Mathematical Reasoning Questions and Answers

Galaxy Virgo Ursa Minor Corona Borealis Bootes Distance 15 200 290 520 Velocity 1600 15 000 24 000 40 000 Data from Acker A and C Jaschek Astronomical Methods and Calculations John Wiley and Sons Karttunen H editor Fundamental Astronomy Springer Verlag The table lists the distances in megaparsecs 1 megaparsec 3 085 x 1024 cm and 1 megaparsec 3 26 million light years and velocities in kilometers per second of four galaxies moving rapidly away from Earth a Does there appear to be a relationship or trend for the data b Find a linear equation in the form y mx that models these data using the points 520 40000 and 0 0 c The galaxy Hydra has a velocity of 60000 km per second How far away to the nearest megaparsec i the galaxy according to the model in part b d The value of m is the Hubble Constant The Hubble Constant can be used to estimate the age of the universe A in years using the formula A 9 5x10 Approximate A using the value of m Round to t nearest hundredth of a billion years

R11 5 Popular kids Who were the popular kids at your elementary school Did they get good grades or have good looks Were they good at sports A study was performed to examine the factors that deter mine social status for children in grades 4 5 and 6 Researchers administered a questionnaire to a random sample of 478 students in these grades One of the questions they asked was What would you most like to do at school make good grades be good at sports or be popular The two way 34 table below summarizes the students responses Goal Grades Popular Sports Gender Female 130 91 30 Male 117 50 60 a Construct an appropriate graph to compare male and female responses Write a few sentences describing the relationship between gender and goals b Is there convincing evidence at the a 0 05 level of an association between gender and goals for elementary school students

Match the appropriate letter beside the words in the word bank with the appropriate statement Word Bank A import s B Export s Your Answer Choice OB A A B OA B B A OA A A B Statement Corn wheat and engineering equipment United States Foreign made goods used in the United States Oil coffee pepper and chocolate United States American made goods sold to other countries

Read these quotations from the excerpt The ground here is muddy and covered in weeds and when I first moved into this house I played here in the dirt paragraph 1 Kneel down in the weeds here This is exactly where I was when I found him I was kneeling just like you are now digging and playing when I made a most incredible discovery paragraph 2 How does the author s use of descriptive language in these quotations affect the reader It captures the narrator s emotional reaction to the discovery It suggests that the backyard is an ideal place to play It places the reader in the moment with the narrator It provides hints to the reader about the narrator s later actions GUEST GUEST How does the author s use of questions in paragraph 3 contribute to the tone of the stor The questions that have no answer contribute to the introspective tone The questions about the narrator s arrival contribute to the cooperative tone The questions about the soldier s lack of fear contribute to the triumphant tone The questions that relate to passing time contribute to the urgent tone

An artisan makes hand crafted painted benches to sell at a craft mall Her weekly revenue and costs not including labor are given in the table Weekly Revenue and Costs for Hand crafted Benches Weekly revenue R dollars 307 872 1365 Number of benches sold each week n 1 3 5 7 9 11 13 1740 1982 1952 b Write the derivative formula for profit Weekly cost C dollars 62 92 115 109 149 174 1709 a Find a quadratic model for revenue Round all numerical values to three decimal places R n dollars 203 Find a cubic model for cost Round all numerical values to three decimal places C n dollars Using the previous models for revenue and cost find a cubic model for profit P Round all numerical values to three decimal places P n dollars

uniform line charge of 16 nC m is located along the e defined by y 3 z 4 a Find E at P 1 2 3 b Find E at that point in the z 0 plane where the direction of E is given by 2 3 ay 1 3 az

Homework Jamie needs a new roof on her hous monthly payments of 656

A tank contains 360 liters of fluid in which 30 grams of salt is dissolved Pure water is then pumped into the tank at a rate of 6 L min the well mixed solution is pumped out at the same rate Find the number A t of grams of salt in the tank at time t 3t A t 400 370e X g

Assignment premium depending on her or his age This table shows the premiums for people between the ages of 20 The Universal Insurance Company sells life insurance For 1 000 000 of insurance a person pays a and 60 For example a person age 30 pays 43 94 per month for their plan which is valid for a 20 year term 1400 1300 35 50 167 06 30 43 94 47 37 Source https www policygenius com life insurance life insurance cost a Use the whole grid below Plot Age horizontally from 0 to 70 years use equal increments Plan your vertical axis such that you have room to extend your curve from 0 to 70 years as well Use your points to draw a smooth curve of best fit Describe the shape of the curve in the space below 1500 12PC 1106 1000 900 800 700 Age Premium LOG Soo 400 300 200 100 20 42 23 25 42 23 S 10 15 25 36 40 Name 40 65 32 90 45 70 75 Age b From the graph not the data table interpolate to estimate the monthly premium for the following ages iii 43 120753 ii 33 i 27 50 iv 52 22000 v 57 280 45 108 15 5 60 65 60 456 42 55 257 14 d What assumption did you make in order to extend your curve in part c c Extend your curve from age 0 to age 70 Extrapolate to estimate the cost of insurance for each age i 61 ii 65 iii 70 iv 10 v 0 newborn 1 1

The graph of a function is given 5 X Determine the average rate of change between the indicated points on the graph

4 19 WP At steady state air at 200 kPa 325 K and mass flow rate of 0 5 kg s enters an insulated duct having differing inlet and exit cross sectional areas The inlet cross sectional area is 6 cm At the duct exit the pressure of the air is 100 kPa and the velocity is 250 m s Neglecting potential energy effects and modeling air as an ideal gas with constant cp 1 008 kJ kg K determine a the velocity of the air at the inlet in m s b the temperature of the air at the exit in K c the exit cross sectional area in cm

4 12 WP As shown in Fig P4 12 air with a volumetric flow rate of 15 000 ft min enters an air handling unit at 35 F 1 atm The air handling unit delivers air at 80 F 1 atm to a duct system with three branches consisting of two 26 in diameter ducts and one 50 in duct The ve locity in each 26 in duct is 10 ft s Assuming ideal gas behavior for the air determine at steady state a the mass flow rate of air entering the air handling unit in lb s b the volumetric flow rate in each 26 in duct in ft min c the velocity in the 50 in duct in ft s ans 20 lb s 2210 ft 3 min 14 6 ft s

The relationship between the number of decibels and the intensity of a sound in watts per square meter is 10 100 10 13 101 Find the difference in loudness between an average office with an intensity of 1 2200 x 10 watt per square meter and a broadcast studio with an intensity of 5 1100 x 10 watt per squan Round your answer to the nearest whole number da

A jar on the desk at a community center contains 1 400 marbles Visitors who guess the number of marbles within 5 of the actual amount receive a discount on activities and merchandise Between what two values must a visitor guess in order to win a discount

Question 13 Multiple Choice Worth 1 points Calculating Net Worth MC The assets and liabilities of a smoothie shop are listed below Owned Inventory Cash Long Term Liabilities Building Mortgage Savings Account Owned Equipment Accounts Receivable Small Business Loan Property Value Other Debt Long Term Investments O 495 120 O 520 120 42 970 545 130 229 682 56 000 110 650 135 327 34 823 10 265 52 495 186 987 If the smoothie shop owner adds 25 000 to the small business loan to cover unexpected equipment repairs what will be the total net worth 25 789 125 000

Budgeting LC A construction worker earns an average bi weekly net pay of 1 764 00 Which compound inequality correctly shows the amount of money t the worker can spend if the monthly budget for food is between 10 and 20 O 176 40 st 352 80 O 352 80 sts 706 50 O 382 20 sts 764 40 O 420 42 sts 573 30

During a war allies sent food and medical kits to help survivors Each food kit helped 6 people and each helped 4 people Each plane could carry no more than 80 000 pounds Each food kit weighed 20 pounds and each medicine kit weighed 10 pounds In addition to the weight constraint on its cargo each plane could carry a total volume of supplies that did not exceed 6000 cubic feet Each food kit was 1 cubic foot and each medical kit also had a volume of 1 cubic foot Assume that those helped by medicine kits were not helped by the food kits and vice versa What was the maximum number of people that could be helped with one plane of supplies The maximum number of people that could be helped was Type a whole number people

5 You were given 1 000 as a graduation present and will invest the full amount in hopes increasing the principal Using the decision making model you learned in Chapter 1 describe how you would make the decision to invest the money A What is the decision that needs to be made B What are the alternatives C What is the best alternative D How can you apply the best alternative E How will you evaluate your solution or decision

16 Percentage of Foreign Bo of foreign born population represented here Find the m the data Do you think the m this set of data Explain 6 5 bottom heavy D

Find the equation of the linear function represented by the table below in slope intercept form X H 2 y 2 0

M 121 P 1 1 What is the finance charge for a 2 year 14 000 loan with a 11 APR Round your ans to the nearest cent Do not include a dollar sign in your answer

3 a Show that and cosh ta r ia 1 i Ta r 1 ia 1 ia sinh ra b Show that a coth ra K a K a where K a K a 1 ia T ia

Quiz 5 3 15 points Consider the following statement All values for c whose distance from 7 is at least 3 that meet this a 5 points Draw a number line below visually represent all values of constraint Clearly label values on your number line C 3 4 10 c 7143 420 410 clo b 5 points Without using absolute values write an equality expression that clearly rep resents all possible values for c c 5 points Using absolute value signs write an inequality expression that clearly represents all possible values for c

2 if answer name Felix 4 elif answer Dog name Fido 6 elif answer Bear name Bob 8 else 10 Variables name Lisa Type the program above identically line per line into the blanks below Use 2 spaces per tab indention level Type the word EMPTY all caps for each empty line Blank 1 Blank 2 Blank 3 Blank 4 Blank 5 Blank 6 Blank 7 N N N A Z A A

The floppy disk drive FDD was invented in 1967 to store information for computer users One model an 8 inch disk and had a radius of 3 95 inches The drive motor would spin at 150 rotations per minute RPM Step 2 of 2 Find the linear speed of a particular point on the circumference of the 8 inch disk in inche per second Round you answer to the nearest hundredth

You and your classmates to raise school In order to pay for the materials you bought to make the abstract paintings you need to sell each of the abstract paintings for 5 00 When transporting the abstract paintings to the auction one of your parents accidentally drops five of the abstract paintings in the street and they are run over by a Community Transit bus What is the new minimum price you need to set for the remaining abstract paintings in order to pay for the materials

A hospital sends an invoice to a patient The patient schedules a payment plan in which she makes an initial payment of 1 451 the first month and then pays one third of the previous month s payment each of the following months until the invoice is paid in full Approximately how much of the invoice will be paid after the fourth month O 1 451 00 O 2 095 89 O 2 149 63

CENGAGE MINDTAP Chapter 13 Aplia Assignment 5 Composing application messages

Attempts Average 3 5 Economic growth and public policy Suppose an American buys stock Issued by an Argentinian corporation The Argentinian firm uses the proceeds from the sale to build a new office complex This is an example of foreign Investment in Argentina Which of the following policies are consistent with the goal of increasing productivity and growth in developing countries Check all that apply Protecting property rights and enforcing contracts Providing tax breaks and patents for firms that pursue research and development in health and sciences Increasing taxes on income from savings Imposing restrictions on foreign ownership of domestic capital In less developed countries what does the term brain drain refer to O The emigration of highly skilled workers to rich countries O Lower productivity due to a malnourished workforce O Rapid population growth that increases the burden on the educational system Rapid population growth that lowers the stock of capital per worker

Solve the given initial value problem y x dy P x y ex y 0 2 where dx P x 0 x 1 x 1 1 1 0 x 1 x 1

Question c The newsprint used to supply the annual needs of 1000 people is 25 100 kg Use this informat in your equation Round to two decimal places if necessary The value of the constant of variation k is 25 10 Alternate Answer The value of the constant of variation k is 25 1 Part 3 4 Part 4 of 4 um parts h and c to find the number of kilograms of newsprint that would be needed to supply a city which has a population

Effects of Adjusting Entries on the Accounting Equation Four adjusting entries are shown below a Wages Expense Wages Payable b Accounts Receivable Service Revenue c Rent Expense Prepaid Rent d Unearned Service Revenue Service Revenue Required 3 320 8 370 2 300 5 230 3 320 8 370 2 300 5 230

3 142 points Skipped eBook Hint Exercise 2 12A Algo Supplies and the financial stateme Pizza Express Incorporated began the Year 2 accounting period with 7 0 earnings Pizza Express was affected by the following accounting events 1 Purchased 13 000 of supplies on account 2 Earned and collected 23 000 of cash revenue 3 Pald 11 500 cash on accounts payable 4 Adjusted the records to reflect the use of supplies A physical count in December 31 Year 2 Required Show the offects of the events on the financial statements using a hor

Preparing and Analyzing Closing Entries At December 31 the ledger of Aulani Company includes the following Earnings 20 000 Interest Expense 3 200 Dividends declared a Required 1 Prepare the closing entries for Aulani at December 31 If an amo

1 1 42 points Skipped Holloway Company earned 4 800 of service revenue on receivable during Year 1 Required Based on this information alone determine the following fo under an accounting equation before satisfying the require a The balance of the accounts receivable that would be re b The amount of net income that would be reported on th c The amount of net cash flow from operating activities th d The amount of retained earnings that would be reported

1 4 next match 15 a Ann entered a raffle at a festival and hopes to win a new TV The odds in favor of winning a new TV are Find the probability of winning a new TV 17 10 X b A sports statistician determined that the probability of a certain rugby team winning its next match is Find the odds against the team winning its S 6 X 0 0 S to 5 Esp

Are you ready for more or serbrug all 1926 2169 8 nevari to ulev gib baik S Jada thinks that the college tuition will increase by 40 each decade Do you agree with Jada Explain your reasoning

5 11 pts First consider what is your context to describe the difference be in this role How do these concepts

UwifadVEZ You have been tasked with collecting 100 pressure transducer to be installed data at an acquisition rate units Hertz

A company estimates that 1 of their products will fail after the original warranty period but within 2 years of the purchase with a replacement cost of 100 If they want to offer a 2 year extended warranty what price should they charge so that they ll break even in other words so the expected value will be O

Mathematics played a crucial role in the development of ancient Greek architecture The Greeks believed that beauty and symmetry were fundamental to architecture and they used mathematical principles to create harmonious designs that embodied these ideals One of the key mathematical concepts used in Greek architecture was the Golden Ratio This ratio also known as the divine proportion is approximately 1 618 and is found in many natural and man made structures The Golden Ratio was used by Greek architects to create buildings that were pleasing to the eye with harmonious proportions that were perceived as beautiful and balanced NDUZ KUNDUZ The Parthenon one of the most famous examples of ancient Greek architecture is a perfect illustration of the use of the Golden Ratio The building s dimensions follow a precise ratio of 9 4 which is very close to the Golden Ratio The columns of the Parthenon also follow a precise mathematical formula with the distance between them being exactly 1 5 times the diameter of each column The use of these precise proportions and measurements gave the Parthenon a sense of balance and symmetry that is still admired and studied today Another mathematical principle used in Greek architecture is the concept of the isosceles triangle This triangle has two sides that are equal in length and it was used by Greek architects to create the sloping sides of roofs and pediments The angle of the isosceles triangle was also important as it had to be precise in order to create a visually pleasing effect The Parthenon for example has a triangular pediment on each end that is filled with detailed sculptures The angle of these pediments was carefully calculated to ensure that they were proportionate to the rest of the building and created a sense of balance and harmony The use of geometry was also important in ancient Greek architecture Architects used geometric shapes such as circles squares and triangles to create patterns and designs that were aesthetically pleasing One of the most famous examples of this is the labyrinth at Knossos on the island of Crete The labyrinth was built in the shape of a complex geometric pattern with a series of interconnected circles and squares that formed a maze like structure The use of geometry in this way created a sense of order and harmony and it is still admired as a masterpiece of ancient engineering In addition to these specific mathematical concepts the Greeks also used general principles of mathematics to design their buildings They used mathematical concepts such as symmetry proportion and harmony to create buildings that were not only functional but also beautiful The Greeks believed that architecture should not only serve a practical purpose but it should also inspire and uplift the human spirit In conclusion mathematics played a crucial role in ancient Greek architecture The use of precise proportions mathematical formulas and geometric shapes created buildings that were not only functional but also aesthetically pleasing The Greeks believed that architecture should embody the ideals of beauty and symmetry and they used mathematics to achieve this goal The Influence of ancient Greek architecture can still be seen today in the buildings and structures that we admire for their beauty and elegance

Form the negation of the stat There is a rainbow Choose the correct answer below OA There is not a rainbow OB There are clouds OC Sometimes there are not rainbows OD There are never rainbows

6 The following table shows fictitious share prices and yields of some companies Symbol TWA PNAA EAL CPQ GEFO STOO RCA STB Company Trans World Airlines Pan American World Airways Eastern Airline Inc Compaq Computers General Foods Corp Standard Oil Radio Corporation of America Studebaker Motor Company Price 27 23 38 30 27 00 6 92 67 33 72 58 60 47 27 18 Yield 3 62 0 12 0 58 0 35 4 0 14 0 61 2 17 You decide to make a small portfolio consisting of four of these compani random a How many possible portfolios of four stocks are possible in which all ha least 0 3 b How many possible five stock portfolios are possible in which three of your portfolio have the property that their price is less than 38 or their 0 3 or both How many possible five stock portfolios are possible in which at lea

Solve the following system of equations 8x 3y 3 6x 5y 5 X 0 010

Problem 4 2 A circular steel rod of diameter d is subjected to a tensile force P 4 0 kN see figure The allowable stresses in tension and shear are 120 MPa and 50 MPa respectively What is the minimum permissible diameter dain of the rod P 4 0 k

Part 3 The wind is not the only factor There are also ocean currents Now calcula part 2 and the ocean currents below in red Using vector addition calcula Month 1 1 square diagonally southwest North America Canada Month 2 1 square diagonally southwest Massachusetts Month 3 1 square west Mont 2 squ south

One disadvantage of having a Traditional Economic System is O Cut off motivation to work hard lacks the potential to generate a surplus of goods O O None of the Above Promotes individual rights

The weekly demand of a slow moving product has the probability mass function shown to the right Find the expected value variance and standard deviation of weekly demand The expected value of weekly demand is Type an integer or a decimal Do not round Demand x Probability f x 0 0 4 1 2 4 or more 6000 NO 0 2 0 3 01 0 0

Problem 2 Renaldo joined a holiday savings club at the neighborhood bank He set aside 10 per week for an eight month period of time this special savings account earned 5 interest compounded weekly How much money did Renaldo have at the end of the 32 weeks Express your approximate answer as currency in dollars and cents with dollar sign For the fraction of a year use 32 out of 52 weeks

The following data show spot speeds collected at a section of highway located in a residential area before and after an increase in speed enforcement activities All speeds are in mi h After Before 27 41 31 31 27 40 Before 44 33 40 41 31 32 32 33 37 44 31 37 www 40 34 42 Before mean speed standard deviation 35 36 27 26 26 85th percentile speed percentage exceeding limit 35 22 22 25 26 37 After mean speed standard deviation 85th percentile speed 30 33 34 39 38 32 34 36 27 36 38 29 29 After 201 17 35 33 29 21 31 19 Using the student s t test determine whether there was a statistically significant difference in the average speeds at a significance level of a 0 05 the 95 percent confidence level OYes there was a statistically significant difference in the average speeds O No there was not a statistically significant difference in the average speeds 24 30 Also report for both the before and after cases the mean speed standard deviation 85th percentile speed and percentage of traffic exceeding the posted speed limit of 30 mi h Enter all speeds and standard deviations in mi h Round your 85th percentile speeds to at least the nearest Integer 16 20 33 28 33 mi h mi h mi h mi h mi h mi h