Basic Math Questions and Answers

30 people were asked What is your favourite fruit Here are the results Fruit banana apple grapes orange Frequency 9 9 6 6 4 banana apple grapes orange Complete the pie chart Click one of the colours in the key then click a sector to colour it What fraction of the people chose grapes Give the fraction in its simplest terms 2

The table shows how Jennifer spent 133 this year at the shops The results are to be shown on a pie chart Amount Angle Product Clothes Games Cinema Other 56 23 16 38 O O O O Fill in the angles Round your answers to the nearest whole number 8 Draw the pie chart for this data by dragging the red buttons 90 90 90 90 Mai 4 EN

The table shows the colours of cars driven by 36 motorists The results are to be shown on a pie chart Colour of car Red Yellow Blue Other Number of Angle motorists 7 11 Fill in the angles 6 12 O Draw the pie chart for this data by dragging the red buttons O 8 O O 90 90 90

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

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

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

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

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

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 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

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

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

Make x the subject of x 5 t

Prove the given identity csc sin 0 cos 0 cot 0 Choose the correct proof below OA csc 0 sin OB csc sin 0 OC csc sin 0 OD csc sin 0 1 sin 0 1 sin 0 1 sin 0 sin 0 sec 0 1 sin 0 sin 0 2 1 sin 0 sin 0 sin 1 sin 0 sin sin 1 sin sin 0 sin 2 1 sin 0 sin 2 Cos 0 sin 0 2 cos 0 cos 0 2 sin 0 2 COS 0 sin 0 cos 0 cot cos 0 cot 0 cos Ocot 0 cos 0 cot 0

verify the identity sin 0 sec 0 tan 0 Which of the following four statements verifies the identity O A sin 0 sec 0 sin 0 cos 0 OB sin 0 sec 0 OC sin 0 sec 0 sin 0 sin 0 COS 0 1 Cos 0 OD sin 8 sec 0 sec 0 1 COS 0 sin 0 sin 0 1 COS 0 COS 0 co 0 sin sin 0 tan 0 Cos 0 sin 0 Cos 0 tan 0 tan 0 tan 0

You may need to use the appropriate appendix table or technology to answer this question The Economic Policy Institute periodically issues reports on workers wages Suppose the institute reported that mean wages for male college graduates were 37 39 per hour and for female college graduates were 27 83 per hour in 2017 Assume the standard deviation for male graduates is 4 60 and for female graduates it is 4 10 Round your answers to four decimal places a What is the probability that a sample of 90 male graduates will provide a sample mean within 1 00 of the population mean 37 39 b What is the probability that a sample of 90 female graduates will provide a sample mean within 1 00 of the population mean 27 83 c In which of the preceding two cases part a or part b do we have a higher probability of obtaining a sample estimate within 1 00 of the population mean Why d Calculate the amount that is 0 60 less than the population mean of 27 83 What is the probability that a sample of 140 female graduates will provide a sample mean less than this amount Step 1 a What is the probability that a sample of 90 male graduates will provide a sample mean within 1 00 of the population mean 37 39 The population mean hourly wage for male graduates was given to be 37 39 with a standard deviation of 4 60 A sample from the population will not necessarily give these same values Let x represent the sample mean hourly wage for a group of 90 males To be within 1 00 of the population mean of 37 39 gives a range of hourly wages between 37 39 1 00 and 37 39 1 00 Therefore the desired probability that a sample mean of 90 males is within 1 00 of the population mean is x

d 2 5x 3y e ex 2x 3 1 3y

On the first day of the fiscal year a company issues 45 000 8 six year installment notes that have annual payments of 9 734 T first note payment consists of 3 600 of interest and 6 134 of principal repayment a Journalize the entry to record the issuance of the installment notes If an amount box does not require an entry leave it blank Cash Notes Payable Feedback Check My Work 88 b Journalize the first annual note payment If an amount box does not require an entry leave it blank Interest Expense

12 Solve the following system of equations 4x 15y 17 x y 13 A 1 3 B 8 1 c 1 8 D 4 3

Verify the identity tan x sec x 1 2 tan x 2 2 Which of the following four statements establishes the identity A tan x sec x tan x tan x 1 1 2 tan x B tan x sec x tan x 1 tan x 1 2tan x OC tan x sec x 1 1 2 tan x OD tan x sec x tan x 1 tan x 1 2 tan x

Prove the given identity 1 tan 0 cos 0 1 Which of the following shows the key steps in proving the identity OA 1 tan 20 cos2 0 sec 0 cos 0 2 OC 1 tan2 e cos 0 sin 0 1 csc 0 O B 1 tan 0 cos 0 cos 0 tan 0 cos 0 cos 0 sin 0 1 cos 0 cos 0 sin 20 2 cos 0 1 cos 0 sin 0 cos 0 sin 0 1 O D 1 tan 0 cos 0 cot 0 cos 0 1 cos 0 tan 20 cos 8 cos 8 1

lan s car gets 34 1 miles per gallon If gas cost lan 2 96 per gallon how much will it cost lan to go 750 miles Round your answer to the nearest penny Input only the number Do not input the dollar sign Example 78 50

Tx R8 11

6 3 8 5 10 7 88 85 toplam n n e iti ka t r

t 0 t 3 2 10 Express f t 0 3 t 5 in terms of unit step functions et t25

A satellite camera takes a rectangle shaped picture The smallest region that can be photographed is a 3 km by 7 km rectangle As the camera zooms out the length I and width wa the rectangle increase at a rate of 2 km sec How long does it take for the area A to be at least 5 times its original size seconds Type an integer or a decimal rounded to the nearest hundredth as needed POLICIS

2 For each line described below is its slope positive negative zero or undefined Justify your answer a As x increases by 3 y decreases by 2 b The line has a negative x intercept and a negative y intercept c The line has a y intercept but does not have an x intercept

Let 3 3 and 8 4 Compute the dot product a b

6 24 32 k l s aralar nda asal ise k nin 20 den k k pozitif ka de eri vard r A 8 B 9 C 10 D 11 E 12

b cos 20 NII 2

12 For each graph below i Determine its slope and y intercept ii Write an equation that describes the graph iii Verify your equation a 6 4 2 2 0 2 N 4 y f x N X b 2 2 N 2 4 y y g x N X

Suppose a charity received a donation of 15 6 million If this represents 46 of the charity s donated funds what is the total amount of its donated funds Round your answer to the nearest million dollars million dollars X G

6 1 1 Determine the slope of each line a b 4 800 E 600 Distance m 0 y 400 y f x 200 0 X 2 For each line described below is its slope positive negative zero or undefined Justify your answer a As x increases by 3 y decreases by 2 b The line has a negative x intercept and a negative y intercept c The line has a y intercept but does not have an intercept 3 A line passes through A 3 1 For each slope given below y g x i Sketch the line through A with that slope ii Write the coordinates of three other points on the line b 14 a 1 4 Determine the slope of a line that passes through each pair of points What strategy did you use a B 6 8 and C 1 2 b D 3 7 and E 5 5 4 5 Gabrielle likes to jog and has a pedometer to measure how far she runs She checks her pedometer periodically and records its readings Gabrielle plotted these data on a grid Graph of Gabrielle s Run 2 5 800 2 320 0 y 6 Time min a What is the slope of the line and what does it represent b How is slope related to rate of change c Assume Gabrielle continues to run at the same rate i How far did Gabrielle jog in 4 min ii How long will it take Gabrielle to jog 1000 m 6 2 6 The slope of line FG is given What is the slope of a line that is i parallel to FG ii perpendicular to FG d 1 6 11 a 3 b c 8 7 The coordinates of two points on two lines are given Are the two lines parallel perpendicular or neither Justify your choice a H 3 3 J 1 7 and K 1 2 M 5 1 b N 4 2 P 1 7 and Q 2 5 R 4 1 8 Is quadrilateral STUV a parallelogram Justify your answer V 4 2 6 4 2 y T 9 Triangle ABC has vertices A 1 1 B 2 5 and C 6 3 Is AABC a right triangle Justify your answer 6 3 10 Sketch graphs to help explain what happens to the graph of y 3x 4 when a the coefficient of x increases by 1 each time until the coefficient is 6 b the constant term decreases by 1 each time until it is 4

4 Determine the slope of a line that passes through each pair of points What strategy did you use a B 6 8 and C 1 2 b D 3 7 and E 5 5