Basic Math Questions and Answers

a Prove that if x 3 18 and ly 2 7 then ry 75 b Prove that if n is a natural number then either n is a multiple of 4 or n 1 is a multiple of 4 c Prove that for any positive real number x there is a natural number such that x

3 PROOF BY INDUCTION a Prove that for for every natural number n the last digit of 6 is either 4 or 6 b Prove that for any natural number n we have 1 2 3 n c Prove that for any natural number n we have 1 1 2 2 3 1 3 4 1 n n 1 d Prove that for any natural number n we have 1 1 1 2 3 e Prove that if n27 is an integer then n 3 n n n 1

A gasoline mini mart orders 24 copies of a monthly magazine Depending on the cover story demand for the magazine varies The mini mart purchases the magazines for 1 53 and sells them for 3 92 Any magazines left over at the end of the month are donated to hospitals and other health care facilities Modify the newsvendor example spreadsheet to model this situation Use what if analysis to investigate the financial implications of this policy if the demand is expected to vary between 10 and 30 copies each month Click the icon to view the newsvendor example spreadsheet The demand must be at least copies for the gasoline mini mart to break even Type a whole number Newsvendor model spreadsheet A 1 Newsvendor Model 2 3 Data 4 5 6 Cost 7 Discount price 8 9 Model 0 11 Demand 12 Purchase Quantity Selling price 13 14 Quantity Sold 15 Surplus Quantity 16 17 The for Profit B 3 92 1 53 0 10 24 MUNDURION X

Consider the market for a new CD where the price is initially 7 00 and 32 thousand copies are sold as indicated in the figure at point A The music company is considering lowering the price to 5 00 at which price 40 thousand copies would be sold What is total revenue at the initial price at point A Revenue is initially thousand

farmer has 150 acres of land suitable for cultivating Crops A and B The cost of cultivating Crop A is 40 acre and the cost of cultivating Crop B is 60 acre The farmer has a maximum of 7400 available for land ultivation Each acre of Crop A requires 20 labor hours and each acre of Crop B requires 25 labor hours The farmer has a maximum of 3300 labor hours available He has also decided that he will cultivate at least 0 acres of Crop A If he expects to make a profit of 120 acre on Crop A and 200 acre on Crop B how many acres of each crop should he plant to maximize his profit rop A rop B No Response acres No Response acres What is the maximum profit No Response

10011011111 2 Question 2 1 point Saved Convert 2855 from decimal to hexadecimal B27 16 Question 3 1 point A

The following function is one to one Find the inverse algeb

A 4 Question 5 1 point Convert 101 0111 1101 0010 2 from binary to octal A Question 6 1 point Find the quotient and remainder when 26 is divided by 7 Put the quotient in box 1 and remainder in box 2

ose that legalizing the use of heroin would decrease its price by 78 percent If the price elasticity of demand for heroin is 2 00 what would be the percentage increase in the quantity of heroin nded from legalizing heroin percent Enter a numeric response using a real number rounded to two decimal places ose instead that the price elasticity of demand for heroin is 0 11 What would be the percentage increase in the quantity of heroin demanded from legalizing heroin Onse rounded to two decimal places thigher the absolute value of the price elasticity of demand for heroin the the increase in heroin use that would result from legalization percent enter your

5 When corn seeds germinate they tend to grow 5 inches in the first week and then 3 inches per week for the remainder of the season The relationship between the height H and the number of weeks since germination W is shown below a Complete the missing values in the table Number of Weeks Since Germination W 1 2 3 4 5 6 Height of Corn Plant H 5 8 11 14

Consider the demand curve illustrated in the figure to the right Is demand elastic or inelastic OA Demand is elastic at all prices above 7 00 and inelastic at all prices below 7 00 B Demand is inelastic at all prices C Demand is elastic at all prices above 5 00 and inelastic at all prices below 5 00 D Demand is elastic at all prices O E Demand is inelastic at all prices above 7 00 and elastic at all prices below 7 00 At what price is total revenue maximized Total revenue is maximized when price equals Enter your response as a real number rounded to two decimal places CID Price 20 18 16 14 12 10 8 6 4 2 6 m ID 8 10 12 Quantity

Question 8 1 point What is the binary number 10 0111 0110 2 written in decimal 631 632 630 A 629

Var II Rosie the Riveter was A a woman who was used as an example to motivate women to work B a real woman that worked creating parts for the military during the early war years C the first woman to actively join the military during World War II

The figure below is dilated with the center of dilation at the origin and a scale factor of 12 What are the coordinates of the image of point X after this transformation 12 11 10 9 8 7 6 5 4 3 2 y 1 12 11 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 c 6 7 8 9 10 11 12 X 1 2 3 4 5 6 7 8 9 10 11 12

Use the regular hexagon to the right to answer the following question 2 Find the m 21 and m 22 Show your work to earn full credit 3 If 22 represents the expression 5x 10 then What is the value of x Show your work to earn full credit 1 2 Maler id or cre Turn in

Parallelogram ABCD A 0 0 B 3 3 C 7 1 D 4 4 Property Word Bank All sides congruent OR Opposite sides congrue All angles are right angles Diagonals congruent

5 The dot plot shows the numbers spent last night on homework by students a What does each value on the represent

Determine whether the argument to the right is valid or invalid You may compare the argument to a standard form or use a truth table Is the argument valid or invalid O Valid P 0

Let p and q represent the following simple statements p The job pays well q The taxes are high Write the symbolic statement paq in words Choose the correct sentence below O The job does not pay well and the taxes are not high It is not true that the job pays well and the taxes are high It is not true that the job pays well or the taxes are high OIt is not true that the job does not pay well and the taxes are not high

Use a truth table to determine whether the statement is a tautology self contradiction or neither p q q Is the statement p q q a tautology self contradiction or neither O Self contradiction Neither O Tautology

Construct the truth table for the compound statement pv q vr Fill in the empty values of the truth table Start with the first four rows Now fill in the final four rows pq r TTT TTF TFT TFF FTT FTF FFT FFF Truth Table pv q vr

Construct a truth table for the following statement pv q Complete the truth table P T q T q pv q N

b dob Fill in the truth table P T T F LL b T F T LL d b b db

Sandhill Distribution markets CDs of numerous performing artists At the beginning of March Sandhill had in beginning inventory 2 500 CDs with a unit cost of 8 00 During March Sandhill made the following purchases of CDs March 5 March 13 a 1 850 9 00 4 000 10 00 Your Answer Correct Answer Used During March 11 900 units were sold Sandhill uses a periodic inventory system Determine the cost of goods available for sale Cost of goods available for sale Weighted average cost per unit b March 21 March 26 Calculate weighted average cost per unit Round answer to 3 decimal places e g 5 125 Ending inventory 4 800 1 850 5 FIFO 151 650 Determine 1 the ending inventory and 2 the cost of goods sold under ach of the assumed cost flow methods FIFO LIFO and average cost Round answers to 0 decimal places e g 125 11 00 12 00 10 110 LIFO AVERAGE COST

What is a national convention O A national convention is a meeting at which the delegates vote to pick their presidential and vice presidential candidates A national convention is a meeting where delegates from each party are chosen The delegates will choose the presidential and vice presidential candidates at the party caucus A national convention is a meeting of members from all parties who vote in a preliminary vote to see who will win Presidency A national convention is meeting at which the newly elected President and Vice President choose their cabinet members

What is the image point of 1 3 after the transformation R90 ory axis

3 2 Choosing the Best Measure of Center Find the mean median and mode of the sneaker prices Which measure best represents the data Mean 20 31 122 48 37 20 45 65 8 Median 20 20 31 37 45 48 65 122 37 45 82 2 2 Mode 20 20 31 37 45 48 65 122 20 30 40 4 Mode 20 Median 41 50 60 or 41 70 Mean 48 5 80 90 388 8 or 48 5 Order from least to greatest The value 20 occurs most often 100 Mean 110 120 130 The median best represents the data The mode is less than most of the data and the mean is greater than most of the data Price dollars On Your Own Find the mean median and mode of the data Choose the measure that best represents the data Explain your reasoning 3 1 93 46 48 34 194 67 55 4 96 150 102 87 150 75 An outlier is a data value that is much greater or much less than the other values Removing an Outlier Identify the outlier in Example 2 Find the mean median and mode without the outlier Which measure does the outlier affect the most The price of 122 is much greater than any other price So it is the outlier Median Mode

Write the negation of the following conditional statement If a fruit is blue then it is not a banana O A fruit is not blue and it is a banana O If it is not a banana then a fruit is blue O If it is a banana then a fruit is not blue O A fruit is not blue and it is not a banana O A fruit is blue and it is a banana O A fruit is blue and it is not a banana O If a fruit is not blue then it is a banana it is not blue

2x B x 6 x 15 x 30 x 60 A 4x E C OA has radius 3 and diameter BC What is the value of x Hint use the semi circle

Circles D and V are congruent circles Quadrilateral DKVL has diagonals of lengths 10 mm and 24 mm Find the length of the radii of the two congruent circles A 26 mm B 12 mm OA OB OC OD C 13 mm D 5 m D D A

2x B X arc DE 120 Oarc DE 150 arc DE 180 arc DE 100 4x E C OA has radius 3 and diameter BC I What is the measure of MINOR ARC DE

x 32 x 1 X 5 15 Use variation of parameters to solve the nonhomogeneous system X x 3 given that the general solution to the homogeneous system X 32 x is X 3 et X Je c l C 1 e t

If 9000 is deposited at the end of each half year in an account that earns 6 4 compounded semiannually after how many half years will the account contain 180 000 Round your answer UP to the nearest half year X half years

For each problem 1 State the hypotheses label the claim 2 Label the level of significance 3 State what function Ztest Ttest 1 PropZtest 2SampZtest or 2SampTtest in the calculator you are using and state the test statistic and p value 4 State your decision show your work for any credit and 5 State the interpretation of your decision Round all p values to 4 decimal places 1 According to an NPD Group report the mean number of meals prepared and eaten at home is less than 700 per year Suppose that a random sample of 76 households showed a mean of 683 meals prepared and eaten at home A previous study indicates that the standard deviation of all meals eaten and prepared at home is 54 Test the NPD Group s claim at a 10 level of significance

5 What s the public opinion of the Affordable Care Act 6 How satisfied are Americans with their healthcare compared to citizens of or countries

Add a comma semicolon or colon if needed Otherwise submit the text without any additional punctuation Mr Buchanan grows a variety of medicinal herbs in his garden chamomile echinacea lavender feverfew and lemon balm

2 A medical professional who supports universal health care outlined a History of Universal Health Care Efforts in the U S She listed some American beliefs values and political ideas that help explain why the United States does not provide government run free universal healthcare the way that many other countries do These beliefs values and ideas include interest group influence ideological differences anti communist and anti socialist views the entrepreneurial character of American medicine a tradition of American voluntarism meaning we don t like to be told what to do and the association of public programs with charity dependence and personal failure Do you think these beliefs values and political ideas exist in the United States today 3 Depending on their political beliefs some may view a law or policy positively while others believe it represents government overreach This is the case with the Affordable Care Act In the United States are there other issues that people tend to view in these two opposite ways 4 Republicans objections to the Affordable Care Act include beliefs that the law will result in increased health care costs and lower quality care What is your take on these objections 5 What s the public opinion of the Affordable Care Act 6 How satisfied are Americans with their healthcare compared to citizens of other countries 7 Have you experienced any challenges with your or your family s healthcare or health insurance If so what laws or policies do you think would have helped the situation 8 Do you think the Affordable Care Act will be successfully implemented

a Patty Stacey deposits 1400 at the end of each of 5 years in an IRA If she leaves the money that has accumulated in the IRA account for 25 additional years how much is in her account at the end of the 30 year period Assume an interest rate of 6 compounded annually Round your answer to the nearest cent b Suppose that Patty s husband delays starting an IRA for the first 10 years he works but then makes 1400 deposits at the end of each of the next 15 years If the interest rate is 6 compounded annually and if he leaves the money in his account for 5 additional years how much will be in his account at the end of the 30 year period Round your answer to the nearest cent c Does Patty or her husband have more IRA money Patty Patty s husband

Find the future value of an annulty of 1400 paid at the end of each year for 15 years if interest is earned at a rate of 7 compounded annually Round your answer to the nearest cent

mr Find the future value of an ordinary annuity of 7 000 paid quarterly for 6 years if the interest rate is 9 compounded quarterly Round your answer to the nearest cem

Match the value with the correct name it represents Use the formula 18668 38 200 1 0 03 12 7 12 1 0 03 12 0 03 18668 38 200 12 7 a the number of years of the investment b the payment c the future value d the number of compoundings per year e the annual interest rate

Find the fifteenth 15th term of an AP with first term of 4 and common difference of 3

elp Lecture 94 Ex 94 2 694 The position x of a ball with respect to time t is given by the following polynomial function x t 6t 9t 1 If x is in meters and t is in seconds find the acceleration ball x t in meters per second per second In other words find d x the change in s over the change in time which is the ball s acceleration dt 1

89 Igor purchased a car for 30 000 He made a down payment of 17 500 and borrowed the remainder at an interest rate of 3 5 compounded continuously for 4 years Estimate his monthly loan payments for the 4 year period rounded to the nearest dollar elect one D 320 300 D 280 O 260

Locate these numbers on the number line 3 1 5 3 0 53 3 2 0 2 3 4 LO 5 6 7 E

Deshaun takes out a loan for his college tuit for 6800 for 4 months Assume each month

8 89 To help him pay for college Roger took out a 20 000 student loan at an interest rate of 6 5 compounded discretely How much would the loan cost if he payed it back over a 4 year period after graduation Round to the nearest dollar Select one 28 322 27 448 24 359 25 729

The following graph shows several aggregate demand and aggregate supply curves for an economy whose potential output is 4 trillion The curves are labeled a b c and d Three points on the graph are also indicated by grey stars and labeled X V and Z PRICE LEVEL 160 150 AD 140 130 120 110 100 90 80 D Description LRAS O Identify which curve on the previous graph corresponds to each of the following descriptions If the curve described is not shown on the graph choose Not Shown In the descriptions AD represents aggregate demand SRAS represents short run aggregate supply LRAS represents long run aggregate supply 2 3 4 6 REAL GDP Trillions of dollars SRAS if the expected price level is 120 SRAS if the expected price level is 140 SRAS if the expected price level is 110 a O O b O 7 000 C O O O d Not Shown O 00 O 00000 Suppose the economy is currently in short run equilibrium at point Z In this case the economy is producing at an output level potential output At current prices and wage levels real wages are to the its what firms and workers expected when they agreed on wage

k in with 1 What c Goal 2 What is JL Explain 3 What triangles are similar to ADEF 4 What is the value of x x 6 P31

6 ETO What is the area of this triangle in square units Explain or show your reasoning