Basic Math Questions and Answers

To simplify the measurement of the acidity or basicity of a solution the pH hydrogen potential measure was developed The pH is given by the formula pH log H where H is the concentration of hydrogen ions in moles per liter in the solution Find the pH value of a solution for which H 0 0000267 The pH value of a solution is approximately Round to the nearest tenth as needed

The formula for pH is pH log H where H is the hydrogen ion concentration The pH of a fruit juice is 3 2 What is the hydrogen ion concentration of the juice The hydrogen ion concentration H is approximately 10 Round to the nearest tenth moles per liter

e Find the inverse of the following matrix show your work 4 2 1 639 A 9 0 3 45 5

A government considers a single person as living in poverty if his or her income falls below the official poverty level which is adjusted every year for inflation The function that models the povert threshold for the years 1987 2008 is f x 3128 3 4054 2 In x dollars where x is the number of years after 1980 a What does this model give as the poverty threshold in 2014 In 20227 b Is this function increasing or decreasing c Graph the function 3128 3 4054 2 Inx for x 5 tox 45

At the end of an advertising campaign weekly sales at an electronics store declined according to the equation y 4500 302 dollars where x is the number of weeks after the end of the campaign a Graph the function for 0 sxs60 b Use the graph to find the weekly sales 10 weeks after the campaign ended c Comment on It pays to advertise for this store a Choose the correct graph below 2500 30 60 Q Q G b The weekly sales 10 weeks after the campaign ended is OB 5000 2500 0 30 60 Q 2 OC AY 5000 1 2500 10 30 Q

1 Consider the experiment of rolling a die Let A be the event getting a prime number A prime number is a whole number greater than 1 that cannot be exactly divided by any whole number other than itself and 1 B be the event getting an odd number Find the following i P A or B ii P A and B 4 mar

c A car begins driving from a stationary position It accelerates at 4m s2 for 10 seconds then travels at a steady speed for another 10 seconds all in the same direction How much distance has it covered since it started driving 5 r

b In triangle XYZ XY 40 cm YZ 57 cm and XZ 81 cm The triangle is illustrated in the following figure Find the size of the angles X Y and Z N 57 81 40 6 ma

During a 10 year period of constant inflation the value of a 400 000 property will increase according to the equation v 400 000 0 0 a What will be the value of the property in 5 years b Use a table or graph to estimate when this property will be worth double its original value a The value of the property in 5 years will be Round to the nearest cent as needed

An antique table increases in value according to the function v x 550 1 03 dollars where x is the number of years after 1980 a How much was the table worth in 1980 b If the pattern indicated by the function remains valid what was the value of the table in 2005 c Use a table or a graph to estimate the year when this table will reach double its 1980 value a The table was worth in 1980 Round to the nearest cent as needed

c Determine the position of any maximum and minimum points of the function y 2t 3 Show your work 6 m

Chau plans to set aside money for his young daughter s college tuition He will deposit money in an ordinary annuity that earns 3 6 interest compounded monthly Deposits will be made at the end of each month How much money does he need to deposit into the annuity each month for the annuity to have a total value of 71 000 after 14 years Do not round intermediate computations and round your final answer to the nearest cent If necessary refer to the list of financial formulas 0

Use the formula S P 1 r to complete parts a and b a Graph the function that gives the future value of 70 000 invested at 5 compounded annually for t years Osts 12 b Find the future value of 70 000 invested for 15 years at 5 compounded annually a Choose the correct graph below 150000 Q b The future value is Round to the nearest cent as needed a 150000 Q Q 0 0 AS 150000 Q Q e

Gordon Sports Authority purchased inventory costing 24 000 by signing a 10 six month short term note payable The purchase occurred on June 1 2021 Gordon will pay the entire note principal and interest on the note s maturity date of December 1 2021 Journalize the company s a purchase of inventory and b payment of the note plus interest on December 1 2021 Record debits first then credits Exclude explanations from any journal entries a Journalize the company s purchase of inventory Date 2021 Journal Entry Accounts CITE Debit Credit

Find the sum of the first 23 terms of the sequence 4 3 10 Sho your work

ii Is 8 8 mod 5 Show your work

Ravi wants to save money to open a tutoring center He buys an annuity with a quarterly payment of 51 that pays 3 4 interest compounded quarterly Payments will be made at the end of each quarter Find the total value of the annuity in 10 years Do not round any intermediate computations and round your final answer to the nearest cent If necessary refer to the list of financial formulas s

e Decide which system has non trivial solutions we say that the system has a non trivial solution if the determinant of the matrix is zero Show your working i 4x y 0 2x 3y 0 ii x 2y 0 3x 6y 0

p Show whether the following function is continuous or discontinuous If it is find the point points of discontinuity of the function discontinuous f x for a 1 0 for x 1 2 x 1 for a 1

n 1 Is an 2n 1 If yes find a a2 a3 3 8 5 9 a general term of a geometric or arithmetic sequence O None of the other options are correct

7 Solve the equation 32 1 36 2 O x 4 0x 0x 0x 1

6 What is the inverse function of k x Ok x y 7 1 2y Ok x 1 2y 7 4 k x 721 Ok x 2 1 2z 7 x

8 If 5x 4 mod6 what is the least positive value of x O 3 05 O None of the other options are correct

1 A function f is said to be onto surjective if and only if O the range of f is a subset to the co domain of f O the range of f is equal to the domain of f the range of f is equal to the co domain of f O f a f b for all a and b in the domain of f 0 10

For each of the situations listed identify which of three principles integrity objectivity and independence or due care from the AICPA Code of Professional Conduct is violated Assume all persons listed in the situations are members of the AICPA Note Refer to the AIC Code of Professional Conduct a Lance recently graduated with an accounting degree and found a job in the payables department of Sawyer Sneaker Company Lance is in charge of adjusting entries for accrued liabilities that have been paid but he does not remember how to treat these because he has not seen them since one of his courses from his junior year in colle Lance assumes the accrued liabilities for this month are the same amounts as last r so he does not enter in the new accrual entries for this month and does not reverse Due care last month s entries b Frankie Candle Co is a small family owned company that only employs one accour Jenny Since Jenny is in charge of all areas of accounting and knows she will not get caught she decides to create fictitious accounts payable entries at Frankie Can for the company she owns Candle Supply Inc Principle from the AICPA Code of Professional Conduct that is violated c April is a newly hired auditor for Penny Blake a CPA firm Her father owns E E Vevermary Supply April is excited to be assigned to work on the account of E E since she understands the business well from working part time during summers there when she was growing up April does not disclose that her father owns E E because she knows she will not have any bias d Anne works in the payables department of Yellow Steel Inc She noticed that her company s current ratio is a little lower than the industry average In an attempt to improve the current ratio she decides not to accrue wages payable for this month Integrity Objectivity and independence

A firm uses a serial assembly system and needs answers to the following a An output of 880 units per shift 8 00 hours is desired for a new processing system The system requires product to pass through four stations where the work content at each station is 32 seconds What is the required cycle time for such a system Round your answer to the nearest whole number Cycle time Answer is complete and correct seconds Efficiency 33 b How efficient is your system with the cycle time you calculated Round your answer to 1 decimal place Answer is complete and correct 97 0 c Station 3 changes and now requires 50 seconds to complete What will need to be done to meet demand assume only 8 00 hours are available What is the efficiency of the new system Round your answer to 1 decimal place Answer is complete but not entirely correct

To help pay for new costumes for a play a theater invests 1600 in a 30 month CD paying 2 3 interest compounded monthly Determine the amour receive when it cashes in the CD after 30 months The theater will receive Round to the nearest cent as needed when it cashes in the CD

The current toll for the use of a certain toll road is 2 75 A study conducted by the state highway department determined that with a toll of p dollars q cars will use the road each day where q 60 000e 0 4p Is demand elastic or inelastic at p 2 75 To determine if demand is elastic or inelastic the elasticity must be computed To compute the elasticity of demand for the given equation use the formula for elasticity What is the formula for elasticity OA E p OB E p OC E p OD E P pf p f p pf p f p pf p f p Notice that f p q 60 000e 0 4p is given in the problem statement but f p is not Calculate f p pf p f p d f p 60 000e 0 4p dp 24000e 0 4p

Fill in the blank to make an equivalent ratio 72 64 9 3 5 7 9 7 8 14 12 7 14 6 4 3 4 2 20 1 63 13 18 27 7 2 19 12 15 1 16 15 15 3 1 17 14 1 2 45 2 2 6 14 4 32 6 30 36 8 1 2 12 24 5 10 6 12 5 14 6 18 11 16 4 20 6 2 1 4 12 18 18 30 9 12 30 24 6 54 27 18

Listen PROBLEM SOLVING The table shows the annual profits in thousands of dollars of a county fair from 2013 to 2016 What must the 2017 profit be in hundreds of dollars to break even over the five year period Profit thousands of dollars Year 2013 2014 2015 2016 2017 2 5 1 4 3 3 1 4 period

Homework Directions Solve each problem below showing ALL work and using MCLE for all word problems Problem 1 644 8 26 2 Find the Lesson 18 Dividing Decimals by Wholes quotient of 185 92 and 56 Solve 3 A high school track is 9 76 meters wide It is divided into 8 lanes of equal width for track and field events How wide is each lane Check 4 In a dozen eggs there are 7 2 milligrams of iron How many milligrams of iron are in each egg

4 What is the slope of a line parallel to the line y 3x 4 46 51 yo 38

In the figure to the right what are the values of x and y

What is the equation of a line that is perpendicular to the line y 2x 1 and passes through the point 4 6

2 x 1 3x 5

3 The value of x solve for the variable 3214 Sellect all the correct answers x 3 x X x log 5 log 3 log 3 log 5 3 1 46 0 68

ii 99 people take a test Their scores out of 100 are 56 79 77 48 90 68 79 92 7156 79 77 48 90 68 79 92 71 Work out the mean median and mode of their scores show you work

Time allowed per column Z Name z 1 8 7 15 2 7 6 13 3 6 5 4 7 4 9 7 16 5 6 8 6 14 7 7 5 12 8 9 8 17 9 9 6 10 8 5 11 9 5 12 8 4 13 9 3 14 8 9 15 4 9 16 6 7 17 7 8 18 6 9 19 4 8 20 9 9 Number o 1 17 9 2 15 6 3 13 8 4 16 7 5 14 6 6 12 5 7 15 8 8 13 6 9 11 5 10 18 9 11 14 5 12 13 9 13 13 7 14 15 7 15 12 6 16 14 8 17 16 9 18 16 8 19 13 5 20 15 9

Persevere with Problems Lannie has 5 cups of chocolate chips She needs 12 cups to make one batch of chocolate chip cookies How many batches of chocolate chip cookies can she make batches X do 90 H 0

Round each number to the correct place value 1 Round to the nearest tenth 2 Round to the nearest tenth 3 Round to the nearest hundredth Round to the nearest tenth 4 Round to the nearest tenth 5 Round to the nearest whole number 146 8 6 Round to the nearest hundredth 9 Round to the nearest tenth Round to the nearest hundredth 7 Round to the nearest whole number 9 88 12 Round to the nearest hundredth 855 788 6 429 15 Round to the nearest hundredth 5 167 677 827 Round to the nearest hundredth 98 949 Round to the nearest tenth 11 Round to the nearest whole number 90 1 33 25 16 118 3 827 13 Round to the nearest whole number 71 7 14 Round to the nearest tenth 481 772 6 36 16 Round to the nearest whole number 2 4 534 212 7 Round to the nearest whole number 71 64 8 Round to the nearest whole number 45 9 98 244 10

Construct a truth table for the given statement q V p A p Complete the truth table P T T F 9 T F LL T P qvp q V p p

Answer Part B Convert 0 87 to a percent Answer Answer to a decimal Part C Convert 0 3 to a decimal Part D Convert 0 225 to a percent Answer Calculator Je

The desired daily output for an assembly line is 480 units This assembly line will operate 640 minutes per day The following table contains information on this product s task times and precedence relationships TASK time ABCDEFGH Workstation cycle TASK TIME SECONDS 40 25 75 15 59 Work Station 30 25 15 IMMEDIATE PREDECESSOR b What is the workstation cycle time 3x Task A B B Answer is complete but not entirely correct seconds per unit D C E G F c Balance this line using the largest number of following tasks Use the longest task time as a secondary criterion Leave no cell blank be certain to enter 0 wherever required Idle Time

Francis Johnson s plant needs to design an efficient assembly line to make a new product The assembly line needs to produce 30 units per hour and there is room for only five workstations The tasks and the order in which they must be performed are shown in the following table Tasks cannot be split and it would be too expensive to duplicate any task TASK TIME TASK MINUTES A TES 1 0 B 8 5 8 5 PUDEFG C 2 0 1 0 2 0 2 0 IMMEDIATE PREDECESSOR Workstation cycle time mmnal A B C b What is the workstation cycle time in minutes Round your answer to 1 decimal place minutes d What is the efficiency of your line balance Use the theoretical minimum number of workstations in your calculation Round your answer to 1 decimal place

Simplify the algebraic expression 10 2 3

Find the least common denominator for the group of denominators using the method of prime numbers 45 75 153 The least common denominator is

b 8a b 14ab 4ab 2ab

Rearrange to isolate variable y in the following equation and choose the correct answer 6 92 3 2

Simplify the algebraic expression 6x 4 2 2x

4x 10 36