Math - Others Questions

6 A bullet fired vertically and will have its height h in meters after t time in seconds given by h t 80t 5t a At what time did the bullet reach the maximum height b What is the maximum height the bullet will reach c What is the height of the bullet after 5 seconds d After how many seconds will the bullet hit the ground el When is the bullet at a height of 240m

Vladimir Guerrero Jr hit a massive homerun The height h in meters of the ball is given by h t 1 2 20t 5t2 where t is the time in seconds a At what height did Vladimir hit the ball at b What is the maximum height of the ball c How long is the ball in the air Smu laring of 16 2 127250 To 800 m ribes

1 For the following functions state the domain a b d 7 5 2 6 3 9 6 8 8 8 f 04 i g j C 00 02367 on or not e 1 2 8 2 1 5 7 8 2 8 h k

8 A robotic submarine is programmed to quickly film a small area of the ocean floor The program a course set to follow the equation d t 5t 75t 70 where d represents the depth belov the surface in meters and t is the time in minutes a Find the depth of the submarine after 10 seconds b How long will the submarine be under water c At what time s is the robotic submarine at 100m Round to 1 decimal place d At what time does the submarine reach the maximum depth e Find the maximum depth the sub is programmed to reach

1 State the domain range for each of the following relations and if it is a function or not a 2 1 1 0 0 1 1 0 2 1 b 2 1 1 0 0 1 1 0 2 1 c 00 M d c x if f x 11 def 11 g f h I WI 2 Given f x 2x 1 and g x x 1 find a f 2 b g 3 e d x if f x 6

P 1 91 0 51 where I is the current in amperes a What value of the current will produce the maximum power b What is the maximum power by a battery is given by the formula 5 A computer software program is sold to students for 20 each A formula that represents the aliment revenue R dollars for an x dollar increase in price is R x 6x 180x 6000 a Calculate the increase in the price of the computer software that produces the maximum revenue DY What is the maximum revenue

equation h t 5t 100t a What is the height of the flare after 3 seconds b What is the maximum height the flare reached

3 Solve for the roots by factoring a x 9x 18 0 d 0 5a 18a 9 g 0 6x 5x 6 b x 3x 26 8 4a 4a 1 e 6x 54 0 h 6a 25 25a 4 Determine the nature of the roots a 4a 3a 7 0 d 04111 c x x 42 0 f 0 8n 20n i 100 16x 60x b 2x 7x 3 0 d 3b 2b 9

5 Emma hll Teight of the ball is given by y 0 01x 0 5x 0 2 where y is the vertical height in yards above the ground and x is the horizontal distance from the tee in yards Round all answers to one decimal place a How far does Emma hit the golf ball

10 5 pts Consider two functions f x and g x Let g x 2f x 3 4 Fill in the blanks with the appropriate numbers To graph g x you take graph of f x and shift it units to the left followed by a concluding with a vertical shift vertical stretch by a factor of units down

5 pts If f x is a linear function f 3 2 and f 1 3 find an equation for f x

8 10 pts Find the average rate of change of f x x x 6 from x 0 to x 3

9x 8 3x 2 8 pts f x 2 pts f 0 7 Consider f x a b and find e

5 Consider the function f x 6x5 5x 4x 3x 2x 1 and answer the following questions a 1 pt State the Remainder Theorem b 4 pts Use the Remainder Theorem to determine the remain when f x is divided by x 1 Don t forget to show your w

Find the solution to the initial value problem y 9y 27 y 0 4 y 0 6

5 5 pts Find all zeros of the function f x 16x 48x 25x 7 factoring Algebraic solutions only

he population of a southern city is growing according to the exponential law Complete parts a and b a If N is the population of the city and t is the time in years express N as a function of t et No represent the initial population of the city and let k be a positive constant that represents the annual growth rate of the city s populatio t Type an exact answer in terms of e

4 10 pts Let f x 5x 4x 2 Find f x h f x h

Find a particular solution to the differential equation 1 y 3y 9 2 y y y 2 sin 3t

3 5 pts Find the polynomial function g x such that all of the following hold a g x has a zero at x 3 with multiplicity 1 b g x has a zero at x 2 with multiplicity 2 g x has a zero at x 1 with multiplicity 2 The graph of g x goes through the point 0 24 Your answer should be a function definition not a graph C

2 Consider f x x 2 x 5 a 2 pts Find the domain of f x Give your answer in interval notation 2 pts State any vertical asymptotes Remember vertical asymptotes should be written as an equation of a line e 2 pts State any horizontal asymptotes Remember horizontal asymptotes should be written as an equation of a line OLLEGE d 2 pts Find any x intercepts algebraically 2 pts Find any y intercepts algebraically

Question Discuss the implications of the Covid 19 pandemic on global logistics and supply chain management How have companies adapted their logistics strategies to deal with disruptions and ensure the continuity of supply chain operations Provide examples and suggest further improvements that can be implemented to fortify logistics against future global disruptions

Do NOT evaluate coefficients Find the form for a particular solution to y 2y 3y f t where f t equals 1 7 cos 3t 2 2tet sint 3 t cos t 4 5e 3t 5 3tet 6 t2 et

The quantity supplied S and quantity demanded D of I shirts at a concert are given below and D P 1000 25P where P is the price of the T shirts a Please draw the demand curve and supply curve on the same axes 2 b What is the equilibrium price 1 c What is the equilibrium quantity demanded and quantity supplied 1 S P 200 50P

1 5 pts Graph one continuous function f x such that all of the following hold a C f x is increasing on 2 f x is constant on 2 4 f x is decreasing on 4 6 f x is increasing on 6 00

Q12 Write 2 T 11 IIK 1 21 as a single summation or product k k Q13 Find the sum of 4 42 43 420

A moment in my life that I learned a lesson about myself is when I had to handle a stressful situations thinking I wasn t strong enough to Handel it My mom got very sick I had to learn how to talk to my family prioritize my tasks and ask for help from friends I overcame many difficulties and challenging situations every day as I developed into a trustworthy provider for my family I ve gained the virtue of resilience from my experiences I realized that strength encompasses not only physical prowess but also emotional resilience I became more adept at managing stress learned how to support people who were having difficulty and ultimately developed a greater confidence in my capacity to face obstacles in life My ability to stay positive despite what appeared to be my weak points was proven by this experience

On Saturday 180 vehicles visited Lana s Car Wash Of those vehicles 3 out of every 4 were cars and the rest were trucks How many trucks visiting Lana s Car Wash on Saturday TYPE THE NUMBER ONLY

O A producer of fine chocolates believes that the sales of two varieties of truffles differ significantly during the holiday season The first variety is milk chocolate while the second is milk chocolate filled with mint It is reasonable to assume that truffle sales are normally distributed with unknown but equal population variances Two independent samples of 18 observations each are collected for the holiday period A sample mean of 12 million milk chocolate truffles sold with a sample standard deviation of 2 5 million A sample mean of 13 5 million truffles filled with mint sold with a sample standard deviation of 2 3 million Use milk chocolate as population 1 and mint chocolate as population 2 Assuming the population variances are equal which of the following is the value of the appropriate test statistic 3 41 18 Multiple Choice z 1 8734 Z 1 8734 t34 1 8734

13 57 A new study has found that on average 6 to 12 year old children are spending less time on household chores today compared to 1981 levels Suppose two samples representative of the study s results report the following summary statistics for the two periods 1981 Levels x 30 minutes s1 4 2 minutes n1 30 Which of the following is the correct value of the test statistic assuming that the unknown population variances are equal Multiple Choice Z 5 73 t59 5 73 t58 5 73 2021 Levels x 24 minutes 23 9 minutes n2 30 z 5 73

38 A veterinarian wants to know if pit bulls or golden retrievers have a higher incidence of tooth decay at the age of three The vet surveys 120 three year old pit bulls and finds 30 of them have tooth decay The vet then surveys 160 three year old golden retrievers and finds 32 of them have tooth decay Number the population of pit bulls and golden retrievers by 1 and 2 respectively Calculate a 90 confidence interval for the difference in the population proportion of pit bulls and golden retrievers that have tooth decay Which of the following is correct Multiple Choice 0 0492 0 1492 0 0332 0 1332 0 0428 0 0572 00199 008011

3 A university wants to compare out of state applicants mean SAT math scores 1 to in state applicants mean SAT math scores 2 The university looks at 35 in state applicants and 35 out of state applicants The mean SAT math score for in state applicants was 540 with a standard deviation of 20 The mean SAT math score for out of state applicants was 555 with a standard deviation of 25 It is reasonable to assume the corresponding population standard deviations are equal Calculate a 95 confidence interval for the difference 1 12 1 56 Multiple Choice O 33 6105 3 6105 25 7961 4 2039 25 8124 4 1876 25 6067 4 3933

B A farmer is concerned that a change in fertilizer to an organic variant might change his crop yield He subdivides his six lots and uses the old fertilizer on one half of each lot and the new fertilizer on the other half The following table shows the results Lot 1 2 3 4 5 6 Crop Yield Using Old Fertilizer 12 9 10 12 8 9 Assume the crop yields are normally distributed Which of the following is the correct value of test statistic Multiple Choice t5 1 22 2 1 22 2 1 22 Crop Yield Using New Fertilizer 14 9 11 10 12 10 t5 1 22

Do men really spend more money on St Patrick s Day as compared to women A recent survey found that men spend an average of 43 87 while women spend an average of 29 54 Assume that these data were based on a sample of 100 men and 100 women and the population standard deviations of spending for men and women are 32 and 25 respectively Which of the following is the correct value of test statistic Multiple Choice O tdf 3 53 Z 3 53 z 3 53

42 16 The student senate at a local university is about to hold elections A representative from the women s sports program and a representative from the men s sports program must both be elected Two candidates an incumbent and a challenger are vying for each position and early polling results are presented next A hypothesis test must be performed to determine whether the percentages of supporting votes are different between the two incumbent candidates In a sample of 100 voters 67 said that they would vote for the women s incumbent candidate In a separate sample of 100 voters 55 said they would vote for the men s incumbent candidate Let p1 and p2 be the proportions of supporting votes for the incumbent candidates representing women s and men s sports programs respectively Which of the following is the correct conclusion for the test at a 0 05 Multiple Choice Reject Ho P1 P2 and therefore do not conclude that the proportions differ Do not reject Ho P1 P2 and therefore do not conclude that the proportions differ Do not reject Ho P1 P2 and therefore conclude that the proportions differ Reject Ho P1 P2 and therefore conclude that the proportions differ

The Institute of Education Sciences measures the high school dropout rate as the percentage of 16 through 24 year olds who are not enrolled in school and have not earned a high school credential Last year the high school dropout rate was 8 1 A polling company recently took a survey of 1 000 people between the ages of 16 and 24 and foun that 6 5 of them are high school dropouts The polling company would like to determine whether the dropout rate has decreased At a 5 significance level the decision is to Multiple Choice O do not reject Ho we can conclude that the high school dropout rate has decreased reject Ho we can conclude that the high school dropout rate has decreased do not reject Ho we cannot conclude that the high school dropout rate has decreased reject Ho we cannot conclude that the high school dropout rate has decreased

A fast food franchise is considering building a restaurant at a busy intersection A financial advisor determines that the site is acceptable only if on average more than 300 automobiles pass the location per hour The advisor tests the following hypotheses Ho H 300 HA H 300 The consequences of committing a Type Il error would be that Multiple Choice O the franchiser builds on an acceptable site the franchiser does not build on an acceptable site the franchiser builds on an unacceptable site the franchiser does not build on an unacceptable site

A statistics professor works tirelessly to catch students cheating on his exams He has particular routes for his teaching assistants to patrol an elevated chair to ensure an unobstructed view of all students and even a video recording of the exam in case additional evidence needs to be collected He estimates that he catches 95 of students who cheat in his class but 1 of the time that he accuses a student of cheating he is actually incorrect Consider the null hypothesis the student is not cheating What is the probability of a Type I error Multiple Choice 5 99

Vermont based Green Mountain Coffee Roasters dominates the market for single serve coffee in the United States with its subsidiary Keurig accounting for approximately 70 of sales Rivals Try to Loosen Keurig s Grip on Single Serve Coffee Market Chicago Tribune February 26 But Keurig s patent on K cups the plastic pods used to brew the coffee is expected to expire this year allowing other companies to better compete Suppose a potential competitor has been conducting blind taste tests on its blend and finds that 47 of consumers strongly prefer its French Roast to that of Green Mountain Coffee Roasters After tweaking its recipe the competitor conducts a test with 144 tasters of which 72 prefer its blend The competitor claims that its new blend is preferred by more than 47 of consumers to Green Mountain Coffee Roasters French Roast Which of the following should be used to develop the null and alternative hypotheses to test this claim Multiple Choice O Ho p 0 47 HA P 0 47 Ho p 0 47 HA P 0 47 Ho 72 HA 72 Ho p 0 50 HA P 0 50

A professional sports organization is going to implement a test for steroids The test gives a positive reaction in 94 of the people who have taken the steroid However it erroneously gives a positive reaction in 4 of the people who have not taken the steroid What is the probability of Type I and Type II errors giving the null hypothesis the individual has not taken steroids Multiple Choice O O Type 1 94 Type II 4 Type 1 4 Type II 6 Type 1 6 Type II 4 Type I 4 Type II 94

A recent report claimed that Americans are retiring later in life U S News World Report August 17 An economist wishes to determine if the mean retirement age has increased from 62 To conduct the relevant test she takes a random sample of 38 Americans who have recently retired and computes the value of the test statistic as t37 1 92 With a 0 05 she Multiple Choice does not reject the null hypothesis and does not conclude that the mean retirement age has increased rejects the null hypothesis and concludes that the mean retirement age has not increased Orejects the null hypothesis and concludes that the mean retirement age has increased does not reject the null hypothesis and does not conclude that the mean retirement age has changed

A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night If this is to happen it will have to move one of its most viewed shows to another slot The network conducts a survey asking its viewers which show they would rather watch The network receives 827 responses of which 428 indicate they would like to see the new show in the lineup Which of the following is an appropriate hypotheses to test if the television network should give its newest show a spot during prime time at night Multiple Choice Ho p 0 50 HA P 0 50 Ho p 0 50 HA P 0 50 Ho p 0 50 HA P 0 50 Ho p 0 50 HA P 0 50 H

The Institute of Education Sciences measures the high school dropout rate as the percentage of 16 through 24 year olds who are not enrolled in school and have not earned a high school credential Last year the high school dropout rate was 8 1 A polling company recently took a survey of 1 000 people between the ages of 16 and 24 and found that 6 5 of them are high school dropouts The polling company would like to determine whether the dropout rate has decreased When testing whether the dropout rate has decreased the appropriate hypotheses are Multiple Choice Ho p 0 065 HA p 0 065 Ho p 0 065 HA P 0 065 Ho p 0 081 HA P 0 081 Ho p 0 081 HA P 0 081

1 point Consider the digraph of a relation R shown below a How many ordered pairs are in the relation R b Which of the following ordered pairs are in the relation R Select Yes if the order pair is in R and No if it is not 2 2 1 3 3 2 3 1 3 5 2 4 2 5 5 5 5 6 4 3 7 5 1 8 4 4 9 4 2 10 4 1 11 1 1 12 2 2 5 3

1 point Let A 2 4 6 and B 3 4 9 12 For each of the elements shown below determine which of the listed Cartesian products the element belongs to Select all that apply a 4 2 OA BX A B AX A C Ax B D Bx B DE None of the above b 4 4 DA Ax B B AX A C Bx A D Bx B E None of the above c 2 3 A Ax B B Bx B OC Bx A D AX A E None of the above d 2 2 DA Ax B DB Ax A C Bx A D Bx B

Mr Sanchez is making punch for a party using a recipe that calls for 4 cups of seltzer for every 6 cups of lemonade If he wants to make a total of 120 cups of punch how many cups of seltzer will he need O 48 cups of seltzer O 300 cups of seltzer O 200 cups of seltzer O 72 cups of seltzer 2

3 5 pts Identify Circle whether the following situations are binomial or not If they are identify n and p If they are not please explain why not Situation We will draw 10 cards from a standard deck without replacement and count how many face cards we picked We will roll a dice 10 times and count how many times we roll a 1 or a 6 A medication has been shown to be 87 effective in the general population In a trial of 100 patients we will count how many of them the treatment is effective for P Probability of success Probability of getting 106 of favorable outcomes total of outcomes Binomial If so what are n and p If not why not Not Binomial Not Binomial Not Binomial Not The probability of drawing a face card changes It follows a hypergeometric distribution since you are drawing without placement from a finite population The trials from each time rolling a die are independent because the probability of success is the same for each trial This is binomial distribution p 1 3 n 10 N of times dice rolled n 10

Lee is saving up money for a down payment on a condominium He currently has 2651 but knows he can get a loan at a lower interest rate if he can put down 3236 If he invests the 2651 in an account that earns 3 9 annually compounded quarterly how long will it take Lee to accumulate the 3236 Round your answer to two decimal places if necessary Answer How to enter your answer opens in new window Keypad Keyboard Shortcuts

Consider the data from the table showing the heights of 15 people at a family gathering 55 Create a stem and leaf plot using the first digit as the stem and the second digit as the leaf for each number Stems 3 4 5 6 17 I Leaves 8 27 0012458 2 56 How many people had a height under 5 feet 7 people had a bright under 60 inches 5 1 57 If we let A represent the set of names of all people at this gathering whose height is under 5 feet write that set using the roster method A Hannah Manuel Luigi Ava John Braxton Entensit 58 Give a verbal description of what would be meant by A in this situation A would be the complement of A This would be the people whose height is 60 mches or more Name Bob Bill Lisa Manuel Hannah Braxton Ava Jake Charlotte Nate Emmett John Mario Ben Luigi Height inches 72 65 60 42 38 55 51 64 62 68 57 54 60 61 47

Progress The movement of the progress bar may be uneven because questions can be worth more or less including zero depending on your answer Joe runs 8 25 times around a track in 1 119 803 seconds If one lap around the track is 402 3 meters which is the best estimate of the runner s average speed in meters per second m s 3 m s O 0 4 m s 30 m s Question ID 97376 0 3 m s