Math - Others Questions

force needed to lift the machine that has a weight of 10 kN 3 m 2 m 10 kN A 20 Prob 3 61 cables 1 25 m 1 25 m

X 4 23 V 1 12 Z n x n What is the graphical representation of

Gwen walks the same route home every day and she often finds coins lying on the ground There is a 42 chance that Gwen will find one dime on her way home Gwen walked home 30 times this past month Is it possible to use the normal approximation to the binomial distribution How do you know Assuming she never found more than one dime each day what is the probability she found more than 8 dimes this past month

3 a Consider a game in which you roll a regular eight sided die When you roll an odd number you win double the amount When you roll an even number you lose half the amount How many points would you expect to win or lose per roll

14 Does the following data show inverse variations 810 5 10 20 O C no yes y 13 26 52

11 Which of the following data sets best represents an inverse variation OF 82 80 78 77 I 1 10 1 4 C y 5 12 1 2 5 2 75 y 0 2 4 I 175 10 172 6 170 10 167 16 10 y Y 160

2 Match the type of discrete probability distribution with the correct definition You will not select all options uniform binomial hypergeometric Choices A B C OD each dependent trial can be either success or failure all outcomes are equally likely the waiting time before success occurs each independent trial can be either success or failure

13 Does the following data show inverse variations 2 18 8 7 04 O yes O no 19 15 2 12 16

4 a 2 5 b 15 of the people in a town have hazel eyes A group of 5 people are randomly chosen Create a probability distribution table and graph for the number of people with hazel eyes in the group Show your work for at least one calculation P x P x 0 6 0 5 0 4 0 3 0 2 0 1 0 0 1 Calculate the expected number of people with hazel eyes in the group 2 3 4 5 Xx

5 Does the following data show inverse variations Round to the nearest tenth in your calculations y 89 335 35 493 12 068 3 873 E 1 597 4 02 11 822 36 837 O no O yes

5 a b A hockey team has 23 players on it consisting of 13 forwards 7 defensemen and 3 goalies The team charity golf tournament is coming up and 8 players are required to play Determine the probability that exactly 3 defensemen are chosen to play in the golf tournament Determine the probability that at least one goalie will play in the golf tournament

3 In business there is a formula used to find simple interest on an account The formula is rate x time x principle interest The rate is the percentage rate usually per year and time is in years with principle being the amount of money put into the account originally The interest will be the money earned on the account Determine whether the following statement is true or false Rate and interest are an inverse relationship assuming the remaining variables are kept constant O True O False

1 In business there is a formula used to find simple interest on an account The formula is rate x time x principle interest The rate is the percentage rate usually per year and time is in years with principle being the amount of money put into the account originally The interest will be the money earned on the account If I put 80 into an account offering 3 interest per year how much interest would I earn in three years

A video game company sends out shipments to its various stores with a mean cargo size of 75 games and a standard deviation of 4 8 games What is the probability that a store chosen at random will receive a shipment of between 65 and 85 games assume a normal distribution

1 Identify each of the following as having either a discrete probability distribution D or a continuous probability distribution C the number of red marbles drawn from a bag the height of the students in this room the volume of lemonade Mr Fisher drinks on a hot day the score in a hockey game

x t cos 4 t 2cos 2 t 3 What are the Fourier series coefficients of this signal

1 2 2 F X n 2 2 Which of the following is the double component of signal x d 2 2 2

A biologist has 400 kg of nutrient A 600 kg of nutrient B and 300 kg of nutrient C These nutrients will be used to make 4 types of food whose contents in percent per kilogram of food and whose growth values are shown on the right Set up the initial simplex tableau that would be used to determine how many kilograms of each food should be produced in order to maximize total growth What is the objective function z 100 x 90 x 70 x3 50 x4 Set up the initial simplex tableau for the problem X X2 X4 S1 S2 S3 0 1 0 0 2 0 625 0 125 0 1 0 8 0 25 0 0 70 50 0 0 Type an integer or decimal for each matrix element 0 0 1 X3 0 0 1 400 ABC 0 Growth Value Let x be the number of kilograms of food type P Let x be the number of kilograms of Q Let x3 be the number of kilograms of R and let x4 be the number of kilograms of S 2008 8 P Q R S 0 12 5 87 5 20 62 5 12 5 100 80 25 0 70 50 100 90

ww aw SETS Interpreting Venn diagram cardinalities with Try Again b Your answer is incorrect A drug trial had 407 participants A survey was taken to determine how many had nausea as a side effect and how many had anxiety as a side effect The Venn diagram below shows the results Each number gives the number of participants who fall into that Venn diagram category All participants in the survey Had nausea 88 63 Had anxiety 197 59 a How many of the participants had anxiety 260 participants b How many of the participants had nausea or anxiety or both 222 participants c How many of the participants did not have both nausea and anxiety 344 participants X 3

8 Long term debt sells at par value 9 10 Balance Sheet 11 Assets 12 Cash 13 Account receivable 14 Inventories 15 Plant and equipment net 16 Total assets 17 18 19 20 21 Market value of total debt Market value of common equity Total capital 22 23 Percentage of debt 24 Percentage of common equity 25 Cash Assets Accounts receivable Inventories Total assets 120 240 360 Plant and equipment net 2 160 Yes Open spreadsheet Calculate Paulson s WACC using market value weights Round your answer to two decimal places Do not round your intermediate calculations 2 880 120 00 240 00 360 00 2 160 00 2 880 00 Liabilities And Equity Accounts payable and accruals Short term debt Long term debt Common equity Total liabilities and equity 10 63 1 100 1 707 Liabilities and Equity Accounts payable and accruals Short term debt 2 880 Long term debt Common equity Total liabilities and equity Formulas N A N A N A N A N A 10 00 63 00 1 100 00 1 707 00 2 880 00

Multiply 810 by 086 using the lattice algorithm identity the correct multiplication lattice Choose the correct answer below OA 8 6 1 0 O 6 S 1 OB OD 4 8 2 4 8 8 7 0 4 7 6 4 9 8 8 6 C 8 0 0 0 0 0 0 0 6 2 4 9 1 2 8 4 7 8 7 1 9 9 8 6

Find the slope of the line graphed below 17 5 3 ca He

Find the slope of the line graphed below S 4 en

6 The table shows Aleksei s December budget Fill in the blanks so that Aleksei s budget is balanced Income December 5 pay December 19 pay Total December Income Expenses 180 Phone 205 Save for driver training Save for car Family expenses Spending money Total December Expensos 55 50 100 100

3 Here are the graphs of f x h x and g x on the same coordinate plane f x S b Write an expression for h x in terms of f x 5 h x g x

Use short division to find the quotient and remainder for the division problems given below Check the result a 5 37 858 b 7 6816 a 5 37 858 R Type whole numbers

Boris s class measured the lengths of 9 leaves Draw a line plot for the lengths of the leaves 3 3 1 3 Lengths of leaves in inches 2 1 4 2 3 2 4 3 3 3 3 4 4 4 2 3 4 3 3 4

If one must always move upward or to the right on the grid shown below how many paths are there from A to B B How many paths are there from A to B

To receive full credit you should show all your work 100 points total 1 Define T R R by T the definition of linearity IL T2 T3 0 11 12 I3 Prove that T is linear by using

1 Find the lengths of the circ Assume r 9 and 0 114 S S 0 arc not 33 74 2 How many revolutions will a car wheel of diameter 18 in make as the car travels a distance of one mile Round your answer to the nearest whole number

Use A to decode the cryptogram A 3 3 1 2 2 7 9 4 1 3 19 50 37 33 67 5 2 18 4 1 23 21 25 17

3 Assuming a credit card bank fee of 2 35 of the net sales find the amount deposited into a tax accountant s checking account based on the following credit card transactions Credit Card Sales 125 00 125 00 125 00 179 00 179 00 652 16 673 00 Credit Card Refunds 35 00 25 00

x 3 matrix Find the k values that make the row vectors of the matrix A orthogonal to 3k A k 1 3k 0 5 Answer Solve the question on this paper below and write down your final answer here k each other

artesian product of finite and nonempty sets can be illustrated by the intersections of a crossing line pattern as shown to the right plain why the number of intersection points in the crossing line pattern for AxB is a b where a n A and b n B w the crossing line pattern for 0 A x ch of the lines coming from set A intersects each of the lines coming from set B GENERED

A study shows the following one generation transition probabilities among four major income groups Eldest Son s Income 10 50 0 35 0 5 0 33 0 1 Father s Income Bottom 10 10 50 50 90 Top 10 Bottom 10 0 47 0 07 0 05 0 01 50 90 0 17 0 39 0 48 0 32 Top 10 0 01 0 04 0 14 0 57 In the long term what percentage of male earners would you expect to find in each category Round your answers to two decimal plac bottom 10 10 50 50 90 top 10

Let L be the line through the point Q 1 8 8 and direction vector a 1 2 2 Find the two distinct points R1 and R2 on L at distance 6 2 to the point P 2 1 4 2 R1 0 0 0 R2 0 0 0

The figure to the right shows two line segments L and L The rays through point P give geometrically a one to one correspondence between the points on L and the points on L For example Q Q Complete parts a and b below a Use similar geometric figures to show that two concentric circles are equivalent sets of points Choose the correct answer below OA l 2 OB e RECED 2 OC P 2 O D

The set C contains 2 and 3 and is closed under addition a What whole numbers must be in C b What whole numbers may not be in C c Are there any whole numbers definitely not in C a Choose the correct set below that C must be O O The priime numbers 2 3 5 7 11 13 17 19 1 2 3 6 2 3 4 5 6 2 3 5

According to behavioral finance markets are always O informationally inefficient informationally efficient O semi strong form efficient weak form efficient

measure of one angle is shown in the figure Given k find the measures of the other seven labeled angles

t 1 a b 1 d 171 2 ise 2 f 1 1 sinyali a a dakilerden hangisidir 7 7 777 1 T 2 f t 1 3 3 76 C d 3 e 2f t 1 1 2f 6 1 T 2f t 1 2 t

8 4x f 4 8 t Which of the following is the complex Fourier series representation of the signal

Service Lube oil and filter 5000 Tire rotation and brake 10000 inspection Wheel alignment inspection 25000 Discount Purchase Price Freight Tire Air Tax Deal Review New car MSRP or List Price Gas Fee Gas Tax Administration Fee Cooling system 50000 Tune up and emission 85000 control Automatic transmission 85000 51 175 In the first 3 years that Jill owns her sports car she drives 63 350 kms Jill maintains her vehicle according to the distance maintenance schedule below taking into consideration both kilometres driven and elapsed time The fuel consumption rating for her sports car is 8 3 L 100 km Each year Jill pays 1960 for insurance and 98 for her vehicle license plate registration During those 3 years Jill renews her driver s licence at a cost of 80 The average cost of fuel is 1 06 L Determine Jill s average monthly operating cost during the 3 years Use the table provided see attached to organize your answers Lien Payout Delivery Price MFG Rebate Down Payment Finance Fee Amount Financed 3 6 Taxable Subtotal Interest Rate Trade in Allowance Loan Term Taxable Total 15 Monthly Payment Module 5 Case Study 1 36 95 63 99 24 30 79 95 84 95 165 00

b Your answer is incorrect A county is planning to expand its train service In studying the current service the county planner looked at which train stations are along or not along various train lines The Venn diagram shows this information for three of the lines All county train stations Green Line stations Ulm Quilmes Explanation Blue Line stations Rechock Fes Graz Jena Trento Orange Line stations Metz Volos Warren Radom York Santos Ponce a Select all the train lines that have a stop at Haifa Green Line Orange Line Blue Line b How many stations are only along the Orange Line 7 c Which stations are along all three lines the Green Line the Orange Line and the Blue Line Choose all that apply Bern Graz Fes Ponce Metz Trento Ulm Quilmes Volos Halfa Jena Radom Santos Warren York 5 8

SETS Interpreting a Venn diagram with 3 sets for a real world situation All animals housed Treated by Dr Scott An animal sanctuary houses a variety of animals To understand the workload of the sanctuary s veterinarians the director looked at which types of animals are treated or not treated by various doctors The Venn diagram shows this information for three of the doctors Snakes Elks Frogs Goats Treated by Dr Hall Cats Otters Treated by Dr Torres Pigs Birds Dogs Llamas Horses Koalas Iguanas Turtles Quails a Select all the doctors who treat otters Dr Scott Dr Torres Dr Hall b How many types of animals are treated only by Dr Scott 0 c Which types of animals are treated only by one of the three doctors Dr Scott Dr Torres or Dr Hall Choose all that apply Cats Elks Birds Goats Dogs Iguanas Koalas Otters Quails Snakes Horses Pigs 10 5 Frogs Llamas Turtles Ang

Use formulas to find the area of the figure 4 km 3 km OA 16 km OB 22 km OC 32 km C 11 km 8 km

A certain field is a rectangle with a perimeter of 886 feet The length is 155 feet more than the width Find the width and length of the rectangular field The width is The length is

If construction costs are 157 000 per kilometer find the cost of building the new road in the figure shown to the right The cost of building the new road is Round to the nearest dollar as needed new road 4 000 m 3 000 m

If you drive 5 miles south then make a left turn and drive 12 miles east how far are you in a straight line from your starting point Use the Pythagorean Theorem to solve the problem Use a calculator to find square roots rounding to the nearest tenth as needed O A 13 0 mi O B 2 6 mi O C 10 9 mi D 4 3 mi

Find the requested term Find the 3rd term of the sequence s 1 13n 1 53