Basic Math Questions and Answers

9 a b The waiting times at a local coffee shop have a mean of 1 25 minutes and a standard deviation of 0 38 What is the z score for a wait time of 1 45 minutes Explain what your answer for part a means If a wait time had a z score of 1 35 what was the original wait time
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9 a b The waiting times at a local coffee shop have a mean of 1 25 minutes and a standard deviation of 0 38 What is the z score for a wait time of 1 45 minutes Explain what your answer for part a means If a wait time had a z score of 1 35 what was the original wait time
Bob is applying for a job at a marketing firm They consider 5 categories for each applicant The manager gives each applicant a score from 1 to 5 in each category and each category is weighted differently Here are Bob s scores Category Education Job Experience Interpersonal Skills Communication Skills References Weighting 2 1 4 4 2 Bob s Scores 2 2 3 3 1 Calculate Bob s weighted mean score Show your work no spreadsheet
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Bob is applying for a job at a marketing firm They consider 5 categories for each applicant The manager gives each applicant a score from 1 to 5 in each category and each category is weighted differently Here are Bob s scores Category Education Job Experience Interpersonal Skills Communication Skills References Weighting 2 1 4 4 2 Bob s Scores 2 2 3 3 1 Calculate Bob s weighted mean score Show your work no spreadsheet
Express as a single logarithm and simplify if possible 3 logcx 4 logy 5log ex log ex 4 log cy 5log x 3 Type your answer using exponen BRACKE CUT
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Express as a single logarithm and simplify if possible 3 logcx 4 logy 5log ex log ex 4 log cy 5log x 3 Type your answer using exponen BRACKE CUT
In which of the following ways would a marketing research firm be least likely to conduct research Record sales data Analyze sales data Compare sales data with other market researchers Conduct market surveys to learn what consumers nood and want
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In which of the following ways would a marketing research firm be least likely to conduct research Record sales data Analyze sales data Compare sales data with other market researchers Conduct market surveys to learn what consumers nood and want
I controlled thousands of city jobs in the police fire department and sanitation department and had power over important institutions such as the courts and municipal agencies I also worked to solved many of the city problems such as building repairing or giving money to schools hospitals orphanages and provided other services like building parks sewer systems and waterworks Who am I O Precinct Workers O City Boss Points 1 Ward Boss Immigrants Q
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I controlled thousands of city jobs in the police fire department and sanitation department and had power over important institutions such as the courts and municipal agencies I also worked to solved many of the city problems such as building repairing or giving money to schools hospitals orphanages and provided other services like building parks sewer systems and waterworks Who am I O Precinct Workers O City Boss Points 1 Ward Boss Immigrants Q
Graph the line that passes through the point 0 3 and has a slope of 4 3 6 5 3 2 1 L 6 5 4 3 2 3 Graph the line that passes through the point 3 4 and has a slope of 1 6 5 4 3 2 1 6 2 0 3 4 5 6 S 4 YA y 3 2 1 0 11 2 3 4 5 6 6 5 4 31 2 1 19 2 3 12 456 2 3 4 5 6 2 Graph the line that passes through the point 4 2 and has a slope of 456 3 2 6 5 4 2 1 5 What is the slope of the line between the 6 What is the slope of the line between the points 3 2 and 4 2 points 0 5 and 3 3 1 4 2 31 4 5 6 i 6 5 4 3 2 1 4 Graph the line the passes through the point 2 4 and has a slope of 2 O 1 2 3 4 5 6 YA 6 5 4 3 2 1 6 5 4 3 2 1 0 1 2 3 14 56 5 6 234 56 123456
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Graph the line that passes through the point 0 3 and has a slope of 4 3 6 5 3 2 1 L 6 5 4 3 2 3 Graph the line that passes through the point 3 4 and has a slope of 1 6 5 4 3 2 1 6 2 0 3 4 5 6 S 4 YA y 3 2 1 0 11 2 3 4 5 6 6 5 4 31 2 1 19 2 3 12 456 2 3 4 5 6 2 Graph the line that passes through the point 4 2 and has a slope of 456 3 2 6 5 4 2 1 5 What is the slope of the line between the 6 What is the slope of the line between the points 3 2 and 4 2 points 0 5 and 3 3 1 4 2 31 4 5 6 i 6 5 4 3 2 1 4 Graph the line the passes through the point 2 4 and has a slope of 2 O 1 2 3 4 5 6 YA 6 5 4 3 2 1 6 5 4 3 2 1 0 1 2 3 14 56 5 6 234 56 123456
Points 1 Question 5 What is patronage O The civil service O Desire of money Government administration jobs Giving jobs as a political reward
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Points 1 Question 5 What is patronage O The civil service O Desire of money Government administration jobs Giving jobs as a political reward
8 Given sin A 9 and cos A B Give an exact answer sin A B cos A B with A in quadrant II and cos B 72 323 90 9 with B in quadrant III find sin A E 10
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8 Given sin A 9 and cos A B Give an exact answer sin A B cos A B with A in quadrant II and cos B 72 323 90 9 with B in quadrant III find sin A E 10
Mia is building a deck around her home Given the following sketch of the deck calculate the area and perimeter 10 ft 8 ft 10 ft
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Mia is building a deck around her home Given the following sketch of the deck calculate the area and perimeter 10 ft 8 ft 10 ft
Given that 10 13 watts meter what is the intensity of a sound for which the decibel level of the sound measures 1137 Round off your answer to three decimal places Keypa
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Given that 10 13 watts meter what is the intensity of a sound for which the decibel level of the sound measures 1137 Round off your answer to three decimal places Keypa
and Hungary Which country do you think won at the Yalta Conference Explain by referencing which possible solutions the country favored and compare it with what resulted from the conference 2 points
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and Hungary Which country do you think won at the Yalta Conference Explain by referencing which possible solutions the country favored and compare it with what resulted from the conference 2 points
1 Identify which scatterplot represents the data from the table 1 point Variable 1 Variable 2 6 10 8 14 2 4 2 10 6 8
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1 Identify which scatterplot represents the data from the table 1 point Variable 1 Variable 2 6 10 8 14 2 4 2 10 6 8
Determine whether A B ACB BCA ACB BCA or if none of A penny dime nickel quarter B penny quarter Which of the following are true statements Select all that apply ACB BCA BCA A B ACB None of the above statements are true
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Determine whether A B ACB BCA ACB BCA or if none of A penny dime nickel quarter B penny quarter Which of the following are true statements Select all that apply ACB BCA BCA A B ACB None of the above statements are true
a college 49 students were members of the marching band or the choir 34 were members of the marching band and 14 were members of the marching ere members only of the choir mere were students who were members only of the choir Type a whole number
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a college 49 students were members of the marching band or the choir 34 were members of the marching band and 14 were members of the marching ere members only of the choir mere were students who were members only of the choir Type a whole number
if the given statement is true or false If it is false give the reason book C book TV radio the correct answer below The statement is false TV book is a subset of the set book TV radio The statement is true TV book is an element not a subset The statement is true TV is not in the set book TV radio The statement is true TV book is a subset of the set book TV radio
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if the given statement is true or false If it is false give the reason book C book TV radio the correct answer below The statement is false TV book is a subset of the set book TV radio The statement is true TV book is an element not a subset The statement is true TV is not in the set book TV radio The statement is true TV book is a subset of the set book TV radio
Which expression is equivalent to 3x 2 3x 2 3x 6x 4 A B C D 11 12 1 This question comes from adding subtracting rational functions Adding and subtracting rational functions means that the denominators must be the 2 Show explain how you would add these expressions 3 Which answer choice would be best B 3x 3x 2 Which scenario could be modeled by the graph of the function f x 100 1 002 A An ant colony that has an initial population of 100 increases by 0 2 per year C X x 2 D A An ant colony that has an initial population of 100 increases at a constant rate of 0 2 per year An ant colony that has an initial population of 100 decreases by 0 2 per year An ant colony that has an initial population of 100 decreases at a constant rate of 0 2 per year 1 Does the equation given represent growth or decay How do you know 2 Write the growth and decay equation 10 times each 3 What is the rate in the given equation
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Which expression is equivalent to 3x 2 3x 2 3x 6x 4 A B C D 11 12 1 This question comes from adding subtracting rational functions Adding and subtracting rational functions means that the denominators must be the 2 Show explain how you would add these expressions 3 Which answer choice would be best B 3x 3x 2 Which scenario could be modeled by the graph of the function f x 100 1 002 A An ant colony that has an initial population of 100 increases by 0 2 per year C X x 2 D A An ant colony that has an initial population of 100 increases at a constant rate of 0 2 per year An ant colony that has an initial population of 100 decreases by 0 2 per year An ant colony that has an initial population of 100 decreases at a constant rate of 0 2 per year 1 Does the equation given represent growth or decay How do you know 2 Write the growth and decay equation 10 times each 3 What is the rate in the given equation
x xEN and x 11 x xEN and x is even and x 11 x x EN and x is odd and x 11 x x E N and x 7 mine the set An B U C the correct answer below and if necessary fill in the answer box to complete your c ANB UC Use a comma to separate answers as needed Use ascending order An B UC is the empty set
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x xEN and x 11 x xEN and x is even and x 11 x x EN and x is odd and x 11 x x E N and x 7 mine the set An B U C the correct answer below and if necessary fill in the answer box to complete your c ANB UC Use a comma to separate answers as needed Use ascending order An B UC is the empty set
the following determine the set A x xEN and x2 1 and x 10 xIxEN and x is odd and x2 1 and x 10 x x EN and x is even and x2 1 and x 10 the correct choice below and if necessary fill in the answer box to complete y ANB Use a comma to separate answers as needed An B is the empty set
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the following determine the set A x xEN and x2 1 and x 10 xIxEN and x is odd and x2 1 and x 10 x x EN and x is even and x2 1 and x 10 the correct choice below and if necessary fill in the answer box to complete y ANB Use a comma to separate answers as needed An B is the empty set
a c d f g i b c d f g a b f i j mine A UC U ANB se the correct answer below and if necessary fill in the answer box in you A UC U ANB Use a comma to separate answers as nee A UC U ANB is the empty set
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a c d f g i b c d f g a b f i j mine A UC U ANB se the correct answer below and if necessary fill in the answer box in you A UC U ANB Use a comma to separate answers as nee A UC U ANB is the empty set
Venn diagram to determine the set A U B U CLES
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Venn diagram to determine the set A U B U CLES
If the ratios of corresponding sides of two 4 sided polygons are and 4 7 are the two polygons similar If so what is the common ratio of their corresponding sides No the two polygons are not similar OYes 1 3 Next Worksheet O Yes 1 2 O Yes 4 7 question 4 of 5 Next Less 4 2 X Coordinate What Are Cor Examples Qui Practice C Ch 6 Basic Ge Ch 7 Basic Gec Ch 8 Basic Geo Ch 9 Basic Geor
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If the ratios of corresponding sides of two 4 sided polygons are and 4 7 are the two polygons similar If so what is the common ratio of their corresponding sides No the two polygons are not similar OYes 1 3 Next Worksheet O Yes 1 2 O Yes 4 7 question 4 of 5 Next Less 4 2 X Coordinate What Are Cor Examples Qui Practice C Ch 6 Basic Ge Ch 7 Basic Gec Ch 8 Basic Geo Ch 9 Basic Geor
Carbon dioxide concentration 410 400 390 380 370 360 350 340 330 lospheric Carbon Dioxide Dissolved Oceanic Carbon Dioxide and Ocean pH Data from NOAA Ocean pH CO ppm Ocean PCO2 uatm 8 13 8 12 8 11 8 10 8 09 8 08 8 07 8 06 8 05 320 8 04 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 Year Hd Predict If the data trends shown in Figure 2 continue on the same trend how might this affect
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Carbon dioxide concentration 410 400 390 380 370 360 350 340 330 lospheric Carbon Dioxide Dissolved Oceanic Carbon Dioxide and Ocean pH Data from NOAA Ocean pH CO ppm Ocean PCO2 uatm 8 13 8 12 8 11 8 10 8 09 8 08 8 07 8 06 8 05 320 8 04 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 Year Hd Predict If the data trends shown in Figure 2 continue on the same trend how might this affect
Gigatons CO equivalent 52 Carbon dioxide concentration 50 48 46 44 40 38 36 Global Anthropogenic Greenhouse Gas Emissions 34 32 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 SEP Use Models Is there enough data in Figures 1 and 2 to draw accurate conclusions abc the future of greenhouse gas emissions and its continued impact on Earth s oceans Explair your reasoning 410 400 390 380 370 360 350 340 M 330 Atmospheric Carbon Dioxide Dissolved Oceanic Carbon Dioxide and Ocean pH Ocean pH CO ppm 8 13 8 12 8 11 8 10 8 09 8 08 8 07 8 06 Ocean PCO 8 05 atm 0 01
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Gigatons CO equivalent 52 Carbon dioxide concentration 50 48 46 44 40 38 36 Global Anthropogenic Greenhouse Gas Emissions 34 32 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 SEP Use Models Is there enough data in Figures 1 and 2 to draw accurate conclusions abc the future of greenhouse gas emissions and its continued impact on Earth s oceans Explair your reasoning 410 400 390 380 370 360 350 340 M 330 Atmospheric Carbon Dioxide Dissolved Oceanic Carbon Dioxide and Ocean pH Ocean pH CO ppm 8 13 8 12 8 11 8 10 8 09 8 08 8 07 8 06 Ocean PCO 8 05 atm 0 01
Gigatons CO equivalent 52 50 48 46 44 42 40 38 36 34 Global Anthropogenic Greenhouse Gas Emissions 32 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Year Data from Olivier J G J et al 2017 Trends in global CO and total greenhouse gas emissions 2017 report PBL Netherlands Environmental Assessment Agency The Hague SEP Analyze Data Look at the data in Figure 1 What general conclusions can you drav bout global anthropogenic greenhouse gas emissions from 1990 2016
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Gigatons CO equivalent 52 50 48 46 44 42 40 38 36 34 Global Anthropogenic Greenhouse Gas Emissions 32 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Year Data from Olivier J G J et al 2017 Trends in global CO and total greenhouse gas emissions 2017 report PBL Netherlands Environmental Assessment Agency The Hague SEP Analyze Data Look at the data in Figure 1 What general conclusions can you drav bout global anthropogenic greenhouse gas emissions from 1990 2016
Select one d 2012 2 1 2 8 O 3 1 O 2 Labor Bureau of Labor Statistics via the US Inflation Calculator https www usinflationcalculator com inflation consumer price index and annual percent changes from 1913 to 2008 Accessed 5 27 20 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 YEAR 218 1 224 9 229 6 233 0 236 7 237 0 240 0 245 1 251 1 255 7 CPI Inflation Rate
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Select one d 2012 2 1 2 8 O 3 1 O 2 Labor Bureau of Labor Statistics via the US Inflation Calculator https www usinflationcalculator com inflation consumer price index and annual percent changes from 1913 to 2008 Accessed 5 27 20 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 YEAR 218 1 224 9 229 6 233 0 236 7 237 0 240 0 245 1 251 1 255 7 CPI Inflation Rate
Find KM M 8 3 4 N 3L W 2 2x 5 K
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Find KM M 8 3 4 N 3L W 2 2x 5 K
Find CE S 10 F 8 O 16 12 E 2x 17 9 D C
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Find CE S 10 F 8 O 16 12 E 2x 17 9 D C
Find HG G 18 O 27 0 10 12 F x 8 H 15 E
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Find HG G 18 O 27 0 10 12 F x 8 H 15 E
The following equation is written in which parabolic form y x 3 1 O Vertex O Parenthetical Next O Standard O Intercept Report an Error question 3 of 5
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The following equation is written in which parabolic form y x 3 1 O Vertex O Parenthetical Next O Standard O Intercept Report an Error question 3 of 5
O Linear function Quadratic equation Next Worksheet Drint Workshoot O Constant function O Quartic polynomial question 4 of 5
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O Linear function Quadratic equation Next Worksheet Drint Workshoot O Constant function O Quartic polynomial question 4 of 5
If the two stars are similar what is the ratio of all of the corresponding sides smaller to larger 5 O 1 5 05 2 25 1 7 O 2 3 Report an Error question 3 of 5 Next Le 4 2 X Coordi What Are Example Pract Ch 6 Bas Ch 7 Bas
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If the two stars are similar what is the ratio of all of the corresponding sides smaller to larger 5 O 1 5 05 2 25 1 7 O 2 3 Report an Error question 3 of 5 Next Le 4 2 X Coordi What Are Example Pract Ch 6 Bas Ch 7 Bas
Oy x 2 2 Oy x 2 2 Next Worksheet Oy x 2 2 Oy x 2 2
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Oy x 2 2 Oy x 2 2 Next Worksheet Oy x 2 2 Oy x 2 2
Are the two triangles similar If so what is the ratio of their corresponding sides Yes 1 6 es 3 4 Next 8 12 O No O Yes 1 4 Report questic
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Are the two triangles similar If so what is the ratio of their corresponding sides Yes 1 6 es 3 4 Next 8 12 O No O Yes 1 4 Report questic
Which of the following statements is true O Similar figures are always the same size Similar figures are always the same color O None of these statements are true Similar figures have the same shane Report an Error question 1 of 5
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Which of the following statements is true O Similar figures are always the same size Similar figures are always the same color O None of these statements are true Similar figures have the same shane Report an Error question 1 of 5
If we reflect a function f x over the y axis it becomes Of x O f x Next f x f x
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If we reflect a function f x over the y axis it becomes Of x O f x Next f x f x
Select one 1 1 Economic Indicators Question 1 What was the inflation rate between 2016 and 2017 01 O 1 O 2 O 1 1 O 2 1 a The following data comes from the U S Department of Labor Bureau of Labor Statistics via the US Inflation Calculator https www usinflationcalculator com inflation consumer price index and annual percent changes from 1913 to 2008 Accessed 5 27 20 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 YEAR 218 1 224 9 229 6 233 0 236 7 237 0 240 0 245 1 251 1 255 7 CPI Inflation Rate X
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Select one 1 1 Economic Indicators Question 1 What was the inflation rate between 2016 and 2017 01 O 1 O 2 O 1 1 O 2 1 a The following data comes from the U S Department of Labor Bureau of Labor Statistics via the US Inflation Calculator https www usinflationcalculator com inflation consumer price index and annual percent changes from 1913 to 2008 Accessed 5 27 20 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 YEAR 218 1 224 9 229 6 233 0 236 7 237 0 240 0 245 1 251 1 255 7 CPI Inflation Rate X
a b c d e f g h i j k b c d f g i c f g i k b d e g k ne AU CnB me correct choice and if necessary fill in the answer box to comples U CnB Use a comma to separate answers as needed AU CNB is the empty set
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a b c d e f g h i j k b c d f g i c f g i k b d e g k ne AU CnB me correct choice and if necessary fill in the answer box to comples U CnB Use a comma to separate answers as needed AU CNB is the empty set
Which of the following would most likely NOT be a part of a formal business letter a postscript a body a signature with the typed name underneath a closing like Respectfully yours
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Which of the following would most likely NOT be a part of a formal business letter a postscript a body a signature with the typed name underneath a closing like Respectfully yours
a b c d e f g h i j k a d e f c d f h j a c e g mine An C h j the correct answer below and if necessary fill in the answer box in yo Anc Use a comma to separate answers as needed AnC is the empty set
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a b c d e f g h i j k a d e f c d f h j a c e g mine An C h j the correct answer below and if necessary fill in the answer box in yo Anc Use a comma to separate answers as needed AnC is the empty set
me the correct answer below AUB a c d t o m a s tv w z AUB a c m a v w z AUB a c v w AUB m q z CELED
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me the correct answer below AUB a c d t o m a s tv w z AUB a c m a v w z AUB a c v w AUB m q z CELED
the set of office supply stores he set of office supply stores that sell paper the set of office supply stores that sell printers the set of office supply stores that sell binders cribe B A ose the correct answer below AB n A is the set of office supply stores that sell paper and do not sell printers 3 B n A is the set of office supply stores that sell printers or do not sell binders C B n A is the set of office supply stores that sell paper or do not sell binders D B n A is the set of office supply stores that sell printers and do not sell paper
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the set of office supply stores he set of office supply stores that sell paper the set of office supply stores that sell printers the set of office supply stores that sell binders cribe B A ose the correct answer below AB n A is the set of office supply stores that sell paper and do not sell printers 3 B n A is the set of office supply stores that sell printers or do not sell binders C B n A is the set of office supply stores that sell paper or do not sell binders D B n A is the set of office supply stores that sell printers and do not sell paper
ANB Use a comma to separate answers as needed cm
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ANB Use a comma to separate answers as needed cm
oose the correct answer below A AUB ak B AUB m p Y C AUB ab c df g ks tv w D AUB d f g s v eccra
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oose the correct answer below A AUB ak B AUB m p Y C AUB ab c df g ks tv w D AUB d f g s v eccra
U be the set of furniture stores A be the set of all furniture stores that sell indoor furniture B be the set of all furniture stores that sell mattresses and C be the set of all furniture stow cal furniture Describe the set B UC in words oose the correct answer from below A The set of all furniture stores that sell mattresses and metal furniture B The set of all fumiture stores that sell mattresses or metal furniture C The set of all furniture stores that sell mattresses D The set of all fumiture stores that sell metal furniture
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U be the set of furniture stores A be the set of all furniture stores that sell indoor furniture B be the set of all furniture stores that sell mattresses and C be the set of all furniture stow cal furniture Describe the set B UC in words oose the correct answer from below A The set of all furniture stores that sell mattresses and metal furniture B The set of all fumiture stores that sell mattresses or metal furniture C The set of all furniture stores that sell mattresses D The set of all fumiture stores that sell metal furniture
the blank with an appropriate word or phrase ets with no elements in common are called ets with no elements in common are called sets sets
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the blank with an appropriate word or phrase ets with no elements in common are called ets with no elements in common are called sets sets
1 A plane intersects a sphere of radius 4cm in a circle Which of the following cannot be the area of this circle A 4 cm B 8 cm C 12 cm D 16 cm T E 24 cm
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1 A plane intersects a sphere of radius 4cm in a circle Which of the following cannot be the area of this circle A 4 cm B 8 cm C 12 cm D 16 cm T E 24 cm
nswer the following with justification A unique polynomial of degree passes through n 1 points What would happen if we try to use an n degree polynomial to interpolate n data points Let f x and g x be polynomials with the degree of f x 3 and the degree of g x 3 Suppo f x g x for x 1 2 3 and 4 What is the degree of g x
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nswer the following with justification A unique polynomial of degree passes through n 1 points What would happen if we try to use an n degree polynomial to interpolate n data points Let f x and g x be polynomials with the degree of f x 3 and the degree of g x 3 Suppo f x g x for x 1 2 3 and 4 What is the degree of g x
Solve the triangle Round your answer to the nearest tenth as neede b 6 c 9 A 117 O A a 12 9 B 24 5 C 38 5 OB a 15 8 B 26 5 C 36 6 OC a 18 7 B 22 5 C 40 6 no triangle
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Solve the triangle Round your answer to the nearest tenth as neede b 6 c 9 A 117 O A a 12 9 B 24 5 C 38 5 OB a 15 8 B 26 5 C 36 6 OC a 18 7 B 22 5 C 40 6 no triangle
TIME REMAIN 55 33 How did the failure of the League of Nations to prevent World War II affect the formation of the United Nations O The US the UK the USSR and China did not think the United Nations would be successful so they refused to join O The US the UK the USSR and China were very determined to create an effective organization that would not fail O The US the UK the USSR and China were afraid to give the United Nations too much power and hindered the organization O The US the UK the USSR and China had not belonged to the League of Nations and therefore had no interest in the United Nations
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TIME REMAIN 55 33 How did the failure of the League of Nations to prevent World War II affect the formation of the United Nations O The US the UK the USSR and China did not think the United Nations would be successful so they refused to join O The US the UK the USSR and China were very determined to create an effective organization that would not fail O The US the UK the USSR and China were afraid to give the United Nations too much power and hindered the organization O The US the UK the USSR and China had not belonged to the League of Nations and therefore had no interest in the United Nations
Show that the function f x is a growth function for x 5 f x 5 x 5 x
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Show that the function f x is a growth function for x 5 f x 5 x 5 x