Basic Math Questions and Answers

1 What technique or steps would you use to factor the expression 4a2 56ab 196b2 Factor as much as possible and explain how you approched this problem 2 Caleb was factori 2

ok mt inces For each of the following products and services indicate whether it is more likely produced in a process operation or in a job order operation 1 Custom tailored dresses 2 Lawn chairs 3 Solar panels 4 Custom home 5 Golf balls 6 Bolts and nuts 7 Football fields 8 Paint cans 9 Headphones Chec

Liquid leaked from a damaged tank at a rate of r t liters per hour The rate decreased as time passed and values of the rate at five hour time intervals are shown in the table t hr r t L h 0 5 10 15 20 25 Find lower and upper estimates for the total amount of liquid that leaked out of the tank in the first 25 hours lower estimate upper estimate Question Help Video liters 9 4 8 6 7 9 7 3 6 7 6 2 liters

5 Provide both the equation and a sketch of the requested function Draw two full periods in your sketch Be sure to label your sketch appropriately so it can be verified to be a sketch of your equation Provide a secant or cosecant function that goes through the point r 4 2

30 Points Jy A 60 ft diameter circular tank foundation carrying a uniform load of 2 000 psf is applied to the ground surface Find the vertical stress due to the foundation load at a depth of 30 ft below the ground surface at the a Tank center b Tank edge SHOW ALL CALCULATIONS

a The depth D of water around a boat in a tidal bay in feet is given by 8 D C 5 sin t where the time t is measured in hours since midnight Find the period of the tide ANSWER What is the depth of the water when it is shallowest ANSWER Find one time when the water is shallowest ANSWER What is the depth of the water when it is deepest ANSWER Find one time when the water is deepest

percent rate of return 8 14 Measuring growth Given that a firm s return on equity is 18 percent and man agement plans to retain 40 percent of earnings for investment purposes what will be the firm s growth rate 8 15 Common stock valuation San

8 13 Common stock valuation Herrera Motor Inc paid a 3 50 dividend last year At a constant growth rate of 5 percent what is the value of the common stock if the investors require a 20 percent rate of return

he stock 8 5 Preferred stock valuation Calculate the value of a preferred stock that pays a dividend of 6 per share if your required rate of return is 12 percent 8 6 Preferred stock valuation You an

3 A company retains 60 of its profits The Return on Equity is 15 What is the growth rate of the earnings

2 a e d b ANSWER Use trigonometric identities to find all trigonometric functions of the angle a arccot that cos a 0 Find cota Find tan a ANSWER Find seca ANSWER Find cos a ANSWER Find sin a ANSWER Find csc such 001 2012

Suppose that the breaking strength of a rope in pounds is normally distributed with a mean of 100 pounds and a standard deviation of 15 What is the probability that a certain rope will break before being subjected to 110 pounds You may need to use the standard normal distribution table Round your answer to four decimal places

A normal distribution has a mean of 85 8 and a standard deviation of 4 85 Find the data value corresponding to the value of z given Enter your answer to four decimal places Z 0 95

A normal distribution has a mean of 85 3 and a standard deviation of 4 85 Find the data value corresponding to the value of z given Enter your answer to four decimal places Z 2 65

Suppose that people s heights in centimeters are normally distributed with a mean of 170 and a standard deviation of 5 We find the heights of 80 people You may need to use the standard normal distribution table Round your answers to the nearest whole number a How many would you expect to be between 170 and 180 cm tall people b How many would you expect to be taller than 178 cm people

What percent of the total population is found between the mean and the z score given Use the standard normal distribution table and enter your answer to two decimal places Z 0 70

What percent of the total population is found between the mean and the z score given Use the standard normal distribution table and enter your answer to two decimal places z 3 44 50 X

Question 10 y 3 Find a formula for the exponential function passing through the points 2 25 and 3 375

What percent of the total population is found between the mean and the z score given Use the standard normal distribution table and enter your answer to two decimal places z 3 44

Consider the following scatter diagrams Match a possible r to each graph a Strong positive correlation b Strong negative correlation Graph a Select Graph by Select Graph c Select y Graph d Select Graph e Select Graph f Select x d Positive correlation 0000000000 e Perfect negative norralation c Negative correlation f No correlation

Question 9 An exponential function f x ab passes through the points 0 7000 and 3 1512 What are the values of a and b a b Question Help Video

Question 8 An exponential function f x ab passes through the points 0 12 and 3 768 What are the values of a and be Q b Question Help Video

X a is used to denote the cutoff between results attributed to chance and results attributed to significant differences

Find the mean the median and the mode of the following scores If an answer does not exist enter DNE mean median mode Test Score 90 80 70 60 50 Frequency 1 7 9 8 5

Answer the following questions about the numbers 217 837 217 838 217 839 217 840 and 217 841 a What is the mean b What is the standard deviation Round your answer to two decimal places

Tent Master produces Pup tents and Pop up tents The company budgets 318 000 of overhead cost and 53 000 direct labor hours Additional information follows Per Unit Pup tent Pop up tent Selling Price Direct Materials 24 27 88 83 Required 1 Compute a single plantwide overhead rate assuming the company allocates overhead cost based on 53 000 direct labor hours 2 Pup tents use 4 direct labor hours DLH per unit and Pop up tents use 3 direct labor hours per unit Compute the overhead cost per unit for each product Pup tent Direct Labor 49 31 3 Compute the product cost per unit for each product 4 For each product compute the gross profit per unit selling price per unit minus the product cost per unit Complete this question by entering your answers in the tabs below Required 1 Required 2 Required 3 Pup tents use 4 direct labor hours DLH per unit and Pop up tents use 3 direct labor hours per unit Compute the overhead cost per unit for each product Required 4 Plantwide Overhead Rate Direct Labor Hours per Unit Overhead Cost per Unit per unit my wor

ok t ces Hydro Sports budgets overhead cost of 570 000 for the year of this amount 304 000 is traceable to the Assembly department and 266 000 is traceable to the Finishing department The company manufactures two types of jet skis standard and deluxe Budgeted direct labor hours for the standard model are 7 in Assembly and 1 in Finishing Budgeted direct labor hours for the deluxe model are 9 in Assembly and 3 in Finishing The company budgets production of 190 units of the standard model and 190 units of the deluxe model for the year 1 Compute each department s total number of budgeted direct labor hours for the year 2 Compute departmental overhead rates for each department using direct labor hours for that department 3 Compute overhead cost per unit for each model using departmental overhead rates Actual direct labor hours for the standard model are 7 in Assembly and 1 in Finishing Actual direct labor hours for the deluxe model are 9 in Assembly and 3 in Finishing Complete this question by entering your answers in the tabs below Required 1 Required 2 Compute each department s total number of budgeted direct labor hours for the year Finishing Department Assembly Department DLHS per Unit Total Hours DLHS per Unit Total Hours Standard Deluxe Totals Check my work Required 3 Number of Units

3 S Book Print erences Wess Company has limited capacity and can produce either its standard product or its deluxe product Additional information follows Standard 66 Per Unit Selling price Direct materials Direct labor 33 23 Required 1 Required 2 1 Using a single plantwide rate the company computes overhead cost per unit of 18 for the standard model and 23 for the deluxe model Which model should the company produce Hint Compute product cost per unit and compare that with selling price to get gross profit per unit 2 Using activity based costing the company computes overhead cost per unit of 2 for the standard model and 49 for the deluxe model Which model should the company produce Hint Compute product cost per unit and compare that with selling price per unit to get gross profit per unit Complete this question by entering your answers in the tabs below Deluxe 102 38 28 Using a single plantwide rate the company computes overhead cost per unit of 18 for the standard model and 23 for the deluxe model Which model should the company produce Hint Compute product cost per unit and compare that with selling price to get gross profit per unit Note A negative gross profit should be indicated with a minus sign Product cost per unit Direct materials Clenderd 33 Direct Labor 23 Check my work Overhead Product Cost per unit

17 These graphs show the temperature T degrees Celsius as a function of time t hours Match each graph with its vertical intercept and rate of change a c Temperature C Temperature C 2 0 2 4 2 0 N T f t Time h i 3 C C h 3 ii 3 C 3 C h Time h T g t 380 3900 b Temperature C 2 6 N T k t Time h 2

5 1 1 This table shows some Northwest Coast artists and their cultural heritage Artist Bob Dempsey Dorothy Grant Bill Helin John Joseph Judith P Morgan Bill Reid Susan Point Heritage Tlingit Haida Tsimshian Squamish Gitxsan Haida Salish a Describe the relation in words b Represent this relation i as a set of ordered pairs ii as an arrow diagram 2 Here is a list of some chemical elements and their atomic numbers hydrogen 1 oxygen 8 iron 26 chlorine 17 carbon 6 silver 47 For each association below use these data to represent a relation in different ways a has an atomic number of b is the atomic number of 5 2 3 Which sets of ordered pairs represent functions What strategies did you use to find out a 4 3 4 2 4 1 4 0 b 2 4 2 4 3 9 3 9 c 2 8 3 12 4 16 5 20 d 5 5 5 5 5 5 5 5 4 Write in function notation a y 4x 9 c D 20t 150 b C 12n 75 d P 4s 5 The function P n 5n 300 describes the profit P dollars for a school dance when n students attend a Write the function as an equation in 2 variables b Identify the independent variable and the dependent variable Justify your choices c Determine the value of P 150 What does this number represent d Determine the value of n when P n 700 What does this number represent 5 3 6 a Laura cycles home from school then walks back to school Which graph best matches this situation Explain your choice Graph A Graph B Distance to Laura s Distance to Laura s Volume L 2 0 3 15 asnoy 1 0 asnoy 0 Time 0 5 Graph C Time 1980 Distance to Laura s b Choose one of the graphs in part a that did not describe Laura s journey Describe a possible situation for the graph Distance to Laura s 7 This graph shows the volume of water in Liam s flask as he hikes the Trans Canada trail Water in Liam s Flask Distance km asnoy asnou Time 12 16 20 Graph D Time a Describe what is happening for each line segment of the graph b How many time did Liam fill hic flack

8 Multinational Enterprises as a Source of Conflict Complete the following paragraph to explain the effect of multinational enterprises on a host nation s economy Assume a large brewing company based in Ireland where the corporate tax is 37 decides to relocate some production of refractometers to Cuba where the corporate tax is 8 If the parent company from Ireland purchases refractometers from its subsidiary in Cuba at grossly inflated prices the result is a impact on Cuba s economy and a impact on Ireland s economy As a result the governments of Ireland regarding the Irish subsidiary locating in Cuba and Cuba are likely to experience Now assume that a major national election takes place in Cuba As a result the Aquamarine party has come to power Assume that the Aquamarine party s main political stance is redistribution of all brewing profits through increased corporate taxes Based on this knowledge of the Aquamarine party s politics businesses in Ireland are likely to the election of the Aquamarine in Cuba Which of the following are the most likely courses of action for Irish brewing businesses with operations in Cuba as a result of the Aquamarine party rising to power Check all that apply The brewing businesses will shift a larger portion of their production to Cuba Over concerns of expropriation the brewing businesses will attempt to interfere with Cuban politics More businesses in the brewing industry will locate multinational enterprise operations in Cuba The brewing businesses will withdraw operations from Cuba The brewing businesses will take no action to engage in Cuban politics

0 0141 A particular type of bacteria is found to be capable of doubling in number about every 48 5 minutes The number N of bacteria present after t minutes could be modeled by N t Noe that No 500 000 is the initial number of bacteria per milliliter Complete parts a and b below a Approximate the number of bacteria per milliliter after 4 hours After 4 hours there are approximately 14 395 000 bacteria per milliliter Round to the nearest thousand as needed b Estimate graphically the elapsed time when there are 11 million bacteria per milliliter U of There are 11 million bacteria per milliliter after approximately minutes Round the final answer to the nearest integer as needed Round all intermediate values to the nearest thousandth as needed S Su

Great Start Preschool operates a not for profit morning preschool Each family pays a nonrefundable registration fee of 105 per child per school year Monthly tuition for the nine month school year varies depending on the number of days per week that the child attends preschool The monthly tuition is 105 for the two day program 120 for the three day program 140 for the four day program and 165 for the five day program The following enrollment has been projected for the coming year Click the icon to view the enrollment data Great Start Preschool Budgeted Revenue For Year Ended Monthly tuition revenue 2 day program 3 day program 4 day program 5 day program Total monthly tuition Months of operations Total tuition revenue Registration fee revenue Lunch Bunch revenue Total revenue CS In addition to the morning preschool Great Start Preschool offers a Lunch Bunch proga where kids have the option of staying an extra hour for lunch and playtime The presch charges an additional 3 per child for every Lunch Bunch attended Historically half of children stay for Lunch Bunch an average of 15 times a month Requirement Calculate Great Start Preschool s budgeted revenue for the school year Data table Two day program Three day program Four day program Five day program Print 72 children 46 children 64 children 30 children Done X

O 2 points 01 14 39 17 300 13 200 Multiple Choice 20 500 halysis and Managerial Acc Google Question 5 Home X M Question 7 Home X ml con con external browser 0 launchUrl https 253A 252F 252Fims mhe MB Body Con Dre Use the cost information below for Laurels Company to determine the total manufacturing costs during the current year G Google Direct materials used Direct labor used Total factory overhead Work in process inventory beginning Work in process inventory ending G Google w Help 5 600 7 600 5 700 3 600 5 200 Saved BUSI310 Princip Learning to Read f W Wikipedi

The crunch to come Social security taxes were raised to build a surplus Mey paid into the system has been greatly exceeding benefits since 1983 Scale in billions of dollars 1 1 1960 65 70 20 billion O 50 billion O 100 billion Collected 1 75 out of money by the year 2036 Scale in billions of dollars I 80 But the baby boomers will break the bank By one government projection the Social Security system will be paying out more than it is taking in by 2015 and the trust fund will run 1 85 Paid out 90 300 250 1 I I 1 1 1995 00 05 10 15 20 25 30 35 200 150 100 50 0 5 000 4 000 3 000 2 000 1 000 0 These taxes have increased at a faster rate than the federal income tax Federal taxes treated as if they were equal in 1982 1982 100 Social Security and Medicare Income tax Because there will be fewer workers to tax 200 150 100 1 1 80 81 82 83 84 85 86 87 88 89 90 91 92 est 50 How many workers pay into Social Security for each person getting benefits 3 7 3 2 3 4 3 2 2 9 2 4 2 0 2 0 1970 1980 1990 2000 2010 2020 2030 2040 at is the difference between the amount of money collected from Social Security taxes and the amount paid out in 1992 10 billion

How will the following transactions affect the U S balance of payments For each transaction in the following table indicate in which U S account it appears as a credit and in which account it appears as a debit Transaction Miguel a U S resident buys an HDTV set for 2 500 and sends it to Mexico as a gift to his parents Arielle a French tourist stays at a hotel in San Francisco and pays 400 for it with her debit card issued by a French bank A U S computer manufacturer purchases hard drives from a South Korean company paying the funds from its bank account in South Korea Account with Credit Capital Current Financial Account with Debit

A particular type of bacteria is found to be capable of doubling in number about every 48 5 minutes The number N of bacteria present after t minutes could be modeled by N t Noe0 014t Suppose that No 500 000 is the initial number of bacteria per milliliter Complete parts a and b below a Approximate the number of bacteria per milliliter after 4 hours After 4 hours there are approximately bacteria per milliliter Round to the nearest thousand as needed XXXB

Use the hypothetical information in the following table to answer the questions that follow Country Currency Canada dollar Eurozone euro Japan yen United Kingdom pound United States dollar Currency Symbol C or EUR On May 1 2016 Per Per 1 26 1 622 0 777 104 8 0 524 Currency The Canadian dollar against the U S dollar The U S dollar against the Japanese yen The British pound against the euro Exchange Rates The U S exchange rate against the British pound on May 1 2017 was Appreciated Over the period of May 1 2016 to May 1 2017 the U S dollar against the Canadian dollar by On May 1 2017 Per Per 1 118 0 792 134 9 0 675 0 548 1 287 113 9 1 412 Using information from the previous table indicate whether each currency listed in the following table appreciated or depreciated against another currency between May 1 2016 and May 1 2017 Depreciated 143 8 0 693 1 263 per pound against the euro by The euro

or equa to half 8 Determine which letter best represents an equivalent fraction A B 9 15 2 16 C 3 5

1 Find the number that makes an equivalent fraction 5 CL 10 80 3 Use or to compare the fractions 5 11 8 12 5 Use or to compare the fractions 4 3 12 m 00 2 Find the number that makes an equivalent fraction 3 7 42 11 4 Determine if the fraction shown is less more or equal to half 3 12 6 Determine if the fraction shown is less more or equal to half 2

On May 17 Shen an American investor decided to buy three month Treasury bills He found that the per annum interest rate on three month Treasury bills is 8 00 in New York and 12 00 in London Great Britain Based on this information and assuming that tax costs and other transaction costs are negligible in the two countries it is in Shen s best interest to purchase three month Treasury bills in because it allows him to earn more for the three months On May 17 the spot rate for the pound was 1 510 and the selling price of the three month forward pound was 1 508 At that time Shen chose to ignore this difference in exchange rates In three months however the spot rate for the pound fell to 1 450 per pound When Shen converted the investment proceeds back into U S dollars his actual return on investment was As a result of this transaction Shen realizes that there is great uncertainty about how many dollars he will receive when the Treasury bills mature So he decides to adjust his investment strategy to eliminate this uncertainty What should Shen s strategy be the next time he considers investing in Treasury bills Avoid investment in foreign institutions T Contract in the forward market to sell the foreign currency in the amount of the proceeds from the investment Exchange half of the anticipated proceeds of the investment for domestic currency Had Shen used the covered interest arbitrage strategy on May 17 his net return on investment relative to purchasing the U S Treasury bills in British three month Treasury bills would be Note Assume that the cost of obtaining the cover is zero

Draw a stem and leaf plot for the data set Enter numbers from smallest to largest separated by spaces Enter NONE for stems with no values Data set A The annual wages of employees at a small accounting firm are given in thousands of dollars 16 25 24 31 37 50 22 32 32 60 23 31 16 11 22 24 25 37 50 x 2 16 31 32 3 112272 NONE 0 456 NONE XXX X

What percent of the total population is found between the mean and the z score given Use the standard normal distribution table and enter your answer to two decimal places z 3 32 X 49 95

A normal distribution has a mean of 85 5 and a standard deviation of 4 83 Find the data value corresponding to the value of z given Enter your answer to four decimal places Z 0 65 X 88 972

Complete the passage to establish the identity 1 cos 2x 1 cos 2x 2 sec x Use double angle formulas 2 sec x

3 Let t 2n and cos t Use a half angle formula to find cos 2 4 1 Give an exact answer Use symbolic notation and fractions where needed COS 7 2

A store orders tubes of glue in the proportions shown in the following table Find the cumulative distribution for the table Size oz 2 6 8 12 16 Proportion 0 28 0 14 0 34 0 06 0 18 Cumulative Percent Find the mean median and mode for the table If an answer does not exist enter DNE Round your mean to two decimal place mean median mode

Find the standard deviation rounded to the nearest unit for the data indicated Test Score 90 80 70 60 50 Frequency 69826

At a well known major university the career choices of 1 500 graduates from an MS program are shown Nuclear industry 6 Industry other than National laboratory nuclear 18 21 Postdoctoral position 21 Continue for Ph D 27 Other research 7 a How many plan to get a job in a national laboratory 270 b How many are planning to continue for a Ph D 405 c How many are planning to enter the nuclear industry or industry other than nuclear 405 d How many are going to continue for a Ph D a postdoctoral position or other research

1 02330 2 88 04300 3 4500 4 00343 5 540500 5 4 3 1 0 022 x 59040 2 5 00 5 3404 CALCULATIONS USING SIGNIFICANT FIGURES 3 120 023 525 3 445 2229 4 66 01 13 89 x 80 5 65 0 0 009000 6 23920 x 1340 6 33 43 7 1 0330 8 525 000 9 9 300 x 104 10 0034300