Basic Math Questions and Answers

Adam s school is a 20 minute walk or a 5 minute bus ride away from his house The bus runs once every 30 minutes and the number of minutes w that Adam waits for the bus varies between 0 and 30 Which of the following inequalities gives the values of w for which it would be faster for Adam to walk to school A w 5 20 B w 5 20 C W 5 20

Anita created a batch of green paint by mixing 2 ounces of blue paint with 3 ounces of yellow paint She must mix a second batch using the same ratio of blue and yellow paint as the first batch If she uses 5 ounces of blue paint for the second batch how much yellow paint should Anita use A Exactly 5 ounces B 3 ounces more than the amount of yellow paint used in the first batch C 1 5 times the amount of yellow paint used in the first batch D 1 5 times the amount of blue paint used in the second batch

The following graph shows the relationship between the number of Frisbees produced and the cost of production The vertical intercept is 40 and the slope of the line is per Frisbee Point d shows that the cost of producing Frisbees is The cost of producing 15 Frisbees is Costs per day Y 180 170 160 150 140 130 120 110 100 90 80 70 60 50 400 30 a 20 10 0 0 T 5 ib 10 C d 15 20 25 30 Frisbees per day X 35 40 O G

Select all numbers that are in engineering notation check all that apply 45 234 10 1 0 325 10 2 701 10 1 0101 2 2 0 1101 2 1 111 235 SUBMIT How do computers deal with numbers Representation of numbers Computers use base 2 only digits are 0 and 1 binary digits are called bits Numbers are stored as binary floating point numbers in engineering notation Floating point numbers in engineering notation we can do the exact same thing in binary 1 bbbb 2 bbbb is the mantissa there always must be a 1 to the left of the point engineering notation the exponent p can be converted to binary but we ll leave it as a decimal number How to convert floating point numbers to engineering notation move the point to the left or right until a single non zero digit is to the left of the moving the point one place to the left increase exponent by 1 moving the point one place to the right lower exponent by 1 Examples in binary p is the exponent 101 11 10 2 10 111 2 1 0111 2 0 01101 0 00 20 21 101 2

Which of the answers for the following conversions contains the correct number of significant figures 2Lx 1 06 gt 1L 12 0 ft x 12in 1 ft 2 543 m x 2 12 qt 24 0 kg x 2 54 cm 1 in 394 in 1 m 1lb 2 20 kg 24 95 min x 100 1942 in 11 lb 370 cm 1 hr 60 min 0 4158 hr

The face of a dam is 10 m high and 20 m wide If the body of water behind the dam is 9 m deep h in the figure at what distance below the surface does the pressure force act V h Fp

1 Here are the first two terms of a geometric sequence 2 4 What are the next three terms 2 What is the growth factor of each geometric sequence a 1 1 1 1 1 b 256 128 64 c 18 54 162 d 0 8 0 08 0 008 0 008 0 08 08

4 7 1 38 1 4 Simplify the improper fractions 10 Convert the improper fractions into whole numbers 2 40 8 5 81 1 28 Solve and simplify the answer 13 2 3 4 2 X 16 5 5 2 43 75 19 2 3 9 22 3 5 5 15 B Decimals Convert the fraction to a decimal 38 10 42 C Percentages Convert to a percentage 10 100 8 5 11 40 3 81 10 14 1 3 2 4 17 47 x 105 20 3 23 4 7 10 21 2 46 10 71 10 2 63 100 5 10 3 205 6 63 9 24 5 12 613 15 5 x 5 18 67 2 21 5 3 14 24 63 4 3 265 6 61 5 3 13 100 6 10

Which of these two analytically equivalent expressions is more prone to round off error if x is very small O 1 64 x 8 O 64 x 8 X both are the same

6 At a restaurant 4 hotdogs cost 68 64 and 5 hamburgers cost 86 00 Which food has the lower unit price

890 400 89 400 8 094 x 10 8 94 x 105 19 The table represents the box office sales of the highest grossing movie in 2019 in various markets Write each number in standard form and in scientific notation

I Ginorme 0 05 per square inch 14 TT 196 TT The Ginorme costs approximately 0 05 for each square inch of pizza 1 Consider Lina s and Michael s work a Explain why Lina s and Michael s unit rates are different but still both correct b How would you decide which pizza was the better buy if yo calculated the unit rate for each pizza using Lina s method versus Michael s method

15 If the quadratic parent function is reflected 16 If the cube root parent function is in the y axis and vertically compressed by a factor of write an equation to represent the new function 17 The absolute value parent function has transformations applied such that it creates an absolute maximum at 2 7 Write an equation that could represent this new function 1 Describe all transformations from the parent function given the function below f x 3 12 x 7 3 x 4 horizontally stretched by a factor of 4 then translated 5 units right and 3 units up write an equation to represent the new function Graph each function and identify all key characteristics 2 f x 22 f x 2 x 3 4 A certain function is vertically stretched by a factor of 2 horizontally compressed by and translated down 6 The new function is represented by f x 618x1 2 Write the equation of the original function 20 Describe all transformations from the parent function given the function below f x x 5 2 Domain x int Extrema Increasing Interval Decreasing Interval End Behavior Domain x int Extrema Range y int Increasing Interval Decreasing Interval End Behavior Range y int

Suppose a new standard MAE384 12 is defined to store floating point numbers using 12 bits The first bit is used to store the sign as in IEEE 754 the next 6 bits store the exponent plus the appropriate bias and the remaining 5 bits store the mantissa As in IEEE 754 an exponent and mantissa of all zero bits is used to indicate true zero and an exponent of all one bits together with a mantissa of all zero bits is used to store infinity Determine by hand in decimal format a the bias for storing exponents in MAE384 12 b the smallest possible non zero positive number c the largest possible finite positive number d the smallest possible difference between 1 0 x 10 and the next larger possible number e the smallest possible difference between 7 0 x 10 and the next larger possible number Problem 5 required submission Handwritten or printed all steps to obtain the answers incl the final answers

a Develop a Matlab function decimal2binary that converts a decimal number z into a binary floating point number in engineering notation The function shall take as input the decimal number x and the number of bits to be used in the mantissa N excluding the hidden bit and shall output the vector m containing the N mantissa bits excluding the hidden bit the exponent p in decimal of the binary floating point number in engineering notation and the remainder r of the transformation Do not print out results to screen within the function b Using the function decimal2binary convert the decimal number 0 1 to a binary floating point number in engineering notation using 10 50 and 60 mantissa bits and report the remainders c Why does Matlab report the remainder as 0 when 60 mantissa bits are used even though infinitely many bits would be required to convert the decimal number 0 1 into a binary floating point number Problem 3 required submission Printout of well commented script you coded included in your Gradescope submission Binary floating point numbers in engineering notation and their remainders Handwritten or printed answer to c

Develop a Matlab function mySquares that calculates the first N squares As input the function shall take the positive integer number N and as output the function shall give a column vectory of length N containing y for i 1 N Function Code to call your function C Reset MATLAB Documentati C Res

People drive on average 14 058 miles per year About how many miles each week is that Note There are 52 weeks in a year People drive about miles each week Type a whole number or decimal rounded to the nearest tenth as needed

of 3 ok int ences Required information The following information applies to the questions displayed below The accounting records of Nettle Distribution show the following assets and liabilities as of December 31 for Year 1 and Year 2 December 31 Cash Accounts receivable Office supplies office equipment Trucks Building Land Accounts payable Note payable Year 1 43 421 23 570 3 718 114 130 44 661 Equity December 31 Year 1 0 0 61 965 0 Year 2 6 561 18 479 2 723 121 570 53 661 148 880 37 151 30 733 86 031 2 Compute net income for Year 2 by comparing total equity amounts for these two years and using the following information During Year 2 the owner invested 35 000 additional cash in the business in exchange for common stock and the company paid a 39 600 cash dividend

4 1 of 3 S eBook Print eferences The accounting records of Nettle Distribution show the following assets and liabilities as of December 31 for Year 1 and Year 2 December 31 Cash Accounts receivable Office supplies Office equipment Trucks Building Land Accounts payable Note payable Year 1 43 421 23 570 3 718 114 130 44 661 0 0 61 965 0 Balance Sheet Balance Sheet Year 1 Year 2 Year 2 6 561 18 479 2 723 121 570 53 661 148 880 37 151 30 733 86 031 Required 1 Prepare balance sheets for the business as of December 31 for Year 1 and for Year 2 Hint Report only total equity on the balance sheet and remember that total equity equals the difference between assets and liabilities Complete this question by entering your answers in the tabs below Prepare the balance sheet for the business as of December 31 for Year 1 Hint Report only total equity on the balance sheet and remember that total equity equals the difference between assets and liabilities NETTLE DISTRIBUTION Ch

10 8 6 4 2 2 4 6 8 10 A Zero 10 8 B Exactly one If a new graph of three linear equations is created using the system of equations shown and the equation x 4y 16 how many solutions x y will the resulting system of three equations have Exactly two 6 8 10 X

Question 5 Points 1 What happened to tone color in the twentieth century Used decreased stringed instruments and rhythms Used decreased brass instruments and rhythms A Used increased percussion instruments and old melodies Used increased percussion instruments and rhythms

Let s do a quick check which way should the internal norma axial load jump when going from left to the right of the horizontal point load of 2000 N applied at point B as shown below Please provide your answer in PlayPosit A 2m B 2m C Fr 1080 N 2000 N A It jumps down from 2000 N to 1000 N B It jumps up from 2000 N to 3000 N C It jumps down from 3000 N to 1000 N D It jumps up from 1000 N to 3000 N

Macmillan Learning Let f x 6x 5 Calculate f x h f x h 0 h Express numbers in exact form Use symbolic notation and fractions where ne f x h f x

Option 2 The Bill of Rights is not only included with the United States Constitution but also state constitutions All states have provisions in their constitutions that protect individual rights Go online and look up your state constitution concerning amendments that are included in the Bill of Rights How does your state constitution protect your individual rights The NJ state constitution protects my individual rights by including the Bill of Rights in their constitution The NJ state constitution includes the first amendment addressing freedom of speech and religion in its first article I believe the NJ state constitution provided more detail on the meaning of freedom of speech and religious rights than the Bill of Rights The NJ state constitution explained there is no racial or religious qualification for public trust or office and that one religion is not more valuable than another NJ State Constitution 1947 I feel this provides more details to the citizens of NJ of the meaning of the First Amendment and protects citizens individual rights Our textbook explained how over time civil liberties have changed and how many of the freedoms we expect today are not explicitly spelled out there Greenberg Page 2018 p 432 The NJ State Constitution does have out of date provisions listed such as allowing the death penalty in certain circumstances NJ currently does not allow the death penalty while the Bill of Rights does not address the death penalty The Bill of Rights 1791 NJ State Constitution 1947 Understanding that state constitutions protect individual rights is essential The article State Constitutional Law The Future of Abortion Rights explained how advocates can use state constitutions to protect abortion rights in the absence of federal protections Wittbrod 2023 p 581 Being aware of our own state s constitution can protect citizens abortion rights being an example My state NJ protects my rights but providing more details about the First Amendment References The Bill of Rights 1791 National Archives https www archives gov files legislative resources education bill of rights images handout insary

Ali a college freshman is deciding on classes for his first term He can choose to take some or none of the six classes from the list below He can t take all of them Astronomy Biology Chemistry Dance Economics Geography In how many different ways can Ali choose the classes to take The order of the classes chosen doesn t matter

Determining the nu Ivan got a train ticket valid for the five cities listed below He can choose to visit some or all of these cities He must visit at least one of them Amsterdam Brussels Lille Paris Rotterdam In how many different ways can Ivan choose the cities to visit The order of the cities chosen doesn t matter X S

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2 What article and section s of the Constitution prove the founding fathers intended to limit the power of government by ensuring citizens have a role in electing those who govern them

for each problem document all steps you took to solve the problem This can be handwritten but must be legible for credit If the problem states By hand do not use any program function to solve the problem however you may use a non programmable calculator to help in determining the numerical results of individual steps submit to Gradescope the requested Gradescope portions listed under each problem on Gradescope associate select your answer pages with the corresponding problem numbers Failure to do so may result in no points given initially and will require a re grade request to fix If the problem header contains MatlabGrader you must submit your solution to Matlab Grader using the Course Navigation Bar Link Matlab Grader Homework F23 Problem 1 MatlabGrader Develop a Matlab function mySquarea that calculates the first N squares As input the function shall take the positive integer number N and as output the function shall give a column vector y of length N containing y 1 for i 1 N Problem I required submission Well commented function source code submitted to Matlab Grader Problem 2 MatlabGrader Gradescope Write a script that generates a plot of the first 20 squares vs i Use your function from problem 1 to generate the data to plot Notes for the MatlabGrader script submission Comment out clear or clear all in your script when submitting to Matlab Grader Generate and store the figure handle examFig1 for the graph before doing any plotting commands using examFigl figure 1 Properly label both axis using the appropriate variable names i e i y Do not include the source code for mySquares in your submission A correct version is used automatically on Matlab Grader Problem 2 required submission Well commented script source code submitted to Matlab Grader Printout of well commented script you coded included in your Gradescope submission

Problem 1 The height of a projectile h is a function of the time t it is in the air The height in feet for t seconds is given by the function h t a What is the domain of the function b What does the domain mean in the context of the problems c Suppose h 2 7 3 interpret the meaning of that statement in the context of the problem and include appropriate units

P7 33 Replace the AND operations by ORs and vice versa by applying De Morgan s laws to each of these expressions a F AB C A D b F A B C D C F A B C A B C d F A B C A B C A B C F ABC A B C A B C e

Prove that the sum of the first n odd 2 positive integers is n

The arterial systolic pressure of an individual at sea level is 119 mm Hg Is this number a gage pressure or absolute pressure Why What is this number in Pascal 3525 10 80 M 886 18s 3s 23

Consider the simple economy that produces only three products Use the information in the following table to calculate the annual rate of inflation for 2022 as measured by the consumer price index CPI BASE YEAR 2010 Quantity 2 Price 10 00 2 00 10 9 15 00 2021 Price 11 00 2 45 15 00 2022 Price 16 20 2 40 14 00 Product Haircuts Hamburgers Movies Using the information in the table the CPI for 2021 with 2010 as the base year is Enter your response rounded to one decimal place

1 862 716 The 6 in the ten thousands place is the value of the 6 in the ones place

A9 foot by 50 foot concrete wall is to be built using concrete blocks Find the area of the wall The area of the wall is Simplify your answer

A computer has the shape of a rectangular solid Find the volume of the computer with dimensions of 3 inches by inches by 3 8 inches The volume of the computer is Simplify your answer Type a whole number or a decimal

Find the volume of the solid The volume of the solid is 2 cm 2 cm 2 cm

Find the surface area of a cube with edges 5 88 cm long The surface area of the cube is Type an integer or a decimal sq cm

exad of bebeen woll to equo to hodinu erti neewied 90 felpaa etalampas ni lawe For Success 4 Nylah can buy any quantity of bracelets at a rate of 15 bracelets send to assol to andmun fron 75 6 pairs of earrings How 72 She can buy any quantity of earrings at a rate of much will she spend if she purchases 4 bracelets and 4 pairs of earrings Represent ratio relationships with a double number line or table bns aixe x erit no ein et nisiqxs bns Inica incont poinsem enler 11 hogona Scrambled Answers Multiply or divide to find equivalent ratios

1 Jorma can peel 4 potatoes in 6 minutes Assuming that Jorma continues to peel potatoes at ans constant rate which of the following graphs shows the relationship between time spent peeling potatoes and the number of potatoes peeled eutangi2 Ines 18 16 14 12 S 10 8 6 4 2 y Graph A em Old 2 g 410 6 8 10 10 aspelnaoing on Minutes EN99W X 18 16 14 12 otatoes 10 8 12 1141016 1801q 82U evios al agirianoijslen olim geleiflum amaldong 6 4 2 y Graph B phowemoH O ebs12 Criteria For Success Identify coordinate points S SSAN a vitnsup s to oinatanpa 6ri8 10 12 14 16 18 ert atsluols ni viilenoihotes to erfgeng zeldet emsipsibenoitsupe lechay bon Write the point as the ratio relationship y x Multiply or divide to test for or generate equivalent ratios Inaleviupo worl2 erth no 2005T ensiq slanib1000

agiriamalielon emoldong 6 8 10 nl vinol Minutes arigenpealdel ameignib arolinu lachsv brs anchiqhoesb give ditolon 2 Which of these expressions is equivalent to 24 a 4 of 6 ga to rigsip erit no x Inlog Jertw nisiqx 9 9 b 10 of 2 4 niniqxe noilsulle eri to amat ni ensem qirianoit c 20 of 48 Jindert el 1 tertw nsem 1 1 brs 0 0 d 25 of 96 219wanA beld ert anewans salono

3 Marcellous sells historical dioramas for a constant rate as shown in the constant of proportionality leupiM bib apsd set ne vsm wo of alone h 10 alamibeb Dioramas x Dollars y is awon 1s 1900M 80 120 160 200 588 41snoihogonq ginanousist 6 TE910 ole s na dw 8 ominu noviqtiuM 10 ebivib Inupe 12 nowanA Answer et ne se ment to 08 Se Criteria For Success Identify the independent x and dependent y variables 588 Solve for the constant of proportionality using the formula y kx

1 346 342 The 4 in the tens place is the value of the 4 in the ten thousands place

1 733 The 3 in the ones place is the value of the 3 in the tens place

2 332 The 2 in the ones place is the value of the 2 in the thousands place

Given the function f x x 6x 5 determine the inverse relation

Most of them went into the program There was just a few farmers that wouldn t have anything to do with it But the majority of people they all went into the program There s a few that said The government isn t going to tell me what to do There was a few of them Now I don t think there was too many Based on your own knowledge the farmer who said these words was talking about O the Agricultural Adjustment Act AAA the Civilian Conservation Corps CCC O the Federal Emergency Relief Administration FERA O the Public Works Administration PWA Pe this Que 1 5 9

1 1 66 points eBook Hint Print Determine the missing amount from each of the separate situations given below 1 2 3 Assets 140 000 102 000 Liabilities 64 000 44 000 Equity 17 000 62 000

Thursday Amanda there are many advantages as well as issues with bureaucracy As you mentioned the bureaucratic red tape is one of them However I also feel like lack of accountability transparency and many other things are major issues as well Edwards 2015 notes tha one third of people believe that it gives competent service and people think that more than half of the tax dollars sent to Washingto are wasted Edwards 2015 found that the US citizens diminished opinion of the federal government does not come as a surprise give the multitude of high profile failures In recent years scandals have erupted at the Department of Veteran s Affairs Internal Revenu Service Secret Service and other agencies Federal auditors regularly uncover waste fraud and abuse in many departments and fede projects often have large cost overruns Edwards 2015 References Edwards C 2015 Bureaucratic Failure in the Federal Government Downsizing the Federal Government Cato Institute https www downsizinggovernment org bureaucratic failure B