Math - Others Questions

e g The area between the curve y 17 7 2 71 Determine whether the following statements are true and give an explanation or counterexample Assume x 0 and y 0 a In xy Inx Iny b In 0 1 c In x y Inx Iny d Part 3 of 7 f 32 for any integer n21 and the x axis on the interval 1 e is 1 OA The statement is false because In 0 0 OB The statement is true because 1 C The statement is false The natural logarithmic function In x is not defined at x 0 D The statement is true because in 0 1 c Choose the correct answer below HW Score 69 05 16 57 of Points 0 14 of 1 OA The statement is false The Product Rule of Logarithms states that in x In y In xy OB The statement is false The Difference Rule of Logarithms states that inx Iny In x y OC The statement is true The Difference Rule of Logarithms states that In x y Inx Iny OD The statement is true The Sum Rule of Logarithms states that in x y Inx Iny

Use the following table to determine the indicated derivatives or state that the derivative cannot be determined 6 3 0 1 4 5 f x 1 f x 2 3 a f 4 b f 1 1 C 3 7 3 2 f 3 d f 3 3 A 1 cannot be determined OB 6 8 A 4 3 Type an integer or a fraction OB 4 cannot be determined b Choose the correct answer below and if necessary fill in the answer box within your choice f 1 Type an integer or a fraction OA 3 cannot be determined 2 A c Choose the correct answer below and if necessary fill in the answer box within your choice

If 15 000 is invested at 12 interest compounded quarterly find the interest earned in 13 years

The value of the first number is

09 27 1 Try the below on your 2 x 3 4 3 8 12 1 3x ex 4 e 5x 1 1 5 x 25 e 2 e 2 4 2x 6x 2 2

The size P of a certain insect population at time t in days obeys the function P t 700e0 041 a Determine the number of insects at t 0 days b What is the growth rate of the insect population c Graph the function using a graphing utility d What is the population after 10 days e When will the insect population reach 840 f When will the insect population double b The growth rate of the insect population is 4 c Graph P t 700e A 0 04t Choose the correct graph below The graphing window is 0 10 1 by 0 1400 100 Q OB d The population after 10 days is approximately 1044 insect s Do not round until the final answer Then round to the nearest whole number as needed e It will take about day s for the insect population to reach 840 Do not round until the final answer Then round to the nearest tenth as needed c oo D o Q

7 9 B E C are the mid points of the sides AP PQ QA of AAPQ If a b c are the position vectors of the points A B C prove that the position vectors of P Q R are 2b a 2c a b c a respectively B

The function f t 600 0 998 represents the change in a quantity over t minutes What does the constant 0 998 reveal about the rate of change of the quantity Answer B

Escherichia coli commonly referred to as E coli is essential for modern biotechnology research One reason for this is the ease and speed at which E coli can be cultivated in the laboratory Under ideal laboratory conditions when this bacterium is grown in a nutrient broth medium the number of cells in a culture doubles approximately every 19 minutes Suppose an initial colony of 150 E coli bacteria are to be used for an experiment Use the exponential growth model Y Yoekt where t is measured in minutes to write an exponential growth function for bacteria colony Round the growth constant k to four significant figures The exponential growth function that models growth of the E coli colony is Approximately how many bacteria will be present in the colony after 135 minutes Round the solution to the nearest whole number Approximately bacteria will be present in the colony after 135 minutes Determine how long it will take for the bacteria colony to reach 100 000 000 bacteria Round the solution to the nearest whole number The bacteria colony will reach a population of 100 000 000 after minutes

15 What percentage of individuals are 45 50 inches tall inclusively 40 45 Answer 50 Height inches 55 Round your answer to the nearest hundredths 60

d 3 3x 2 2x 4x

How many years will it take for an initial investment of 20 000 to grow to 70 000 Assume a rate of interest of 2 compounded continuously It will take about years for the investment to grow to 70 000 Round to two decimal places as needed

Med ed 10 8 Refer to Exercise 10 7 a Place a 99 confidence interval on the proportion of false negatives produced by the test b Is there substantial evidence a 01 that the test produces less than 2 false negatives c Which of the two types of errors false positives or false negatives do you think is more crucial to public safety Explain your reasoning 10 7 The test for screening donated blood for the presence of the AIDS virus was developed in the 1980s It is designed to detect antibodies substances produced in the body of donors carrying the virus however it is not 100 accurate The developer of the test claimed that the test would pro duce fewer than 5 false positives and fewer than 1 false negatives In order to evaluate the accuracy Test Result Positive test Negative test Total of the test 1 000 persons known to have AIDS and 10 000 persons known to not have AIDS were given the test The following results were tabulated True State of Patient Has Aids 993 7 1 000 Does Not Have Aids 591 9 409 10 000 Total 1 584 9 416 11 000 a Place a 99 confidence interval on the proportion of false positives produced by the test b Is there substantial evidence a 01 that the test produces less than 5 false positives

10 29 The quality control department of a motorcycle company classifies new motorcycles according to the number of defective components per motorcycle at an initial inspection An improvement to the production process has been implemented and hopefully there will be a change from the historical defective distribution 7 80 72 10 773 05 74 03 and 5 02 A random sample of 300 motorcycles produced under the new system is classified as follows Number of Defectives Number of Motorcycles n 0 238 1 32 2 12 3 13 4 or more 5 Total 300 At the ax 05 level does there appear to be a change in the historical proportions of defectives

a Place 95 confidence intervals on the proportions of the production falling into the five classifications b Do the confidence intervals support the conclusion reached in Exercise 10 29 c Why may the conclusion reached using the confidence intervals differ from the conclusion reached in Exercise 10 29

A graph of a function f is given below y 15r f 1 4 f 9 9 10 5 Find f 1 4 and f 1 9 4 X X 2 8 X

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

A statisican that is a sports enthusiast estimated the mean cost upper level NBA tickets They determined the mean cost to be between 52 and 78 L What is the sample mean X What is the margin of error E estion 4 6 points large airline wants to estimate the mean number of unoccupied seats per flight ow many flight records must they select to be 90 confident that their estimate is thin 0 5 unoccupied seats Assume o 4 3

A grocery store clerk put only packages of flour tortillas and packages of com tortillas on a shelf The ratio of the number of packages of corn tortillas to the total number of packages on the shelf was 7 to 16 Which number could be the number of packages of flour tortillas the clerk put on the shelf F G H J 23 18 14 32

Tritium is a radioactive isotope of hydrogen that has the desirable characteristic of radioluminescence which allows it to glow in the dark without the need for an external light source Thus tritium filled tubes are often used for applications such as airplane cockpit instrument dials watch hands and emergency lighting The half life of tritium is 12 32 years Suppose you recently purchased a premium watch with tritium hands How many years will it take for the watch hands to lose 95 6 of their original brightness Round your solution to the nearest year years

Two variables appear to have an exponential relationship What pattern s does the scatterplot suggest for the model Select the two correct answers 1 point It is only increasing or only decreasing It has a point of inflection It is only concave up or only concave down It has one or more extrema It is both concave up and concave down Ite

K Determine which numbered regions make up the indicated set XUY U T1 X 72 13 T4 COLLE A This question 1 point s possible Select all regions contained in the given set A B C TA D 13

K In the set of the ten top grossing movies of all time define the sets shown below E the set of movies that earned more than 900 million A the set of movies that won a movie award B the set of movies that were made before 1970 Describe the set En B in words and then find the set Click on the icon to view the table of the ten top grossing movies of all time Define the set En B in words Choose the correct answer below OA The set of movies that earned more than 900 million and were made before 1970 OB The set of movies that earned less than 900 million or were made after 1970 OC The set of movies that earned more than 900 million or were made before 1970 OD The set of movies that earned more than 900 million and were made after 1970 Identify the elements of the set En B Type the letter s of the movie s that are in the specified set For example an answer could be En B a b m En B Use a comma to separate answers as needed Data table Movie Movie a Movie b Movie c Movie d Movie e Movie f Movie g Movie h Movie i Year 1985 1980 1940 1968 1959 1965 1976 I 1935 1975 Inflation Adjusted Gross millions 1 346 1 219 982 949 906 887 880 856 761 Won Movie Award Yes No Yes Yes Yes No Yes No

K Use the Venn diagram to determine whether the statements are equal for all sets A and B A UB and A U B Are the statements equal for all sets A and B O O Yes No CHE This question 1 point s possible A 100 I II U IV B II

K In the universal set U a b c h define subsets of cars with the characteristics shown to the right Describe the following set in words and then find the set POC 0 Click on the icon to view the table of new car features Define the set PnC in words Choose the correct answer below OA The set is the set of cars that cost more than 20 000 and are not compact OB The set is the set of cars that both cost more than 20 000 and are compact OC The set is the set of cars that either cost more than 20 000 or are compact OD The set is the set of cars that cost 20 000 or less and are not compact Identify the elements of the set Pn C Select all that apply A g C h E d G e 1 1 PnC is the empty set P price is above 20 000 C is compact G A has a good safety rating has antitheft package W warranty is at least three years B b D c F f H a Data table Car a b C d T e f g h Cost 23 000 16 500 21 600 21 000 20 400 18 900 18 100 23 800 poss Size midrange subcompact compact compact compact subcompact subcompact midrange Print Warranty years 3 2 3 3 2 3 4 4 Done Sat

Determine whether the following pair of sets is equivalent Justify your answer x x is a letter in the word cat and x x is a letter in the word scar Are the sets equivalent OA No the two sets do not have any of the same elements OB Yes the two sets consist entirely of letters OC No the two sets have a different number of elements OD Yes both sets are subsets of larger sets

Describe the following set as either finite or infinite x x is a word in a poem written by Emily Dickinson The set is because the number of elements in the set infinite a whole number

Determine whether the set is well defined x x has many possessions Choose the correct answer below O not well defined O well defined

Let U 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 A 1 2 3 4 7 9 10 11 13 15 17 B 1 3 6 8 9 10 12 13 14 16 17 and C 2 3 5 7 12 13 14 15 Find B CUA Select the correct choice below and if necessary fill in the answer box to complete your choice OA B CUA BILL Use a comma to separate answers as needed B B C UA 9

Use the following table of electives to describe the set below in an alternative way World Culture Cultural Diversity Humanities No Yes Yes Yes No Writing No Yes Yes Yes No Yes No Class A Class B Class C Class D Class E Class F Yes Class G Yes Class B Class C Class D Class F Class G Choose the correct answer below OA x x is a world culture elective OB x x is a writing elective OC x x is a humanities elective OD x x is a cultural diversity elective Yes Yes No No Yes Yes No No Yes Yes No No Yes Yes

Use the table to answer the question Consider the set V GPA above 3 0 Which set is equal to V Choose the set equal to V OA Brenda Dana Elston OB Carmen Elston Gina OC Carmen Frank Brenda Dana Elston Gina This question 1 point s possible Major Carmen History Frank Physics Senior Brenda Business Freshmen Dana History Senior Elston History Junior Gina Business Junior Class Rank GPA Act Junior 3 7 Ban 1 9 Yea 2 8 Bas 1 7 So 3 2 Ter 3 1 Ch

List all the two element subsets of the following set 2 4 6 8 Choose the correct answer below OA 2 4 2 6 2 8 4 6 4 8 6 8 OB 2 4 4 6 6 8 OC 0 2 4 2 6 2 8 4 6 4 8 6 8 2 4 6 8 OD 0 2 4 2 6 2 8 4 6 4 8 6 8

Find n A for the following set A x x is a letter in the word unconsciousness n A

Find an element of set A that is not an element of set B A y y is a consumer product B y y is an electronic device Choose the correct answer below O mp3 player O pan O O computer cell phone

Below is a graph of the Sun s azimuth at sunset every single day for an entire year However the person recording the data neglected to record the dates of each observation of azimuth Using their graph which number represents a date when there was 12 hours of daylight and 12 hours of darkness Azimuth in Degrees 310 300 290 280 270 260 250 240 230 01 04 0 5 02 O2 and 4 O1 and 3 and 5 O1 and 5 Azimuth of the Sun 3 Month

9 5x y 5 6 5 4 2 1 Ay 10 x 5y 20

RE 6 5 Notes 2023 notebook Graphing Vertical and Horizontal Lines Graph y 2 ox y 2 Graph x 5 3 3 Graph x 3 4 x 7 orizontal Line Vertical Line Graphing y mx b Graph y 3x 4 M 3 5 4 Assignment find slope Graph y 6 3 81 6 1 2 x 09 5 6 6 y 9 Graph y 2 3x 1 count risc runt 6 2 Parallel Par pendicular LINS Parallel Somestore y x 1 2 2 Perpendicular opposite re ciplants M Y 7137 71 Label ports substitute in formul

6 4 Slope as Rate of Change MATHPOWER M 10 Western Edition pp 270 272 1 Jake cycled 7 5 km in 25 min and 22 5 km in 75 min Rhona cycled 8 75 km in 35 min and 16 25 km in 65 min a Plot the points time distance for Jake on the grid shown b Plot the points time distance for Rhona on the same grid c Use the graph to indicate who cycled faster d Calculate Jake s rate of cycling in kilometres per hour e Calculate Rhona s rate of cycling in kilometres per hour 2 One year Lillian paid 4250 in taxes on a taxable income of 25 000 In the previous year she paid 3740 in taxes on a taxable income of 22 000 a Determine the rate of income tax as a percent of taxable income b Describe the rate of income tax in words c If Lillian had a taxable income of 26 500 in the next year and the income tax rate did not change how much income tax did she pay d If Lillian paid 3612 50 in income taxes the next year and if the income tax rate did not change what was her taxable income that year 3 During a trip to Belgium Toni exchanged three amounts of Canadian dollars for Belgian francs Included in the amount he paid for each transaction was a handling charge He received 5000 Belgian francs for 205 Canadian 3750 Belgian francs for 155 Canadian and 6250 Belgian francs for 255 Canadian a Plot the points Canadian dollars Belgian francs on the grid shown b What does the slope of the graph represent c Use the graph to find the exchange rate for the number of Belgian francs that is equivalent to one Canadian dollar that week d What is the handling charge for each transaction

5 3x 2y 2 7 x y 4 49 6 x 2y 6 8 x 4y 4 LT Ay find the slope of the line with poir C 3 7 and C4 1 1 Y x2112 m 42 41

Your dad mentioned that he had 100 000 in his retirement account 20 years ago If inflation has been 4 per year for those 20 years by how m would the account have needed to GROW to have the same purchasing power today as 20 years ago O 65 980 O 88 098 O 101 902

9 The slope of a line is 2 The line passes through 1 k 0 4 and m 4 Find the values of k and m

is The line passes through 4 1 Name the coordinates of two other possible points on the line 8 The slope of a line is

Find the slope of a line that has these points 1 3 2 4 8 2 and 11 3 xz y 2 y 5 8 0 and 8 6 m y2 X2 3 2

Your dad mentioned that he had 100 000 in his retirement account 20 years ago If the account has grown by the market rate of 10 per year by how much would the account have grown O 276 980 379 098 O 572 750 890 076

Make the subject of this formula k n 12

Make x the subject of x 5 t

3 The value in millions of dollars of transactions processed by an online payment platform is modeled by the function M The value is expected to increase by 6 1 each year At time t 0 54 million dollars of transactions were processed Write the equation of a function M t that represents this situation ins last

Simplify the given expression The result will be one of sin x cos x tan x cotx secx or csc x cos x sec x cot x cos x sec x cot x I

Verify the identity 2 sin x sinx cot x csc x Choose the sequence of steps below that verifies the identity OA OB O C 2 sin x sinx cot x sinx cot x 1 2 sin x sinx cot x sinx 1 cot x 2 sin x sinx cot x sin x 1 cot x SO D sin x sin x cot x 1 cot x csc x 1 CSC X 1 CSC X 1 2 CSC X CSC X 2 CSC X CSC X 2 CSC X CSC X CSC X MIN

Prove the given identity sin 0 1 cot e 1 2 Which of the following shows the key steps in proving the identity 2 2 O A sin 1 cot e sin 0 sin 0 cot 0 sin 2 OB sin 0 1 cot e sin 0 tan 0 sin 0 O c sin 0 1 cot 0 os 0 c COS COS sin 0 2 COS 0 O D sin2 0 1 cot2 0 sin 0 csc 0 sin 0 2 1 cot 0 sin 1 2 2 sec 0 0 cos cos 0 1 2 sin 0 2 sin 0 0 cos 0 1 2 sin 0 1 2 sin 0 1