# Mathematical Reasoning Questions and Answers

Math - Others
Mathematical Reasoning
The following diagram shows a 4 step process that begins with Operation 1 and ends with Operation 4 The rates shown in each box represent the effective capacity of that operation 12 hr Operation 1 Capacity 15 hr Operation 2 a Determine the capacity of this process per hour 11 hr Operation 3 14 hr Operation 4 b Which action would yield the greatest increase in process capacity 1 increase the capacity of Operation 1 by 15 percent 2 incroce the capacity of Operation 2 by 10 percent or 3 increase the capacity of Operation 3 by 10 percent
Math - Others
Mathematical Reasoning
wooden artifact from an ancient tomb contains 60 percent of the carbon 14 that is present in ving trees How long ago to the nearest year was the artifact made The half life of carbon 14 is 730 years
Math - Others
Mathematical Reasoning
3 Are individuals likely to face increasing risks from wildfires in the future a No wildland fire suppression techniques are very sophisticated so wildfire poses little danger in modern times b No modern construction techniques and materials make buildings virtually fireproof c No zoning laws and regulations prevent development in areas where wildfires may occur d No modern scientific forest management practices have eliminated most of the risk from wildfire e Yes climate change resulting in higher atmospheric temperatures is a o occurring
Math - Others
Mathematical Reasoning
A government agency reported that in 2020 5 4 of people with a bachelor s degree and 8 8 of people with a high school diploma but no college were unemployed Suppose that the reported percentages were based on independently selected representative samples of 500 people with a bachelor s degree and 500 people with a high school degree but no college Construct a 95 confidence interval for the difference in the proportion who were unemployed for these two groups Use Bachelor s Degree High School Diploma Only Enter your answer using interval notation Round your numerical values to four decimal places 0 054 0 088 USE SALT Submit Answer Interpret the interval We are 95 confident 0 that the true difference in the proportion of people with a bachelor s degree who are unemployed and the same proportion for people with a high school diploma but no college falls within this interval The bounds of the interval suggest the proportion was higher for those with a high school diploma but no college 2 6 6 Points X DETAILS PREVIOUS ANSWERS PECKSTAT3 11 R 041 S MY NOTES d too much time on their cell phones Of the 750 teens 02
Math - Others
Mathematical Reasoning
3 Migraine is a neurological disorder that affects about 15 of the world s population according to estimates Among people with this disease 95 regularly suffer from headaches Among people who do not suffer from this disease 90 do not have regular headaches A 5 points What is the probability that a randomly chosen person regularly suffers from Headaches Suffers from migraine B 5 points If a person regularly has headaches what is the probability that he
Math - Others
Mathematical Reasoning
Determine if the rates are equivale 25 hours to 5 days 8 hour in 2 Explain 2 days
Math - Others
Mathematical Reasoning
Savings Minding the gap refers to the 3 6 months of savings you should have at the ready in case of an emergency The goal is to determine your job security which leads you to the month range you think you will need Example Teachers have high job security so I keep three months salary in savings but my wife is in sales so she keeps six months savings for her job Minding the Gap is that space you keep between you and the danger that forces you into debt I recommend 5 monthly to this category till you reach your monthly goal You use these savings for emergencies but remember it is not an emergency if you are tapping this amount monthly What is the 5 amount How many months total do you think you should have for emergency savings and why How many months will you need to save till you meet your savings goal What should you consider doing with that savings money after you reach your goal
Math - Others
Mathematical Reasoning
16 AKS 2b The graph of the function f x log x 4 characteristics of h x llertical Asymptore X 4 5 4 2 10 left 2 3 2 3 Domain 4 x y f Positive left hight is shown below List the Negative Decreasing Increasing Kight X intercept s 30 Y intercept s 0 2 Vertical Asymptote X 4 Horizontal Asymptote 4 logo s X Range x y P 17 AKS 2c 2d Bryan decides that he would like to invest his money Determine the number of years it will take Bryan s initial investment of 5 000 to reach a value of 7 500 when he invests the money in an account in which the interest is compounded continuously at an annual interest rate of 8 A Per 18 AKS 2c 2e The value of a car depreciates over time Your friend purchased a car in October of this year The value V of his car after t years can be modeled by the V 20 000 t logo s equation log 0 5 20 000 4 20 000 How much would your friend s car be worth after 4 years Putin desmos Find the line 19 AKS 2d In the year 2000 Inman Park in Atlanta GA had a squirrel population of 500 For the next 15 years the squirrel population grew at a rate of 4 5 What was the squirrel population in the year 2020 A PCI rit f growth decay
Math - Others
Mathematical Reasoning
While lifting the heavy boxes I hurt my back A comma splice B run on C sentence D fragment
Math - Others
Mathematical Reasoning
MAT8003 0108 F23 Simplify the given expressions using Boolean algebra and verify your results by truth table a bar L M bar N L bar M L M N 0 0 0 0 0 1 0 1 0 0 11100101110111
Math - Others
Mathematical Reasoning
suppose the odometer on our car is broken and we want to estimate the distance driven over a 30 second time interval We take the speedometer readings every five seconds and record them in the following table Time s 0 5 10 15 20 25 30 Velocity mi h 16 20 22 29 31 30 28 In order to have the time and the velocity in consistent units let s convert the velocity readings to feet per second 1 mi h ft s Round your answers to the nearest whole number 5280 3600 5 Time s 0 Velocity ft s 23 10 15 32 During the first five seconds the velocity doesn t change very much so we can estimate the distance traveled during that time by assuming that the velocity is constant If we take the velocity during that time interval to be the initial velocity 25 ft s then we obtain the approximate distance traveled during the first five seconds If we had wanted ar 20 25 30 23 ft s x 5 s Similarly during the second time interval the velocity is approximately constant and we take it to be the velocity when t 5 s So our estimate for the distance traveled from t 5 s to t 10 s is 29 ft s x 5 s If we add similar estimates for the other time intervals we obtain an estimate for the total distance traveled ft 45 44 41 ft 23 x 5 29 x 5 32 x 5 43 x 5 45 x 5 44 x 5 We could just as well have used the velocity at the end of each time period instead of the velocity at the beginning as our assumed constant velocity Then our estimate becomes 29 5 32 5 43 5 45 5 44 x 5 41 x 5 ft ft e we could have taken velocity readings every two seconds or
Math - Others
Mathematical Reasoning
You measure the weights of 47 watermelons and find they have a mean weight of 77 ounces Assume the population standard deviation is 14 4 ounces Based on this construct a 95 confidence interval for the true population mean watermelon weight use 3 decimal places State in words what this means in context of the problem F
Math - Others
Mathematical Reasoning
Which of the following international transactions would be recorded in the U S current account and which would be recorded in the U S capital account Items 5 items Drag and drop into the appropriate area below sale of a U S Treasury bond to a resident of Ontario Canada Categories purchase of a condo in Mexico by a U S resident purchase of an airplane ticket from United Airlines a U S company by a Chinese student Capital account purchase of a Canadian government bond by a resident of Pennsylvania purchase of a Samsung television by Best Buy a U S company Current account
Math - Others
Mathematical Reasoning
Mean S GROUP 1 30 9 N 36 X 8 1 Is there any evidence of a difference in the average between the two groups Ho Hi Critical Value s Computed Value s Decision 2 Is there any evidence of a difference in the proportion between the two groups Ho Hi Decision Critical Value s GROUP 2 20 3 Is there any evidence that the average in Group 1 is higher than 40 Critical Value s 10 Ho Hi Decision 4 Set up a 90 C I E for the difference of two population proportions 16 Computed Value s 6 Computed Value s Graph Graph Graph
Math - Others
Mathematical Reasoning
Figure 39 Price level a b F c G LRAS d H SRAS SRASO SRAS Real GDP 39 Starting from long run equilibrium at point F in Figure 39 at which o following points would short run equilibrium occur following a drought in Midwestern states H G ADO
Math - Others
Mathematical Reasoning
What is NOT the example for the group not in labor force discouraged workers overqualified employees stay at home parents
Math - Others
Mathematical Reasoning
The long run aggregate supply LRAS curve O is a vertical line is a horizontal line Oslopes downward slopes upward
Math - Others
Mathematical Reasoning
Head movement evaluations are important because disabled individuals may be able to operate communication aids using head motion A paper reported the accompanying data on neck rotation in degrees both in the clockwise direction CL and in the counterclockwise direction CO for 14 subjects For purposes of this exercise you can assume that the 14 subjects are representative of the population of adult Americans Subject 1 H CL CO 2 3 57 6 35 7 54 5 USE SALT 13 R 084 S 4 5 6 7 56 8 51 1 8 9 70 877 3 51 6 54 7 63 6 59 2 59 2 55 8 38 3 44 6 52 1 60 2 52 7 47 2 65 6 71 4 48 8 53 1 66 3 59 8 47 5 64 5 34 4 10 Find the test statistic Round your answer to two decimal places 11 12 13 14 Based on these data is it reasonable to conclude that mean neck rotation is greater in the clockwise direction than in the counterclockwise direction Carry out a hypothesis test using a significance level of a 0 01 Use for clockwise for counterclockwise and g M State the appropriate null and alternative hypotheses in degrees Enter for as needed Ho MY NOTES Use technology to find the P value Round your answer to four decimal places P value State the conclusion in the problem context We fail to reject Ho It is not reasonable to conclude that mean neck rotation is greater in the clockwise direction than in the counterclockwise direction We fall to reject Ho It is reasonable to conclude that mean neck rotation is greater in the clockwise direction than in the counterclockwise direction We reject Ho It is not reasonable to conclude that mean neck rotation is greater in the clockwise direction than in the counterclockwise direction rotation is greater in the clockwise direction than in the counterclockwise direction
Math - Others
Mathematical Reasoning
Math - Others
Mathematical Reasoning
Figure Policy Alternatives Panel a Price level P3 P P LRAS SRAS AD Y Yp Y Real GDP SRAS Price level P3 P P Panel b LRAS SRAS AD Y Yp Y Real GDP AD 17 Figure Policy Alternatives In Panel b the economy is initially in short run equilibrium at real GDP level Y and price level P2 If the government decides to intervene it would most likely A increase taxes B C decrease the quantity of money available increase the level of government purchases of goods and services D decrease the level of government purchases of goods
Math - Others
Mathematical Reasoning
13 Let p q be simple logical statements Construct a truth table for the conditional statement p q q 9 pts
Math - Others
Mathematical Reasoning
2 Let p q be simple logical statements Construct a truth table for the condit statement p q 9 pts
Math - Others
Mathematical Reasoning
Joan s Nursery specializes in custom designed landscaping for residential areas The estimated labor cost associated with a particular landscaping proposal is based on the number of plantings of trees shrubs and so on to be used for the project For cost estimating purposes managers use two hours of labor time for the planting of a medium sized tree Actual times from a sample of 10 plantings during the past month follow times in hours 1 8 1 5 2 6 2 1 2 4 2 3 2 6 3 0 1 4 2 3 With a 0 05 level of significance test to see whether the mean tree planting time differs from two hours a State the null and alternative hypotheses Ho 2 Hai 2 O Ho 2 Ha 2 Ho 2 H 2 Ho 2 H H 2 Hoi H2 H 4 2 b Compute the sample mean c Compute the sample standard deviation Round your answer to three decimal places d What is the test statistic Round your answer to three decimal places What is the p value Round your answer to four decimal places p value e What is your conclusion diffors from two hours There is no reason to change from the two hours for cost estimating purposes
Math - Others
Mathematical Reasoning
Use PMT C 91 nt to determine the regular payment amount rounded to the nearest dollar The price of a small cabin is 40 000 The bank requires a 5 down payment The buyer is offered two mortgage options 20 year fixed at 6 5 or 30 year fixed at 6 5 Calculate the amount of interest paid for each option How much does the buyer save in interest with the 20 year option Find the monthly payment for the 20 year option Round to the nearest dollar as needed Find the monthly payment for the 30 year option Round to the nearest dollar as needed Calculate the total cost of interest for both mortgage options How much does the buyer save in interest with the 20 year option Use the answers from parts 1 and 2 to find this answer
Math - Others
Mathematical Reasoning
The scores on a psychology exam were normally distributed with a mean of 70 and a standard deviation of 4 What is the standard score for an exam score of 75 The standard score is Round to the nearest hundredth as needed
Math - Others
Mathematical Reasoning
Which of the lines on the given graph have a negative slope d a b C Select all lines with a negative slope 0 000 e f d b C This question 1 point s possible a None of the lines have a negative slope
Math - Others
Mathematical Reasoning
4 10 Find an equation of the tangent plane to the surface sin xyz at the point 7 1
Math - Others
Mathematical Reasoning
2 5 Give a parametric representation for the line through the point 2 5 3 that is perpendicular to both u 1 1 2 and the x axis
Math - Others
Mathematical Reasoning
A company estimates that its sales will grow continuously at a rate given by the function S t 12e where S t is the rate at which sales are increasing in dollars per day on day t a Find the accumulated sales for the first 8 days b Find the sales from the 2nd day through the 5th day This is the integral from 1 to 5 a The accumulated sales for the first 8 days is Round to the nearest cent as needed
Math - Others
Mathematical Reasoning
Assume two satellites A B are in the same orbital plane Compute the in plane satellite positions XA YA for A and XB YB for satellite B given rA is 26 705 km and B is 27 512 km and the true anomaly fA 22 80 and f 95 30 respectively Compute the baseline distance between the two satellites O 27892 km O 12547 km 32065 km 10786 km
Math - Others
Mathematical Reasoning
A research group conducted an extensive survey of 2931 wage and salaried workers on issues ranging from relationships with their bosses to household chores The data were gathered through hour long telephone interviews with a nationally representative sample In response to the question What does success mean to you 1457 responded Personal satisfaction from doing a good job Let p be the population proportion of al wage and salaried workers who would respond the same way to the stated question Find a 90 confidence interval for p Round your answers to three decimal places lower limit upper limit USE SALT
Math - Others
Mathematical Reasoning
ing par stock On January 22 Jefferson County Rocks Inc a marble contractor issued for cash 230 000 shares of 20 par common stock at 25 an on February 27 it issued for cash 12 000 shares of preferred stock 8 par at 14 a Journalize the entries for January 22 and February 27 If an amount box does not require an entry leave it blank Jan 22 Cash Common Stock Paid In Capital in Excess of Par Common Stock Feb 27 Cash Preferred Stock Paid In Capital in Excess of Par Preferred Stock Feedback Check My Work 000 000 100 000 X X X
Math - Others
Mathematical Reasoning
Use Newton s method to find the roots of the equation log x 4 x Start with 3 Report your answers to 4 decimal places 21 x2 23
Math - Others
Mathematical Reasoning
Choo Choo Paper Company makes various types of paper products One of their products is a 30 mils thick paper In order to ensure that the thickness of the paper meets the 30 mils random cuts of paper are selected and the thickness of each cut is measured A sample of 256 cuts had a mean thickness of 30 4 mils with a standard deviation of 5 mils a Compute the standard error of the mean b At the 0 05 level of significance using the critical value approach test to see if the mean thickness is significantly more than 30 mils State the null and alternative hypotheses in mils Enter for as needed Ho Ha C Find the value of the test statistic State the critical value s for this test Round your answer s to three decimal places If the test is one tailed enter NONE for the unused tail test statistic s test statistic 2 State your conclusion O Do not reject Ho There is insufficient evidence to conclude that the mean thickness is significantly more than 30 mils O Reject Ho There is insufficient evidence to conclude that the mean thickness is significantly more than 30 mils O Reject Ho There is sufficient evidence to conclude that the mean thickness is significantly more than 30 mils O Do not reject Ho There is sufficient evidence to conclude that the mean thickness is significantly more than 30 mils c Show that the p value approach results in the same conclusion as that of part b Find the p value Round your answer to four decimal places p value State your conclusion O Do not reject Ho There is insufficient evidence to conclude that the mean thickness is significantly more than 30 mils O Reject Ho There is insufficient evidence to conclude that the mean thickness is significantly more than 30 mils oro is sufficient evidence to conclude that the mean thickness is significantly more than 30 mils
Math - Others
Mathematical Reasoning
You like pizza and you like cola Which of the graphs in the figure below represents your happiness h as a function of how many pizzas p and how much cola c you have if a There is such a thing as too many pizzas and too much cola figure b There is such a thing as too much cola but no such thing as too many pizzas figure 1 2 3 4
Math - Others
Mathematical Reasoning
6 Complete a frequency chart for the test scores no work to show 7 For the above data set hind the mean median mode and standard deviation WILL BE NO WORK 8 For the above data set find Range Q1 and Q3 and draw a box whisker plot Range
Math - Others
Mathematical Reasoning
Simplify the given expression 4 sin 3x cos 3x 4 sin 3x cos 3x
Math - Others
Mathematical Reasoning
cos a sin 2 cos 1 2 2 Using the identity sin a cosa 1 make the appropriate substitution Which of the following substitutions proves the identity OA cos2 a 1 cos2 a 2 cos a 1 2 cos 1 2 cos a 1 OB cos2 1 sin a 2 cos a 1 2 cos a 1 2 cos 1 O C OD COS cos 2 a 1 sin a 2 cos 1 2 cos 1 2 cos a a 1 1 cos2 a 2 cos a 1 2 cos a 1 2 cos 1
Math - Others
Mathematical Reasoning
Identical twins come from a single egg that split into two embryos and fraternal twins are from separate fertilized eggs Also identical twins must be of the same sex and the sexes are equally likely and sexes of fraternal twins are equally likely Use the data table to complete parts a and b below Identical Twins Fraternal Twins boy boy 8 3 boy girl 0 3 girl boy 0 3 Sexes of Twins girl girl G 8 3 a After having a sonogram a pregnant woman learns that she will have twins What is the probability that she will have identical twins The probability is Type an integer or a simplified fraction
Math - Others
Mathematical Reasoning
Math - Others
Mathematical Reasoning
4 According to a data intelligence company that specializes in the short term rental market 76 of listings by a website specializing in renting properties are for entire homes or apartments as opposed to shared spaces Do the listings in a particular city have the same distribution of housing types Using publicly available data suppose you take a random sample of 100 listings in this particular city Of those 80 were for entire homes or apartments Is there sufficient evidence to conclude that the percentage of listings in this particular city that are for entire homes or apartments is different from 76 Using the five step process for hypothesis testing HMC3 and a significance level of a 0 05 test the appropriate hypotheses LUSE SALT State the appropriate null and alternative hypotheses Let p be the population proportion of listings that are for entire homes or apartments Enter for as needed Ho H Find the test statistic Round your answer to two decimal places Use technology to find the P value Round your answer to four decimal places P value MY NOTES State the conclusion in the problem Reject H We do not have sufficient evidence to conclude that the percentage of listings in this particular city that are for entire homes or apartments is different from 76 Reject Ho We have sufficient evidence to conclude that the percentage of listings in this particular city that are for entire homes or apartments is different from 76 Fail to reject Ho We do not have sufficient evidence to conclude that the percentage of listings in this particular city that are for entire homes or apartments is different from 76 Fail to reject Ho We have sufficient evidence to conclude that the percentage of listings in this particular city that are for entire homes or apartments is different from 76
Math - Others
Mathematical Reasoning
Math - Others
Mathematical Reasoning
The extreme temperatures for each continent for a given year are listed in the da a table Usir dicted a cubic model a location with a maximum temperature of 95 degrees Fahrenheit is have a minimum temperature of 86 degrees How reliable is this prediction Give a reasons to defend your answer ast two Continent Maximum F Minimum F Africa Antarctica Asia Australia Europe Oceania North America South America 136 59 129 128 122 108 134 120 11 129 90 9 67 14 81 27
Math - Others
Mathematical Reasoning
A leasing firm operates on the belief that the annual mean number of miles driven in its leased cars is 18 500 To see whether this belief is valid a random sample of 15 one year old cars were checked and the sample mean was 19 100 and standard deviation 3 750 miles Which assumptions or conditions are not met for this hypothesis testing problem If all are okay then choose None Randomization Assumption Independence Assumption n big enough
Math - Others
Mathematical Reasoning
At a movie premiere the moviegoers were asked whether they liked or did not like the movie Of the 100 adults asked 74 said they liked it Of the 25 teenagers asked 17 said they liked it Fill in the blanks below to make the statement the most reasonable possible At the movie premiere choose one moviegoers enjoyed the movie more because liked the movie whereas only of the choose one moviegoers liked the movie
Math - Others
Mathematical Reasoning
Anormal distribution has a mean of 20 and a standard deviation of 5 Use the 68 95 99 7 rule to find the percentage of values in the distribution between 20 and 35 What is the percentage of values in the distribution between 20 and 35 Save
Math - Others
Mathematical Reasoning
A woman with her employer s matching program contributes 300 at the end of each month to her retirement account which earns 7 interest compounded monthly When she retires after 4 years she plans to make monthly withdrawals for 26 years If her account earns 5 interest compounded monthly then when she retires what is her maximum possible monthly withdrawal without running out of money The maximum possible monthly withdrawal is approximately Simplify your answer Round to the nearest cent as needed
Math - Others
Mathematical Reasoning
12 ints eBook Hint Print References Nombre Company management predicts 1 656 000 of variable costs 2 338 000 of fixed costs and income of 146 000 in the next period Management also predicts that the contribution margin per unit will be 54 1 Compute the total expected dollar sales for next period Contribution margin Income 2 Compute the number of units expected to be sold and produced next period Numerator Denominator 1 Units Units Check my
Math - Others
Mathematical Reasoning
7 B moints eBook Hint Print References Bloom Company predicts it will incur fixed costs of 259 000 and earn income of 493 100 in the next period Its expected contribution margin ratio is 69 1 Compute the amount of expected total dollar sales 2 Compute the amount of expected total variable costs Complete this question by entering your answers in the tabs below Required 1 Required 2 Compute the amount of expected total dollar sales Numerator Dollar Sales Denominator Total Dollar Sales Total dollar sales
Math - Others
Mathematical Reasoning
Use the accompanying 200 Los Angeles commute times to test the claim that the mean Los Angeles commute time is less than 35 minutes Assume that a simple random sample has been selected Use a 0 05 significance level Compare the sample mean to the claimed mean of 35 minutes Is the difference between those two values statistically significant Click the icon to view the Los Angeles commute times Identify the null and alternative hypotheses Ho H Type integers or decimals Do not round