Permutations and Combinations Questions and Answers

Identify the end behavior of the polynomial function x 2x 9 Hint It may help to graph the polynomial function with your calculator first As x decreases the function f x increases As x increases the function f x increases As x decreases the function f x increases As x increases the function f x decreases As x decreases the function f x decreases As x increases the function f x increases As x decreases the function f x decreases As x increases the function f x decreases

Factor the following polynomial by grouping T 3x 3x 9 Which of the below is a factor of the polynomial x 3 0 x 9 x 3 x 9

The following polynomial identity is commonly used to create Pythagorean Triples x y 2x x y What would be the Pythagorean triple created using the identity and x 4 and y 1 5 12 13 6 8 10 7 24 25 8 15 17

Simplify the expression 5x 3x Evaluate using properties of exp 16 2

Rationalize the denominator 13 2 7 13 2 7 Simplif

Which of the below is a factor of a 64 a 4 a 8 a 4a 8 a 4a 16

Determine whether the following relation represents a function Give the domain and range for the relation 1 3 2 5 9 9 5 5 Does the given relation represent a function OYes O No What is the domain Use a comma to separate answers as needed What is the range Use a comma to separate answers as needed ww

Rationalize the denominator 0 Use sqrt to input a square root into WeBWorl For example sqrt 5 to represent 5

Find the open interval s where the following function

circle with an equation of x 2 4x y 2 2y 4 then plot any point on the circle To draw a circle fir

A slot machine has 3 dials Each dial has 40 positions two of which are Jackpot To win the jackpot all three dials must be in the Jackpot position Assuming each play spins the dials and stops each independently and randomly what are the odds of one play winning the jackpot B 1 40 1 X 3 40 1 1 X 40 40 1 X 20 20 20 8000 1 1 1 1 X X 3 3 3 27 1 1 X 3 40 X 1 64000 3 9 0 0000156 0 00156 0 037 3 7 61000 0 000125 0 0125 10 Points 0 00014 0 014

Rectangle ABCD has a width of 5 units and a length of 6 units Use point A located at 2 2 to construct rectangle ABCD

TOTIC CE LIVOLUTION Question 4

Fill in the blanks with the an appropriate a When converting from gallons to liters b When converting from liters to gallons

Price dollars 160 120 80 40 0 120 8 Quantity According to the figure above the total cost of producing 5 units is 24 40 2 80 3 5

The points on the graph show the population data in millions of the state of Florida for each decade from 1900 to 2000 The data are modeled by the function P x 506975 1 43 shown on the graph What is the domain of the graph of P x that is shown A B x 0 1900 x 2000

Read this excerpt from the prologue of Shakespeare s play Henry V in which King Henry is referred to as Harry A kingdom for a stage princes to act And monarchs to behold the swelling scene Then should the warlike Harry like himself Assume the port of Mars and at his heels Leash d in like hounds should famine sword and fire Crouch for employment Which best describes the purpose of this excerpt of the prologue OIt predicts what will happen to Henry at the end OIt states the conflict that occurs at the end of the play It introduces the characters of Henry s enemies OIt builds suspense about the war in the play

For Gundy Company units to be produced are 5 290 in quarter 1 and 6 200 in quarter 2 It takes 1 5 hours to make a finished unit and the expected hourly wage rate is 15 per hour Prepare a direct labor budget by quarters for the 6 months ending June 30 2020 GUNDY COMPANY Direct Labor Budget 1 Quarter 2 Six Montl

aw a rough graph of the polynomial function Use degree end behavior and zeros bounce or cross to help f x x 2 x 1 x 3 O 54 VA it W O O 4 3 2 1 543 wi S

Show the end behavior using directed arrows 7 g x 5 Off OH ON OM 2 37 2

Approximate the area of a circle with the gi round the result to the tenths place Use t r 2 5 m

cost dollars 250 200 150 100 50 a 1 2 3 5 6 3 4 or the time hours How much does A Plus Plumbing cost for each hour of work and what is the one time fee Explain or show your reasoning

Federal Income Taxes and Piecewise Functions MC The piecewise function represents the amount of taxes owed f x as a function of the taxable income x Use the marginal tax rate chart or the piecewise function to answer the questions Tax Bracket Marginal Tax Rate 0 10 275 10 10 276 41 175 12 41 176 89 075 22 89 076 170 050 24 170 051 215 950 32 215 951 539 900 35 37 539 901 0 10x x 10 275 10 276 x 41 175 41 176 x 89 075 89 076 x 170 050 0 32x 9 070 32 170 051 x 215 950 0 35x 26 187 32 215 951 x 539 900 0 37x 36 985 67 x2 539 901 0 12x 205 50 0 22x 4 323 00 f x 0 24x 6 105 50 Part A Using the method of your choice demonstrate how to calculate the amount of taxes owed on a taxable income of 31 000 Show all work 4 points 1 Part B Using the taxes owed from part A determine the effective tax rate Show all work 4 points Part C Compare the piecewise function to the marginal tax rate chart How is the marginal tax rate chart represented in the piecewise function 2 points

Ms Suzuki invested 36 000 in two accounts one yielding 6 interest and the other yielding 8 If she received a total of 2 540 in interest at the end of the year how much did she invest in each account The amount invested at 6 was COS

Select one At a school play children s tickets c cost 3 each and adult tickets a cost 7 each The total amount of money earned from ticket sales is 210 Write an equation that represents this algebraically Oa 210 7 3 c O a 7 3c Oc 7a 3 O210 3c 7a

12 24 6 al f 15 18 21 3 Question 14 4 points Solve the rational inequality 3x X 4 O 52 xs 8 orx 4 8 x 4 0 20 67 No Solution Question 15 4 points Consider the function f x X 2 x 6 x 0 x 2 x 3 find the vertical asymptote 57 H Question 16 4 points Identify any horizontal asymptotes of the function f x x 4x 4x 52 t

Previous the enhanced profitability tha responsible activities Previous In supplying private label footwear to chain retailers the sizes of a company s margins direct costs as reported on p 6 of each issue of the FIR should be viewed as Question 2 how much the company received from each pair of private label footwear sold that cam used to help cover the company s dividend payments how many dollars the company earned from each pair of private label footwear sold could in turn be allocated to a helping pay the company s administrative expenses interest costs and 2 boosting the company s pretax profits how much the company received from each pair of private label footwear sold that can the be applied to helping pay the company s marketing expenses warehouse expenses a administrative costs which boosts the profit margins on branded footwear sales the net profit a company earned on each pair of private label footwear sold how much the company received from each pair of private label footwear sold over a above materials costs and direct labor costs those dollars can be used to cover supervision costs plant maintenance costs and plant depreciation none of allocated to the costs of producing private label footwear and supplying it to chain retalers Previous Question 3 Next The most attractive way to reduce or eliminate the impact of paying tariffs on pairs imported to an company s distribution warehouse in Latin America is to raise the company s selling price of footwear in Latin America by the full amount of the tariff and pass all tariff costs along to the Latin American purchasers of the company s footwear this strategy has the advantage of completely eliminating the company s exposure to import tariffs in Latin America build a plant in Latin America and then expand its capacity as may be needed so that the plant has the capability to supply all or at least most of the pairs the company intends to try to sell in Latin America lower the S Q rating on all pairs sold in Latin America no tariffs have to be paid on branded footwear having an S Q rating of 3 stars or below pursue a strategy of selling fewer pairs in Latin America than rival companies which will them keep the company s costs for import tariffs lower than those of rivals and give the company a low tariff cost advantage on its sales in Latin America lower the company s selling prices of pairs sold in Latin America to levels low enough to escape having to pay the import tariff Next

You have an equally likely chance of choosing any integer 1 through 50 Match each of the given events with the correct probability An even number is chosen A number less than 35 is chosen A perfect square is chosen Choose Choose Choose Choose 17 25

If you toss a coin 60 times and you end up with 40 heads the experimental probability of getting a head is 0 66 True False

Three volunteers are chosen at random from a group of 12 to help at a summer camp a What is the probability that you your brother and your friend are chosen Express your answer as a fraction in simplest form The probability is b The first person chosen will be a counselor the second will be a lifeguard and the third will be a cook What is the probability that you are the cook your brother is the lifeguard and your friend is the counselor Express your answer as a fraction in simplest form

19 There are 62 miles in one kilometer How many miles are there in eight kilometers

Solve the following by FACTORING and using the ZERO PRODUCT PROPERTY X 46 40 0 x 10 4 X 8 5 X 10 4

Solve for the unknown by using the quadratic formula 3 x 8X 5 0 4 2x 3x 6 0

Part I Imagine you are hired to consult on different types of organizational structures for a mid sized company with 135 employees In 3 5 sentences describe the company the company product and or service industry and geographical service area Be creative this is a very flexible assignment designed to allow you to select any type of product or service industry that you would like to explore Choose a company that would work well with this scenario and learning activity Refer to the information of Chapter 7 of Introduction to Business for more information on organizational structures before you begin Part II Begin by briefly explaining the following structures 1 Traditional departmentalization 2 Matrix 3 Committee and 4 Team based Part III Compare the advantages and disadvantages for each organizational structure and identify which structure you recommend for their specific business Be sure your answer refers to their specific product and or service industry the

4 The peanut butter manufacturers are expecting an unusually large peanut crop this year This will cause the supply of peanut butter to What determinant of supply causes this change Which way will the supply curve shift A Shifts Left Price per Can B 400 500 Quantity Copyright www economicsonline co uk Per week D1 A Shifts Left Price per Can 400 D 500 D1 B Stays the Same Price Quantity 500 700 Supply Price 5 The peanut butter manufacturers are all buying equipment that can make peanut butter two times faster than before This will cause the supply of peanut butter to What determinant of supply causes this change way will the supply curve shift B Stays the Same Quantity 500 700 C Shifts Right Supply QI Quantity 02 C Shifts Right 51 www sp g 02 52 Which 52

directly upward at 64 feet per second f t s from a plat high Its height is represented by the equation s t 16t 2 64t 80 What will be the object s maximum height

In an experiment where a pair of indistinguishable dice is thrown and the numbers facing up are multiplied the sample space 2 3 4 5 6 7 8 9 10 11 12 The set of all integers from 1 to 36 36 13 A 1 2 3 4 5 6 C E G 1 2 3 4 5 6 4 6 8 9 10 12 15 16 18 20 24 25 30 36 11 21 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6 B D F H 1 1 1 2 1 3 1 4 1 5 1 6 2 2 2 3 2 4 2 5 2 6 3 3 3 4 3 5 3 6 4 4 4 5 4 6 5 5 5 6 6 6

Let E be the event that the sum of the numbers is odd The event E is A C 1 1 3 1 5 1 2 2 1 3 3 3 2 4 4 2 4 4 5 3 1 5 3 5 5 5 2 6 2 2 2 4 2 6 4 2 4 4 4 6 6 2 6 4 6 6 4 6 6 2 6 4 6 6 B D 1 1 1 3 1 5 3 1 3 3 3 5 5 1 5 3 5 5 2 1 4 1 6 1 1 2 1 4 3 2 2 3 4 3 3 4 6 3 2 5 4 5 1 6 5 2 5 4 5 6 6 5 3 6

Approximate the definite integral using the Trapezoidal Rule and Simpson s Rule with n 4 Compare these results with the approximation of the integral usin graphing utility Round your answers to four decimal places 8 1 x dx Trapezoidal Rule n 4 Simpson s Rule n 4 Graphing Utility

Hawkes Learning Home CODECIMUNITAT Use the graphs below to compare the heights of the San Antonio S 72 Question M Heights of San Antonio Spurs ba Gu Forw 74 Cen 76 78 80 82 8 Player heights inches

4 The value of a collectible toy is increasing exponentially The two po graph show the toy s initial value and its value 3 weeks afterward Value in Dollars 40 2 30 20 10 3 10 0 5 1 2 3 4 5 6 7 8 9 10 Weeks Since Purchase t 1 Express the toy s value t in dollars as a function of time w in weeks after purchase 3 so Write an expression to represent the toy s value 10 days after purchase

Choose the two statements that are true about the rational function f x O There is no horizontal asymptote O There is no vertical asymptote O The vertical asymptote is x 0 O The horizontal asymptote is y O The function is undefined at x 4 x 4 3x 12x

Simplify X x 7 2 10 Rubric 2 Show all work for full credit 7x 14 1 point for correct answer 1 points for appropriate work

Determine which of the following vector spaces are isomorphic to one another M24 RS P1 M22 R P3 P4

Consider the curve given by the equation xy 3 cos y 2 a Find the slope of the tangent line to the curve at 1 Answer M b Find an equation of the tangent line to curve at 1 21 M

Evaluate without using a calculator Write undefined or imaginary if your result is not a rea number a a b a5 c Va d

Simplify the following expression Write your answer using positive exponents only m 1 2 1 n 4 5 10

10 12 ERROR ANALYSIS correct answer in each case a x x x8 6w5 2v w6 x y Explain the error in each simplification below What is the c x x x b x4 x9 11 3m m n 5m n 13 3x 3 6x

Maximize p 5x 5y 5z 5w subject to x y z 3 y z w 4 X Z W 5 x y w 6 x 0 y 0 z 0 w 0 p x y z w

1 cu decimetre is the same as litrola