Mathematical Reasoning Questions and Answers

vectors A B C D E Let a 10i 4j and b 8i 4j Find the dot product of the two vectors and the angle between the two a b 72 and 0 41 38 a b 96 and 0 131 33 a b 4 096 and 0 131 40 a b 64 and 0 131 38 a b 64 and 0 41 33 80 67000 ME

Depression and insomnia often go hand in hand Mendoza Company a national pharmaceutical firm has positioned itself as a specialist in the production of both antidepressants and sleeping pills Mendoza s current business model describes the following breakdown of America s approximately 50 million adults suffering from insomnia 17 use both antidepressants and sleeping pills regularly 24 use only antidepressants regularly 15 use only sleeping pills regularly and the remaining 44 use neither antidepressants nor sleeping pills regularly In a recent study on insomnia in a psychiatry journal 160 American adults suffering from insomnia but otherwise chosen at random were asked about their use of antidepressants and sleeping pills The breakdown of their answers is given by the top row of numbers in the table below These numbers are the frequencies observed for the sample of 160 insomniacs The second row of numbers gives the expected frequencies under the hypothesis that Mendoza s model is correct The bottom row of numbers contains the following value for each of the categories of medication use So E JE Part 1 Fill in the missing values in the table Round your responses for the expected frequencies to two or more decimal places Round your Jo JE responses to three or more decimal places Send data to Excel Observed frequency fo Observed frequency Expected frequency Expected frequency Expected frequency JE Both 29 0 Only antidepressants 31 38 40 1 426 Only sleeping pills 19 0 0 Neither Total a Determine the type of test statistic to use 81 70 40 1 596 160 Part 2 Answer the following to summarize the test of the hypothesis that Mendoza s model is correct Use the 0 10 level of significance for the test Type of test statistic Choose one b Find the value of the test statistic Round your answer to two or more decimal places 0 c Find the critical value Round your answer to two or more decimal places d Can we conclude that the percentages given in Mendoza s model are incorrect 19 B M

converse inverse and contrapositive only the contrapositive of the conditional statement is to the co

Here is a graph of a function f and graphs of two transformations of f g and h Y YA 3 da 1 Write an equation for g x in terms of f x 2 Write an equation for h x in terms of f x 5X 3 h

1 point Consider the following statement Some people are allergic to cats For the following questions Let X people P x be the predicate x is allergic to cats Write the statement in quantified form OA VxEX P x OB Ex EX P x OC VxEX P x OD Ex EX P x Negate the quantified statement OA VxEX P x OB Ex EX P x OC VxEX P x OD Ex EX P x Translate the negated statement into English OA Nobody is allergic to cats OB There exists someone that is not allergic to cats C Everyone is allergic to cats OD There exists someone that is allergic to cats

1 point Consider the following statement Everyone likes playing games For the following questions Let X people P x be the predicate x likes playing games Write the statement in quantified form OA VxEX P x OB VxEX P x OC Ex EX P x OD 3x EX P x Negate the quantified statement OA Ex EX P x OB VxEX P x OC VxEX P x OD Ex EX P x

1 point Are the following statements true or false 1 Every graph has a Hamilton path 2 Every complete graph has an Hamilton circuit 3 Every graph with a Hamilton circuit has a Hamilton path 4 If Km n has an Euler circuit then m and n are both even order to got orodit for this problem all opowOKO

Which graph shows the weakest correlation O A O C D They are all the same correlation U

Removing point A from the scatterplot will a change the correlation but not the regression equation b change the regression equation but not the correlation c not change the correlation or the regression equation d change the correlation and the regression equation O A OB O C OD A

Researchers wanted to study how quickly lclcles grow They measured the amount of time from the initial measurement hrs and the length of the Icicle cm The data was examined and plotted What conclusion can we make from the data below Amount of time from initial measurement hr 28 24 46 60 83 107 Length 35 36 5 22 5 29 32 34 35 36 36 5 40 42 40 30 20 10 Length cm 80 Time hrs 100 120 O There is a strong positive linear relationship between the time and length of the icicle O There is a strong negative linear relationship between the time and length of the icicle O There is a wak positive linear relationship between the time and length of the icicle There is a weak negative linear relationship between the time and length of the icicle

Hint Compare their z scores Last year s Scholastic Assessment Test SAT mean was 500 with standard deviation 100 David scored 350 Last year s ACT mean was 20 with standard deviation 5 Justina scored 15 When comparing these scores to others who took the same test who scored at a higher percentile a These are two different tests there is no way to tell b They both scored in the same percentile and so are the same c David scored higher d Justina scored higher O A OB Oc OD

A survey seeks to find if adults in Minnesota feel women have better job opportunities than they did 20 years ago Which survey is likely to produce the best results a An online survey that is announced on all local TV News programs b An online survey that is announced on a popular women s TV program c A survey given to 500 randomly chosen adult Minnesotan s d A survey given to 1000 randomly chosen adult Minnesotan s O A OB O C O D

Suppose the number of cigarettes a person smolles in a day is our x variable and the number of times the cough in a day is the y variable a The number of cigarettes smoked in a day acts as the Ocorrelation coefficient O response variable O true variable explanatory variable GY b The number of coughs in a day acts as the Otrue variable response variable O explanatory variable O correlation coefficient 6 P Suppose that we have the following data of Cigarettes 2 57 9 3 Coughs 5 12 13 19 6 6 32 c Use StatCrunch to create a scatterplot Looking at the scatterplot is a linear regression appropriate for this data sot O No the data shows randomness O No the data follows a curved line instead of a straight line Yes the data seems to follow a linear trend c What is the y Intercept Round to 3 decimal places d Use StatCrunch to find the equation of the regression line What is the slope Round to 3 decimal places 24 33 11 2 52 68 20 6 f What is the correlation coefficient Round to 2 decimal places 85 Ostrong negative O moderate negative Omoderate positive O weak positive strong positive Oweak negative 10 11 8 24 30 15 8 What level of correlation strength does this correlation coefficient suggest between these variables d 3 2 5 1 1 Which is the interpretation of this Re h What is the coefficient of determination IT Answer as a percent and round to 1 decimal place 98 0 of the variability in the number of times a person coughs in a day is explained by the number of cigarettes they smoke 098 0 of the variability in the number of cigarettes a person smokes in a day is explained by the number of times they cough in a day O About 0 980 of the variability in the number of cigarettes a person smokes in a day is explained by the number of times they cough in a day 00 980 of the variability in the number of times a person coughs in a day is explained by the number of cigarettes they smoke 1 If a person smokes 30 cigarettes in a day predict the number of times they will cough Round to 1 decimal places

11 55 33 13 14 94 15 63 68 17 33 4 19 3 84 21 55 18 23 86 78 25 22 3 27 55 25 29 90 18 12 51 95 14 3 76 16 58 45 18 3 4 20 75 27 22 50 19 24 11 94 26 68 91 28 20 36 30 7 85 Math Aids Com C20 FRAGEN

6 Extra credit 1 pt Consider a real matrix bed bmn P n qr T 8 such that x Ax 0 for any non zero vector x Let x t be a solution to the system x t Ax t A a C d p Is it correct to say that any solution is bounded x t M for all t 20 Prove answer

2 Solve 4ABC with ZA 51 a 12 cm b 8 cm Hint first check how many triangles are formed

Calculate the regular payment amount for the following a 12 000 to be accumulated over 7 years in an account paying 1 9 compounded quarterly b 18 600 to be accumulated over 5 years in an account paying 94 compounded monthly

A 2 75 KN tensile load is applied to a test coupon made from 1 6 mm flat steel plate E 200 GPa v 0 30 Determine the resulting change in a the 50 mm gage length b the width of portion AB of the test coupon c the thickness of portion AB d the cross sectional area of portion AB 2 75 KN Fig P2 64 A 12 mm 50 mm B 2 75 kN

Determine a the compressive force in the bars shown after a temperature rise of 180 F b the corresponding change in length of the bronze bar 0 02 in 14 in Bronze A 2 4 in E 15 x 106 psi a 12 x 10 6 F 18 in Aluminum A 2 8 in E 10 6 x 106 psi a 12 9 x 10 F

PROBLEM 2 4 A cast iron tube is used to support a compressive load Knowing that E 69 GPa and that the maximum allowable change in length is 0 025 determine a the maximum normal stress in the tube b the minimum wall thickness for a load of 7 2 kN if the outside diameter of the tube is 50 mm

Question 3 Mr Smith and Mr Stein were driving to a business meeting 270 miles from their office Mr first a miles then Mr Stein drove the rest of the way Write an algebraic expression for how many miles Mr Stein drove

What is the error message in the IFERROR function below IFERROR A1 B1 C1 Table was not completed CAD 0 00 0 11

14 Which of the following is a private organization representing the interests of all Utah REALTORS O a the Real Estate Commission O b a multiple listing service c the Division of Real Estate O d the Utah Association of REALTORS

Aiden picks a marble at random Without putting the first marble back he picks a seco marble at random Are these two events dependent or independent dependent independent

What is the volume of the 3D figure formed by rotating the triangle about the axis shown below 10 feet 7 feet O732 67 square feet 2930 67 square feet O2051 45 square feet 512 87 square feet

Part Answer all 4 questions in this part Each correct answer will receive 4 credits charts etc Utilize the information provided for each question to determine your a part Note that diagrams are not necessarily drawn to scale For all questions in this numerical answer with no work shown will receive only 1 credit All answers should written in pen except for graphs and drawings which should be done in pencil 16 33 Marilyn collects old dolls She purchases a doll for 450 Research shows this doll s value wa increase by 2 5 each year Write an equation that determines the value V of the doll t years after purchase a com Assuming the doll s rate of appreciation remains the same will the doll s value be doubled in 20 years Justify your reasoning

35 The following numbers represent 15 randomly chosen students in AP Statistics who shared the average number of minutes they spend getting ready every morning O A OB O C OD E 13 35 23 30 35 10 27 35 15 17 25 65 10 20 Which measure of center shows the best representation of how long a typical AP Statistics student takes to get ready in the morning A The mean because there is an outlier B The median because there is an outlier C The mode because it is the most D All of them are good E None of them are good 20

32 Using the set of data collected from eight golfers which shows the distance a golf ball travels versus the speed with which the club head hit it O A B C Club head speed mph x 100 102 103 101 105 100 99 105 Distance yards y 257 264 274 266 277 263 258 275 Which of the following statements best describes the distribution A There is a strong positive linear relationship between the club head speed and distance a golf ball travels with no visible outliers B There is a strong negative linear relationship between the club head speed and distance a golf ball travels with no visible outliers C There is a weak positive linear relationship between the club head speed and distance a golf ball travels with no visible outliers D There is a weak negative linear relationship between the club head speed and distance a golf ball travels with no visible outliers

If it turns out that the woman who wrote 29 pairs of jeans actually meant to write down 19 pairs of jeans which statistics would change Another question asked of the females as they were entering the Katy Perry concert was how many pairs of jeans they owned The results are listed below Calculate the mean median mode IQR and range for this data 9 4 10 O IQR and Range O Mean and Median O Mean and Mode Mean and Range O Median and Range 8 8 14 11 14 3 8 4 8 7 7 29 6 12 2 17 9 7 21

5 Maiki has a 65 free throw average on her basketball team What is the probability that she will make 2 free throws in a row A 0 2275 B 0 4225 C 0 65 D 1 30 O A OB C D

2 There are 15 runners in a race How many outcomes are possible for 1 2nd and 3rd place winners to finish Assume there are no ties A 6 B 455 C 2730 D 3375 O A O B O C O D

e letters to represent each non negated simple statement and rewrite the given compound If the octopus does not scare you you will visit the aquarium et p represent the simple sentence The octopus does scare you and q represent You will visit the aquarium me compound statement written in symbolic form is

P p q Determine whether the statement p p A q is an implication OA The statement is not an implication OB The statement is an implication OC It is impossible to tell

s tv u in the missing values in the table Fill in the blanks below S T t T u T S u tv u s tv u

sive F 3 10 D 14 11 m 12 n 15 when 4x when x 7 Solve as math out 17 4y when y 2 an n 10 40 x 5 when m 36 when n 17 true or false X 1 P 20 when X 8 when X 7

15 Which of the following is all right to do without a license O a collect rents on a duplex across town b lease your own commercial property c sign contracts for office leases d serve as a property manager for industrial properties

April has a 100 50 10 insurance policy limit What is the per person bodily injury limit on her policy O 100 000 1 000 O 100

M M 4 4 4 0 Find formulas for the entries of M where n is a positive integer Your formulas should not contain complex numbers 1 1

Write an inequality representing the problem and 14 A router for a wireless network on a floor of an office building has a range of 35 feet The router is located at the point 30 30 The lettered point in the coordinate diagram represent computers in the office Which computers will be able to connect to the network through the router B C D Router 14 The inequality is G Which computers will be able to connect to the router list in alphabetically order with no spaces or commas

What would be TRUE regarding a security with a LOW Sharpe ratio relative to similar investments It provides a relatively low risk return O It provides a relatively high return compared to similar investments O If combined with risk free assets in a Complete Portfolio the Sharpe would be higher O This is insufficient information to compare with other securities O The return as risk premium relative to its risk is low

If mWV 44 and mBX 126 find m F Answer m F V F W B

Read the question carefully and select the best answer Which of the following most closely matches what Katniss means when she says I suppose a cannon goes off after the supplies explode and another tribute dies A Katniss is so depressed that she does not notice the cannon B Katniss still has tracker jacker venom in her system so she cannot tell if the cannon sound is real or if she hallucinated C Katniss still cannot hear O D Katniss hid so well that she is far away from the cannon fire and therefore cannot hear it

t the correct choice that completes the sentence onjunction p q is true only when both p and q a

11 6 Study the graph Then answer Part A and Part B The line graph shows the number of diners at a food court between 1 P M and 6 P M Diners Visiting a Food Court Between 1RM and 6 PM Number of Diners 200 180 160 140 120 100 80 60 40 20 0 1PM 2PM 1 P M to 2 P M Part B 2 P M to 3 P M 4 P M to 5 P M 3 FM 5 P M to 6 P M Part A During which 1 hour interval was the decrease in the number of diners greatest 4PM 5 PM 6PM

The scores for 20 students on a 50 point math test are 44 37 42 35 34 38 46 50 41 36 30 48 49 39 45 31 47 40 4 and 32 Part 1 of 3 a Find the percentile rank for a score of 42 A test score of 42 is equivalent to the 55 Part 1 3 Part 2 of 3 th st nd rd b Find the percentile rank for a score of 47 471 cuiustent to the percentile th st nd rd percentile

En an evening statistics class the ages of 20 students are as follows 38 35 42 33 19 37 Part 1 of 3 a What is the percentile rank of 32 An age of 32 is equivalent to the 45 Part 1 3 21 25 Part 2 of 3 41 34 th st nd rd b What is the rank from the top of 32 An age of 32 has a rank of 26 36 39 43 percentile in this data set 24 31 23 20 30 32

Match the type of checking account with the correct description For people who use checking accounts but do not maintain a high balance Designed for low income customers Offer special checking deals if you are 55 or older or a student Earn interest if a minimum monthly balance is kept in the account OI IV II III 11 IV I III III I IV II 1 No Frills checking accounts II Basic checking accounts III NOW accounts IV Lifeline checking accounts

ii Let R be a rotation and S be a reflection of the euclidean plane E2 Give a precise deion of RS relating it to the classification of isometries of E2 Be careful of special cases

What happen if you press 1 in the input while a 1 X X y printf d n y printf d n x A B C D No answer print the value of y and then x anyway after it exit the loop while print the value of x anyway after it exit the loop while No output it exit the loop while print the value of y anyway after it exit

3 2 points Find the smallest number a such that A BB is regular for all a