Mathematical Reasoning Questions and Answers

Complete the following derivation using the following selection of derived rules only none of the basic rules DNE DNI Comm CommV DeM DSL DSR MT Trans HS Def E and Def I 1 P Q 2 P R 3 PV Q n Q R Premise Premise Premise Goal

Complete the following derivation using the following selection of derived rules only none of the basic rules DNE DNI Comm CommV DeM DSL DSR MT Trans HS Def E and Def I 1 A B 2 Q P 3 4 Q PV S T n T S Premise Premise Premise Premise Goal

using exactly one application each of E DeM CommV and Def E 1 P 2 P P A D n D A Premise Premise Goal

A baseball team plays in a stadium that holds 55 000 spectators With the ticket price at 10 the average attendance at recent games has been 21 000 A market survey indicates that for every dollar the ticket price is lowered attendan increases by 3000 a Find a function that models the revenue in terms of ticket price Let x represent the price of a ticket and R represent the revenue R x b Find the price that maximizes revenue from ticket sales c What ticket price is so high that no revenue is generated

A multiple choice exam has seven possible answers for each question For each correct answer you are awarded 7 points For each incorrect answer 1 point is subtracted from your score For answers left blank no points are added or subtracted a If you do not know the correct answer to a particular question is it to your advantage to guess Explain b If you do not know the correct answer but can eliminate one possible choice is it to your advantage to guess Explain b Select the correct choice below and if necessary fill in the answer box within your choice OA No it is neither an advantage nor disadvantage to guess because the expectation is 0 No it is a disadvantage to guess because the expectation is Simplify your answer OB www O C Yes it is to your advantage to guess because the expectation is Simplify your answer

2 At a 99 confidence level what is the confidence interval for a data set consisting of five measurements with a mean and standard deviation of 5 42 0 03 mg L 5 36 to 5 48 mg L 5 37 to 5 47 mg L C 5 38 to 5 46 mg L d 5 39 to 5 45 mg L a b e The correct answer is not given

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5 Aligned curriculum with stage of development creating the interdisciplinary approach

What is the sequence in the High Scope Approach that encourages children to be deliberate in selecting activities and materials active in implementing their plans and reflective in their subsequent reviews Plan Review Do

Devise a preference schedule with three candidates three rankings and seven voters in which the point system Borda count violates Fairness Criterion 1 Explain your work Choose the correct answer below O A First A Second B Third OC First Second Third C 4 C A C B 1 AB03 AB02 C CBA2 CAB2 B First Second Third D First Second Third ABC4 A 4804 B C A B C 1 B C A 2 A B C 2 C B A 1 TI

When a company discontinues an operation and disposes of the discontinued operation component the transaction should be included in the income statement as a gain or loss on disposal reported as O a bulk sale of plant assets included in income from continuing operations O an amount after continuing operations O a prior period adjustment an unusual item

A certain statistics instructor participates in triathlons The accompanying table lists times in minutes and seconds he recorded while riding a bicycle for five laps through each mile a 3 mile loop Use a 0 05 significance level to test the claim that it takes the same time to ride each of the miles Does one of the miles appear to have a hill Click the icon to view the data table of the riding times Determine the null and alternative hypotheses Ho H Find the F test statistic F Round to four decimal places as needed Find the P value using the F test statistic P value Round to four decimal places as needed What is the conclusion for this hypothesis test A Fail to reject Ho There is insufficient evidence to warrant rejection of the claim t OB Pelect H There is sufficient evidence to warrant rejection of the claim that the Riding Times minutes and seconds 3 20 Mile 1 3 15 3 24 3 22 3 22 Mile 2 3 19 3 23 3 20 3 17 3 20 Mile 3 3 34 3 31 3 28 3 30 3 29 Note when pasting the data into your technology each mile row will have separate columns for each minute and second entry You will need to convert each minute second entry into seconds only Print Done X

The operating cycle for a merchandiser that sells only for cash moves from Multiple Choice O Purchases of merchandise to inventory to cash sales Purchases of merchandise to inventory to accounts receivable to cash sales Inventory to purchases of merchandise to cash sales Accounts receivable to purchases of merchandise to inventory to cash sales Accounts receivable to inventory to cash sales

Havermill Co establishes a 250 petty cash fund on September 1 On September 30 the fund is replenished The accumulated receipts on that date represent 73 for Repairs Expense 137 for merchandise inventory and 22 for miscellaneous expenses The fund has a balance of 18 On October 1 the accountant determines that the fund should be increased by 50 The journal entry to record the reimbursement of the fund on September 30 includes a Multiple Choice Debit to Repairs Expense for 73 Credit to Merchandise Inventory for 137 Credit to Cash for 250 Debit Petty Cash for 232 Credit to Cash for 18

Look at the graphs and their equations below Then fill in the information about the coefficients A B C and D y A x y B x a For each coefficient choose whether it is positive or negative b Choose the coefficient with the least value c Choose the coefficient closest to 0 y C x Choose one y D x B Choose one B C D Choose one B Choose one B

Choose the best answer to the following question Explain your reasoning with one or more complete sentences Which line does the letter A have reflection symmetry along Choose the correct answer below OA It has reflection symmetry going diagonally through its middle The letter A remains unchanged when reflected across this line B It has reflection symmetry going diagonally through its middle A pattern composed of the letter A remains unchanged when translated in this direct OC It has reflection symmetry going horizontally through its middle A pattern composed of the letter A remains unchanged when translated in this direc OD It has reflection symmetry going vertically through its middle The letter A remains unchanged when rotated across this line OE It has reflection symmetry going vertically through its middle The letter A remains unchanged when reflected across this line OF It has reflection symmetry going horizontally through its middle The letter A remains unchanged when rotated across this line O

20 Which players in the coalition P1 P3 P4 are critical A P1 only B None of the players C P1 and P3 only D All three players E none of these 21 The Banzhaf power distribution of the weighted voting system is A P1 40 P2 20 P3 20 P4 20 B P1 70 P2 10 P3 10 P4 10 C P1 25 P2 25 P3 25 P4 25 D P1 60 P2 20 P3 10 P4 10 E none of these as steyeganov beinglaw adi 20 21

Ricardo believed that the government should not interfere with wages Wage should be determined solely by unhindered market forces O True O False

For problems 17 21 use the weighted voting system 25 22 12 6 3 and the Banzhaf definition of power The four players are P P2 P3 and P4 17 The weight of the coalition P2 P3 P4 is 17 A 25 B 22 C 21 D 40 E none of these 18 The number of winning coalitions is A 15 B 1 C 8 D 7 E none of these 19 Which players in the coalition P1 P2 are critical A P only B P1 and P2 C P2 only DNone of the plauora 18 19

Consider the weighted voting system 10 10 5 3 1 Identify which players Are dictators Have veto power but are not dictators Are dummies Identify players by their number only For example if the answer is P and P2 enter 1 2 If there are no players that fit the description leave the space blank

s the use of letters of credit a necessary and effective tool in international trade promoting trust between buyers and sellers or do they impose unnecessary complexities and costs on transactione Debate the adus

Question 1 Consider a law firm with 15 lawyers and 3 paralegals The firm is struggling to keep up with the high demand for its services particularly during the busy litigation seasons It has been observed that the lawyers spend a significant amount of their time on administrative tasks that could potentially be handled by paralegals After a careful study of the work distribution within the firm it was determined that 35 of the activities carried out by the lawyers are administrative in nature Given that each lawyer works 50 hours a week please determine a How many additional paralegals should the firm hire to handle the administrative tasks currently performed by the lawyers b If the lawyers time spent on administrative tasks is redirected to billable legal work by what percentage could the firm potentially increase its billable hours

The weekly demand for Math Wars The Force Multiplies video games is given by 560 X 7 11 43 where x is the number of thousands of video games produced and sold and p is in dollars Using the Marginal Revenue function R x approximate the marginal revenue when 14 000 video games have been produced and sold X dollars Submit Answer 1 1 Points DETAILS p PREVIOUS ANSWERS 3500 MY NOTES

3 8 The cash flow associated with making self locking fasteners is shown below Determine the net pres ent worth year 0 at an interest rate of 10 per year Year Income 1000 Cost 1000 01 2 3 4 5 20 20 20 20 30 30 30 30 30 8 8 8 8 12 12 12 12 12 6 7 8 9 30 25

Marginal Analysis Elasticity Course Packet on elasticity of demand and finding the unitary price point Given the demand equation x5 10p 108 where p represents the price in dollars and x the number of units determine the value of p where the elasticity of demand is unitary Price p dollars If the current price is 10 dollars and price is increased by 1 then total revenue will O decrease O increase

I Analysis Elasticity Course Packet on marginal analysis If the demand function for math self help videos is given by 40 0 6x and the total cost function to manufacture the videos is given by 3x 28 evaluate the marginal profit function at x 10 Marginal Profit This means that if production and sales increase by one unit then total profit will O increase O decrease by approximately dollars

S T V W U A B C D S T V W U S T V W S T V S T E O U F O W G S H OT I OU J OV K OW

G K V J H E F A O G KV J H E F B O KV J H E F C H E F D O KV J E H E F O K G E H OF I OG J OH K OJ

from this horse in mg 100 ml The sample mean is x 94 50 Let x be a random variable representing glucose readings taken from Gentle Ben We may assume that x has a normal distribution and we know from past experience that 12 5 The mean glucose level for horses should be 85 mg 100 ml Do these data indicate that Gentle Ben has an overall average glucose level higher than 85 Use a 0 05 95 90 84 103 101 110 86 87 a What is the level of significance 0 05 State the null and alternate hypotheses in mg 100 ml Enter for as needed Ho 85 H 85 Will you use a left tailed right tailed or two tailed test left tailed Oright tailed Otwo tailed X b What sampling distribution will you use Explain the rationale for your choice of sampling distribution We ll use the standard normal since we assume that x has a normal distribution with known Compute the z value of the sample test statistic Round your answer to two decimal places X O We ll use the Student s t since we assume that x has a normal distribution with known o We ll use the Student s t since n is large with unknown o We ll use the standard normal since we assume that x has a normal distribution with unknown c Find the P value Round your answer to four decimal places P value X O Sketch the sampling distribution and show the area corresponding to the P value 3 2 1 0 1 2 3 3 2 1 0 1 2 3 OM 3 2 1 3 2 1 0 1 0 1 2 2 3 3

1 Using categories Kaley asked her classmates about their favorite types of music The results are shown in the chart provided Make a frequency table of the data then answer the questions below Step 1 Draw a table Label three columns Tally Frequency Cumulative Frequency Step 2 Complete the table using the data Music Rock R Jazz J Country C Top 40 F Rap P a What is the most popular type of music b What is the least popular type of music c How many students were polled Favorite Types of Music PRF PF PFFUD FR F P C F C F C J PP P J RR F RPP F

construct a confidence interval from sample data Let a be the level of significance for a two tailed hypothesis test The following statement applies to hypothesis tests of the mean For a two tailed hypothesis test with level of significance a and null hypothesis Ho k we reject Ho whenever k falls outside the c 1 a confidence interval for based on the sample data When k falls within the c 1 a confidence interval we do not reject Ho A corresponding relationship between confidence intervals and two tailed hypothesis tests also is valid for other parameters such as p M M or P P which we will study in later sections Whenever the value of k given in the null hypothesis falls outside the c 1 alpha confidence interval for the parameter we reject Ho For example consider a two tailed hypothesis test with 0 05 and Hoi H 21 H 21 A random sample of size 13 has a sample mean x 22 from a population with standard deviation 8 a What is the value of c 1 a 0 95 Using the methods of Chapter 7 construct a 1a confidence interval for from the sample data Enter your answer in the form lower limit to upper limit Include the word to Round your numerical answers to two decimal places X What is the value of given in the null hypothesis i e what is k k 21 Is this value in the confidence interval Yes O No Do we reject or fail to reject H based on this information Fail to reject since 21 is not contained in this interval O Fail to reject since 21 is contained in this interval O Reject since 21 is not contained in this interval O Reject since 21 is contained in this interval b Using methods of Chapter 8 find the P value for the hypothesis test Round your answer to four decimal places P value Do we reject or fail to reject Ho O Reject the null hypothesis there is sufficient evidence that differs from 21 O Fail to reject the null hypothesis there is insufficient evidence that differs from 21 O Fail to reject the null hypothesis there is sufficient evidence that differs from 21 O Reject the null hypothesis there is insufficient evidence that differs from 21 Compare your result to that of part a These results are the same O We rejected the null hypothesis in part b but failed to reject the null hypothesis in part a O We rejected the null hypothesis in part a but failed to reject the null hypothesis in part b

Let A x y z w and MR the Boolean matrix of the relation R on A If MR O a R is a poset O b R is an equivalence relation O c None O d R is asymmetric 0 1 1 1 0 0 0 1 0 1 00 0 0 0 0 Then

The maximum inplane shear stress ksi in the element shown below is most nearly 20 ksi 10 ksi 40 ksi

cipal axis 2 3 Verify the value of Z for a W18 50 that is tabulated in the dimensio and properties tables in Part 1 of the Manual

What percent of 84 is 21 of 84 is 21

In a random sample of 500 judges it was found that 287 were introverts USE SALT a Let p represent the proportion of all judges who are introverts Find a point estimate for p Round your answer to four decimal places b Find a 99 confidence interval for p Enter your answer in the form lower limit to upper limit Include the word to Rou your numerical values to two decimal places Give a brief interpretation of the meaning of the confidence interval you have found We are 1 confident that the true proportion of judges who are introverts falls above this interval We are 99 confident that the true proportion of judges who are introverts falls within this interval We are 1 confident that the true proportion of judges who are introverts falls within this interval We are 99 confident that the true proportion of judges who are introverts falls outside this interval c Do you think the conditions np 5 and ng 5 are satisfied in this problem Explain why this would be an important consideration No the conditions are not satisfied This is important because it allows us to say that p is approximately normal Yes the conditions are satisfied This is important because it allows us to say that p is approximately binomial Yes the conditions are satisfied This is important because it allows us to say that p is approximately normal No the conditions are not satisfied This is important because it allows us to say that p is approximately binomial

15 9 D Multiply by 1 using an appropriate notation to express each number in terms of the least common denominator Multiply by 1 using an appropriate notation 14 15 Multiply 4 14 3 4 5 9 15 3 9 5 14 3 4 5 15 3 9 5 www 45 45 to express each number in terms of the least common denominator n

What price do farmers get for their watermelon crops In the third week of July a random sample of 41 farming regions gave a sample mean of x 6 88 per 100 pounds of watermelon Assume that is known to be 1 94 per 100 pounds a Find the margin of error for a 90 confidence interval for the population mean price in dollars per 100 pounds that farmers in this region get for their watermelon crop What is the margin of error Round your answer to two decimal places Find a 90 confidence interval for the population mean price in dollars per 100 pounds that farmers in this region get for their watermelon crop Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to two decimal places b Find the sample size of farming regions necessary for a 90 confidence level with maximal error of estimate E 0 45 for the mean price per 100 pounds of watermelon Round your answer up to the nearest whole number farming regions c A farm brings 15 tons of watermelon to market Hint 1 ton is 2 000 pounds Find a margin of error for a 90 confidence interval for the population mean cash value of this crop in dollars Round your answer to two decimal places Find a 90 confidence interval for the population mean cash value of this crop in dollars Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to two decimal places

Thirty four small communities in Connecticut population near 10 000 each gave an average of x 138 4 reported cases of larceny per year Assume that o is known to be 43 7 cases per year a Find the margin of error for a 90 confidence interval for the population mean annual number of reported larceny cases in such communities Round your answer to one decimal place Find a 90 confidence interval for the population mean annual number of reported larceny cases in such communities Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to one decimal place larceny cases b Find the margin of error for a 95 confidence interval for the population mean annual number of reported larceny cases in such communities Round your answer to one decimal place Find a 95 confidence interval for the population mean annual number of reported larceny cases in such communities Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to one decimal place larceny cases c Find the margin of error for a 99 confidence interval for the population mean annual number of reported larceny cases in such communities Round your answer to one decimal place Find a 99 confidence interval for the population mean annual number of reported larceny cases in such communities Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to one decimal place

How much do wild mountain lions weigh Adult wild mountain lions 18 months or older captured and released for the first time in the San Andres Mountains gave the following weights pounds X 72 108 134 130 60 64 Assume that the population of x values has an approximately normal distribution a Use a calculator with mean and sample standard deviation keys to find the sample mean weight x and sample standard deviation s in pounds Round your answers to four decimal places lb lb S USE SALT b Find a 75 confidence interval for the population average weight in pounds of all adult mountain lions in the specified region Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to one decimal place

Suppose we have two strings ABCBDAB and BDCAB What is the longest common subsequence of them B BC ABAB

sinx 0789 7 X 107 0 8 x 7 The standard factored form of integer r 5 733 sinxx lim 20 71 e e 0 q 1 X O using the unique factorization theorem is d 04 O a 23 3 72 O b 13 441 O c 32 72 13 O d 73 32 2 0 Ra 40 40x2 va vb lak laksa azoto 201 20 vb 1 2u 1 e ej ze 0 Ud

7 10 8 3 100 What is the first step in adding fractions when denominators are different A Add the numerators keeping the same denominators n OB Multiply by 1 using an appropriate notation to express each number in terms of the LCD n OC Simplify if possible D Find the least common multiple of the denominators That number is the least common denominator LCC The LCD is

survey of magazine subscribers showed that 45 4 rented a car during the past 12 months for business reasons 53 rented a car during the past 12 months for personal reasons and 30 rented a car during the past 12 months for both business and personal reasons What is the probability that a subscriber rented a car during the past 12 months for business or personal reasons to 3 decimals b What is the probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons to 3 decimals

A ball is thrown horizontally from a height of 18 m and hits the ground with a speed that is five times its initial speed What is the initial speed

Question 8 Construct a circuit that is equivalent to the given expression a xy yz 3 points