Basic Math Questions and Answers

Beginning with the Koch curve with a lin step 0

To ensure reliable performance of vital computer systems aerospace engineers sometimes employ the technique of triple redundancy in which three identical computers are installed in a space vehicle If one of the three computers gives results different from the other two it is assumed to be malfunctioning and is ignored This technique will work as long as no more than one computer malfunctions Assuming that an onboard computer is 99 reliable that is the probability of its failing is 0 01 what is the probability that at least two of the three computers will malfunction Round your answer to four decimal places

You are interested in finding a 90 confidence interval for the mean number of visits for physical therapy patients The data below show the number of visits for 10 randomly selected physical therapy patients Round answers to 3 decimal places where possible 9 27 13 27 6 27 17 10 27 7 a To compute the confidence interval use a distribution b With 90 confidence the population mean number of visits per physical therapy patient is between and visits c If many groups of 10 randomly selected physical therapy patients are studied then a different confidence interval would be produced from each group About percent of these confidence intervals will contain the true population mean number of visits per patient and about percent will not contain the true population mean number of visits per patient

Ch 10 Quiz 6 1 points TB MC Qu 10 37 Static Regardless Regardless of the specific type of long term deb

1 point We usually write numbers in decimal form or base 10 meaning numbers are composed using 10 different digits 0 1 9 Sometimes though it is useful to write numbers hexadecimal or base 16 Now there are 16 distinct digits that can be used to form numbers 0 1 9 A B C D E F So for example a 3 digit hexadecimal number might be 2B8 a How many 3 digit hexadecimals are there in which the first digit is E or F b How many 6 digit hexadecimals start with a letter A F and end with a numeral 0 9 c How many 4 digit hexadecimals start with a letter A F or end with a numeral 0 9 or both

etry 1 9 2 Homework K Transform the pola coordinates Ther

Let f x y 144 x A Describe the cross sections of the surface z f x y produced by cutting it with the planes y 1 y 4 and y 7 B Describe the cross sections of the surface in the planes x 1 x 4 and x 7 C Describe the surface z f x y y 2 A Choose the best description of the cross sections in the planes y 1 y 4 and y 7 OA Upper semicircles whose centers lie on the y axis OB Up opening parabola in the xz plane OC Down opening parabola in the yz plane D Lower semicircles whose centers lie on the x axis

Qu aph of the equation r 2a cos 0 a

Housing Prices Going into the Real Estate Bubble The following table shows the average percentage increase in the price of a house in 9 regions of the United States X X X X New England Middle Atlantic X Pacific South Atlantic West North Central West South Central Mountain East North Central East South Central P X X Frequency 175 75 200 Let X be the percentage increase in the price of a house in a randomly selected region a What are the values of X Enter your answers from smallest to largest Do not enter redundant values X 125 250 125 75 200 b Compute the frequency and probability distribution of X 175 175 125 175 200 250

In the following exercises given L or R as indicated express their limits as n as definite integrals identifying the correct intervals 64 Ln 1 n n 1 1 n

A business operated at 100 of capacity during its first month and incurred the following costs Production costs 20 500 units Direct materials Direct labor Variable factory overhead Fixed factory overhead Operating expenses Variable operating expenses Fixed operating expenses 173 300 236 100 259 900 90 700 Oa 293 368 b 58 768 c 301 391 Od 66 732 125 900 44 500 760 000 170 400 170 400 If 1 800 units remain unsold at the end of the month and sales total 1 165 000 for the month the amount of operating income reported on the absorption costing in statement would be

A fitness center is interested in finding a 98 confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center Records of 229 members were looked at and their mean number of visits per week was 3 3 and the standard deviation was 2 7 Round answers to 3 decimal places where possible a To compute the confidence interval use a distribution b With 98 confidence the population mean number of visits per week is between and visits c If many groups of 229 randomly selected members are studied then a different confidence interval would be produced from each group About percent of these confidence intervals will contain the true population mean number of visits per week and about percent will not contain the true population mean number of visits per week

work ansform the polar equation to 9

ework Transform the polar equation to an equati 5n 6

Which of the following values cannot be probabilities 3 5 5 3 0 03 0 2 1 0 41 1 15 Select all the values that cannot be probabilities A 2 B 5 53 3 C 3 5 D 0 03 E 1 15 F 0 41 G 0

Identify the symbols used for each of the following a sample standard deviation b population standard deviation c sample variance d population variance If sample data consist of weights measured in grams what units are used for these statistics and parameters a The symbol for sample standard deviation is b The symbol for population standard deviation is c The symbol for sample variance is d The symbol for population variance is

Suppose that the universal set is U 1 2 3 4 5 6 7 8 9 10 Express each of the following subsets with bit strings of length 10 where the ith bit from left to right is 1 if i is in the subset and zero otherwise a 3 4 5 b 1 3 6 10 c 2 3 4 7 8 9 d 1 2 4 8 10 e 3 f 4 5 7 9

1 point A woman is about to build her own home computer She decides she has three different possible brands of chip four possible hard drives three choices of RAM manufacturer and five brands of DVD writer to consider How many different ways are there for the woman to build her computer

Use the table to determine a solution of the equation Use synthetic division to verify that this number is a solution of the equation Then solve the polynomial equation 20x 49x 19x 2 0 X 3 2 The solution is W1473 Y 20x 49x 19x 2 1040 396 90 2 12 0 154 Which solution of the equation can be determined from the table

England Journal of article by Dr Douglas Jorenby and colleagues comparing different treatments to help patients stop smoking Two of the four treatments were a placebo and a nicotine patch The subjects were treated and the number of subjects not smoking after 6 months was recorded The results are summarized in the table below Treatment Subjects participating Subjects not smoking After Six Months 30 52 Placebo 160 Nicotine Patch 244 Note that using the above data a 95 confidence interval for the proportion of patients using a placebo who were not smoking 6 months later is 0 127 p 0 248 Calculate the 95 confidence interval for the proportion of patients using a nicotine patch who were not smoking 6 months later Show all work Round to 3 decimal places 8 pts b Using a scale appropriate for the two confidence intervals draw the two confidence intervals for the placebo and the nicotine patch on a number line Label each so that they can be distinguished from each other Use a ruler and

Consider a sample of 55 football games where 29 of them were won by the home team Use a 0 05 significance level to test the claim that the probability that the home team wins is greater than one half Identify the null and alternative hypotheses for this test Choose the correct answer below O A Ho p 0 5 H p 0 5 OB Ho p 0 5 H p 0 5 OC Ho p 0 5 H p 0 5 O D Ho p 0 5 H p 0 5 G

The accompanying table shows the ages in years of 11 children and the numbers of words in their vocabulary Complete parts a through d below Click here to view the data table Click here to view the table of critical values for the Pearson correlation coefficient Vocabulary si 2400 1800 1200 600 0 0 2 4 6 8 Age years Vocabulary si 1500 Age years BEDIEN 3000 b Calculate the sample correlation coefficient r Vocabulary si 24004 1800 1200 600 0 02 4 6 8 Age years Vocabulary si 6 4 2 0 P r 0 975 Round to three decimal places as needed c Describe the type of correlation if any and interpret the correlation in the context of the data There is a strong positive linear correlation Interpret the correlation Choose the correct answer below T A 1500 3000 Age years

Determine the reactions at A and B for the beams loaded as shown Beam weight may b neglected 08 ban A 21sdmsm to einignih bod son 1 1 19 A 5 200 lb ft 800 lb B77 2 4 2 4 M1 008 m 8

linear relation may exist between the two variables If the relation is linear determine whether it indicates a positive or negative association between the variables Use this information to answer the following Do the two variables have a linear relationship OA The data points have a linear relationship because they do not lie mainly in a straight line OC The data points have a linear relationship because they lie mainly in a straight line Response OD 30 20 10 04 0 20 Explanatory Do the two variables have a positive or a negative association OA The two variables have a positive association OB The two variables have a negative association OC None of the above 40 B The data points do not have a linear relationship because they do not lie mainly in a straight line The data points do not have a linear relationship because they lie mainly in a straight line Q ON

Tom has taken 5 of the 8 equally weighted tests in his U S History class this semester and he has an average score of exactly 78 0 points How many points does he need to earn on the 6th test to bring his average score up to exactly 80 0 points vilo91100 wold no delgur babside 6 00 2 3

The data show the time intervals after an eruption to the next eruption of a certain geyser Find th egression equation letting the first variable be the independent x variable Find the best predicted of the interval after an eruption given that the current eruption has a height of 69 feet Use a signific level of 0 05 84 76 Height ft Interval after min Click the icon to view the critical values of the Pearson correlation coefficient r 122 78 108 73 105 122 77 67 87 61 77 87 What is the regression equation y x Round to two decimal places as needed What is the best predicted time for the interval after an eruption that is 69 feet high The best predicted interval time for an eruption that is 69 feet high is Round to one decimal place as needed minutes 78 A 70

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Inequalities Which system of inequalities below correctly represents the shaded region on the graph below y R 2 2 A x y 1 y 1 B x y 1 y 1 C x y 1 by 1 D x y 1 y 1

at is coterminal with 288 coterminal with B 14x 3

What does it mean to say that two variables are positively associated Choose the correct answer below OA There is a linear relationship between the variables OB There is a linear relationship between the variables and whenever the value of one variable increases the value of the other variable increases OC There is a linear relationship between the variables and whenever the value of one variable increases the value of the other variable decreases D There is a relationship between the variables that is not linear

The height of the triangle is h and AD x Complete the steps below to prove the Law of Cosines When filling in the blanks you may use the letters a b c x and h C a 1 h B Part 1 Use the Pythagorean Theorem to find a Oa c x h Oa c x Od x h Oa b x h Part 2 Use the answer from Part 1 to fill in the blanks a 2 0 0 Part 3 Use the Pythagorean Theorem to find b Ob a x h Ob x h Ob c x h Ob c a Part 4 Use the answers from Parts 2 and 3 to fill in the blanks 2 2 0 0 Part 5 Use trigonometry to fill in the blank x cos A Part 6 Use the answers from Parts 4 and 5 to fill in the blanks 2

8 y 9 15 8 13 X 10 KX TO OA 10 8 6 4 2 0 Click here to view a table of critical values for the correlation coefficient a Construct a scatterplot Choose the correct graph below 0 13 9 11 8 73 8 77 9 26 O 4 8 12 16 OB Ay 10 8 6 4 2 0 0 O 4 8 12 16 14 6 4 12 8 09 6 14 3 09 9 13 The linear correlation coefficient is r O C 0 05 10 8 6 4 2 0 48 12 16 OD 10 8 6 2 0 NYNO ww 7 7 27 10 4 O 5 4 75 O 8 12 16 b Find the linear correlation coefficient r then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables

Choose the correct answer below OA r 0 722 represents a stronger correlation because 0 722 0 893 OB r 0 722 represents a stronger correlation because 0 893 0 722 OC r 0 893 represents a stronger correlation because 0 893 0 722 D r 0 893 represents a stronger correlation because 0 722 0 893

Find the value of the linear correlation coefficient r The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew in millimeters Temperature 62 76 50 51 71 Growth 36 39 50 OA 0 210 B 0 OC 0 196 D 0 256 46 51 13 33 33 17 46 44 79 16

Show that e Solution e ei e e iye cos y isin y e cos y i sin y cos y i sin y cos y i sin y e e y

II 2 3 Show from the definition that the functions r Rez and y Im z are not complex differentiable at any point Solution Differentiation f 2 x Rez from the definition z A f z lim A 0 lim A 0 lim A 0 g z Az g z Re z Az Re 2 A 0 Az Differentiation g 2 y Imz from the definition lim lim A 0 Re Az Im Az lim A 0 Az Im z Az Im 2 Az Jo i 1 0 The functions r Rez and y Im z are not complex point because the functions have different limit as Az imaginary axis if Az Ar if Az iAy if Az Ar if Az iAy differentiable at any 0 through real and

1 Find and plot log z for the following complex numbers z Specify the principal value a 2 b i c 1 i d 1 i 3 2

al This table shows the number of lorries passing a checkpoint each hour between 6 am and 8 pm one day Find the median and interquartile range IQR of the checkpoint times Enter your first answer as a 4 digit number e g 0738 median IQR hrs mins 3 4 i m time 0600 0700 07000800 0800 0900 0900 1000 1000 1100 1100 1200 1200 1300 1300 1400 1400 1500 1500 1600 1600 1700 1700 1800 1800 1900 1900 2000 lorries 6 2 10 5 9 9 10 8 3 5 3 6 8 7 01 V cum freq Mark it

18 points Write the equation of the ellipse in standard form State the center vertices co vertices and foci 16x 9y 96x 36y 36 0

1 Find all values and plot a 1 i b i i c 2 2 d 1 i 3 1 1

2 Show that cos z cos z sinh y where z x iy Find all zeros and periods of cos z

What is the rate of movement for the Pacific Plate between the Abbott Seamount and Lo ihi in cm yr Rate of plate movement cm yr Type only numbers no letters Be aware of the decimal Round to the nearest tenths place

3 A cougar is standing in a forest and scents a deer grazing in the boundary of the forest The cougar is 3km due East from the edge of the forest and the deer is 9km North of that point If the cougar can run through the forest at a rate of 8km hr but can run through the field at a rate of 10km hour where should the cougar exit the forest in order to reach their prey in the least amount of time

0 14 22 0 8 otal cubes Fill the gaps in this sequence 16 25 49 64 2 Work out the cube root of 216 then square it and 2 When you subtract one square number from another the answer What are the two square numbers 2 Write down a number you can cube to give an answer bigger than 200 but smaller than 400

Find the circumcenter of A ABC y O B A C X

21 Two step equations Solve these equations 3m 5 20 5y 11 29 8m 21 59 a 6 5 15 m 10h 3 103 y m a t 4 5 11 t h 6 Noah says I am thinking of a number s When I multiply it by 7 and subtract 41 the answer is 78 What is Noah s number S 4

Solve these equations 5x 10 35 5y 15 15 NO X 5 5 4z 10 1 5 3 12y 8 24 8 7 X y Z X y Z You need to make p loaves of bread Each loaf requires 415 grams of flour 1 You also need 160 grams for sprinkling 1 2 2 2 Choose the expression for the total amount of flour you need in terms of p P 415 P 415 160 160 415p 160 415p 160 If you have 2800 grams of flour what is the maximum number of 2 loaves you could make

Find the matrix product if possible 2 4 1 3 0 3 1 2 3

Use Integratior by parts to solve xx x xe 1 doc So X

2 147 3 Refer to the graph of the function and complete