Basic Math Questions and Answers

Find the exact value of the trigonometric function at the given real number 57 3 a sin b sin O sin 7T 6

8 Prove the following trigonometric identity secx secx csc r ser r

Which expression has the restrictions O O y 1 0 7272 3y y 2 X 5y 2y 1 6u 5y y 3 4y 3 y 2 6y X 4 y 7 6y 6y X y 5 y 3 y y 1

Identify the sequence that is not geometric 30 6 1 2 0 24 5 5 5 5 4 16 64 256 2 6 7 21 22

If f x 4x 7 evaluate f 1 f 2 3 6 94 26

expressed as a single power is O O O 5 LO x3 3x5 3 X 5 LOC 5 n

2 Mr Hemley stands next to the Illinois Centennial Monument at Logan Square in Chicago and casts a shadow that is 18 feet long The shadow of the monument is 204 feet long If Mr Hemley is 6 feet tall how tall is the monument le X

Suppose a base 4 place value system has its digits represented as shown to the right a Determine the value of GOBGR in base 10 b Write 205 in the base 4 system using only the symbols shown to the right a The value of GOBGR in base 10 is Simplify your answer

Graph the trigonometric function 1 y COSX Plot all points corresponding to x intercepts minima and maxima within one cycle Then click on the graph a function button Tha X

In an alternate method of converting a number to base b divide the number by b recording the quotient and remainder Then repeat the procedure using the quotient as the number Continue the process until the quotient The digits of the answer are the remainders from last to first a Convert 2642 to base 5 by this method b Convert 3275 to base 8 by this method a 2642 05

a Where is f continuous b f 6 e lim f x h lim f x x 1 10 9 8 7 k lim f x n f 5 20 to answer the remaining questions 10 9 3 c f 2 NT Evaluate the following if possible If the limit is infinite use co or 00 as appropriate Otherwise if the limit does not exist use DNE i f 1 8 7 6 1 lim f x x 3 4 o lim f x X 8 3 2 3 f lim f x 7 8 9 10 9 IC d lim f x x 1 g lim f x x 2 j lim f x x 3 m lim f x

2 Given the function f x x 3x 2 x 3 x 12 x 3 a lim f x x 3 b lim f x c lim f x x 3 d f 3 find each of the following each part worth 2 points

Investor Matt has 461 000 to invest in bonds Bond A yields an average of 9 7 and the bond B yields 5 4 Matt requires that at least 4 times as much money be invested in bond A as in bond B You must invest in these bonds to maximize his return What is the maximum return per year Round to the nearest cent

0 10 1 2 11 3 www 12 13 4 5 14 15 16 he equivalent Hindu Arabic numeral is 17 8 9 18 19

each mathematical function indicated reduce each answer to the lowest possible terms and change any improper fraction to a mixed number 32 1 1 84 7 2 7 97 18 3 16 2 3 4 138 2 3 5 234 21 13 7 89 13 5 8 71 3 62 3 9 1223 x 1 4 32 18 4 6 671 8 x 1 4 537 32 24 99 76 No 2 3 S 9 367 12 216 72 1 18 7 214 9 2 783

Ikerd Company applies manufacturing overhead to jobs on the basis of machine hours used Overhead costs are estimated to total 290 030 for the year and machine usage is estimated at 126 100 hours For the year 308 530 of overhead costs are incurred and 130 100 hours are used a Your answer is correct Compute the manufacturing overhead rate for the year Round answer to 2 decimal places e g 1 25 Manufacturing overhead rate S eTextbook and Media List of Accounts 23 per machine hour Attempts 1 of 5 used

JOB NO ITEM FOR Date 7 10 222 12 3 15 24 27 31 Total cost Unit cost 469 White Lion Cages Todd Company Direct Materials 700 Cost of completed job Direct materials Direct labor Manufacturing overhead 900 1 640 1 600 Job Cost Sheet Quantity Date Requested Date Completed Direct Labor 500 300 700 2 000 7 2 7 31 Manufacturing Overhead Source Documents 600 360 940 Answer the following questions 1 What are the source documents for direct materials direct labor and manufacturing overhead costs assigned to this job

Write the Babylonian numeral as a Hindu Arabic numeral 1 The equivalent Hindu Arabic numeral is Symbols Hindu Ar Symbols

Write the Babylonian numeral as a Hindu Arabic numeral wwwww www Babylonia Symbols Hindu Ar Symbols

now lim sin 0 72 What is the rate of convergence of this sequence

Graph the trigonometric function y cos X 1 2 Plot all points corresponding to x intercepts minima and maxima within one cycle Then click on the graph a function button 2 MH 2x 3k An x X

The following are the job cost related accounts for the law firm of Colaw Associates and their manufacturing equivalents Supplies Salaries and Wages Payable Operating Overhead Service Contracts in Process Cost of Completed Service Contracts Cost data for the month of March follow 1 2 3 4 5 Law Firm Accounts 6 a Manufacturing Firm Accounts Raw Materials Factory Wages Payable Manufacturing Overhead Work in Process Cost of Goods Sold Purchased supplies on account 2 100 Issued supplies 1 600 60 direct and 40 indirect Assigned labor costs based on time cards for the month which indicated labor costs of 74 100 80 direct and 20 indirect Operating overhead costs incurred for cash totaled 47 300 Operating overhead is applied at a rate of 90 of direct labor cost Work completed totaled 82 000 Journalize the transactions for March Credit account tities are automatically indented when amount is entered Do not indent manually

Lott Company uses a job order cost system and applies overhead to production on the basis of direct labor costs On January 1 2020 Job 50 was the only job in process The costs incurred prior to January 1 on this job were as follows direct materials 20 200 direct labor 12 120 and manufacturing overhead 16 160 As of January 1 Job 49 had been completed at a cost of 90 900 and was part of finished goods inventory There was a 15 150 balance in the Raw Materials Inventory account During the month of January Lott Company began production on Jobs 51 and 52 and completed Jobs 50 and 51 Jobs 49 and 50 were also sold on account during the month for 123 220 and 159 580 respectively The following additional events occurred during the month Purchased additional raw materials of 90 900 on account Incurred factory labor costs of 70 700 Of this amount 16 160 related to employer payroll taxes Incurred manufacturing overhead costs as follows indirect materials 17 170 indirect labor 20 200 depreciation expense on equipment 12 120 and various other manufacturing overhead costs on account 16 160 4 Assigned direct materials and direct labor to jobs as follows 1 2 3 Job No Direct Materials 50 51 52 10 100 39 390 30 300 Direct Labor 5 050 25 250 20 200 Calculate the predetermined overhead rate for 2020 assuming Lott Company estimates total manufacturing overhead costs of S848 400 direct labor costs of 707 000 and direct labor hours of 20 200 for the year

une 99999 What is the equivalent Hindu Arabic numeral 3506 Type an integer What is the equivalent Roman numeral MMMDVI O A Tals in the Hindu Arabic Roman traditional Chinese and Greek systems of numera Choose the correct equivalent Chinese numeral below HA OB K O C O D

Write the Mayan numeral as a Hindu Arabic numeral FI 0 10 11 EEN 3 www 13 4 wwww 14 www 5 15 6 TE 16 nquivalent Hindu Arabic numeral is 7 LEE 17 8 www 18 9 19

Stine Company uses a job order cost system On May 1 the company has a balance in Work in Process Inventory of 3 510 and two jobs in process Job No 429 2 150 and Job No 430 1 360 During May a summary of source documents reveals the following Job Number 429 430 a 431 General use Materials Requisition Slips 2 970 4 100 4 540 11 610 900 12 510 Labor Time Tickets 2 100 3 200 8 100 13 400 1 590 Stine Company applies manufacturing overhead to jobs at an overhead rate of 68 of direct labor cost Job No 429 is completed during the month No Date Account Titles and Explanation May 14 990 Prepare summary journal entries to record 1 the requisition slips 2 the time tickets 3 the assignment of manufacturing overhead to jobs and 4 the completion of Job No 429 Credit account titles are automatically indented when amount is entered Do not indent manually Debit Credit

Your answer is partially correct During January its first month of operations Dieker Company accumulated the following manufacturing costs raw materials 5 400 on account factory labor 6 100 of which 5 900 relates to factory wages payable and 200 relates to payroll taxes payable and factory utilities payable 2 500 Prepare separate journal entries for each type of manufacturing cost Credit account titles are automatically indented when amount is entered Do not indent manually Date Account Titles and Explanation Jan 31 31 31 Raw Materials Inventory Accounts Payable To record purchase of raw materials on account Finished Goods Inventory Factory Wages Payable Employer Payroll Taxas Payable To record factory labor costs Manufacturing Overhead Utilities Payable To record entry for utilities payable Debit CULANT TO 5400 6100 2500 Credit TO DA DO 5400 5900 200 2500

Sam Peters is the sole proprietor of Charismatic Cats a business specializing in the sale of high end pet gifts and accessories Charismatic Cats sales totaled 1 060 000 during the most recent year During the year the company spent 53 000 on expenses relating to website maintenance 33 200 on marketing and 28 500 on wrapping boxing and shipping the goods to customers Charismatic Cats also spent 636 000 on inventory purchases and an additional 19 500 on freight in charges The company started the year with 19 800 of inventory on hand and ended the year with 13 100 of inventory Prepare Charismatic Cats income statement for the most recent year Begin by calculating the cost of goods sold for the year Charismatic Cats Cost of Goods Sold For Current Year Beginning inventory Plus Purchases and freight in Cost of goods available for sale Less Ending inventory Cost of goods sold 19 800 13 100

Write the Babylonian numeral as a Hindu Arabic numeral The equivalent Hindu Arabic numeral is Babylonian Symbols Hindu Arabic Symbols

20 x 5 If there is no solution type no solution Type your answer below as a number example 5 3 1 4 1 2 or 3 2

Part B 47 x 2 4 If there is no solution type no solution Type your answer below as a number example 5 3 1 4 1 2 or 3 2

53 Finding Years to Double How long would it take to dou ble your money in an account paying 4 compounded quarterly Answer in years plus days ignoring leap years 17 years 152 days 54 Comparing Principal and Interest Amounts After what time period would the interest earned equal the origi nal principal in an account paying 2 compounded daily Answer in years plus days ignoring leap years 34 years 240 days

A number system has base in expanded form ADO with digits represented by the symbols A and Write the expression below Choose the correct answer below OA A XO D Q 1 B A OC 0 x A 0 OD x A 0

Write the Babylonian numeral as a Hindu Arabic numeral TTTTT T The equivalent Hindu Arabic numeral is

What is the orthographic drawing of the isometric drawing at the right Assume there are no hidden cubes Choose the correct orthographic drawing below OA Top Front Right B Top Front Right Front Right C f Top Front Right

A friend of yours who is not taking statistics wonders why it is that anyone would choose to take a sample Obviously he says you would get better information from a census Consider the following two explanations on why statisticians take samples rather than taking a census i Although we may get better information from a census it is usually far too costly and time consuming to contact every member of the population ii A large random sample will be nearly as good as census for far less cost Which of the above statements is correct Both i and ii are incorrect ii is correct i is incorrect i is correct ii is incorrect Both i and ii are correct

1 1 2 w Ill 23 4 Ft to 3 1 5 6 7 8 9 10 100 1000 The Hindu Arabic numeral is Type an integer or a fraction

Fill in the blank with the appropriate phrase As you read a Roman numeral from left to right if a smaller number comes before a larger number you should As you read a Roman numeral from left to right if a smaller number comes before a larger number you should divide the larger number by the smaller number subtract the smaller number from the larger number multiply the smaller number by the larger number add the smaller number to the larger number

Determine the quadrant in which the terminal side of 0 lie a sine 0 and tane 0 Choose one b sin 0 and cos0 0 Choose one

There are three graduated cylinders shown in the picture at right The graduated cylinder on the far left has scale markings that are 0 1 mL apart so it can be read to the nearest 0 1 mL Hence we can estimate a volume of 5 75 mL 0 05 mL note that 0 05 mL in 5 75 mL constitutes the estimated digit and 0 05 mL is the uncertainty which was calculated as half of the smallest division of the scale of the measurement device 0 1 mL 2 0 05 mL Based on this example what is the measurement of volume in the center and rightmost graduated cylinders shown in the picture assuming each scale is in mL 269m er to ainu adi bus osig erit ferly amuzzA Swolsd mwora 10 points Center cylinder volume 10 points Rightmost cylinder volume anlog 5 2

To Alberto Subject Planning our slime project Hi Alberto Here are my notes from when we tried making the two types of slime Gooey Slime Mass of empty cup 0 007 kg Mass of water 0 36 kg Total mass after adding glue 0 492 kg Total mass after adding borax 0 5 kg Here is the glue and borax I saw at the store 0 5 kg BORAX 1 84 kg Firm Slime 0 005 kg 0 36 kg 0 525 kg 0 55 kg PLEASE LET ME KNOW Which kind of slime do you want to make with the science club How many boxes of borax and how many bottles of glue should we bring to the science club meeting There are 24 members How many batches of slime will the club be able to make Find a solution to the Making Slime problem Choose one type of slime Then calculate how much glue and bor is needed to make it Determine how many bottles of glue and boxes of borax to bring to the science club meeting Tell how many batches of slime the science club will be able to ma with the materials

Find the reference angle for radians TU 9

Nightclub Management You have just opened a new nightclub Russ Techno Pitstop but are unsure of how high to set the cover charge entrance fee One week you charged 5 per guest and averaged 300 guests per night The next week you charged 6 per guest and averaged 290 guests per night a Find a Jinear demand equation showing the number of guests q per night as a function of the cover charge p q p b Find the nightly revenue R as a function of the cover charge p R P c The club will provide two free non alcoholic drinks for each guest costing the club 3 per head In addition the nightly overheads rent salaries dancers DJ etc amount to 1 000 Find the cost C as a function of the cover charge p C p d Now find the profit in terms of the cover charge p TICE ANOTHER P p Determine the entrance fee you should charge for a maximum profit in dollars p per guest

Find the reference angle for radians Elin 3

Graph the inequality below on the number line x 7 4 H 11 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11

Write the numeral as a Hindu Arabic numeral XMMCCLXVI

Graph the inequality below on the number line y 10 Ve 11 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1

Using the table write the given Roman numeral as a Hindu Arabic numeral Roman Numerals Hindu Arabic Numerals CXLVII I 1 V 5 X 10 L 50 C 100 D 500 M 100

Mia currently has 10 email subscribers to her blog and gains an average of 10 new subscribers per day Julie currently has 100 email subscribers to her blog and loses an average of 5 email subscribers per day Use this information to answer questions 7 10 EMAIL SUBSCRIBERS 5 8 8 8 8 8 8 8 8 100 1 2 3 4 5 6 7 8 9 10 DAYS 7 Write an equation to represent y the total number of subscribers after x days for each girl Mia Julie 8 Graph each equation on the grid at the left 9 What is the solution to the system of equations 10 What does the solution mean in the context of the situation

Select one Newton s 3rd Law and Conservation of Momentum Study the image Question 6 Is there an action reaction pair in this image Yes The ball is pushing against the ground and the ground is pushing the ball back No The ball is not in motion Action reaction pairs only happen during motion No The ball is at ground level Action reaction pairs form when an object is above ground level Yes The ball is round Round objects always have an action reaction pair acting on them