Basic Math Questions and Answers

The number of barrels of crude oil produced per day in a certain country from 2005 through 2013 is shown in the following table Barrels Produced thousands 5 9 5 6 5 4 5 3 5 6 5 8 5 9 6 7 7 4 Construct a time series plot of the data in which the horizontal axis represents the number of years since the year 2000 and the vertical axis begins at 5 0 and ends at 7 4 Barrels Produced in thousands Barrels Produced in thousands 7 4 7 2 7 6 8 6 6 6 4 6 2 6 5 8 5 6 5 4 5 2 5 7 4 7 2 7 6 8 6 6 6 4 6 2 6 5 8 5 6 Year 2005 2006 2007 2008 2009 2010 2011 2012 2013 5 4 5 2 5 L 5 4 6 7 1 5 6 8 9 10 11 Years Since 2000 7 8 Years Since 2000 12 13 9 10 11 12 13 Barrels Produced in thousands Barrels Produced in thousands 7 4 NA 7 2 7 6 8 66 6 6 6 4 6 2 6 5 8 5 6 5 4 5 2 5 7 4 7 2 7 6 8 6 6 6 4 6 2 6 5 8 5 6 5 4 5 2 5 5 5 6 6 7 8 9 10 11 12 13 Years Since 2000 7 8 9 10 11 Years Since 2000 12 13

A pizza delivery driver records the number of deliveries made from her pizzeria over a 10 day period The results are shown following table C Number of Deliveries Number of Deliveries 35 30 25 20 Construct a time series plot of the data 15 10 5 35 30 235 20 15 10 Day 1 5 2 3 4 5 60 7 8 9 10 00 Number of Deliveries 12 13 19 25 28 24 18 13 11 5 1 2 3 4 567 8 9 10 Day 1 2 3 4 5 6 7 8 9 10 Day Number of Deliveries Number of Deliveries 35 30 25 20 15 10 5 35 30 25 20 15 10 5 1 2 3 4 5 1 2 3 4 Day 16 7 J 8 5 6 7 8 Day 9 10 9 10

The annual number of motor vehicle deaths in a certain country from 2000 to 2012 is shown in the following table O Motor Vehicle Deaths in thousands Construct a time series plot of the data in which the horizontal axis represents the number of years since the year 2000 and the vertical axis begins at 30 and ends at 50 Motor Vehicle Deaths in thousands 50 45 40 35 30 50 45 40 35 Year 2000 2001 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 30 Motor Vehicle Deaths thousands 46 46 45 44 43 45 44 40 37 36 35 37 1 2 3 4 5 6 7 8 9 10 11 12 Years Since 2000 1 2 3 4 5 6 7 8 9 10 11 12 O 200 Motor Vehicle Deaths in thousands Motor Vehicle Deaths in thousands 50 45 40 35 30 50 45 40 35 30 1 2 3 4 5 6 7 8 9 10 11 12 Years Since 2000 1 2 3 4 5 6 7 8 9 10 11 12 O 000

Determine the ordered pair for the point labeled D in the figure below Here the x and y axes are labeled from 0 to 5 in 0 5 unit increments x y 1 y 5 4 3 2 1 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 e

Eight patients in a hospital had their heart rate and diastolic blood pressures recorded The results are shown in the following table Diastolic Blood Pressure mm HG Diastolic Blood Pressure mm HG Construct a scatterplot of the data in which the horizontal axis corresponds to heart rate and the values start at 55 and end at 85 and the vertical axis corresponds to diastolic blood pressure and the values start at 55 and end at 130 130 125 120 115 110 105 100 95 90 85 80 75 70 65 60 55 3281188288FR 85 130 125 120 115 110 105 100 95 Pulse Rate beats per minute 72 68 80 55 60 75 55 65 90 80 75 70 65 60 55 Diastolic Blood Pressure mm Hg 55 60 65 70 116 110 55 60 65 70 75 80 85 Pulse Rate beats per min 127 90 101 121 97 105 75 80 85 Diastolic Blood Pressure mm HG Diastolic Blood Pressure mm HG 130 125 120 115 110 105 100 95 90 85 80 75 65 60 55 130 125 120 115 110 105 100 95 90 85 80 75 70 65 60 55 55 60 65 70 75 80 85 Pulse Rate beats per min 55 60 65 70 75 80 85

Plot P 2 5 1 on the rectangular coordinate system whose x and y axes are labeled from 0 to 5 y y O 3 N 1 5 aga 19 3 2 P2 5 1 2 3 P 2 5 1 N 3 4 4 10 5 10 O 3 2 1 5 4 3 2 1 1 P 2 5 1 P 2 5 1 2 2 3 3 4 4 5 10 5 X X G

Find the exact values of the six trigonometric functions of the angle 8 shown in the figure sin 8 cos 6 tan 6 CSC 6 sec 6 cot 6 7 7 2 72 7 X XX X 7 2 7

Use the scatterplot to answer the question SK Time in minutes 22 20 18 16 20 50 30 40 Miles Ran per Week Identify the independent variable and the dependent variable The independent variable is Select ne time in a 5 km race in minutes ne number of miles ran per week ne time in a 5 km race in minutes 60 he number of miles ran per week the dependent variable is Select

Average Price of Residential Natural Gas in dollars per million Btu 5432109765432 HO 0 1 2 3 4 5 6 7 8 9 10 Number of Years Since 2000 Classify the scatterplot as generally increasing generally decreasing or neither generally increasing generally decreasing neither

Use the scatterplot to answer the question 25 5 Hourly Wage in dollars 20 10 5 0 1 2 3 4 5 Number of Years of Work Experience 6 From inspecting the graph as the number of years of work experience increases what generally happens to the hourly w The hourly wages generally increase The hourly wages generally decrease The hourly wages do not generally increase or decrease

Use the time series plot to answer the question Number of Biodiesel Cars Owned in the U S in thousands 400 350 300 250 200 150 100 50 0 1 2 3 4 567 8 9 10 Number of Years Since 2000 During which years were the data recorded Enter your answers as a comma separated list

Use the scatterplot to answer the question Final Exam Score 100 95 90 70 60 55 50 0 1 2 3 4 5 6 7 8 9 10 Hours Studying for a Final Exam According to the graph how long in hours did a person study who scored a 96 on the final exam

Let x represent the number of years since 1990 and let y represent the amount spent to purchase a car exported to that country in thousands of dollars Identify the marginal change b and the given ordered pair x Y b x x Write an equation in point slope form using the given ordered pair x y for the amount spent to purchase a car exported to that country from 1990 to 1999 Sketch a graph of the equation for x 0 to x 9 y 35 30 25 20 15 10 5 y 35 30 25 From 1990 to 1999 the amount spent to purchase a car exported to a certain country increased at a rate of 1 780 each successive year In 1995 the average amount spent to purchase a car exported to that country was 25 400 20 15 10 5 1 1 2 2 3 3 4 4 5 6 7 5 6 7 L 8 8 9 9 X X y 35 30 25 20 15 10 5 y 35 30 25 20 15 10 5 1 1 2 3 2 3 4 4 5 5 6 6 7 8 9 7 8 9 X X 1

A marginal change and an ordered pair are given b 3 5 2 Write the equation of the line in point slope form Let x be the independent variable and y be the dependent variable

Determine whether x y3 7 is a linear equation If it is not explain why it is not The given equation is a linear equation The given equation is not a linear equation because at least one of the variables has an exponent which is not one The given equation is not a linear equation because it does not involve two variables and an equal sign The given equation is not a linear equation because at least one of the variables is in the denominator of the fractic

Calculate 1 1

Use the formula A s 251 4 h for the surface area A of a right square pyramid whose base side measures s and whose height is h This formula yields the surfac area in square units Suppose a particular skyscraper has a glass encased pyramid roof which is 20 meters wide at its base and 30 meters high Compu the surface area of the pyramid roof to determine how much glass was used to construct the roof in m2 Round the result to the nearest whole number m

Determine the ordered pair for the point labeled E in the figure below n y 4 3 2 1 E X 5 4 3 2 1 1 2 3 4 5 1 2 3 in e

Part 1 of 3 HW Score 70 14 of 20 points O Points 0 of 1 Determine the following estimate without using a calculator Then use a calculator to perform the computation necessary to obtain an exact answer How reasonable is your estimate when compared to the actual answer The estimate of the total cost of the grocery items is Type a whole number Save Estimate the total cost of six grocery items if their prices are 11 05 1 43 9 88 9 07 2 25 and 14 51 by rounding each price to the nearest dollar and then adding

EV Part 1 of 3 HW Score 70 14 of 20 points O Points 0 of 1 The estimated product is Type an integer Save Estimate the product by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in your head Then use a calculator to perform the computation How reasonable is your estimate when compared to the actual answer 47 of 391 631

U a b c d e f g h Let sets A B and C be subsets of U where A a b c d B b c d e g C a c d e f Complete a Venn diagram for the sets and then answer the question following A B List the elements in the set ANC U BNA U a

Review the prevention levels slides and the reading on prevention levels from the Module 2 Learning Guide Using the information provided match each activity to its correct prevention level Breast cancer screening Teaching children how to wear bike helmets as part of bike safety Pregnancy prevention education for 6th graders Smoking cessation programs Medication strategies for Alzheimer s Vaccinations Surgical strategies to treat heart disease Choose Choose Tertiary prevention Secondary prevention Primary prevention Choose Choose Choose Choose Choose

Driver s education in high schools Exercise programs for people living with disabilities Choose Tertiary prevention Secondary prevention Primary prevention Choose

The following questions highlight how changes in numbers can be measured in both absolute and relative or percentage terms Two stores in a mall are having promotions The first Annie s Attic is offering 10 00 off any purchase The other Betty s Breakables is offering 40 off any purchase Each store offers a music box at a non discounted price of 60 and a faux Ming vase for 30 00 as summarized in the following table Determine the promotional price of each item at each store Item A music box A faux Ming vase Original Price Dollars 60 30 00 S 10 00 Off Dollars Discount What advice should you give your friend in this situation 40 Off Dollars Suppose a friend of yours wants to buy a crystal candlestick You remember seeing this item at both Annie s Attic and Betty s Breakables but you do not remember the price O Go to Betty s Breakables if the price is above 25 00 Go to Betty s Breakables 40 off is always better than 10 00 off Go to Betty s Breakables if the price is below 25 00

A performance evaluation for new sales representatives at Office Automation Incorporated involves several ratings done on a scale of 1 to 10 with 10 the highest rating The activities rated include new contacts successful contacts total contacts dollar volume of sales and reports Then an overall rating is determined by using a weighted average The weights are 2 for new contacts 3 for successful contacts 3 for total contacts 5 for dollar value of sales and 3 for reports What would the overall rating be for a sales representative with ratings of 4 for new contacts 5 for successful contacts 3 for total contacts 9 for dollar volume of sales and 3 for reports Round your answer to two decimal places

Use the Critter Sitters chart of accounts to analyze the transaction and complete a T account Chart of Accounts Un June 3 Michelle Sanchez paid QuickSigns 350 in cash to apply a vinyl graphic on her car to advertise 1 Critter Sitters Animal Care and has provided you with the receipt Complete the chart below for this transaction Amount Account Type 2 Accounts Complete the T accounts for the transaction Increase Decrease Debit Credit

soil water content and the spread of the disease in fields of bell It is thought that too much water helps spread the disease The fields were divided into rows and quadrants The soil water content percent of water by volume of soil was determined for each plot An important first step in such a research project is to give a statistical description of the data Soil Water Content for Bell Pepper Study 6 8 8 8 8 8 8 9 9 9 10 10 10 10 10 10 10 11 12 12 12 12 12 13 13 13 13 14 14 14 12 14 14 14 15 17 16 15 14 13 12 11 10 9 LAUSE SALT a Make a box and whisker plot of the data Find the interquartile range IQR 15 15 15 15 15 16 17 17 16 15 14 13 12 11 10 9 9 9 9 9 9 8 11 17 16 15 14 13 12 11 10 9 8 11 11 16 15 14 13 12 11 10 9 8

Look at the two histograms below Each involves the same number of data The data are all whole numbers so the height of each bar represents the number of values equal to the corresponding midpoint shown on the horizontal axis Notice that both distributions are symmetric Histogram i Frequency Frequency M Histogram ii 5 mode 3 0 3 4 5 5 10 N a Estimate the mode median and mean for each histogram Histogram i Histogram ii 8 00 8 9 9

4 pts Social Security numbers are comprised of nine digits Assuming no two people can use the same social security number what is the population limit for the social security number constraint

3 pts If n A 4 n B 5 and n AUB 9 find n An B

What percentage of the general U S population are high school dropouts Suppose the percentage of high school dropouts by are as follows For convenience the data are sorted in increasing order in O 5 9 66 6 16 15 14 13 12 11 10 9 8 765 9 10 10 10 LUSE SALT a Select the box and whisker plot 6 12 12 12 12 12 13 13 13 13 b Find the interquartile range IQR 10 10 10 10 7 7 78 16 15 14 13 12 11 10 9 8 7 6 8 00 00 8 00 13 14 11 11 11 11 9 14 14 9 11 9 9 9 16 15 14 13 12 11 10 9 8 II 6 12 12 15 15 16 c A particular state has a dropout rate of about 8 Into what quartile does this rate fall below Q between Q and the median between the median and Q3 above Q3 16 15 14 13 12 11 10 9 12 e

Do bonds reduce the overall risk of an investment portfolio Let x be a random variable representing annual percent return for Vanguard Total Stock Index all stocks Let y be a random variable representing annual return for Vanguard Balanced Index 60 stock and 40 bond For the past several years we have the following data x 10 0 35 23 29 22 23 13 12 22 a Compute Ex Ex 95 y Compute Ex Ex 4505 Compute y Ey 89 Compute Ey Ey2 2383 9 K b Use the results of part a to compute the sample mean variance and standard deviation for x Round your answers to four decimal places X 9 5 s 360 2500 X S 18 9802 x Use the results of part a to compute the sample mean variance and standard deviation for y Round your answers to four decimal places 8 9 y s 159 09 x S 12 6131 X K 2 31 15 21 17 15 2 3 12 USE SALT x V c Compute a 75 Chebyshev interval around the mean for x values Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to two decimal places y X Your answer s should be in the form of expression s 00 Compute a 75 Chebyshev interval around the mean for y values Enter your answer in the form lower limit to upper limit Include the word to Round your numerical values to two decimal places 1 0 X Your answer s should be in the form of expression s Use the intervals to compare the two funds O 75 of the returns for the balanced fund fall within a narrower range than those of the stock fund O 75 of the returns for the stock fund fall within a narrower range than those of the balanced fund O 25 of the returns for the balanced fund fall within a narrower range than those of the stock fund O 25 of the returns for the stock fund fall within a wider range than those of the balanced fund d Compute the coefficient of variation in percent for fund x Round your answer to the nearest whole number Compute the coefficient of variation in percent for fund y Round your answer to the nearest whole number Use the coefficients of variation to compare the two funds

For mallard ducks and Canada geese what percentage of nests are successful at least one offspring survives Studies across five states in a country give the following percentages of successful nests x percentage success for mallard duck nests y percentage success for Canada goose nests a Use a calculator to find Ex Ex Use a calculator to find Ex Ex USE SALT Use a calculator to find Ey y Use a calculator to find Zy Ey2 H S 55 87 58 16 38 21 54 b Use the results of part a to compute the sample mean as a percent variance and standard deviation as a percent for x the percent of successful mallard nests Round your answers to four decimal places 60 73 24 c Use the results of part a to compute the sample mean as a percent variance and standard deviation as a percent for y the percent of successful Canada goose nests Round your answers to four decimal places y s d Use the results of parts b to compute the coefficient of variation in percent for successful mallard nests Round your answers to one decimal place

Simplify each expression Classify each answer b degree and number of terms 1 3u 5u 9 5u u 7 2 2k k 6 3k e 3 3m 8 3m 8 4 2 5y

In this problem we explore the effect on the standard deviation of multiplying each data value in a data set by the same constant Consider the data set 17 4 13 8 16 USE SALT a Use the defining formula the computation formula or a calculator to compute s Round your answer to four decimal places S b Multiply each data value by 7 to obtain the new data set 119 28 91 56 112 Compute s Round your answer to four decimal places S c Compare the results of parts a and b In general how does the standard deviation change if each data value is multiplied by a constant c Multiplying each data value by the same constant c results in the standard deviation remaining the same Multiplying each data value by the same constant c results in the standard deviation being Icl times smaller Multiplying each data value by the same constant c results in the standard deviation being Icl times as large Multiplying each data value by the same constant c results in the standard deviation increasing by c units d You recorded the weekly distances you bicycled in miles and computed the standard deviation to be s 2 6 miles Your friend wants to know the standard deviation in kilometers Do you need to redo all the calculations Yes No Given 1 mile 1 6 kilometers what is the standard deviation in kilometers

Exponent Rules Evaluate each expression 1 4 2 4 5 18m n4 32m n 2 5 Simplify each expression Final answers must contain positive exponents 3 x y 4 3a b 7 6 3p q 2 6 2p q 2

The Grand Canyon and the Colorado River are beautiful rugged and sometimes dangerous A physician has recorded for a 5 year period the number of visitor injuries at different landing points for commercial boat trips down the Colorado River in both the Uppe and Lower Grand Canyon Upper Canyon Number of Injuries per Landing Point Between North Canyon and Phantom Ranch Lower Canyon Number of Injuries per Landing Point Between Bright Angel and Lava Falls 7110783 13 LUSE SALT What is the median 4 JI a Compute the mean median and mode for injuries per landing point in the Upper Canyon What is the mean Round your answer to four decimal places What is the mode 0114 1 1

In this problem we explore the effect on the mean median and mode of multiplying each data value by the same number Consider the following data set 5 5 6 9 13 a Compute the mode median and mean What is the mode 5 LUSE SALT What is the median 6 What is the mean 7 6 b Multiply each data value by 3 Compute the mode median and mean What is the mode 15 What is the median 10 What is the mean 22 c Compare the results of parts a and b In general how do you think the mode median and mean are affected when each data value in a set is multiplied by the same constant Multiplying each data value by the same constant c results in the mode median and mean increasing by a factor of C Multiplying each data value by the same constant c results in the mode median and mean remaining the same Multiplying each data value by the same constant c results in the mode median and mean decreasing by a factor of C There is no distinct pattern when each data value is multiplied by the same constant d Suppose you have information about average heights of a random sample of airline passengers The mode is 66 inches the median is 71 inches and the mean is 75 inches To convert the data into centimeters multiply each data value by 2 54 What are the values of the mode median and mean in centimeters What is the mode 167 04 x cm What is the median 180 34 cm

Give the ordered pair that corresponds to the point shown in the figure What are the coordinates of the point Type an ordered pair 6 4 3 2 3 2 1 2

The Grand Canyon and the Colorado River are beautiful rugged and sometimes dangerous A physician has recorded for a 5 year period the number of visitor injuries at different landing points for commercial boat trips down the Colorado River in both the Upper and Lower Grand Canyon Upper Canyon Number of Injuries per Landing Point Between North Canyon and Phantom Ranch 3411457 8414 Lower Canyon Number of Injuries per Landing Point Between Bright Angel and Lava Falls 7110783 13 4 0 1 14 11 USE SALT a Compute the mean median and mode for injuries per landing point in the Upper Canyon What is the mean Round your answer to four decimal places What is the median What is the mode b Compute the mean median and mode for injuries per landing point in the Lower Canyon What is the mean Round your answer to four decimal places What is the median What is the mode c Compare the results of parts a and b The Lower Canyon mean is greater while the median and mode are the same The mean median and mode are greater for the Upper Canyon The Lower Canyon mean is greater while the median and mode are less The mean median and mode are greater for the Lower Canyon d The Lower Canyon stretch had some extreme data values Compute a 5 trimmed mean for this region Round your answer to four decimal places Compare this result to the mean for the Upper Canyon computed in part a The trimmed mean is closer to the Upper Canyon mean The trimmed mean is the same as the Upper Canyon mean

Consider the following numbers 2 3 4 4 5 a Compute the mode median and mean What is the mode What is the median What is the mean b If the numbers represented codes for the colors of T shirts ordered from a catalog which average s would make sense Select all that apply mode median mean c If the numbers represented one way mileages for trails to different lakes which average s would make sense Select all apply mode median mean d Suppose the numbers represent survey responses from 1 to 5 with 1 disagree strongly 2 disagree 3 agree 4 ag strongly and 5 agree very strongly Which average s make sense Select all that apply mode median mean

Find the mean median and mode of the data set Enter DNE for any values that do not exis 24 3 30 9 56 8 67 3 71 7 90 4 What is the mean Round your answer to two decimal places What is the median What is the mode

Write the equation y 2x 8 in the form of Jawapan Answer X y b 1

Consider the data in the table for the amount of oil used annually to generate electricity in a certain country from 2000 to 2011 Amount of Oil Used millions of gallons Interpret Years since 2000 Xo 0 X 1 x 2 Calculate Y i 0 4 X5 5 X7 7 X8 8 x9 9 10 10 X11 11 Yo 2 216 Y 2 213 9 Y 2 211 8 Y3 2 209 7 Y4 2 207 6 Y 2 205 5 Y6 2 203 4 Y 2 201 3 Y8 2 199 2 Yg 2 197 1 10 2 195 Y11 2 192 9 The value represents the amount of oil used in millions of gallons to generate electricity in that country in 2005 The value represents the amount of oil used in millions of gallons to generate electricity in that country from 2000 to 2011 The value represents the amount of oil used in millions of gallons to generate electricity in that country from 2000 to 2005

Consider the data in the table for the amount of oil used annually to generate electricity in a certain country from 2000 to 2011 Amount of Oil Used millions of gallons 2 612 Y 2 609 9 Y 2 607 8 Y3 2 605 7 Y4 2 603 6 Ys 2 601 5 Y6 2 599 4 Y 2 597 3 Y8 2 595 2 Y 2 593 1 10 Interpret Years since 2000 x0 0 x 1 x 2 1 5 10 Calculate Y X3 4 4 X5 5 3 X6 6 x 7 Xg 8 x 9 10 10 11 11 10 2 591 11 2 588 9 The value represents the amount of oil used in millions of gallons to generate electricity in that country from 2000 to 2011 The value represents the amount of oil used in millions of gallons to generate electricity in that country from 2005 to 2010 The value represents the amount of oil used in millions of gallons to generate electricity in that country in 2010 The value represents the number of years that passed from 2000 to 2011

Consider the data in the table for the amount of oil used annually to generate electricity in a certain country from 2000 to 2011 Amount of Oil Used millions of gallons Yo 2 114 O 11 C i 0 i 5 TIME M i 5 O X Years since 2000 0 1 2 3 Xo X3 X4 4 X10 Write the total amount of oil used to generate electricity in that country from 2005 to 2007 as a sum X5 X6 6 Xy 7 8 x9 9 5 10 11 11 Y 2 111 9 Y 2 109 8 Y3 2 107 7 Y4 2 105 6 Ys 2 103 5 Y6 2 101 4 Y 2 099 3 Y8 2 097 2 Yg 2 095 1 10 2 093 11 2 090 9

Consider the data in the table for the number of confirmed cases of Lyme disease in a certain state annually from 2005 to 2014 Years since 2000 Cases of Lyme Disease X5 5 53 6 13 1 8 14 1 5 Oxi i 8 13 O XiXi i 8 x6 14 Xy 7 X8 8 x9 9 X10 10 X11 11 Y5 X12 12 13 13 14 X14 Write a sum to represent the total number of confirmed cases of Lyme disease in that state from 2008 to 2013 Y8 105 Y7 Yg 138 330 322 270 Y10 Y11 475 Y12 387 Y13 675 599

Use the given n 5 ordered pairs to calculate xy Round to two decimal plac X y 3 15 16 73 14 15 0 05 1 66 1 98 28 91 18 30 2 27 1 67

Consider the following group of bivariate values 1 46 X 1 42 Y2 1 34 Compute 1 1 44 x3 1 52 3 1 42 X4 1 5 Y4 1 45 1 41 X5 Ys 1 38 Y6 1 46 1 39 x7 Y7

Consider the bivariate data shown in the table x 8 9 10 2 9 3 y Compute ExEy 10 8 8 11 12 13 14 7 1 6 6 5 3 4 2 15 3 2