Basic Math Questions and Answers

Question 22 Round these numbers to three significant figures as shown in class 1 566 38 2643468 374 649 2 11972 0 07052

Precision and Accuracy Four samples were taken from a population with a true population percentage of p 53 The number lines below show the sample percentages that resulted Determine precision and accuracy of the sample percentages 52 52 Select an answer 53 Select an answer Question Help Ro 53 e 54 54 52 52 0000 53 Select an answer Select an 53 54 54

1 23 67 6 62 0 4 2 5 8 Name Mark an X for each category that applies Number Real Rational Irrational 2 7 2 5 7 25 1 4 75 3 4 September 2023 Group Work The Real Number System 9 10 11 12 4 13 5 2 14 2 3 15 12 5 8 16 4982 17 17 1 18 3 9 9 0 3 0 Integer Whole Natural

cubic inches Convert 898 59 cubic meters into cubic inches Round your answer off to the nearest hundredth if necessary Measurement and Conversion Table

estion 15 What is the percent uncertainty of the given measurement 137 5776 0 0005 sec onds Question Help Merca

Question 14 More accurate More precise First determine which number x or y is more accurate then which is more precise x 5 000 y 0 0070

on 10 Use the conversion factor 1 gallon 3 785 liters Convert 21 gallons per minute to liters per hour 21 gallons per minute liters per hour Round your answer to the nearest tenth Question Help Message instructor

Question 8 miles per gallon While researching vehicles Elias finds that the fuel economy of a particular vehicle is given as 12 68 kilometers per liter Convert this into miles per gallon Round your answer off to the nearest hundredth if necessary Measurement and Conversion Table

Question 16 How many significant figures does 9 984 860 0000 have Question Help Message instructor

Question 19 Determine the accuracy i e the number of significant figures of this number 37000 Select an answer Question Help Message instructor Submit Question

Question 23 Calculate the sum below and express the result with the correct number of significant figures 69 60 0 7780 256 900 Question Help Message instructor

Core 1732 1 32 answered Question 2 Complete the following table by filling in the missing metric prefixes abbreviations or multiplication factors The multiplication factor may be entered as a decimal a fraction or a power of 10 Metric Prefix Choose no prefix Choose B Choose Choose B nano Question Help Message instructor Abbreviation Choose base unit d Choose P Choose Multiplication Factor 10 10 10 3

32 answer Simplify this number and write the answer in appropriate scientific notation with the mantissa rounded to 3 decimal places Question Help Message instructor Submit Question 8 640 10 1 242 10 1 2 208 10 14 Note There are no questions that combine converting units with rounding rules Please remember to complete the practice worksheet to ensure you understand how to combine those concepts There will be instances on exams where you will need to do a unit conversion and round to the correct number of significant figures

Question 29 Rewrite this number in appropriate scientific notation 0 0073 108

Question 4 Convert 233 9 feet per minute into centimeters per second Round your answer off to the nearest hundredth if necessary centimeters per second Measurement and Conversion Table

Question 31 Multiply the following and express your answer in appropriate scientific notation 6 5 x 10 26 x 8 2 10 7 product Questi

The farmer decided that he ordered enough planks for an arena that measured 1151 ft by 631 ft Is he correct Explain

Determine whether the functions y and y2 are linearly dependent You can use the definition or the Wronskian 1 y t e t y t e 4t 2 y t te t y2 t e t 3 y t e t cos 2t y2 t e t sin 2t

How long will it take Jasmine and Ralph working together at the same individual rates to peel one pound of apples Be sure to include units in your answer

Solve Several different bus routes stop at the corner of Second St and Lincoln Ave A Wilkenson bus arrives every 33 minutes a Fifth Avenue bus arrives every 21 minutes and a Harris Road bus arrives every 77 minutes If both buses arrive at the stop at 5 07 AM how many minutes will pass before both buses arrive at the same time again O231 minutes 21 minutes 77 minutes

It takes Jasmine of an hour to peel a pound of apples It takes Ralph of an hour to peel a pound of apples If each person continues to work at the same rate how many pounds of apples can Jasmine and Ralph peehin one hour 12

solution Problem 7 y y 0 Problem 8

5 2 Here is one way to solve the equation 5x 45 Explain what is done in each step 5x 45 2 x 9 x 9 Original equation Step 1 Step 2 x 3 or x 3 Step 3

3 Write a statement and an expression to represent the tape diagram Then evaluate your expression 22 9 22 9 22 9 22 9 22 9 22 9 Statement Expression Value of Expression

2 y 1 2 x 4

Given the following illustration find the TIME in all locations ALSO Bases upon the location of the Sun Identify what portion of the Earth is currently DARK you can say top or bottom given given EACH position THE INFORMATION BELOW FIND THE TIME OF DAY FOR 6AM 6PM 12 Am 12 pm Am apm 3AM 3pm of EARTH 2 shade the dark side 3 SUN 4 A 2 1 1 2 3 4 7

stralia s Great Barrier Reef The map shows disease conditions on coral reefs at six study sites of white syndrome an infectious disease of coral was investigated in a six year study on Key Number of colonies with white syndrome per 1500 m of reef 50 O 26 50 1 25 0 Cooktown Lizard Island Cairns Townsville a i Identify the site with the highest incidence of diseased colonies 1 a ii Deduce whether there is a trend in the incidence of white syndrome over the north south range of latitude 1

7 9 3 5 1 Solving Rational Equations Solve each equation Remember to check for extraneous solutions 312 45X11 4r 2 15r 4 55r 5r 5r 1 x 3 3r r 6 2 6 x 3 1 3 a 5 3a 15a 18 r 19 1 r 3 3 a 6 Simplify each expression 5 5 x 4 x 3 4 v 9v 20 v 9v 20 4 2 3x 9 3 1 2X17 x 2x 2x r a 4 a 5a 6 v 3 v 4 Name ro 4 1 2 6 2 b 1 8 k 6 2k 8k 6 k 6k Date 1 n 5 10 b 56 4 n 5n 6r 3r 9 4 3 Period 5b 20 b 56 4 n 10n 24 n 5n

10 IB QUESTION The following graph represents a function y f x where 3 x 5 The function has a maximum at 3 1 and a minimum at 1 1 2 3 2 0 F3 a The functions u and v are defined as u x x 3 v x 2x where x R i State the range of the function uo f

1 a Use Taylor s theorem to show that if a 2 1 then 0 1 x e b Let m 0 Is the following statement True or false Explain why If 0 1 z e then 0 1 2 e

Revenue Cost of Revenue Gross Profit Operating Expenses Operating Income Loss Non Operating Income Loss Pretax Income Loss Adjusted Abnormal Losses Gains Pretax Income Loss GAAP Income Tax Expense Benefit Net Income Interest Expense In Millions of USD Cash Cash Equivalents STI Accounts Notes Receiv Inventories Other ST Assets Total Current Assets Property Plant Equip Net Property Plant Equip Accumulated Depreciation LT Investments Receivables Other LT Assets Total Noncurrent Assets Total Assets Liabilities Shareholders Equity Payables Accruals ST Debt Other ST Liabilities Total Current Liabilities LT Debt Other LT Liabilities Total Noncurrent Liabilities Total Liabilities Total Equity 274 515 365 817 394 328 169 559 212 981 223 546 104 956 152 836 170 782 43 887 51 345 108 949 119 437 26 334 119 103 0 38 668 66 288 721 67 009 82 67 091 9 680 57 411 2 873 42 296 15 229 47 867 105 392 107 049 108 923 284 109 207 119 103 14 527 19 300 94 680 99 803 FY 2020 FY 2021 09 26 2020 09 25 2021 90 943 62 639 16 120 26 278 4 061 6 580 32 589 39 339 143 713 134 836 45 336 49 527 112 096 119 810 66 760 70 283 100 887 127 877 33 952 38 762 180 175 216 166 323 888 351 002 46 108 153 157 258 549 65 339 2 645 54 763 17 141 53 577 FY 2022 09 24 2022 48 304 28 184 4 946 2 931 53 971 135 405 52 534 124 874 72 340 120 805 44 011 217 350 352 755 64 115 22 773 67 094 153 982 109 707 38 394 125 481 119 381 43 050 162 431 148 101 287 912 302 083 63 090 50 672

In Millions of USD except Per Share 12 Months Ending Revenue Cost of Revenue Gross Profit Operating Expenses Operating Income Loss Pretax Income Loss Adjusted Abnormal Losses Gains Pretax Income Loss GAAP Income Tax Expense Benefit Net Income Interest Expense In Millions of USD Total Assets Cash Cash Equivalents STI Accounts Notes Receiv Inventories Other ST Assets Total Current Assets Property Plant Equip Net Property Plant Equip Accumulated Depreciation LT Investments Receivables Other LT Assets Microsoft Corp MSFT US Standardized Total Noncurrent Assets Total Assets Liabilities Shareholders Equity Payables Accruals ST Debt Other ST Liabilities Total Current Liabilities LT Debt Other LT Liabilities Total Noncurrent Liabilities Total Liabilities FY 2020 FY 2021 FY 2022 06 30 2022 06 30 2020 06 30 2021 143 015 0 168 088 0 198 270 0 46 078 0 52 232 0 62 650 0 96 937 0 115 856 0 135 620 0 43 528 0 45 940 0 52 237 0 53 409 0 69 916 0 83 383 0 53 420 0 69 870 0 83 255 0 384 0 1 232 0 461 0 53 036 0 71 102 0 8 755 0 9 831 0 44 281 0 61 271 0 Total Equity Total liabilities Equity 2 591 0 FY 2020 06 30 2020 2 346 0 FY 2021 06 30 2021 136 527 0 130 334 0 32 011 0 38 043 0 1 895 0 2 636 0 11 482 0 13 393 0 181 915 0 184 406 0 52 904 0 70 803 0 96 101 0 122 154 0 43 197 0 51 351 0 2 965 0 5 984 0 63 527 0 72 586 0 119 396 0 149 373 0 301 311 0 333 779 0 118 304 0 301 3110 27 394 0 10 825 0 50 438 0 88 657 0 71 453 0 83 716 0 10 978 0 72 738 0 141 988 0 333 779 0 2 063 0 22 534 0 33 728 0 5 905 0 6 037 0 43 871 0 55 317 0 72 310 0 95 082 0 76 205 0 72 363 0 34 492 0 31 681 0 30 853 0 110 697 0 103 134 0 103 216 0 183 007 0 191 791 0 198 298 0 FY 2022 06 30 2022 104 757 0 44 261 0 3 742 0 16 924 0 169 684 0 87 546 0 147 206 0 59 660 0 6 891 0 100 719 0 195 156 0 364 840 0 166 542 0 264 940 al

a Let f y t y sin t and let D R Show that f is a Lipschitz function in y on D and state the Lipschitz constant b Let f y t 1 12 and let D y t MSys M teR for some M 0 Show that f is Lipschitz continuous in y on D and state the Lipschitz constant Hint it will be useful to remember the triangle inequality 121 221 121 22

Answer the following Poisson exercises using the Excel function Poisson in your equation Enter your Excel equations in the highlighted cells 1 a b C d e A textile manufacturer process finds that on average four flaws occurs per every 60 yards of material produced Write the Excel equation using an Excel function that will calculate the probability of exactly three flaws in a 60 yard piece of material Write the Excel equation using an Excel function that will calculate the probability of three or less flaws in a 60 yard piece of material Write the Excel equation using an Excel function that will calculate the probability of five or more flaws in a 60 yard piece of material Write the Excel equation using an Excel function that will calculate the probability of two or less flaws in a 30 yard piece of material Write the Excel equation using an Excel function that will calculate the probability of two or less flaws in a 15 yard piece of material

Adjustment for prepaid expense The prepaid insurance account had a beginning balance of 7 340 and was debited for 3 230 of premiums paid during the year Journalize the adjusting entry required at the end of the year assuming the amount of unexpired insurance related to future periods is 4 120 If an amount box does not require an entry leave it blank Insurance Expense

Adjustment for accrued expense City Realty Co pays weekly salaries of 13 375 on Monday for a six day workweek ending the preceding Saturday Journalize the necessary adjusting entry at the end of the accounting period assuming that the period ends on Friday Round your answers to nearest whole dollar If an amount box does not require an entry leave it blar 88 Salaries Expense Salaries Payable

Use PMT P nt to determine the regular payment amount rounded to the nearest dollar The price of a home is 125 000 The bank requires a 20 down payment and three points at the time of closing The cost of the home is financed with a 30 year fixed rate mortgage at 10 Complete parts a through e below a Find the required down payment b Find the amount of the mortgage c How much must be paid for the three points at closing Round to the nearest dollar as needed d Find the monthly payment excluding escrowed taxes and insurance Round to the nearest dollar as needed e Find the total cost of interest over 30 years Round to the nearest dollar as needed

One safe investment pays 7 per year and a more risky investment pays 9 per year a How much must be invested in each account if an investor of 96 000 would like a return of 7 240 per year b Why might the investor use two accounts rather than put all the money in the 9 investment a is invested in the 7 account is invested in the 9 account b Why might the investor use two accounts OA Investing in two accounts always yields more money than investing in just one account OB Although the 9 account earns more interest the 7 account has no hidden fees OC The 9 investment is riskier than the 7 investment There is a greater chance the investor will lose money if it is all placed in the 99 OD The 9 account does not earn as much interest as the 7 account

Write the equation for the stated transformation on the following function A reflection in the x axis f x x 6

Perform the stated operation on the following functions f x 2x g x x 1 2 f g 2

Question 13 Perform the stated operations on the following functions f x 2x g x x g f 1

Perform the stated operation on the following functions x 2 f x x g x 2x 4 f x g x

Professor L Question 3 Completely simplify the following expression 6x y z4 z

The following table gives the number of women age 16 years and older in millions in a country s Kovillan workforce for selected years from 1950 and projected to 2050 Complete parts a and b below Women in the Year Workforce millions Year 1950 2010 1960 2015 1970 2020 1980 2030 1990 2040 2000 2050 a Use x as the number of years past January 1st 1950 to create a cubic model y using these data 0x 0x 0x0 Type integers or decimals rounded to five decimal places b During what year does the model indicate that the number of women in the work force will reach its maximum 10 Round down to the nearest year 18 6 21 1 30 6 45 8 56 4 65 9 Women in the Workforce millio 75 3 77 2 79 8 80 8 86 1 91 9

12 Months Ending Revenue Cost of Revenue Gross Profit Operating Expenses Operating Income Loss Non Operating Income Loss Pretax Income Loss Adjusted Abnormal Losses Gains Pretax Income Loss GAAP Income Tax Expense Benefit Net Income Interest Expense In Millions of USD Cash Cash Equivalents STI Accounts Notes Receiv Inventories Other ST Assets Total Current Assets Property Plant Equip Net Property Plant Equip Accumulated Depreciation LT Investments Receivables Other LT Assets Total Noncurrent Assets Total Assets Liabilities Shareholders Equity Payables Accruals ST Debt Other ST Liabilities Total Current Liabilities LT Debt Other LT Liabilities Total Noncurrent Liabilities Total Liabilities 09 26 2020 09 25 2021 09 24 2022 274 515 365 817 394 328 169 559 212 981 223 546 104 956 152 836 170 782 38 668 43 887 51 345 66 288 108 949 119 437 721 26 334 67 009 119 103 82 0 67 091 9 680 57 411 2 873 FY 2020 09 26 2020 90 943 16 120 4 061 32 589 143 713 45 336 112 096 42 296 15 229 47 867 108 923 284 109 207 14 527 94 680 FY 2021 09 25 2021 62 639 26 278 6 580 39 339 134 836 49 527 119 810 66 760 70 283 100 887 127 877 33 952 38 762 180 175 216 166 323 888 351 002 105 392 107 049 46 108 2 645 54 763 17 141 53 577 125 481 119 381 43 050 153 157 162 431 258 549 287 912 119 103 19 300 99 803 2 931 FY 2022 09 24 2022 48 304 28 184 4 946 53 971 135 405 52 534 124 874 72 340 120 805 44 011 217 350 352 755 64 115 22 773 67 094 153 982 109 707 38 394 148 101 302 083

A concert promoter needs to make 108 000 from the sale of 1900 tickets The promoter charges 60 for some tickets and 40 for the others Complete parts a through e a If there are x of the 60 tickets and y of the 40 tickets Write an addition equation that states that the total number of the tickets sold is 1900 Type an equation Do not simplify b How much money is made from the sale of x tickets at 60 each c How much money is made from the sale of y tickets at 40 each d Write an equation that states that the total amount made from the sale is 108 000 Type an equation Do not simplify e Solve the equations simultaneously to find how many tickets of each type must be sold to yield the 108 000 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The promoter should sell tickets at 60 each and tickets at 40 each OB There are infinitely many solutions If the promoter sells y tickets at 40 each then Type an expression using y as the variable OC There is no solution tickets at 60 each should be sold

The matrix associated with the solution to a system of linear equations in x y and z is given Write the solution to the system if it exists 10 COD Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA xa y and z Simplify your answers OB There are infinitely many solutions If z is allowed to be any real number then x Type expressions using z as the variable OC There is no solution and y

7 OPEN RESPONSE Use the figure If AB 3 15 what is BD Write the answer in simplest radical form Lesson 4 4 A B 1 D

Use the graph of the polynomial function f x a to solve f x 0 and b find the factorization of f x x 2x 6x 10x 6x 8 a Choose the correct solution for f x 0 OA x 1 andx 4 B x 1 x 1 and x 4 OC x 1 x 1 and x 4 OD x 1 andx 4 b The factorization of the polynomial function f x is Type your answer in factored form CIT 60 40 20 20 60 80 Ay

K The total number of a particular chain store in the world can be modeled by the cubic function y 10 4x 402x 5595x 8698 where x is the number of years aft 2000 and y is the total number of stores Complete parts a through c below a Graph the function on the window 2 20 2 by 8000 23000 1000 OA B O No OYes GILD b What does the model predict the number of stores will be in 2025 The model predicts that there will be A Round to the nearest whole number as needed c Does the number of stores ever decrease over this period of years ending in 2020 according to the model stores in 2025 O C OD