Basic Math Questions and Answers

Question 3 290 54 4 3 209 45 5 6 7 8 9 10 11 12 13 14 15 16 17 6 of 20 Benji has 3 100 in a savings account which earns 7 interest compounded quarterly He made no additional withdrawal deposits What was the amount in the account after two quarters D Save

QUESTIO a Find how many natural numbers under 100 are not divisible by either 2 3 5 or 7 b Use this result to determine how many prime numbers less than 100 there are For the toolbar press ALT F10 PC or ALT FN F10 Mac

Consider the implication Anyone who knows Peter likes him a Translate this into predicate logic Clearly label the necessary predicates b Compute the negation in predicate logic in such a way that no negation precedes a quantification symbol c Give a version of the negation in simple English For the toolbar press ALT F10 PC or ALT FN F10 Mac

Give a closed form expression for the element an of a sequence with initial condition a0 1 and recurrence relation an an 1 n 1 and prove your answer is correct by induction For the toolbar press ALT F10 PC or ALT FN F10 Mac

Define the fibonacci numbers by f 0 0 f 1 1 and then recursively for natural numbers n 2 by f n f n 1 f n 2 a Prove by induction that for n 0 the nth fibonacci number satisfies f n 2n b Asymptotically what does this tell us about the growth of f n with respect to n For the toolbar press ALT F10 PC or ALT FN F10 Mac

Find a general solution y y 8y 10y 0 y t Do not use d D e E i or I as arbitrary constants since these letters already have defined meanings

Solve the given initial value problem y 6y 25y 0 y 0 2 y 0 3 y t

Find a general solution to the following higher order equations a y 5y 6y 12y 0 b y 5y 4y 10y 0 iv c y 5y 4y 0

3 points The equation of the function y x compressed vertically by a factor of 0 25 translated 2 units left and 4 units up and reflected in the x axis

10 4 points Factor Show all your steps a y 81 25x b y 12x 8x 7

8 2 points a Make an example of a quadratic function in standard form b What is the y intercept of your function

Solve the given initial value problem y 3y 2y 0 The solution is y t y 0 1 y 0 52 9199

Determine whether the equation is exact If it is then solve it e 9y 7t dt 8 9e dy 0 For the given equation write out the condition for exactness d dy d et 9y 7t 8 get Select the correct choice below and if necessary fill in the answer box to complete your choice Type expressions using t and y as the variables OA The equation is exact because N t y at t y M dy OB The equation is not exact because M dy t y An implicit solution in the form F t y C is N at t y C where C is an arbitram

1 Use Mathematical Induction to show that when n is an exact power of 2 that the solution to the recurrence relation with base condition is T n 2T 2 2 n T 2 2 T n nlog n

Best of luck on the 80 points required to earn the Bootcamp Certification and begin COMPETING GAME TIME Question 1 Jhulio is evaluating the purchase of a 2 000 square foot 5 unit apartment building in the Bronx A broker just advised him that a nearby building was sold for 800 per square foot implying a 5 cap rate Using the Sales Comp Approach what is the estimated value of the building 1 600 000 O 16 000 000 1 pts 60 000 160 000

The following information applies to the questions displayed below Sanyu Sony started a new business and completed these transactions during December December 1 Sanyu Sony transferred 66 288 cash from a personal savings account to a checking account in the name of Sony Electric in exchange for its common stock December 2 The company paid 1 900 cash for the December rent December 3 The company purchased 13 788 of electrical equipment by paying 5 588 cash and agreeing to pay the 8 200 balance in 30 days December 5 The company purchased supplies by paying 980 cash December 6 The company completed electrical work and immediately collected 1 288 cash for these services December 8 The company purchased 2 598 of office equipment on credit December 15 The company completed electrical work on credit in the amount of 5 100 December 18 The company purchased 480 of supplies on credit December 28 The company paid 2 590 cash for the office equipment purchased on December 8 December 24 The company billed a client 1 000 for electrical work completed the balance is due in 30 days December 28 The company received 5 100 cash for the work completed on December 15 December 29 The company paid the assistant s salary of 1 500 cash for this month December 30 The company paid 570 cash for this month s utility bill December 31 The company paid 950 cash in dividends to the owner sole shareholder Required 1 Enter the amount of each transaction on individual items of the accounting equation Note Enter reductions to account balances with a minus sign Date December 1 December 2 Balance after December 1 and December 2 December 3 Balance after December 3 Cash 0 0 Accounts Receivable 0 0 Assets Supplies 0 0 Office Equipment 0 0 Electrical Equipment B 0 0 Liabilities Accounts Payable 0 0 Common Stock 0 D

ompany manufactures and sells x cellphones per week The weekly price demand and cost equations are given below p 600 0 1x and C x 15 000 130x What price should the company charge for the phones and how many phones should be produced to maximize the weekly revenue What is the maximum weekly revenu company should produce phones each week at a price of und to the nearest cent as needed

The total daily cost in dollars of producing x park benches is given by C x 3125 15x 0 2x A Sketch the graphs of the average cost function and the marginal cost function on the same set of coordinate axes B Find the minimum average cost A Choose the correct graph below A Ay 100 0 0 100 B The minimum average cost is B 100 0 0 100 X O C Ay 100 0 0 100 D Ay 100 0 0 100

GAMES A contestant won two spins of the wheel 100 500 1000 5000 0 0 a Construct a relative frequency table Sum 100 Relative Frequency Sum 2600 2500 3000 200 500 3500 5000 600 5100 Relative Frequency b What is the expected value of two spins 1000 1100 5500 6000 2000 1500 2500 7500 10 000

Explain why I H pital s rule does not apply If the limit exists find it by other means Use co and co when appropriate X 7 lim X 7 x 7 Explain why I H pital s rule does not apply A Although the limit of the denominator is o the limit of the numerator is not B Although the limit of the numerator is 0 the limit of the denominator is not C Although the limit of the denominator is 0 the limit of the numerator is not D Although the limit of the numerator is o the limit of the denominator is not If the limit exists find it by other means Select the correct choice below and if necessary fill in the answer box to complete your choice x 7 lim OA X 7 x 7 Type an exact answer in simplified form B The limit does not exist

Find two numbers whose sum is 23 and whose product is a maximum The two numbers are Simplify your answer Use a comma to separate answers as needed

For the function below find A f x B the partition numbers for f C the critical numbers of f 7 x 8 f x A f x

The network diagram and task times for a project are shown below A Task A1 A2 A3 A4 A5 A 2 A3 Duration days 7 1 4 4 7 A4 What is the early finish time for activity A5 A days

5 Solve for g Graph the solution on a number line 36 20

20 Solve cos x 1 in the interval 0 x 2 A O B C 2 D 0 2

19 Evaluate 1 2 sin 3 using exact values 8 A 1 B 2 2 2 C 1 2 2 20 Solve cos x 1 in the interval 0 x 2 A O B T C 2 D V 230 2 D 0 2

14 The range of y csc 0 is A y ER B 1 y y 1 C 1 y 1 D 1 y 1

Use the trigonometric function y f x 4 sin x 3 2 to solve the following questions from 1 to 8 1 The amplitude of the function y f x is A A 0 B A 1 C A 4 2 The phase shift of the function y f x is A PS 0 I B PS 2 3 The period of the function y f x is A T B T 2 4 The equation of the axis is A y 1 B y 2 5 The y intercept A Y int 3 is C PS B Y int 0 C T 3n C y 1 C Y int 2 6 The x intercept s in the interval 0 x 2 A X int B X int 0 C X int D A 2 2 D PS D T 6T D y 2 D Y int 2 3 2 D X int 7 The solution of the equation f x 2 in the interval 0 x 2 is A x 0 T 3 B x C x x 3 732 D no solution 2 2 8 From the function y sin x and the following transformations except A vertical stretch by 4 B horizontal stretch by 3 C vertical shift down by 2 D horizontal compression by 1 3

9 Which value is a solution to cos x 31 B 275 4 A 2 4 3 10 If tan x 4 A 24 25 C 7 B 25 1 what is cos 2x given that x 31 4 C 25 31 2 4 T D 3 D 2014 25

11 The maximum value of y 4sin x 2 1 A 5 B 4 C 3 radians in degree measure 12 Express A 252 71 5 B 225 C 25 D 4 D 52

You randomly remove one card from a deck to see if it is a heart You place the card back in the deck and repeat the process five times Oa This experiment can be reduced to a binomial experiment Success is a heart failure is not a heart a trial is removing a card and the random variable is the number of hearts n 5 p 0 75 q 0 25 Ob This experiment cannot be reduced to a binomial experiment because the events are not independent The probability of choosing a heart changes after each selection Oc This experiment can be reduced to a binomial experiment Success is a heart failure is not a heart a trial is removing a card and the random variable is the number of hearts n 5 p 0 25 q 0 75 Od This experiment can be reduced to a binomial experiment Success is a heart failure is not a heart a trial is removing a card and the random variable is the number of hearts n 5 p 0 5 q 0 5

5 The y intercept is A Y int 3 B Y int 0 C Y int 2 6 The x intercept s in the interval 0 x 2 A X int T B X int 0 C X int I 2 D Y int 2 D X int 3T 2

3 The period of the function y f x is A T B T 2n 4 The equation of the axis is A y 1 B y 2 C T 3n C y 1 D T 6 D y 2

Project portfolio management office serves as a source of decision making in organizational IT projects True False

HIT strategies must be aligned with organizational strategic planning and the dictate of external environment True False

HIT value analysis should include metrics that will identify the value of the system to the user True False

State restrictions and simplify a x 9 x 4x 4 X x 4 x 6x 9

x 1 2x 3 x 25 2x 13x 15 State restrictios

Knowledge management applications are not cost effective for healthcare organizations True False

A discount clothing store is selling a 70 sport jacket for 10 off the regular price What is the discount rate 14 3

3 1 point The graph of y 2x 6 is shown below 27 Which change in the equation would shift the entire graph to the left Replacing the 2 with a 3 Replacing the 2 with a 1 Replacing the 6 with a 9 Replacing the 6 with a 4

Consider the equation 2 10 t 8 When this equation is solved for t what is the approximate result O t 0 15 t 2 41 t 3 11 t 0 19

The graph of a polynomial function f x is shifted j units to the left and k units up What is the function of the resulting graph Of x k j Of x k j Of x j k Of x 1 k

Let f x x 10x 9x 64 and g x 2x 14x 20 What is the solution to the equation f x g x x 2 and 5 x 7 4 and 3 x 5 and 2 x 3 4 and 7

2 to Problem 3 25 pts Follow the steps to determine the range of acceptable initial diameter of a cylindrical metal bar having a final diameter of 10 cm with at least 65 000 psi in tensile strength 60 000 psi in yield strength and 5 EL in ductility 5 1 What is the range of cold work in CW needed to give at least 60 000 psi in yield strength 2 pts obcw 410 2 What is the range of cold work needed to give at least 65 000 psi in tensile strength 2 pts CWB2 3 Strength psi 100 000 90 000 80 000 70 000 60 000 50 000 40 000 30 000 20 000 10 000 1 4 x100 A6 0 2 1 1 100 106 0 Tensile strength 3 What is the range of cold work needed to give at least 5 EL in ductility 2 pts 010 CW 480 pts 6 90 cw 10 1 1000 1 Ao Do 4 What is the range of cold work needed to meet all requirement for mechanical properties 6 pts 282 w 48 41 23 5 How to correlate the initial and final cross section area of the cylindrical rod to the amount of cold work 5 pts 0 CW Ao Ad Ad 1 Ao x 100 Yield strength Elongation T 20 40 60 80 Percent cold work H 010 au 100 obcw 100 41 Ao Ao Ad Ao 100 6 What is the range of initial diameter should be used to start the cold work process 8 TT 102 DX100 TT 100 90 80 70 60 50 40 30 20 10 100 486 96 01000 100 Ad 40 Ad 0100w A 010080 771 78 54 0100w 1 78 54 2007 100 4 Elongation 4T Do 10 986 90

Select the appropriate vowel for each of these singular nouns Then indicate whether each noun is maschile or femminile 1 2 3 4 5 6 7 8 class 9 citt 10 attor 11 dottoress 12 attric person esam donn caff problem alberg stazion

A soccer team has 20 members The team wants to purchase a mixture of sweatshirts and jackets so that each team member receives either a sweatshirt or a jacket The soccer team spends 816 Each sweatshirt costs 32 and each jacket costs 54 If x represents the number of sweatshirts and y represents the number of jackets which system of equations represents the situation x y 20 32x 54y 816 x y 20 54x 32y 816 x y 20 54x 32y 816 x y 20

The graph of the function m x x 3x 2x 4 has a zero at 1 What are the other zeros of the function A B C D 2 and 2 1 and 4 1 5 1 2 3 1 What does the word zeros refer to 2 What kind of division could you use to break down the equation 3 How could you find the remaining zeros 4 Show work Which answer choice is best

Solve the initial value problem dx 4tx t Int 3 x 1 0 dt The solution is x t

Obtain the general solution to the equation dy y dx X 4x 7 What is an integrating factor for the equation Do not include arbitrary constants in the a H X