Mathematical Induction Questions and Answers

8 Your parents give you 700 to spend on books and supplies for this semester Your math book is 114 your biology book is 132 your biology lab book is 50 your English books are 142 and your drama book is 44 After you buy your books how much is left for supplies 9 Which property is represented by the following equation 23 7 2 23 7 2 Associative property of addition b Commutative property of addition c Distributive property of multiplication over addition d Additive inverse and additive identity A 10 The endpoints of a diameter of a circle C on the Cartesian plane are 5 2 and 0 2 Find the circumference of the circle C 11 The scores for your math tests are 88 81 97 97 83 78 85 95 79 82 What is your average score 12 Write 30 as the product of two odd numbers and one even number each of which is greater than 1 13 On a scavenger hunt you are supposed to cover an area on a map represented by a 2 cm by 5 cm rectangle to find clues for your hunt If the scale drawing on the map is 1 cm equals 20 feet what is the area in square feet you are supposed to cover 14 Find the answer to the following 13 5x3 3x6 2 12 15 True or False a a a xa 0 b a a a a 0 c axa axa 1 d aa xa 0

Set up the eigen value equation that would be used to get the linear momentum for a 1 dimensional particle in a box in the ground state Use the handout of operators

1 3 Playing a game with a pair of dice you win 2 if you roll a 7 or an 11 You pay 5 to roll the dice each time What is the expected value of this game

Maximize the function P 5x 2y subject to Y 5x 9y 9x 5y ALALVIAI 0 0 45 45 What are the corner points of the feasible set The maximum value is None in the blanke provided if th and it occurs at T

A factory received a shipment of 24 bolts and the vendor who sold the items knows there are 7 bolts in the shipment that are defective Before the receiving foreman accepts the delivery he samples the shipment and if too many of the bolts in the sample are defective he will refuse the shipment For each of the following give your responses as reduced fractions If a sample of 7 bolts is selected find the probability that all in the sample are defective If a sample of 7 bolts is selected find the probability that none in the sample are defective

This exercise uses the radioactive decay model A wooden artifact from an ancient tomb contains 70 of the carbon 14 that is present in living trees How long ago was the artifact made The half life of carbon 14 is 5730 years Round your decay rate r to 6 decimal places Then round your answer to the nea whole number yr

U X 24 58 38 W

105 84 g e

65 0 127

X Rectangle O Rhombus Trapezoid O Parallelogram

The following represents the probability distribution for the daily demand of computers at a local store Demand Probability 0 0 05 1 0 20 2 0 35 3 0 25 0 15 What is the expected daily demand 01 1 65 2 2 25

Estimate cos x2 da using a the Trapezoidal Rule and b the Midpoint Rule each with n 4 Give each answer correct to five decimal places a T 0 84549 b M 0 5373 c By looking at a sketch of the graph of the integrand determine for each estimate whether it overestimates underestimates or is the exact area 1 T Underestimate Overestimate 2 M4 d What can you conclude about the true value of the integral A TA cos x dx M4 B T4 C TA cos x2 dx and M4 cos x dx cos x dx and M4 f cos x dx D No conclusions can be drawn E MA cos x2 dx T

List all halfway points on the graph of y cot x on the interval 3 3 2 2 The points are Type an ordered pair Use a comma to separate answers as needed Simplify your answer Type an exact answer using it as needed Use integers or fractions for any numbers in t

Jim Smith is a salesman who receives a 1 100 draw per week against his commission He receives a 12 commission as an incentive on all sales Sales for Jim were 205 000 for the month Assuming a four week month Jim s commission is 24 600 20 200 23 500 26 400 None of these

Lisa Richter made a one time deposit of 5 000 at 4 compounded semiannually for 5 years What would her balance be at the end of five years assuming she is still earning 4 compounded semiannually 5131 8131 8 800 6 095

Banks and other financial institutions sometimes calculate simple interest based on Exact interest method Using 30 days for each month Using 366 days in the year Bankers rule ordinary interest None of these

The mortgage company requires a 14 down payment on houses it finances If the Sumis bought a house for 114 000 how much down payment did they have to make The Sumis had to make a down payment of

An airline ticket cost 280 without the tax If the tax rate is 7 what is the total bill for the ticket The total ticket cost is Simplify your answer Type an integer or a decimal Round to the nearest cent if needed

Are f and g orthogonal in the inner product space C a b with the inner product O Yes b f g flx f x g x dx C n 2 2 f x sin x g x COS X O No

In the diagram e W P t Angle 33 and p 6 87 m Find the length of side t in meters Round to 2 decimal places

An identification code is to consist of 4 letters followed by 3 digits Determine the following a How many different codes are possible if repetition is not permitted b How many different codes are possible if repetition is permitted c How many different codes are possible if repetition of letters is permitted repetition of numbers is not permitted and the first 4 letters must be the same letter d How many different codes are possible if the first letter must be R S or T and repetition of letters and number is not permitted b How many different codes are possible if repetition is permitted Choose the correct answer below OA 258 336 000 OB 456 976 000 OC 12 OD 457 976 c How many diff rent codes are possible if repetition of letters is permitted repetition of numbers is not permitted and the first 4 letters must be the same letter Choose the correct answer below

Prove the following statement If AA and B2B ard AB BA then AB AB

Construct a set of six pieces of data with mean median and midrange of 61 and where no two pieces of data are the same Choose the correct answer below OA 51 54 55 67 69 70 OB 58 59 60 62 63 64 OC 53 56 59 63 67 69 OD 55 57 59 62 66 67

A distinct group of objects without regard to their arrangement is called a A distinct group of objects without regard to their arrangement is called a permutation list

Nine red balls and seven blue balls are in a bag If two balls from the bag are to be selected at random determine the probability of selecting two red balls Assume that selection is to be done without replacement Set up the problem as if it were to be solved but do not solve P 2 red balls selected

Evaluate the expression a 10 C4 b 10P4 al Simplify our answer

Lester Co produces toys kites It has a fixed cost of 62 150 If the selling price per unit is 9 50 and the variable cost per unit is 6 25 the breakeven point is 9 207 6 542 22 600 29 860 None of theco

An LCD flat screen TV at Best Buy increased in price from 900 to 1 200 What was the percent of increase 33 1 3 50 60 70 None of these

Find the area and the perimeter of the landing area of the pole vault pit shown to the right The landing area is Type a whole number or a decimal The perimeter is 13 1 Landing a

Solve 150 y 6 The solutic

Find a particular solution to the differential equation 4y 4y 1y 2t 2t 6e 4t

The number of salespeople assigned to work during a shift is apportioned based on the average number of customers during that shift Apportion 22 salespeople using Webster s method given the information below Afternoon Evening 510 Shift Morning Midday 300 375 Average number of customers 125 Salespeople to assign What modified divisor did you use

A teacher wishes to distribute 50 identical pieces of candy among 4 students based on how many pages of a book they read last month using Hamilton s method The table below lists the total number of pages read by each student Child Alexei Pages 380 Alexandria 480 Trymaine 180 Miranda 130 Answer the following questions Give all answer to at least 4 decimal places as appropriate Find the divisor

Evaluate the expression 9P5

By conversion of the markup formula solve the following Note Round your answer to the nearest whole percent Percent markup on Percent markup on cost selling price 26

An inorganic soil has the following characteristics The soil has a liquid limit of 30 and plastic limit of 10 Using the USCS classification system what is the classification of the soil Sieve No 8 No No 200 10 No 4 Percent passing 64 78 86 A 20 acre parcel of land has a rainfall intensity of 3 in hr and a rational method runoff coefficient C of 0 10 The flow rate cfs for this site is most nearly O A 3 0 O B 5 0 O C 7 5 O D 9 0

5 15 pt Water containing 0 1 lb gal of salt enters a tank at a rate of 3 gal min and leaves the tank at a rate of 1 gal min Suppose the tank initially contains 100 gallons of solution in which the salt is 20 lb Find the amount of salt in the tank

For the set of numbers find the mean the median and any modes that exist 22 16 23 17 25 25 The mean is Type a whole number or decimal rounded to the nearest tenth as needed The median is Type a whole number or a decimal Find the mode Select the correct choice below and if necessary fill in the answer box to complete your choice OA The modes are Type a whole number or a decimal Use a comma to separate answers as needed The mode is Type a whole number or a decimal OC There is no mode B

A federal state or federation is one in which countries unite toward a common economic or sometimes military goal in which governmental power is disbursed to units of local government in which governmental power and control is centralized in which local city and county units of government work to adopt uniform rules and regulations

2 Total and marginal utility Charles enjoys buying shoes The following table contains information on Charles s utility from shoes each month Fill in the two missing cells of the table Shoes Total Utility Pairs Utils 0 0 TOTAL UTILITY Ut 50 45 40 35 30 25 1 20 2 3 4 in 5 6 12 30 36 40 42 On the following graph use the purple points diamonds symbol to plot Charles s total utility TU curve if he consumes zero one two three four five or six pairs of shoes per month Note Plot your points in the order in which you would like them connected Line segments will connect the points automatically Marginal Utility Utils per pair 12 10 8 0 4 2

Find the area bounded by the graphs of the indicated equations over the given interval Compute answers to three decimal places Y x 11 y 0 0 x 2 the area calculated to three decimal places is Square units

The Flotterons plan to purchase paint for the walls and for the trim in their living room They select one color for the walls and one color for the trim at random from following colors Walls Taupe Mahogany Sable Burgundy Trim Oyster White Alabaster Complete parts a through e C List the sample space Choose the correct answer Delow A TM TS TB MS MB SB OW OA WA OB TO TW TA MO MW MA SO SW SA BO BW BA TM TS TB MS MB SB OW OA WA OC T M S B O W A D TO TW TA MO MW MA SO SW SA BO BW BA c Determine the probability that they select Alabaster The probability is Simplify your answer

The following frequency distribution was constructed from data collected from a sample of 46 students at a college Calculate the Relative Frequency Distribution and the Percent Frequency Distribution Round the Relative Frequency to four decimal places and Percent Frequency to two decimal places wherever applicable Weight in Frequency Relative Percent

1 Find the perimeter of a rectangle that is 7 yd by 8 yd The perimeter of the rectangle is Type a whole number or a decimal yd yd

5 Let set A be the set of even integers strictly between 12 and 19 and let B be the set of integra greater than 15 and less than or equal to 20 If the universe of discourse is the set of integers that are at least 10 and at most 25 find the following a A b B c An B d AUB

Determine which functions are solutions of the linear differential equation Select all that apply y y y y 0 X ex e x xe X

Katie a single taxpayer is a shareholder in Engineers One a civil engineering company This year Katie s share of net business income from Engineers One is 200 000 net of the associated for AGI self employment tax deduction Assume that Katie s allocation of wages paid by Engineers One to its employees is 300 000 and her allocation of Engineers One s qualified property is 150 000 unadjusted basis of equipment all purchased within past three years Assume Katie has no other business income and no capital gains or qualified dividends Her taxable income before the deduction for qualified business income is 400 000 Required a Calculate Katie s deduction for qualified business income b Assume the same facts provided above except Katie s net business income from Engineers One is 400 000 net of the associated for AGI self employment tax deduction and her taxable income before the deduction for qualified business income is 350 000 Part a Part b

On August 2 Jun Company receives a 6 000 90 day 12 note from customer Ryan Albany as payment on his 6 000 account receivable 1 Compute the maturity date for this note 2 Prepare Jun s journal entry for August 2 Complete this question by entering your answers in the tabs below Required 1 Required 2 Prepare Jun s journal entry for August 2 View transaction list Journal entry worksheet

1 A pharmaceutical lab developed a method for determining the amount of morphine hydrochloride in tablets and obtained the following data for two different dosages Sample 1 2 3 4 5 Average Standard Deviation 100 mg tablets mg tablet 99 17 94 13 95 92 94 55 93 83 96 2 10 mg tablets mg tablet 12 06 8 83 9 08 10 2 a In either experiment is there any evidence that there is a blunder Briefly explain your reasoning worth 2 5 points b Choose one data point that may be a blunder and use a statistical test to determine whether the data point can be rejected worth 2 5 points e Is a bias occurring in the analysis of either tablet concentration or in other words is there evidence for a systematic error Please perform a statistical test or tests to confirm your answers for both tablet concentration worth 10 points

y 1 47 e 0 22t cos 4 9t ere y is the displacement in feet and t is the time in seconds Use a graphing utility to graph the displacement function for 0 t 10 Find t e beyond which the distance between the weight and equilibrium does not exceed 0 85 ft Round your answer to 2 decimal places S