Math - Others Questions

List the set in roster form Enter only the first five values of this set 3 5 I

uragging statements from the left column to the right column below give a proof by induction of the following statement For all n 1 4 7 10 3n 1 n 3n 5 2 The correct proof will use 8 of the statements below Statements to choose from Thus P k 1 is true Let P n be the statement 4 7 10 3n 1 4 7 10 3 k 1 1 k 3k 5 3 k 1 1 3k 5k 2 3k 5k So 3k 4 6k 8 2 2 3k 11k 8 2 k 1 3 k 1 5 2 Observe that 4 Therefore by the Principle of Mathematical Induction P n is true for all nz 1 n 3n 5 2 By the inductive hypothesis 4 7 10 3k 1 Note that 4 7 10 3 k 1 1 4 7 10 3k 1 3 k 1 1 k 3k 5 2 Now assume that P k is true for an arbitrary integer k 1 1 3 1 5 is true So the base case P 1 Your Proof Put chosen statements in order in this column and press the Submit Answers button

1 point Below are the steps of a proof by induction that 2n 1 2 for all integers n 3 Arrange the given steps in the correct order 2k 1 2 2k 2 by inductive hypothesis By the principle of mathematical induction we conclude that the statement is true for all integers n 3 Assume that 2k 1 2k for some integer k 3 2 k 1 1 2k 1 2 by algebra The statement is true for n 3 because 2 3 1 7 8 2 2k 2 2k 2k because k 3 v 2k 2k 2 2k 2k 1 by algebra Therefore 2 k 1 1 2k 1 which shows the statement is true for k 1

oblem 4 The concentration C of a drug in the bloodstream is given by 5 C t 2 3t 1 where t is the time in hours after ingestion of the drug and C is measured in milligrams per liter a State the domain of C t b Evaluate the average rate of change of C t on the interval 4 5 include units and interpret the answer c Graph the function Page 1 of 2

1 point Let P n be the predicate 8n7 n where the domain of n is all integers Suppose you are using induction to prove P n is true for all integers n 9 Which of the following do you prove in the basis step A 8n n for some integer n B 8 9 O c 8n n for n 8 OD 8n n for n 9 E If 8n7 n for n 9 then 8n7 n for n 10 OF None of the above Which of the following is the inductive hypothesis OA If 8k7 k for some integer k9 then 8 k 1 7 k 1 8 B 8k7k for all integers k with 9 k n C 8k7k8 for all integers k 9 O D 8k7 k for some integer k 9 E None of the above Which of the following do you prove in the inductive step OA 8n n for all integers n k B 8 k 1 k C 8k7 k 1 8 D 8n n for all integers n 9 E 8 k 1 7 k 1 OF None of the above

1 point By dragging statements from the left column to the right column below give a proof by induction of the following statement For all n 0 8 divides 32 1 The correct proof will use 8 of the statements below Statements to choose from We have 32 k 1 13 32k 1 9 3 k 1 9 3 k 9 9 1 9 32k 1 9 1 9 3 k 1 8 Now assume that P k is true for an arbitrary integer k 0 Then 32k 1 8j for some integer j Let P n be the statement 8 divides 32 1 Therefore by the Principle of Mathematical Induction P n is true for all n 0 Thus P k 1 is true So 32 k 1 1 9 8j 8 8 9j 1 which is divisible by 8 Note that the base case P 0 is true since 32010 which is divisible by 8 Your Proof Put chosen statements in order in this column and press the Submit Answers button

At June 30 Assets Cash Accounts receivable net Inventory IKIBAN INCORPORATED Comparative Balance Sheets 2021 Prepaid expenses Total current assets Equipment Accumulated depreciation Equipment Total assets Liabilities and Equity Accounts payable Wages payable Income taxes payable Total current liabilities Notes payable long term Total liabilities Equity Common stock 5 par value Retained earnings Total liabilities and equity Sales Cost of goods sold Gross profit 105 700 69 500 66 800 4 700 Other gains losses Cain en 246 700 127 000 28 500 345 200 28 000 6 300 3 700 38 000 33 000 71 000 IKIBAN INCORPORATED Income Statement For Year Ended June 30 2021 226 000 48 200 345 200 Operating expenses excluding depreciation Depreciation expense 2020 47 000 54 000 91 000 6 000 198 000 118 000 10 500 305 500 34 500 15 600 4 400 54 500 63 000 117 500 163 000 25 000 305 500 693 000 414 000 279 000 70 000 61 600 147 400

1 point Suppose you wanted to prove the following statement by mathematical induction 2 4 6 2n n n 1 for all n 1 What would the first line of a proof by induction be OA Let P n be the statement 2 4 6 2n n n 1 B Let P n 2 4 6 2n C Suppose P n n n 1 for all n 1 D Assume P n is true for all n 1 E Let P n be the statement 2 4 6 2n n n 1 for all n 1 What would you need to show to establish the base case OA Show that P 1 is true that is that 2 1 1 1 B Show that P 2 is true since the sum starts with 2 OC Show that 2 4 6 2n P 1 D Show that P 0 P 1 and P 2 are true E There is no need to establish a base case since the sum has at least four terms What is the first line of the inductive case for this proof OA Assume P k is true for some arbitrary k 1 that is that 2 4 6 2k k k 1 B Assume P k is true for some large k 1 say that 2 4 6 432 216 217 C Assume P k implies P k 1 for all k z 1 OD Assume P k is true for all kz 1 that is that 2 4 6 2k k k 1 OE Assume P k and P k 1 are both true for an arbitrary k 1 that is that 2 4 6 2k k k 1 and 2 4 6 2k 2k 2 k 1 k 2 www

1 point Let P n be the predicate 7 6 7 6 7 5 Suppose you are using induction to prove P n is true for all integers 0 Which of the following is the basis step OA 7 7 n B 7 6 1 0 71 C 7 6 7 61 7 I 0 n D 7 6 0 7 6 1 7 5 n E Hf7 6 B 7 6 0 5 7 6 1 7 10 OF None of the above D 7 6 C H7 6 7 6 10 1 0 A 8 7 6 7 6 1 7 5 7 6 1 7 5 Which of the following is the inductive hypothesis 7 6k 1 7 A 7 6 for all integers k 0 5 ANO 1 0 k 1 c 7 6 10 INO E None of the above 7 6 1 7 5 7 6 1 7 5 7 61 7 5 7 6 2 7 5 D 7 6 7 6 2 7 1 0 k 1 IO for n 1 5 E 7 6 7 6 7 1 0 OF None of the above for some integer n is true for 72 0 5 Which of the following do you prove in the inductive step A 7 6 7 6 7 for all integers n 0 for r 0 then 7 6 7 6 10 for some integer k 0 where the domain of it is all integers k 1 for some integer k 0 then 7 6 7 6 2 7 5 for all integers nk for all integers k with 0 k n 1 0 for n 1

balance my family responsibilities During this course I aim to dever and how culture and social norms influence our lives When it comes to addressing a local issue my primary concern would be poverty Poverty is a complex problem with underlying factors such as unemployment lack of educational opportunities and unaffordable housing Researching these specific causes in my community can provide valuable insights Moreover poverty isn t confined to one region it has global connections highlighting broader issues of income differences and financial gaps When we take action against poverty in our local area we become part of a global initiative to fight inequality and develop strategies that can benefit more than just our community

1 On a map the scale is 3 4 cm 8 miles The actual the distance between these cities on the map Scale 3 48 miles 0 75cmX 8 miles Zsumiles 2 Jacob made a drawing of his land using a scale 1 inch 14 yards The actual length of his land is 84 yards long What is the length of Jacob s land in the drawing 75 140 3 A scale drawing of a basketball court has a scale of 1 inch 9 feet The basketball court is 94 feet by 50 feet Find the dimensions of the court in the drawing VLength and width 5x10 6 5x Yo 142 X 24mles 4 Andrew draws a scale drawing of his office On the drawing his office is 6 cm by 7 cm If the scale of the drawing is 5 cm 10 ft what is the actual area of Andrew s office Stepiti Scale 5cm lopt 56 197 5 26 x width Step 5cm tcm 10PX 5 X 27 5cm 10 F 12 14 168 F 5 Finley has blueprints of her house that use a scale of 1 cm 2 5 m The actual distance between two rooms in Finley s house measures 28 m How far apart are these roons on the bluerint Scale 1cm 2 5m 2 5 28 1 2 5 28 2 5 2 5 6cm Toms 2 2 5 m2 28m X 11 2 6 The scale on a set of blueprints of a house is 1 in 3 ft On the blueprint one of the bedrooms measures 3 75 in wide and 4 5 in long What is the perimeter of the actual bedroom 7 Jill s room is 12 5 feet long and 11 5 feet wide She made a scale drawing of the room with a scale of 0 5 inch 2 feet What is the perimeter of Jill s room in the drawing 8 Taylor made a scale drawing of his room using a scale of 0 25 inch 1 foot On the drawing the length

By dragging statements from the left column to the right column below give a proof by induction of the following statement For all n 1 1 22 n n n 1 2n 1 6 The correct proof will use 8 of the statements below Note that 1 Statements to choose from 1 1 1 2 1 1 6 Now assume that P k is true for an arbitrary integer k 1 1 2 P 1 is true Let P n be the statement 1 2 k 1 k k 1 2k 1 6 So the base case n n 1 2n 1 6 Then we see that k 1 k k 1 2k 1 6 k 1 6 6 2k 3k k 6k 12k 6 6 6 2k 9k 13k 6 6 k 1 k 2 2k 3 Then 12 22 k 6 k 1 k 1 1 2 k 1 1 Note that 12 22 k 1 2 12 2 k k 1 k k 1 2k 1 6 Therefore by the Principle of Mathematical Induction P n is true for all n 1 Thus P k 1 is true Your Proof Put chosen statements in order in this column and press the Submit Answers button

In a proof by mathematical induction that a statement P n is true for all n 0 what are you trying to prove in the induction step Select all that apply A That P k and P k 1 are true for all k 0 B That P k implies P k 1 for some k 0 C That P k implies P k 1 for all k 0 D That P k 1 implies P k for some k 0 E That assuming P k 1 is true for an arbitrary k 0 we can prove that P k is true F That assuming P k is true for an arbitrary k 0 we can prove that P k 1 is true

a Equipment with a book value of 80 000 and an original cost of 162 000 was sold at a loss of 33 000 b Paid 118 000 cash for a new truck c Sold land costing 315 000 for 405 000 cash yielding a gain of 90 000 d Stock investments were sold for 96 300 cash yielding a gain of 17 000 Use the above information to determine cash flows from investing activities Note Amounts to be deducted should be indicated with a minus sign Answer is complete but not entirely correct Statement of Cash Flows partial Cash flows from investing activities Cash paid for new truck Cash received from the sale of equipment Cash received from the sale of land Cash received from the sale of stock investments Net cash provided by investing activities 33 000 X 33 000 X 405 000 17 000 X 488 000 Return t

Problem 3 According to data from the National Traffic Safety Institute the stopping distance y in feet of a car traveling a miles per hour can be described by the equation y 0 0560572 1 06657z Source National Traffic Safety Institute a Find the stopping distance for a car traveling 40 mph b How fast can you drive if you need to be certain of stopping within 150 ft

oped Book Hint Print erences Hampton Company reports the following information for its recent calendar year Selected Year End Balance Sheet Data Accounts receivable increase 75 000 Inventory decrease 41 000 Salaries payable increase 13 000 7 000 14 000 Income Statement Data Sales Expenses Cost of goods sold Salaries expense Depreciation expense Net income Required Prepare the operating activities section of the statement of cash flows using the indirect method Note Amounts to be deducted should be indicated with a minus sign Statement of Cash Flows partial Cash flows from operating activities indirect method Adjustments to reconcile net income to net cash provided by operating activities Income statement items not affecting cash 6 000 3 000 800 Changes in current operating assets and liabilities

ces a Equipment with a book value of 80 000 and an original cost of 162 000 was sold at a loss of 33 000 b Paid 118 000 cash for a new truck c Sold land costing 315 000 for 405 000 cash yielding a gain of 90 000 d Stock investments were sold for 96 300 cash yielding a gain of 17 000 Use the above information to determine cash flows from investing activities Note Amounts to be deducted should be indicated with a minus sign Statement of Cash Flows partial Cash flows from investing activities

If 12 000 is invested at 4 5 for 30 years find the future value if the interest is compounded the following ways Round your answers to the nearest cent a annually b semiannually c quarterly d monthly e daily N 360 f every minute N 525 600 9 continuously h simple not compounded

A payday loan provides short term loans ranging from 250 to 2 000 Assume the cost of the loan is 1 00 per day per 100 borrowed until the loan is repaid What is the cost of a 650 payday two week loan

0 047619 0 952381 5 1 U1 At least one of the answers above is NOT correct v 1 20 21 21 5 1 and incorrect incorrect Find two vectors and 2 whose sum is 5 1 where is parallel to 5 4 while 72 is perpendicular to 5 4 The first coordinate is incorrect The second coordinate is incorrect The first coordinate is incorrect The second coordinate is incorrect

Convert the credit card rate to the APR Oregon 1 per month 11

Consider the following loan purchase a refrigerator for 1 900 at 15 add on interest for 3 years Give the formula used to approximate the annual percentage rate or APR for an add on loan where r is the annual interest rate as a decimal and N is the number of monthly payments APR Determine the following values for this loan r N Find the APR rounded to the nearest tenth of a percent for the loan 6

Consider the present value of the following achieve 6 000 in three years at 2 5 simple interest Determine the future value A in dollars the annual interest rate r as a decimal and the time t in years A r Find the present value using the present value formula and a calculator Round your answer to the nearest cen th

Consider the amount of simple interest earned 1 000 at 7 for 6 years Give the formula for simple interest where I is the interest in dollars P is the present value in dollars r is the annual interest rate as a decimal and t is the time in years I p r t 100 Determine the following values P 1000 r 0 07 t 6 1000 7 6 100 p r t 100 Calculate the amount of simple interest earned 420 Need Help Read It X Your answer cannot be understood or graded More Information

Consider the total amount that must be repaid on the following note described 8 523 borrowed at 15 5 simple interest for 3 years 125 days Give the future value of simple interest formula where A is the future value in dollars P is the present value in dollars r is the annual interest rate as a decimal and it is the time in yea A Determine the following values for the note For t first enter the total number of full years then enter the remaining days as a fraction of a 360 day year P r t 360 What is the total amount to be repaid Round your answer to the nearest cent

1 point A and B are n x n matrices Check the true statements below A Adding a multiple of one row to another does not affect the determinant of a matrix OB The determinant of A is the product of the pivots in any echelon form U of A multiplied by 1 where r is the number of row interchanges made during row reduction from A to U c If the columns of A are linearly dependent then det A 0 OD det A B det A det B

1 point Let a 3 4 3 and b 2 1 4 Show that there are scalars s and t so that sa tb 8 14 20 You might want to sketch the vectors to get some intuition S II

Find the point P such that v PQ has the components 9 9 25 13 Q 3 4 25 5 P help points

assign6 Problem 20 1 point Let a 8 6 7 and b 3 6 8 be vectors Compute the following vectors b 000 A a b B 0a 000 C a b 0 Dal

Let a Compute det 4 b Use Cramer s rule to solve the following system 1 x2 23 A 1 5 4 25 5 25 5 0 5x2 X3 21 41 25x2 5 3 5x1 25x2 4 5 4

Let A 2 2 11 2 3 2 2 3 a Find the determinant of A det 4 3 b Find the matrix of cofactors of A adj A c Find the adjoint of A A A d Find the inverse of A 00

1 point Let u 5 3 3 3 and 4 1 Find the vector that satisfies 8u v 4x w In this case

Let A 4 1 0 4 7 8 5 3 2 9 8 9 10 7 8 10 K Then tr A and A 1 2

1 point Suppose 3 0 5 and 3 5 3 Then u v u v vu 2u 2u 4v

assign6 Problem 9 1 point A and B are n x n matrices Check the true statements below A If det A is zero then two rows or two columns are the same or a row or a column is zero B If two row interchanges are made in succession then the determinant of the new matrix is equal to the determinant of the original matriz C The determinant of A is the product of the diagonal entries in A D det AT 1 det A

1 point What is the vector between the point 10a 36 and the point 5a 106 Answer

The answer above is NOT correct 1 1 4 0 1 0 0 0 1 A Enter a 3 x 3 skew symmetric matrix A that has entries a12 1 a13 4 and a23 0 1 1 4 0 1 0 0 0 1

If then uu 0 and uu U

Your task is to create your own Carnival Game similar to the Pick Up Ducks game Research the types of games that are played at a Carnival Remember games at a carnival are based on chance not skill Come up with a theme for your Carnival Game and include the amount to play the game and the prizes associated with the game Also the percentage probability of winning a prize should be different do not make all or probabilities equal Class comments

5 60 Present value of a complex stream Don Draper has signed a contract that will pay at the end of year 6 If 8 percent is the appropriate discount rate what is the present him 80 000 at the end of each year for the next 6 years plus an additional 100 000 value of this contract 5 61 Present value of a complex stream Don Dias his retirement

annual payments be repay in five equal annual end of year payments of 10 000 with the first payment to 5 29 Solving for r of an annuity You lend a friend 30 000 which your friend will be received 1 year from now What rate of return does your loan earn

5 26 Future value of an annuity In 10 years you are planning on retiring and buying a house in Oviedo Florida The house you are looking at currently costs 100 000 and is expected to increase in value each year at a rate of 5 percent annually Assuming you can earn 10 percent annually on your investments how much must you invest at the end of each of the next 10 years to be able to buy your dream home when you retire

You can get a car loan with a term of three years at an APR of 6 If you can afford a monthly payment of 330 how much can you borrow Round your answer to the nearest cent

he position of a weight attached to a spring is s t 4 cos 3t What are the frequency and period of the syste

Write as a percent If necessary round to the nearest tenth of a percent 17 4 I X Enter a number orial Learn It Write a decimal or a fraction as a percent

On Friday Charlie starts reading a book with 450 pages and he reads 4 of the pages How many pages does Charlie have left to read

12 of 15 Macmillan R x and S x are rational functions then R x S x is after common factors are canceled also a rational function Suppose the vertical asymptotes of R x are x 1 and x 4 and that the only vertical asymptote of Six is x2 What are the vertical asymptotes of R x S x Give your answer as a comma separated list of equations if needed Express numbers in exact form Use symbolic notation and fractions where needed Enter DNE if fonction has no vertical asymptotes vertical asymptotels of R S

5 complete statement of cash flows using a spreadsheet under the indirect method Note Enter all amounts as positive values Balance sheet debit balance accounts Cash Accounts receivable Inventory Equipment Balance sheet credit balance accounts Accumulated depreciation Equipment Accounts payable Income taxes payable Common stock 2 par value 11116 GOLDEN CORPORATION Spreadsheet for Statement of Cash Flows For Current Year Ended December 31 December 31 Prior Year 115 800 79 000 534 000 307 000 1 035 800 108 000 79 000 29 100 576 000 170 000 Analysis of Changes Debit Credit December 31 Current Year 172 000 172 000

es Required information Cash flows from operating activities FORTEN COMPANY Statement of Cash Flows For Current Year Ended December 31 Adjustments to reconcile net income to net cash provided by operations Income statement items not affecting cash Changes in current assets and current liabilities Cash flows from investing activities 0

In the absence of immunization a certain disease is contracted at an average age a If b percent of the population is immunized at birth then the average age at which the disease is contracted is given by 99a A 100 b We think of a as a constant so A is a function of b Find the vertical asymptote for A Express numbers in exact form Use symbolic notation and fractions where needed Give your answer in terms of b vertical asymptote Wh contracting the dicence