Permutations and Combinations Questions and Answers

8 Prove by induction that S 1 23 n 1 2 n 3 24

TB MC Qu 07 45 Static Hoff Company uses the allo Hoff Company uses the allowance method An account that had bee the receivable affect the elements of the financial statements when

1 point Find all rational zeros of the polynomial Its rational zeros are P x 42 182 62 18z 10 23 with a Say S3 SA Note If the polynomial has o ly three rational zeros input them at 2 2 and input them at a and if the polynomial has only one rational zero input it at a and 3 If the polynomial has only two rational zeros

1 Solve the equation over the interval 0 2 2 sin x sin x 1 2 Solve the equation over the interval 0 360 1 2 sin 20 0

A cell phone company charges 42 per month of service The cost of a new cell phone plus 8 months of service is 415 99 How much does it cost to buy a new cell phone and 3 months of service

You invest 40 000 to start a nacho stand in a shopping mall You can make each basket of nachos for 0 70 How many baskets must you sell before your average cost per basket is 1 50

8 Lucia and John will work together to make 60 paper flowers for a school party The line shown represents the possible combinations of time in hours spent by Lucia and John to fulfill this task Time spent by Lucia hours 12 10 A 4 B 5 C 12 D 15 8 6 4 2 0 02 4 6 8 10 12 14 16 Time spent by John hours X According to the graph on average how many paper flowers will Lucia make per hour

A bag contains red green and blue marbles One sixth of the marbles are red there are as many blue marbles as green marbles 1 4 and there are 24 fewer red marbles than green marbles Determine the number of marbles in the bag in these two approaches a Use algebraic reasoning i e introduce variables form equations and then solve the equations b Use the set model of fractions labeling a Venn diagram

Give the domain of r x x 16 in interval notation

Note In order to get credit for this p Problem 4 1 point The expression In x 2 ln t 1

g csc E14 j sin 7 6 TC CF 2 m sec 117 12 h sec k cos n csc 7tt 4 570 i cot 1 tan 5T 6 25m 3 o cot T

1 Let A 2 4 6 8 B 3 5 7 9 11 find An B A 3 4 5 6 7 8 9 10 11 B 2 3 4 5 6 7 8 9 11 C 4 5 6 7 11 D o A and B are disjoint sets

2 The ISO Personal Auto Policy does not allow which means that the limits of multiple vehicles covered on a policy can not be added together to increase the limit availability for a loss A Combined single limits B Split limits C Stacking limits D None of the above

The cost of legal defense like Lawyers and Court Fees is paid the policy limits A As a part of B As a portion of C In addition to D None of the above

6 There is no liability coverage for ownership maintenance or use of A Motorcycles B Three wheeled vehicles C Mopeds D All of the above E None of the above

14 There is an exclusion that removes liability coverage for a vehicle that is also capable of flight A True B False

Find the number to add to x 18x to make it perfect square trinomial Write that trinomial as the square of a binomial O add 81 x 9 O add 324 x 18 O add 18 x 9 O add 36 x 18

3 A mother has 7 children What is the probability that she has a All girls 128 b The first child is a girl and the rest are boys c One girl 7 d At least one boy in those 8 births

Expand the expression r t 4 using the binomial theorem

26 What are the factors of 64x3 8y Box final answer

C 1 A C A 2 Simplify 5 3x 2 3x 10 15x 10 Simplify 2x 2x 3 4x 3 4x 6x x 2 x 3 x2 5x 6 x2 5x 5 B D B D B 15x 10 D 3x 10 x 3 4x 6 x x 6 x 6x

ey inter pt 2 y 2 5 3 5 AY 1 A O 5 244 Co y intercept

Use a number line to find the LCM 3 3 a 3 6 b 4 7 c 2 5 Need Help 0 4 2 Read It 4

Identify the period and determine where two asymptotes occur for the function 30 5 y tan

A B X 80 0 1 2 f x f x 49 0 2 The table above gives selected values for a differentiable and decreasing function fand its derivative If f is the inverse function of f what is the value of 2 8 1 80

Factor out a Greatest Common Factor GCF 15x 20y 12y 21y

Ex x 2 x 6 Ex x 3 6 t x 1 x 2 X x 2 10 x x 6

Three children go to the ice cream store that serves 34 flavors In how many different ways can the children be served one di ice cream each if the following is true a Each child receives a different flavor ways b The same flavor can be served to more than 1 child ways

Question 2 25 points Solve the equation for x 2x 6 30 x 288 Ox 2 3 O O No Solution Question 3 25 points Completely solve the following equation for x X O x 0 O 4x 4 x 4 x 1 4 x 2 x 2 X

Graph of the Week 7 March 3 Analyze the graphs below and write a reflection on what you think the graph is communicating to you To guide you with your response start with some observations What is the topic of the graph What surprises you about the graph What do you wonder What are some observations that you can make based on the graph What do you foresee happening in the next 10 years Costs to Raise a Child in 2022 Estimated expenses to raise a child from birth to age 17 in the U S Housing Food CHM Came Education Tansportation Healthcare Clothing AN 18 52 343 Bend mamed couple with two children and an average 104 127 belove n 76 346 723 14 141 002 45 531 282 7 20 441 12 521 21 SALASS Total 292 017 Source US Department of Agriculture s Expenditures on Chlten by Familles 2015 30 000 Future costs of raising a child A new USDA report found that parents in each Income bracket will spend vastly different sums of money each year as their children grow from infance to age 17 This chart shows the estimated annual cost of raising a child bore 2015 for married parents in each income group 20 000 Questions to ask when reading graphs 10 000 Is there an upward or downward trendi Are there any sudden spikes in the graph What is being compared in the graph What prediction can I make for the future What inferences can I make about the graph 454 770 total for parents making more than 107 4 284 570 total for parents mak 50 200 to 10 212 300 tota for parents mal less than 50

Question 4 20 points Which function has a domain of x 3 g x x 3 g x x 3 g x x 3 g x x 3 Question 5 20 points Consider the two functions below Function 1 f x 5 4 3 15 S et 31 2 11 2 31 4 st f x 1 2 3 4 5 24 Function 2 g x g x 4 x 3 2

Question 3 1 point How could you restrict the domain of f x 6 x 4 2 5 to make it s inverse a function

A class of 24 students wants to choose 3 stud set of 3 students should have an equal chanc will result in a fair decision 1 t

You toss a fair coin 3 times Let Eo Event that the outcome is an even number of heads and an even number of tails note that 0 is an even number E Event that the outcome is an even number of heads and an odd number of tails E2 Event that the outcome is an odd number of heads and an even number of tails E3 Event that the outcome is an odd number of heads and an odd number of tails Q Fill in the following probability distribution table and press Check Event Probability Eo E1 Check Clear Help E2 E3 phobility that either the outcome is an even number of heads and an odd number of tails or the outcome is an odd number of heads and an even number of tails is

INTERACTIVE Tower of Hanoi The Tower of Hanoi is a mathematical puzzle that has inspired many myths about its origins one version priests were tasked with solving this puzzle using 64 disks and when the puzzle was completed the world would end Explore this classic puzzle to see what patterns you can discover 1 Complete the puzzle using 3 disks Try to complete it in the minimum number of moves possible 7 2 Complete the puzzle using 4 disks and then 5 disks Record any observations below like how many moves you took or what patterns you noticed 3 Patrice says she used the solution for 3 discs to help her solve the puzzle for 4 discs How coul

ar bu Benjamin s Backpacks can sell backpacks for 34 per backpa per backpack a Write the cost and revenue equations Granh both equations for 0 to 50 backpacks on the same ir of backpacks Benja

Which of the slopes below represents a line that is parallel to the line y 5x 2 Om Om 1 Om 5 Om 5

Complete the expansion of 2 5y 3 Use before exponents x2 would be written as x 2 Step 1 Determine the binomial coefficients from row 3 of Pascal s Triangle 1 Step 2 Write each a term and each b term in parenthesis after the coefficients 1 2 5y 3 2 5y Step 3 Assign exponents to each term Step 4 Simplify each term 3 2 5y 2

Expand the binomial 5 3y 3 For the toolbar press ALT F10 PC or ALT FF BIUS Paragraph

54 R Byron opened a new bank account and immediately started depositing d dollars per week He also withdrew w dollars per week to pay expenses The total amount of money in the account M after n weeks is represented b the equation M nd nw Which of the following is a factor of M Ad w Bn w d n

Part A Your grandmother opened an account when you were born with 1000 The account earns 3 interest compounded quarterly How much money will be in the account when you turn 18 Part B You had a part time job when you were 16 and saved all the money you made 1500 You put those earnings in an account earning simple interest at a rate of 2 5 How much will the account be worth 2 years later when you are 18 Part C You decided to buy at car using all of this money you have saved but realize you will still need to borrow 5000 If you get a standard loan using an APR of 4 for 5 years how much will your nonthly payment be on the loan h will you end up repaying after the 5 years if you pay the exact monthly payment you have paid in interest

1 Factor Completely x 8x 4x 32 2 Factor Completely 2q 9q 18q

Simplify the expression 64x10yz mplify the expression 16x4y8 Write the radical in simplest form 120 Write the radical in simplest form 72 on enominator by m rom the denom

Graph the solution set of the inequality where x i x 6 3

solving the equation 7x 9 x 39 If sh sent the final step

D Graph the solution set of the inequality where 4 x 2 Choose the graph of 4 x 2

Find the probability of exactly four successes in five trials of a binomial experiment in which the probability of success is 40 p

From inspecting the density histogram a student concludes that 33 of all statistics students in the United States work less than 5 hours per week What would you tell the student

The late fee for library books is 2 00 plus 154 each day for a book that is late If Maria s fee for a late book was 53 20 write and solve a linear equation to find how many days late the book was

Question 1 of 7 Step 1 of 1 Four scenarios of statistical studies are given below Answer The average finish time for the Ironman Kona was time of 4 14