Math - Others Questions

2 Here are graphs of x 4 and x y 12 Complete the graphs by shading regions and adjusting line types as needed to show all the allowable numbers of widgets and zurls that the factory can produce in one day 11 1 12 4 12 10 8 6 4 2 3 Does each ordered pair represent an allowable combination of widgets and zur produced in one day 4 5 10 12 3 9

M MEASUREMENT AND MATTER Counting significant digits when measurements are added or Add or subtract the following measurements Be sure each answer you enter contains the correct number of significant digits 2 800 g 1 57 g g 0 670 g 1 07 g g 7 82 g 0 500 g g X

3 5 pts Identify Circle whether the following situations are binomial or not If they are identify n and p If they are not please explain why not Situation If so what are n and p If not why not We will draw 10 cards from a standard deck without replacement and count how many face cards we picked Binomial Not Binomial Not

Be sure to fully justify your responses when appropriate Show where all your numbers came from if not explicitly written Don t forget Units and use complete sentences when appropriate asked for 1 10 pts We bought a pack of 10 lightbulbs from a garage sale and 6 of them don t work If we were to collect a random sample of 2 lightbulbs no replacement and count the number of lightbulbs that are defective create a probability distribution for this discrete random variable a First define your random variable X

Construct a Binomial probability distrubtion table using n 5 and P 0 24 Next record the mean and standard deviation of the distribution below Where necessary round all numbers to four decimal places P x 0 1 2 3 st 4 5 X OF 0 0 2536 0 4003 0 2529 0 0798 0 0126 0 0008

Wages and Salaries Personal Income Taxes Payroll Taxes e g Social Security tax Income Receipts from Rest of the World Income Payments to Rest of the World Indirect Business Taxes Corporate Income Taxes Government Transfer Payments US Exports Undistributed Corporate Profits Gov t Purchases of Goods and Services 188 Gross Private Domestic Investment US Imports Net Private Domestic Investment Statistical Discrepancy Personal Consumption Expenditure 1300 90 85 128 147 50 240 522 78 237 257 96 112 8 1220

14 8 If the 50 kg crate is subjected to a force of P 200 N determine its speed when it has traveled 15 m starting from rest The coefficient of kinetic friction between the crate and the ground is 0 3 14 9 If the 50 kg crate starts from rest and attains a speed of 6 m s when it has traveled a distance of 15 m determine the force P acting on the crate The coefficient of kinetic friction between the crate and the ground is p 0 3

Wages and Salaries Personal Income Taxes Payroll Taxes e g Social Security tax Income Receipts from Rest of the World Income Payments to Rest of the World Indirect Business Taxes Corporate Income Taxes Government Transfer Payments 1300 90 85 128 147 522 US Exports 78 Undistributed Corporate Profits 237 Gov t Purchases of Goods and Services 188 Gross Private Domestic Investment 257 US Imports Net Private Domestic Investment Statistical Discrepancy Personal Consumption Expenditure 50 240 96 112 8 1220

Consider the proposition over Z2 given by g x y x y x y That is the variables and y take integer values Put a checkmark next to those propositions which are true OA VI y q x y B q 1 1 OC Ey q 1 y OD 32 3y q z y E V Vy q z y DE 3r Vyg z y

Which of the following are equivalent to the proposition p q pr Select all that apply OA p q Vr OB p q r OC p V q r OD p q OE p qVr

Consider the proposition p x y Student a has taken class y over the universe where x is any student at UML and math class at UML Express each quantified proposition in English 1 3x 3y p x y 2 Ey Vx p x y 3 3x Vy p x y 4 Vy Vx p x y A Every class has been taken by at least one student B Every student has taken every math class C Every student has taken a math class D There is a student who has taken some math class E There is a student who has taken every math class I There is a math class that has been taken by every student

Match each quantified proposition over R with its negation 1 3x x 2 x 0 2 3x y x y 17 3 Vx 2 2 V x 0 4 3 Vy x y 17 5 Vr Vy x y 17 2 A 3x Vy x y 17 B 3x y x y 17 C Vac x 2 V x 0 D Vx x 2 A x 0 E V Vy x y 17 F 3x x 2 x 0 G Ve y x y2 17 H Va Vy x y 17 I 3x x 2 x 0

Let p n be the following proposition over Z the set of integers p n n 7n 12 0 Consider the following propositions over Z Which of the following propositions does p imply i e which a satisfy p q Select all that apply A g n n is a divisor of 24 OB g n 4n 12 OC g n tn 16 OD g n n 8 n 8 n 64 Be able to justify your answers using truth sets

Let p x q r be propositions over Z p x x 10 q x x 2 6 a Translate the following statement into English 3x z p a q x O A 10 and 2 2 6 for some integer a OB There exists a rational number a so that x2 10 and x 2 6 OC For all integersa a 2 10 and x 2 6 OD For all rational numbers a x 2 10 and x 2 6 OE None of the above b Translate the following statement into English Va z p x q x OA For all rational numbers x x 10 or x 2 6 OB 10 or x 2 6 for some integer a OC For all integers x x 10 or x 2 6 OD Every integer x satisfies x 10 and x 2 6 OE None of the above

Suppose that p 91 92 96 are propositions over the set of integers with the following truth sets Tp 3 7 10 Tq 3 Tq2 7 10 Tq 1 3 7 10 Tq 1 2 7 10 Tas 3 7 10 Tq 1 7 a Which of the following propositions imply p That is for each proposition does q p Select all that apply DA 92 B q OC 94 OD 96 b Which of the following propositions does p imply That is for each proposition does p qi Select all that apply DA gs B 92 OC 93

Which of the following propositions over R are tautologies over R Select all that apply OA q x x B q z x 7 x 7 x 49 OC q z x 1 2 1 OD q z x 1 x 2x 1 OE q z x 0 Be able to justify your answers using truth sets

Which of the following propositions are OA p q OB pV q OC p q OD q OE pa OF P implied by p p q Select all that apply

Consider the following propositions over R Which of these propositions are contradictions Select all that apply OA q x 10 x 100 OB q z x 0 OC g x x 6 x 6 x 36 OD q z 10 6 Be able to justify your answers using truth sets

Consider the following proposition p over the set S 1 2 10 p x x 16 10x a Compute the truth set of p Answer Tp b Which of the following propositions over S is equivalent to p OA g x 8x 16 OB q x 3 x 66 OC q x x 5 3

Solve 7 3 4

15 1 point Frogh measures the amount of water in her backyard well each day during a dry spell in her area 6 4 7 1 3 0 2 26 22 34 46 50 42 38 Day Amount of Water L 5 30 The rate of change of the amount of water with respect to the number of days is measured in units of

1 1 point Tracy reads part of her novel between 15 min and 30 min each day and the time she spends reading varies each day What type of relation best describes how Tracy s reading time is related to the price of gasoline BLERTEL IN

3 1 point A scatter plot is created for a set of data A linear model for the data has a coefficient of determination of R 0 7106 A quadratic model for the data has a coefficient of determination of R 0 7531 An exponential model for the data has a coefficient of determination of R 0 7278 Which model best fits the data

3 1 point Consider the data in the following table This relationship is 3 4 5 137 192 269 y 1 70 98 CEREEEEEE

1 point Mareta and Mikias are having a race The distance in metres that Mareta can travel while riding her bike in seconds follows a quadratic model d 22 The distance in metres that Mikias can travel on his motorized scooter in t seconds follows a linear model d 81 Who is ahead in the race at 4 s

14 1 point A mobile phone company offers a phone plan that allows 600 min of airtime per month The revenue generated from this plan depends on the price of the plan according to the data in the table 10 30 35 Monthly Plan Price Revenue 1000s 15 20 1560 1740 1180 1500 1080 25 1720 The first differences for this data imply a rate of change of revenue with respect to monthly plan price that is constant increasing or decreasing ARESIO

7 1 point More than one model can sometimes seem to fit a set of data is this statement true or false

1 point A relation can be modelled using a quadratic relation when the differences are constant

Section 4 Application Directions For each of the questions in this section show all work to get full marks 19 4 points The table shows the number of visitors to a Web site since it was put online Days 1 2 Daily Visitors 750 780 810 3 4 840 870 5 900 Determine a linear and an exponential model for the data How many more visitors does the exponential model predict on the 10th day than the linear model

1 point The following number sequence is an example of 1 3 9 27 81 TELITI growth

9 2 points Sasi roller blades at a constant speed travelling 8 km from her home to the library in 0 5 h What was the rate of change of distance with respect to time

0 1 point A bacteria population quadruples every hour What type of relation best describes how the population is related to time

0 4 points The value of Nazanin s baseball card collection has been increasing by 7 each year If it is worth 934 now how much will it be worth after 2 years

5 1 point In a linear model the first differences are IELIETE

2 1 point Which relation best describes this graph ES

18 3 points Solve 7 3 4 1

Directions For each of the questions in this section show all work to get full marks 16 2 points Solve Give the answer as a fraction 5 1 5 50

8 1 point In y mx b the letter b is THEEEEEE

17 3 points Solve

irections For each of the questions in this section write your final answer

2 Let f x 5x 1 Find f 0 3 Given f x 2x 3 x 5 x 2 answer the following question a List the zeros of the function b What is the degree of f x c As x o f x d As x f x MIDDLESEX

Simplify the following Show the steps PEMDAS 2 5 16 7 2 5 16 57 2 Evaluate the expressions Show the substitution and the steps z x y use x 6 y 8 and z 6 10 p q 5 5 use p 1 and q

Use the following to answer questions 18 19 Figure Demand and Supply of Gasoline Price per gallon 5 4 3 2 50 2 1 50 1 0 S2 D 100 200 300 400 500 600 Quantity of gasoline per month Figure Demand and Supply of Gasoline Look at the figure Demand and Supply of Gasoline A factor that may have changed supply from S to S is A better technology in the production of gasoline B increased demand C lower labor productivity in gasoline production D increased prices of substitutes for gasoline Figure Demand and Supply of Gasoline Look at the figure Demand and Supply of Gasoline Given the initial equilibrium of S and D any price lower than W create pressure for the price to A 2 00 fall B 2 50 rise C 3 00 rise

Use the following to answer questions 24 25 Figure The Supply of DVD Rentals Rental price of DVDs Rental price of DVDs 0 0 A K C Quantity per period S S Quantity per period A to o in panel A B p to q in panel B C s tot in panel D to v in panel D Rental price of DVDs A 7 to o in panel A B p to q in panel B C s to fin panel C Rental price of DVDs 0 0 B D Quantity per period S1 S 24 Figure The Supply of DVD Rentals Look at the figure The Supply of DVD Rentals A decrease in the price of DVD rentals would result in a change illustrated by the move from Quantity per period 25 Figure The Supply of DVD Rentals Look at the figure The Supply of DVD Rentals A decrease in the price of DVDs sold by movie producers to rental stores would result in a change illustrated by the move from

27 Important factors that can cause supply curves to shift include input prices technology and A consumer preferences B imports C taxes D demand

51 Most introductory economics textbooks have a section on market failure It is here that students learn that markets may fail to achieve their potential leaving people worse off than they theoretically could be The existent of market failure is often taken as an excuse for government intervention to do whatever markets fail to do In just a couple of sentences explain why economists and others particularly politicians must accept the possibility of government failure as well That is tell me why government solutions to perceived market failures may themselves fail to achieve their own stated goals The U S Drug war is an apt example of a discrepancy between a stated political policy goal and the actual attainment of that goal

37 Hugo Ch vez is the president of Venezuela Venezuela is a major producer of oil products which remain the keystone of Venezuela s economy Suppose President Ch vez wants to increase his popularity with the citizens of Venezuela and enacts a government policy that reduces the customer price of gasoline sold at state owned gas stations to 50 of the previous price This policy is called a A price control B price floor C price ceiling D quota

46 What type of economic system does the United States have A traditional economy B free market economy C command economy D mixed economy

47 In Mark Skousen s article What is Economics Anyway he bemoans the apparent fact that the modern definition of economics is incomplete What does he say is missing A relationship between means and ends B the concept of scarcity C the process of transformation of resources D allocation toward competing ends

36 To be binding a price ceiling must be set at a price lower than the equilibrium price higher than the equilibrium price C the same as the equilibrium price D any price ceiling is binding A B