Mathematical Induction Questions and Answers

A 15m 58 N B161 18m C In the diagram three points A B and C are on the same horizontal ground B is 15m from A on a bearing of 053 C is 18m from B on a bearing of 161 A vertical pole with top T is erected at B such that angle ATB 58 Calculate correct to three significant figures a the length of AC b the bearing of C from A c the height of the pole BT

Incremental Analysis of Special Sales Order Decision Ludolph Industries has an annual plant capacity of 74 000 units current production is 59 000 units per year At the current production volume the variable cost per unit is 31 00 and the fixed cost per unit is 4 40 The normal selling price of Ludolph s product is 46 00 per unit Ludolph has been asked by Bramwall Company to fill a special order for 11 000 units of the product at a special sales price of 23 00 per unit Bramwall is located in a foreign country where Ludolph does not currently operate Bramwall will market the units in its country under its own brand name so the special order is not expected to have any effect on Ludolph s regular sales Read the requirements Revenue from special order Less expenses associated with the order Less Variable manufacturing cost Contribution margin Less Additional fixed expenses associated with the order Increase decrease in operating income from the special order Incremental Analysis of Special Sales Order Decision Total Order 11 000 units 253 000 Revenue from special order Less expenses associated with the order Less Variable manufacturing cost Contribution margin Less Additional fixed expenses associated with the order Increase decrease in operating income from the special order 0 Total Order 11 000 units possible CO Ludolph should accept the special sales order because it will increase operating income Requirement 2 How would your analysis change if the special order sales price were to be 38 00 per unit and Ludolph would have to pay an attorney a fee of 17 000 to make sure it is complying with export laws and regulations relating to the special order Enter a 0 for any zero balances Use parentheses or a minus sign to indicate a decrease in contribution margin and or operating income from the special order test

The function T x 17 4 In shows the relationship bety and the amount of time the money is invested For this function x represents the starting amount of the investment and T represents the amount of time in years The function measures the amount of time needed for the starting amount to grow to 8000 Luis is interested in a 13 year investment and wants to know what his starting investment should be A Draw a graph that shows the function as it intersects the time value 13 years and state the window you used Graph Window used Format is Xmin Xmax X Xin Ymax B According to your graph what is the starting value of the investment needed x for the 13 year investment Round your answer to the nearest 0 01 algebraic couation that would determine the initial investment x needed for the 13 year

Consider a 400mm long beam with a pinned left and simple roller right supports at each end respectively The beam is subjected to three concentrated forces P P and 3P as shown in the figure below The beam cross section with detailed dimensions is shown in the figure right Take E 200 GPa Length unit mm X 100 P 100 A 3P 50 50 4 100 12 Figure 2 Beam with concentrated loads and cross section 16 Neutral axis a Find the location of the neutral axis on the beam cross section and the moment of inertia about the neutral axis b If Ex 50 x 10 5 at A determine how much P is given that the applied forces are P P and 3P The point A see the red dot right is 3 mm from the top edge of the cross section and the section containing the point A is shown in the figure i e at 150 mm from the roller support c Draw the shear and bending moment diagrams for the beam using the value of P you found in part b Use the graphical method to get full credit Label your diagrams with appropriate values and justify them showing your calculations d Find the maximum tensile and compressive stresses max in the beam and indicate their locations e If the cross section is flipped 180 from the inversed T to T shape how much would the maximum compressive and maximum tensile stresses be

The price demand equation and the cost function for the production of table saws are given respectively by x 12 800 32p and C x 60 000 50x where x is the number of saws that can be sold at a price of p per sav and C x is the total cost in dollars of producing x saws Complete parts A through 1 below A Express the price p as a function of the demand x and find the domain of this function The price function is p

Express the following number in exponential form 2 5j What is the exponential form of the given number Use integers or decimals rounded to the nearest hundredth for any numbers in the expression as needed Express complex numbers in terms of j The argument should be between C

Using DeMoivre s theorem find 1 2 1 21 cos j sin Simplify your answers Round to two decimal places as needed Type any angle measures in degrees Use angle measures greater than or equal to 0

Use the table to find the number of subsets of the set of students who are neither upperclassmen juniors or seniors nor have a GPA below 3 2 The number of subsets is Type a whole number Major Class Rank GPA Activitie Elston Music Freshman 3 8 Band Carmen Physics Senior 2 5 Yearboc Frank Business Freshman 1 3 Basebal Gina Music Senior 2 9 Soccer Dana Music Freshman 3 9 Tennis Brenda Business Freshman 3 8 Choir

Question 1 Theresa wants to buy a house so she has decided to save one quarter of her salary Theresa earns 48 00 per hour and receives an extra 28 00 a week because she declined company benefits She wants to save at least 550 00 each week How many hours must she work each week to achieve her goal 15 p

Suppose T R R is a linear transformation that first rotates a point about the origin through 11T radians clockwise and then reflects points through the horizontal axis Find the standard matrix A of T Answers should be in exact form i e do not use a calculator to get a decimal approximation 6

Use a standard normal distribution table to find a z score such that 33 00 of the area under the standard normal curve is above that score Click the icon to view the standard normal distribution table Z Round to the nearest hundredth as needed

The following chart shows the most popular choices for a girl s name In a certain group each person was asked to vote for one name and the results are shown If an answer does not exist enter DNE Number 9 9 7 6 1 Find the mean the median and the mode for the number of votes mean median mode Names Emma Oliva Sophia Ava Isabella

Question 1 Draw the graph of f z 3 2 10 9 6 5 10 9 8 7 6 5 4 3 2 1 B 2 1 2 s523 3 4 5 6 7 co 1 2 3 4 5 6 7 8

4 6 1 2 3 5 1 1 004050 2 0 00549500 4 42 050 5 1230 00 6 100 3 5600 7 0 030400 55 604 X 0 0995 O Calculate the following problems and give the answer in correct sig figs 843 00 0 05542 1123 7 554 333 3 24 8854 443 4 125 943 686 000 543 345543 2 0540 0 5540 X x 43 4 8 80 500 9 35 93 10 2 0000 11 123 0200 12 000439300 13 8584 300 14 5432 320 4 400 21 0 08535

Silvia is left an annuity of US 4000 in her uncle s will The annuity is for five years at 4 per annum and is to be paid out monthly Find the monthly payments

lowing figure depicts the aggregate demand curve AD and the long run aggregate supply curve LRAS for the United States The economy is initially at long run equilibrium at point A In 2015 Mexico was the second largest importer of goods produced in the United States importing approximately 236 billion in goods Now suppose that Mexico experiences a substantial economic boom in 2016 that greatly increases Mexico s demand for U S made products In the figure below first shift the appropriate curve to depict the change in the U S economy that is due to the economic boom in Mexico According to classical economics the economy will self correct Now using your knowledge of classical economics move the equilibrium point to depict the self correction of the economy To refer to the graphing tutorial for this question type please click here COO Price Level P LRASI O

1 point Problem 8 The distance d of a point P to the line through points A and B is the length of the component of AP that is orthogonal to AB as indicated in the diagram So the distance from P 0 4 3 to the line through the points A 4 2 4 and B 3 5 1 is Brouiou Mu Angum

ind the regression line for the data points Round your values to two decimal places y X 85 90 100 102 105 y 75 40 35 28 25

6 4 Expected rate of return and risk Summerville Inc is considering an investme one of two common stocks Given the information that follows which investme better based on the risk as measured by the standard deviation and return of e COMMON STOCK A COMMON STOCK B PROBABILITY 0 30 0 40 0 30 RETURN 11 15 19 PROBABILITY 0 20 0 30 0 30 0 20 RETURN 5 6 14 22

mputing holding period returns a From the price data here compute the holding period returns for Jazman a Solomon for periods 2 through 4 PERIOD JAZMAN 1 9 2 11 3 10 4 13 b How would you interpret the meaning of a holding period return SOLOMON 27 28 32 29

a Copy and complete the table of values for the relation y x x 2 for 3 x 3 X y 3 2 1 0 1 2 4 2 3 4 b Using scales of 2cm to 1 unit on the x axis and 2cm to 2 units on the y axis draw a graph of the relation y x x 2 c From the graph find the i minimum value of y ii roots of the equation x x 2 0 iii gradient of the curve at x 0 5

a Copy and complete the table of values for the relation y x x 2 for 3 x 3 X y 3 2 1 4 0 1 2 2 3 4 b Using scales of 2cm to 1 unit on the x axis and 2cm to 2 units on the y axis draw a graph of the relation y x x 2 c From the graph find the i minimum value of y ii roots of the equation x x 2 0 iii gradient of the curve at x 0 5

A Ih S Paragraph 15 Use the following to answer question 34 Figure Market for Loanable Funds II Interest rate 8 E 0 O 300 A 8 be greater than B 8 be less than C 8 equal Supply than mal Demand Quantity of loans Styles 34 Figure Market for Loanable Funds II If the interest rate is greater than the quantity supplied of loanable funds will demanded then the quantity of loanable tunds F

Goods Pizzas Rent Car Phone a b c Qty 20 1 1 1 2001 Price 10 00 600 00 100 00 50 00 Qty 30 2 4 0 5 2002 Price 11 00 640 00 Qty 40 2 120 00 5 40 00 0 25 2003 Price 12 00 700 00 150 00 30 00 Calculate the Nominal GDP in 2001 2002 and 2003 respectively 2001 20 10 1 600 1 100 1 50 950 2002 30 11 2 640 4 120 5 40 2110 2003 40 12 2 700 5 150 25 30 2637 50 Assume 2001 is the base year What is the CPI in 2002 I Assume 2001 is the base year What is the CPI in 2003 2

a If a raw score corresponds to a z score of 1 75 what does that tell you about that score in relation to the mean of the distribution b What if the raw score corresponds to a z score of 0 85 These problems are worth 10 points Please answer the questions in complete sentences

of ea set of numbers 10 15 13 17 14 61 82 64 68 75 68 78 78 73 69 4 5 4 6 2 1 3 4 2 2 2 7 1 5 2 1 8 2 2 2

Thirty small communities in Connecticut population near 10 000 each gave an average of x 139 0 reported cases of larceny per year Assume that a is known to be 44 3 cases per year a Find a 90 confidence Interval for the population mean annual number of reported larceny cases in such communities What is the margin of error Round your answers to one decimal place lower limit X 125 54 152 46 upper limit X margin of error 13 5 X b Find a 95 confidence interval for the population mean annual number of reported larceny cases in such communities What is the margin of error Round your answers to one decimal place lower limit 123 93 154 07 15 1 upper limit margin of error X X c Find a 99 confidence interval for the population mean annual number of reported larceny cases in such communities What is the margin of error Round your answers to one decimal place lower limit 120 55 upper limit 157 45 18 45 margin of error X d Compare the margins of error for parts a through c As the confidence levels increase do the margins of error increase O As the confidence level increases the margin of error remains the same O As the confidence level increases the margin of error decreases As the confidence level increases the margin of error increases

This question 1 point s possible K The professor assigns grades in the modern poetry class according to where a student s average is located in the following diagram The averages in a class are 80 77 81 77 85 74 75 78 78 and 88 Suppose the professor assigns grades using the method shown below Averages on the border are assigned the higher grade F D C B mean 1 11 standard deviations mean standard deviation What grade does the person earning the 80 get The person will get a n A D C F mean mean standard deviation mean 14 standard deviations Submit quiz

FitTime produces two types of exercise treadmills Regular and Deluxe The exercise craze and related demand is such that FitTime could use all of its available machine hours producing E The two models are processed through the same production department Click the icon to view the data What product mix will maximize operating income Hint Use the allocation of fixed manufacturing overhead to determine the proportion of machine hours used by each product Prepare the product mix analysis FitTime Product Mix Analysis Sale price per unit Variable costs per unit Contribution margin per unit Units produced with equivalent number of machine hours Contribution margin for equivalent number of machine hours Deluxe 1 010 775 235 1 235 Regular 580 447 133 3

Kasper s puppy ran out of the house It ran 18 meters turned and ran 23 meters and then turned 140 to face the house How far away from the house is Kaspers puppy Round to the nearest bundredth

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

The sale prices for homes in a certain city are as follows Location 415 First Street 957 Locust Street 114B First Street Cytrus Heights 814 Duncannon 482 Circle Court 1580 De Soto Dr 118 Moss Road Find the mean the median and the mode If an answer does not exist enter DNE median mode mean mean Which measure seems to best describe the home price median mode Need Help Price 285 000 460 000 130 000 2 590 000 Read It 240 000 315 000 130 000 230 000

20 of all college students volunteer their time Is the percentage of college students who are volunteers different for students receiving financial aid Of the 318 randomly selected students who receive financial aid 76 of them volunteered their time What can be concluded at the a 0 05 level of significance Use che p value approach a For this study we should use Select an answer b The null and alternative hypotheses would be Ho Select an answer H Select an answer c The test statistic please enter a decimal Please enter a decimal Please round your answer to 2 decimal places Please round your answer to 2 decimal places d The p value e The p value is a f Based on this we should Select an answer the null hypothesis

K Use a standard normal distribution table to find the percentage of area above the standard normal curve that is specified Above z 1 47 Click the icon to view the standard normal distribution table What is the percentage of the area above z 1 47 Round to the nearest tenth as needed

The cyclists X and Y leave town Q at the same time Cyclist X travels at the rate of 5km h on a bearing of 049 and Cyclist Y travels at the rate of 9km h on a bearing of 319 a Illustrate the information on a diagram b After travelling for two hours calculate correct to the nearest whole number the i distance between cyclists X and Y ii bearing of Cyclist X from Y c find the average speed at which cyclist X will get to Yin 4 hours

k ces Sofia Gomez runs a mobile pet grooming service She charges 30 direct labor per grooming hour She applies overhead to jobs on the basis of grooming hours She predicts 1 000 grooming hours for the year Her estimated overhead costs for the year follow Van depreciation Van maintenance 9 700 Van insurance expense 1 600 Indirect materials 1 Predetermined overhead rate 2 Total job cost 3 Price quote 1 200 Tool depreciation 800 Other overhead 550 1 150 1 Compute the predetermined overhead rate using estimated grooming hours 2 Sof a has been asked to groom 3 large dogs She expects this job to require a total of 9 direct labor grooming hours Compute her total cost direct labor plus applied overhead for this job 3 If Sof a targets a markup of 20 on the total cost for each job what price should she quote for the job in part 2 Check my w

Select the correct choice below and if necessary fill in the answer box to complete your choice Simplify your answer Type an integer or decimal rounded to the nearest hundre as needed OA For the time period between and not inclusive of OB For the time period between and inclusive of sec and sec and sec the ball will be at least 41 ft above the ground sec the ball will be at least 41 ft above the ground

Question Tent Provide your answer below 11 km 3 km Coral reef Shoreline A visitor is staying in a tent that is 11 kilometers west of the closest point on a shoreline to a coral reef Th coral reef is 3 kilometers due south of the shoreline The visitor plans to travel from the tent to the coral reef by running and swimming If the visitor runs at a rate of 7 kmph and swims at a rate of 2 kmph how f should the visitor run to minimize the time it takes to reach the coral reef Round to two decimal places

7 What is the constant of proportionality in the equation y 5x

Suppose that the functions fand g are defined as follows 1 x 2 4 x 4 g x 4x 3 Find fig and f g Then give their domains using interval notation f g x Domain of fig 8 x 8 OVO X 0 0 C 0 0 C S

The function f is defined by f x 2x 7 Find f 4a f 4a

Now we substitute our function of x C x ln 9x 1 250 Step 6 Now we know the fixed costs are 250 Thus we have the following C 0 250 Plugging this into the cost function we can find K 250 C 0 In 0 C x 9 250 K In 19x 1 K 0 X 0 0 1 K 1 Step 7 Finally we can determine the cost function K

The following statistical study gives a sample statistic and a margin of error Find the confidence interval and answer any additional questions A national survey of 1513 respondents reached on land lines and cell phones found that the percentage of adults who favor legalized abortion is 43 The study claimed that the error attributable to sampling is 6 percentage points Would you claim that a majority of people are not in favor of legalized abortion The confidence interval for the study is to docimale Hea necending order

ppose that you are given the task of learning 100 of a block of knowledge Human nature is such that we retain only a percentage P of knowledge t weeks after we have learned it The Ebbinghaus learning model asserts that P is given by P t Q 100 Q where Q is a percentage that we would never forget and k is a constant that depends on the knowledge learned Suppose that Q 40 and k 0 6 Complete parts a through e below Find the percentage retained after 0 weeks 1 week 2 weeks 6 weeks and 10 weeks Complete the table to the right 4 Time Passed Percentage 0 weeks 1 week 2 weeks 6 weeks 10 weeks

A Simplify 2x 3x 5 x

Find the solution to the initial value problem y 9y 27 y 0 4 y 0 6

Progress The movement of the progress bar may be uneven because questions can be worth more or less including zero depending on your answer Joe runs 8 25 times around a track in 1 119 803 seconds If one lap around the track is 402 3 meters which is the best estimate of the runner s average speed in meters per second m s 3 m s O 0 4 m s 30 m s Question ID 97376 0 3 m s

Eric is driving on the highway He begins the trip with 12 gallons of gas in his car The car uses up one gallon of gas every 20 miles Let G represent the number of gallons of gas he has left in his tank and let D represent the total distance in miles he has traveled Write an equation relating G to D and then graph your equation using the axes below Equation 0 0 X 00 12 G X

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

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