts EL SL 30 000 N 10 mm IMPa 10 pa 300000p xlmpa 10 Pa WO 0 1 10 1mm 100 mm 10 mm

11 During the Reconstruction period how many amendments were added to the Constitution OA Two OB Six OC Three OD Four

7 Why did many Southerners dislike carpetbaggers OA They worked with new arrivals from the North and betrayed their fellow Southerne OB They took advantage of the economic chaos in the South after the Civil War OC They went around the South freeing enslaved people after the Civil War OD They won most of the high political offices in the North after the Civil War

Set An C in roster form is Type a whole number Use a comma to separate answers as needed

shows the top 10 countries for production of com rice and wheat in a recent year The universal set is the set ries in the world Indicate in which region I VIII in the figure country G belongs belongs in region Ta Com 1 R 2 A 3 G 4 W 5 F 6 P 7 C 8 N 9 S 10 L Rice 1 E 20 3 A 4 R 5 M 6 L 7 G B T 9 J 10 K Wheat 1 8 2 W 3 S 4 P 5 E 6 N 7 H 8 A 9 Q 10 R Com NV VII When

4 Which one of the following is the correct sign diagram for the function Y 3 O O O O O x 1 x 1 x 1 1 3 y 0 0 0 y T I 3 1 1 0 0 0 1 3 y 00 0 1 13 y 0 0 0 T r 3 1

work results of a survey of customers at a pet supply store showed that 37 owned lizards 42 owned cats and 19 owned both lizards and cats How many owned the customers surveyed owned either a lizardor a cat pe an integer or a decimal

en the following determine the set B nC U x x EN and x 13 B x x EN and x is even and x 13 C x x EN and x 13 ect the correct choice below and if necessary fill in the answer box to complete your A Bnc Use a comma to separate answers as needed Use ascending order B Bn C is the empty set

bilowing sets U x x E N and x 10 A x x EN and x is odd and x 10 B x x E N and x is even and x 10 etermine ect the correct choice below and if necessary fill in the answer box to complete your a An B Use a comma to separate answers as needed B An B is the empty set A

Given the following determine the set A U B n AUB U 1 2 3 4 5 6 7 8 A 1 2 3 7 8 B 1 3 4 6 Select the correct choice below and if necessary fill in the answer box to complete your choic OA A UB n AUB Use a comma to separate answers as needed Use ascending order OB AUB n AUB is the empty set

I the set Anc U 1 2 3 4 5 6 7 8 9 A 2 4 5 9 C 2 3 4 5 9 ect the correct choice below and if necessary fill in the answer box to comp A An C B An C is the empty set Use a comma to separate answers as needed

b c d e f g h i j k j b c d f g i c f g i k b d e g k mine AU Cn B t the correct choice and if necessary fill in the answer box to complete your cho AU COB Use a comma to separate answers as needed AU Cn B is the empty set

hoose the correct answer below A p y B c o e ta h u g r d Oc a b OD p y L c o e L u g r d

A Use a comma to separate answers as needed GEEN

A 0 Use a comma to separate answers as needed

J is the set of cities in a country A is the set of cities that have a science museum 3 is the set of cities that have a professional sports team Describe B in words Choose the correct answer below OA B is the set of cities in a country that have a science museum and do not have a professional sports team B B is the set of cities in a country that do not have a science museum C B is the set of cities in a country that do not have a professional sports team D B is the set of cities in a country that have a professional sports team and do not have a science museum

For the sets U A and B construct a Venn diagram and place the elements in the proper regions U 1 2 3 4 5 6 7 8 A 1 4 5 B 1 2 3 6 8 Choose the correct answer below A U A 7 B B U A B C U 6 B D

t the correct choice that completes the sentence below et containing all the elements that are members of set A or set B or of both is called the of set

ect the correct choice that completes the sentence below set of all elements in the universal set that are not in set A is called the

IV 1 5 1 111 Show that 23 PL K KKK 138 Thus e 11 1 1 Solution We begin with parametrizize the circle z1 1 as z 1 eit 1 cost i sint where 0 t 2 For the nominator in the integrand e z 1 we have dz 2 Im e eRez i Imz eRezeilmz eRez e since Re z 2 on the circle And for the denominator in the integrad we have 1 z 2 cost isint Re 2 cost isint 2 cost 1 M 8 1541 2 1 0 e e Becauce the integrationcontour is a circle with radius 1 we have that L 2 ML estimate gives

a How many subsets does it have b How many proper subsets does it have a The set has 1024 subsets Simplify your answer b The set has proper subsets Simplify your answe

list 3 21 a How many subsets does it have b How many proper subsets does it have a The set has subsets Simplify your answer

0 is true or false If it is false give the Choose the correct answer below A The statement is false two sets can never be equal B The statement is true the set is equal to the empty set OC The statement is true the empty set is a subset of every set OD The statement is false the set contains the element

Solve the given radical equation Check all proposed solutions 2x 18 x 5 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is Use a comma to separate answers as needed Simplify your answer OB The solution set is the empty set

6 Ages of people in a movie theater 2 H 8 24 14 20 6 8 26 32 38 Age 7 Rachel and Tiana are both dancers preparing for an audition The box and whisker plot below shows the number of hours each girl practiced each week over the last few months 10 44 Rachel 50 56 62 12 14 16 18 20 22 more 25 a Identify the minimum and maximum ages b What percent of the people are no more than 8 years old c What percent of the people are between 8 and 38 years old a Which girl has the greatest range of practice hours b Based on the number of hours practiced which dancer do you feel is most prepared for the audition Explain your reasoning