Basic Math Questions and Answers

P D P R E Key Concepts P R E where P is profit R is revenue and E is expenses The vertex of a profit function lies on the axis of symmetry The vertex of a profit function contains the maximum profit Maximum profit can be found on the graph where the difference between the revenue and expense functions is the greatest Guided Exercises FunFleece Incorporated manufactures fleece hats It is considering making a new type of weatherproof fleece hat The expense and revenue functions are E 300p 150 000 and R 300p2 29 000p 1 Determine the profit function P Date Substitute the expense function for E and the revenue function for R P 300p2 29 000p 300p 150 000 P Mod The profit function is P 2 Use the equation from Exercise 1 Determine the maximum profit to the nearest cent Determine the price that yields maximum profit Find the maximum of the profit equation Axis of symmetry b 2a Substitute the price p into the profit equation from Exercise 1 Axis of symmetry 2

1 n n 12 4n 16 16n 2 3x 3x 9x 8x

A data set includes weights in grams of 40 Reese s Peanut Butter Cup Miniatures The accompanying Statdisk display shows results from using all 40 weights to test the claim that the sample is from a population with a mean equa to 8 953 g Test the given claim by using the display provided from Statdisk Use a 0 01 significance level Click the icon to view the Statdisk display Identify the null and alternative hypotheses Ho H Type integers or decimals Do not round

A random sample of 839 births included 430 boys Use a 0 05 significance level to test the claim that 51 1 of newborn babies are boys Do the results support the belief that 51 1 of newborn babies are boys Identify the null and alternative hypotheses for this test Choose the correct answer below OA Ho p 0 511 H p 0 511 OB Ho p 0 511 H p 0 511 OC Ho p 0 511 H p0 511 OD Ho p0 511 H p 0 511

1 Assume that the solution to y 3xy y 0 is given as a power series about x 0 that is 8 y x n 0 Write a2 a3 and a4 in terms of ao and or a Anxn

1 A shallow foundation supported by a silty sand is shown in the figure below Estimate the elastic settlement of the foundation given Length L 3 m Width B 3 m Depth of foundation D 1 5 m Thickness of foundation t 0 25 m Load per unit area Ao 150 kN m Ef 15 x 106 kN m The silty sand has the following properties H 20 m Mg 0 3 Eo k 400 kN m m 16 000 kN m Compressible soil layer Es s Be A H Rigid layer Eo Depth z NOTE Show all the calculation steps Es Es Eo kz

QUESTION 3 All Sundry Ltd commenced business on June 1 2019 The business financial year ends on May 31st The policy of the business is to depreciate all non current assets according to the months of ownership using the Reducing Balance Method at a rate of 20 per annum The following information was provided relating to its non current assets register over the first two financial years 2019 August 1 2019 October 1 2020 Nov 30 2021 Feb 28 2021 March 1 Bought a machine for 45 000 by cheque Bought an additional machine for 30 000 paying in cash I All Sundry Ltd traded the machine that was acquired in October 2019 for a newer model The newer model cost 36 000 and a trade in allowance of 18 700 was agreed upon All Sundry Ltd settled the balance due by cheque Sold the machine that was originally purchased on August 1 2019 for 34 130 cash Purchased a machine for 55 000 by debit card Required Prepare the following for All Sundry Ltd to reflect the two year period i Machinery Account ii Accumulated Depreciation Machinery Account iii Disposal Accounts iv separate account for each disposal Income Statement extracts 4 marks 16 marks 5 marks 2 marks

a Us and them b We and them c Us and they d We and they 33 Joel is one of the fanatical sports fans about nothing else a Who talks b Who talked c Who talk 1 Who is talking 34 I will see you tomorrow When I return b After I have returned c After I might have returned d When I have returned But for the night guard s vigilance the factory burgled a Would be b Will be c Would have been d Will have been 36 No sooner It started to rain a Did he arrive home when b Had he arrived home than c Than he arrived home d When he an He doesn t think of her 37 Hardly a day goes by J a That b When c While d Without 38 Scarcely had I opened the door the dog came running in a As b Before c Than d When 39 Several Attended the two day summit a Head of state b Heads of states c Heads of state J Head of states 40 You haven t seen this man before Searned with CamScanner a Isn t so b Have you c Is it so d Isn t it 41 I saw him again week a Soine time b Sometimes c One time d Sometime 42 She bought a a Red beautiful leather b Beautiful leather red c Beautiful red leather d Leather beautiful red 43 It was the head boy that took the book away a Didn t he b Wasn t he c Wasn t it d Isn t it 44 My father took me to England a At the age of ten b Being ten years old c When I was ten d At ten years old 45 The teacher wanted to know if all our homework submitted a Have been b Has been c Had been d Is being 46 The man denied the company property a Stolen To have stolen c To be stealing d Stealing 47 The day I won a visa lottery was the Day of my life a Happy b Very happy c Happiest d Happier 48 Ebiere invited to her birthday party a Bola and I b My self and Bola c Bola and me d Bola and myself 49 The company employs only experienced mature workers a And b But c Well d Very 50 Adamu looked at his watch and said it s high time we Home a Must go h Went c Should go d in

Suppose that during a recession the government borrows money to provide free wireless Internet access in urban areas Which of the following statements are correct Choose one or more A Crowding out will occur as individuals choose to rely on free Internet service instead of purchasing their own B This policy will likely be accompanied by an impact lag as the policy takes time to make its way to the people C The free wireless Internet access in urban areas will likely raise interest rates as the government borrows more money to finance the purchase D The provision of free Internet service is an example of an automatic stabilizer E The government is engaging in contractionary fiscal policy 4

the fall of 2007 the United States economy began a descent into deep recession As a result the federal government and the Federal Reserve took action to stimulate economic growth Which of the following would have been an appropriate fiscal policy Choose one or more A the federal government beginning to close failing banks B the Federal Reserve increasing the money supply to reduce the interest rate C the federal government spending more money to build more infrastructure D the federal government providing tax refunds to many taxpayers DE the federal government increasing its regulation of banks

Assume the economy is operating beyond the full employment output level as shown in the graph below The government want to use contractionary fiscal policy to correct the situation Drag the appropriate line to the correct position to show the change To refer to the graphing tutorial for this question type please click here IG Price Level 16 15 14 13 12 11 10 9 8 7 X ERAS 9 B 9 63 SRAS AD1

and 2010 Year 2001 2010 1st attempt Part 1 2 points 2001 2010 In the first decade of this century The table below shows the data on the national debt from both 2001 Part 2 1 point Total U S debt billions of 5 807 13 561 Nominal GDP billions of Using the table provided compute the U S debt to GDP ratio in both 2001 and 2010 Give all answers to two decimals be aware that your answer is not a percentage 10 286 14 499 Which of the following are contributing factors for the increase in the debt to GDP ratio See Hint Choose one or more A increased taxes due to changes in the tax code B increased defense spending for wars in Afghanistan and Irag See Hint

8 of 13 30 area 6 Resources Find the area of the given region The area can be expressed as a sum of areas of rectangles triangles or circles Note that the are in the figure is a semicircle 8 Use decimal notation Give your answer to three decimal places ExGive Up Hint Check Answer

of 13 Find the area of the given region The area can be expressed as a sum of areas of rectangles triangles or circles Note that the are in the figure is a semicircle 6 area 40 4 9 4 Use decimal notation Give your answer to at least three decimal places Answer

given triangle 25 A 15 13 C degree measure C Use decimal notation Give your answers to three decimal places Include the degree symbol in your answers where need

Which of the following policies would dramatically and permanently reduce government outlays Choose one or more A reducing the number of individuals eligible for food stamps B reducing the cost of living increase for Social Security recipients C lowering wages for workers involved in all government construction projects D reducing the number of overseas military bases E lowering Medicare and Social Security taxes

Find the length of the side marked c of the given triangle 8 C 60 C 7 Give an exact answer Use symbolic notation and fractions where needed

Truman an industrious worker is faced with the following tax table Income level 0 8 700 8 700 35 350 35 350 85 650 85 650 178 650 178 650 388 350 Greater than 388 350 If Truman earns 73 000 what is his tax bill Marginal tax rate 10 15 25 28 33 35

The government announced that last year it spent 179 million in mandatory outlays and 416 million in discretionary outlays It received 612 million in revenue Last year the government had a budget surplus surplus deficit of million

The budget of the federal government is dramatically different than it was 50 years ago In what way is it different Choose one A Mandatory spending has increased as the population has gotten older and the Social Security and Medicare programs have expanded B Discretionary spending has increased due to the expansion of the Social Security and Medicare programs OC Mandatory spending has decreased dramatically OD Spending on defense as a percentage of the federal budget has dramatically increased

Assume n is a positive integer Count the number of operations in the loop below x 0 for i 1 to n for j 1 to i for k 1 to j x i j k next k next j next i 1 Start by counting the number of operations performed in the innermost loop the k loop This total will depend on j In each iteration of the innermost loop The inner loop runs operations are performed times so the total number of operations performed in this loop is 2 Now we want to count the number of operations the middle loop the j loop performs in a complete run of it In the ith iteration of the middle loop The middle loop runs a total of times To get the total number of operations we need to add up the number of operations performed for each value of j That is the total number of operations performed in the middle operations are performed This total depends on the value of j start adding from the smallest value of j 3 Finally we compute the total number of operations this algorithm performs In the ith iteration of the outer loop The outer loop runs a total of times To get the total number of operations we need to add up the number of operations performed for each value of i That is the total number of operations performed in the algorith operations are performed This total depends on the value of i

K Determine whether the following pair of sets is equivalent Justify your answer 4 8 12 and a e i Are the sets equivalent OA No the two sets do not have any of the same elements B Yes both sets are subsets of larger sets OC Yes both sets have the same number of elements O D No neither set is a subset of the other C

K Decide whether the following statement is true or false x x is a letter in the word baggy y y is a letter in the word baggier Is the statement true or false OA The statement is false because not every element of the second set is an element of the first set OB The statement is true because every element of the first set is an element of the second set OC The statement is false because not every element of the first set is an element of the second set OD The statement is true because at least one of the elements of the first set is an element of the second set

8 Stephen sets up an IRA with an APR of 4 at age 26 At the end of each month he deposits 57 in the account How much will the IRA contain when he reaches 65

15 A 7000 deposit in an account with an APR of 3 6 compounded continuously for 5 years

K Use an alternative method to express the following set y y is a day of the week that begins with S Choose the correct answer below OA Saturday B Sunday Monday Tuesday Wednesday Thursday Friday Saturday OC Saturday Sunday OD Sunday OE

1 100

9 You invest 500 in an account that pays simple interest of 2 for 7 years

10 You invest 8000 in an account that pays simple interest of 3 for 13 years

7 Keiko pays 340 per month for food a semiannual health insurance premium of 1600 and an annual car insurance premium of 650 Find the monthly cost for budgeting

2 The container holds 4 gallons of water How many fluid ounces is that

A warehouse is 42 yards long and 26 yards wide with a height of 13 yards What is the volume of the warehouse

1 A car is driving at 180 miles per hour What is its speed in miles per minute

Moments after Mortimer thought of Gertrude Gertrude telephoned him Therefore his thinking of her caused her to call This argument is O Strong O Weak O Valid O Sound

Educators have frequently noted the connection between education level and salary The higher a person s education level is the higher his or her annual salary is likely to be Education increases people s earning power This argument exemplifies which of Mill s methods Concomitant Variation O Agreement O Joint Method of agreement and difference Difference

Whenever we have great roses like this it s always been after a long period of cloudy weather Must be they don t like direct sun Which of Mill s methods is exemplified in this passage O Agreement O Difference O Concomitant Variation O Residues

Two hundred samples of water taken from many sites all concentrations of toxic chemicals Obviously the water in the Charles River is unsafe This argument is an example of O inductive generalization O causal reasoning O modus tollens analogical reasoning Question 11 The above argument is strong weak 1 pts

Two hundred samples of water taken from many sites all along the Charles River show unsafe concentrations of toxic chemicals Obviously the water in the Charles River is unsafe This argument is an example of inductive generalization Ocausal reasoning O modus tollens Oanalogical reasoning

A random nationwide poll of several thousand gun owners shows that 80 of them are opposed to gun control laws Thus most adults oppose gun control laws This argument is an example of O inductive generalization Ocausal reasoning O modus tollens analogical reasoning

Find the value of the given trigonometric function Hint Convert the radian measure to degree first 5x tan 12 A 3 732 B 3 554 C 3 961 D 3 294 I

The above argument commits O no fallacy O the fallacy of biased sample O the fallacy of hasty generalization O the fallacy of post hoc ergo propter hoc

I notice that the old people in an assisted living facility are dying frequently I conclude that it is the facility itself that is causing their deaths This argument commits which fallacy biased sample Onon causa pro causa post hoc ergo propter hoc

A V 0 03 Nm Its potential energy V is given by the equation mentioned below V Whe2 where 0 is in radians 2 B V 0 02 Nm migur Find V if W 8 75N b 0 75m and 0 5 5 V 0 04 Nm Fig 8 28 D V 0 05 Nm W Copyright 2015 Pearson Canada Inc I

x 30 for i n 2 to n x 5 next i The number of operations performed by this algorithm depends on whether n is even or odd Case 1 n is even There are oop is Case 2 n is odd There are oop is operations performed in each run of the loop and the loop runs operations performed in each run of the loop and the loop runs times so the total number of operations performed in times so the total number of operations performed in

Find the area of the parcel of land shown in figure below It is a right angle triangle attached to a circle sector A 1040 m B 1120 m 1260 m D 1180 m Fig 8 51 20 0 40 0 m 30 0 m Copyright 2015 Pearson Canada Inc X S Time 240 r Atter 3 atte Grading M Description Please revie for Assignm check what closest ansv recorded T 11 30 PM sheet at the deducted if and drop the

8 I pledge allegiance to the flag of the United States of America and to the republic for which it stands one nation under God indivisible with liberty and justice for all What is this O Argument O Not an argument O No answer text provided

14 Earl collided with another car because he was texting while driving What is this Argument O Explanation No answer text provided

15 The First Amendment is fundamentally important because it guarantees freedom of speech and freedom of religion What is this O Argument O Explanation O No answer text provided No answer text provided

18 Among the reasons for the American Revolution were taxation without representation and the quartering of British troops in American homes What is this O Argument O Explanation O No answer text provided O No answer text provided

20 Martin Luther was saved persecution by the Church authorities because of the time intervention of Frederick the Wise Elector of Saxony What is this O Argument O Explanation