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Math - Others
Functions
A random variate has the following triangular density f x 1 16 min x 8 x 0 x 8 Develop algorithms to generate this variate using Inverse transformation 1 Write the density function f x in two parts 2 Find f 4 f 8 3 Find the expectation of x 4 Draw f x 5 Find CDF F x 6 Draw F x 7 Find F 4 F 8 and F 10 8 Find the inverse of F x 9 Find the random variate 10 Find the value of the random variate for U 0 0 5 8 and 1
Statistics
Statistics
mosquito repellent claims that it will effectively repel mosquitoes for at least 6 hours A local biologist thinks that the company s claim is exaggerated and the length of time for which this brand of mosquito repellent is effective is actually less than 6 hours To test her hypothesis the biologist devised a randomized sample of 107 trials and found that the mosquito repellent was effective for 5 61 hours on average Use the p value method to test the hypothesis that the mean effective length of time of this brand mosquito repellent is less than 6 hours using a significance level of 2 5 Assume the standard deviation of the distribution of all times for which this brand of mosquito repellent is effective is known to be 1 76 hours State the null and alternative hypothesis for this test OH 6 H p 6 O Ho p 6 H p6 OH 6 H p 6 O Ho 6 H p 6 Determine the test statistic for the hypothesis test 0 1 82 0 2 29 0 0 32 0 1 07 Determine the p value for the hypothesis test 00 0110 00 9890 00 2194 00 0374 Determine the appropriate conclusion for this hypothesis test O The sample data provide sufficient evidence to reject the alternative hypothesis that this brand of mosquito repellent is effective for less than 6 hours on average and thus we conclude that the company s claim that the mosquito repellent is effective for at least 6 hours is likely true O The sample data do not provide sufficient evidence to reject the null hypothesis that this brand of mosquito repellent is effective for at least 6 hours and thus we conclude that the company s claim that that the mosquito repellent lasts for at least 6 hours is likely true The sample data provide sufficient evidence to reject the null hypothesis that this brand of mosquite repellent is effective for at least 6 hours and thus we conclude that the company s claim that that the mosquito repellent lasts for at least 6 hours is likely false
Algebra
Quadratic equations
The graph shows stopping distances for trucks at various speeds on wet roads Use this information to complete parts a and b below f x x x opping Distance feet Stopping Distances at Selected Speeds 700 620 600 500 445 400 305 300 185 200 85 100 0 25 35 45 59 55 a Use the statistical menu of your graphing utility and the quadratic regression program to obtain the quadratic function that models a truck s stopping distance f x in feet on wet pavement traveling at x miles per hour
Geometry
Solution of triangles
An official major league baseball has 108 stitches in it What three dimensional figure describes the baseball Rawlings OFFICIAL MAJOR LEAGUE BASEBALL Allen Holy Cone Sphere Cube O Cylinder
Geometry
2D Geometry
63
Statistics
Statistics
average daily volume of a computer stock in 2011 was 35 1 million shares a able source A stock analyst believes that the stock volume in 2018 is different fro l Based on a random sample of 30 trading days in 2018 he finds the sample me 3 million shares with a standard deviation of s 11 7 million shares Test the hypo structing a 95 confidence interval Complete parts a through c below D h ic U 35 1 million shares 35 1 million shares 5 confidence interval about the sample mean of stocks traded in 20 nce the mean stock volume in 2018 is between ecimal places as needed million shares a P
Geometry
2D Geometry
K This question 1 point s possible According to government data the probability that a woman between the ages of 25 and 29 was never married is 40 In a random survey of 10 women in this age group what is the pr eight were married A 1 002 OB 0 161 OC 0 013 OD 0 167
Math - Others
Basic Math
Choose which reasoning process is shown in the following example Explain your answer An HMO does a follow up study on 1329 randomly selected patients given a flu shot None of these people became seriously ill with the flu The study concludes that all HMO patients be urged to get a flu shot in order to prevent a serious case of the flu B Choose the correct answer below OA It is deductive reasoning because additional information may prove that other patients may not have taken the flu shot and still did not catch a serious case of the flu B It is deductive reasoning because a general conclusion is drawn based on specific observations C It is inductive reasoning because a general conclusion is drawn based on specific observations D It is inductive reasoning because the flu is epidemic If someone does not take the flu shot there is a great possibility for that person to catch a serious case of the flu
Calculus
Differentiation
dw dt For the given functions a express as a function of t both by using the Chain Rule and by expressing w in terms of t and differentiating directly with respect to t Then b evaluate w 6ye Inz x In 1 y tant z 1 1 dw at the given value of t dt by dw dt
Biology
Evolution
A mule is an example of polyploidy but unlike many polyploid plants the mule is A less fit than P generation B larger than P generation C fertile D sterile
Geometry
2D Geometry
Given 15 10 and x 5 find all x such that the distance between these two points is 17 Separate multiple answers with a comma Answer
Biology
Ecology - Biodiversity & Conservation
In October 2019 after prolonged droughts around the country Australia experienced wide spread bushfires In Australia the summer of 2019 is known as the Black Summer and the bushfires were deemed one of the biggest natural disasters The extent of damage was an estimated 18 million hectares Which of the following best predicts the effect that the bushfires had on the biodiversity of ecosystems in Australia A B C D The biodiversity of ecosystems in Australia increased immediately after the bushfires due to the fires returning nutrients to the soil The biodiversity of ecosystems in Australia was so high that the bushfires did not affect biodiversity much The biodiversity of ecosystems in Australia was unaffected by the bushfires because most ecosystems do not contain much vegetation The biodiversity of ecosystems in Australia decreased due to many organisms dying be
Biology
The Living World
Spallanzani s effort to refute abiogenesis failed as he let in which unbeknownst to him carried organisms A the vital force air B the vital force red humour C DNA D carbon dioxide
Biology
Human Health and Diseases
List the 4 stages of neutrophil extravasation at a site of injury when the neutrophil exits the capillary into the tissue Explain what is happening at each stage
Geometry
2D Geometry
19 1 point E What would be the first step in this construction Label point D Place the compass at point B and draw an arc Place the compass at point C and draw an arc Place the compass on point a and draw arc CB
Geometry
2D Geometry
Q 7 cm
Calculus
Differentiation
40Write a 40 Write your answer as a fraction or a whole or
Statistics
Statistics
A sample of 1300 computer chips revealed that 39 of the chips fail in the first 1000 hours of their use The company s promotional literature claimed that less than 42 fail in the first 1000 hours of their use Is there sufficient evidence at the 0 01 level to support the company s claim tate the null and alternative hypotheses for the above scenario swer He Tables Key Keyboard Sh
Math - Others
Mathematical Reasoning
4 A stereo is marked down 75 If this is a 15 decrease find the sale price
College Algebra
Matrices & Determinants
b Determine whether or not the vectors 1 1 1 1 2 3 and 2 1 1 form a basis for the vector space R c Solve the following system of equations by row echelon form 2x y 2z 8 3x 2y 4z 15 5x 4y z 1
College Algebra
Complex numbers
1a Show that the set S is consisting of all four vectors whose first and last components are equal to zero is a subspace of R4
College Math - Others
Trigonometry
3 22 0 5 4 3 2 1 1 2 3 4 5 6 2 H 3 Identify the function whose graph appears above f x
Biology
Human Physiology - Neural Control & Coordination
What is the difference between a memorized presentation and an extemporaneous presentation Which one is more effective Why
College Algebra
Quadratic equations
Use synthetic division to divide x4 3x 2x 2x 7 by x 2 The quotient is and the remainder is Use integers or fractions for any numbers in the expression
College Algebra
Permutations and Combinations
Divide using synthetic division x 9x 3x 2 X 5 x3 9x2 3x 2 remainder X 5
College Algebra
Quadratic equations
f x x x 1 x 2 Choose the correct graph below O A 50 a 10 10 10 Confusing the techniques relating to end behavior zeros and multiplicity intercepts symmetry and turning points OB 50 C 50 10 10 E 10 10 G 50 OD 50 10 EMMAN 50 10
College Algebra
Complex numbers
If the polynomial f x has x 2 as a factor then f 2 0 Choose the correct answer below OA True because by the Factor Theorem if x 2 is a factor of f x then f 2 0 OB False because by the Factor Theorem if x 2 is a factor of 1 x then f 2 f 0 OC False because by the Factor Theorem if x 2 is a factor of f x then f x 2 0 OD False because by the Factor Theorem if x 2 is a factor of f x then f 2 0
College Algebra
Quadratic equations
Find the real zeros of f and state the multiplicity for each zero State whether the graph of f x 3 x 4 x 5 The real zeros of f are x 4 5 Use a comma to separate answers as needed The multiplicity of the smaller zero is Type a whole number The multiplicity of the larger zero is Type a whole number Does the graph of f cross or touch the x axis at the smaller zero The graph crosses the x axis The graph touches but does not crosses the x axis Does the graph of f cross or touch the x axis at the larger zero The graph crosses the x axis O The graph touches but does not crosses the x axis
College Algebra
Quadratic equations
Determine whether the following statement is true or false A polynomial function of degree n has at most n 1 zeros Choose the correct answer below OA The statement is false because a polynomial function of degree n has at most n 1 turning points and n 1 real z OB The statement is false because a polynomial function of degree n has at most n 1 turning points and 2n real zer OC The statement is false because a polynomial function of degree n has at most n 1 turning points and n real zeros OD The statement is true because a polynomial function of degree n has at most n turning points and n 1 real zeros
College Math - Others
Basic Math
1 True or False a 4x 2y 4y 2x b 4x 1 4y 4y 1 4 x c x y y x d 4xy 4yx
College Algebra
Sequences & Series
Use the factor theorem to determine whether the first polynomial is a factor of the second polynomial x 6 x3 8x 9x 18 Is x 6 a factor of x3 8x 9x 18 O No Yes www
College Statistics
Statistics
A data set includes weights in grams of 36 Reese s Peanut Butter Cup Miniatures The accompanying Statdisk display shows results from using all 36 weights to test the claim that the sample is from a pop with a mean equal to 8 953 g Test the given claim by using the display provided from Statdisk Use a 0 05 significance level Click the icon to view the Statdisk display Identify the null and alternative hypotheses Ho H H H 8 953 8 953 Type integers or decimals Do not round Identify the test statistic Round to two decimal places as needed
College Algebra
Quadratic equations
the division 2x 5x2 x 2x 3 2x 1 2x 5 x 2x 3 the dividend is the divisor is the quotient is and the remainder is e dividend is the divisor is the quotient is and the remainder is
College Algebra
Sequences & Series
Consider the polynomial f x 2x 3x x 6 Write the degree of this polynomial its leading term its leading coefficient and its constant term The degree of the given polynomial is 5 The leading term is 2x The leading coefficient is The constant term is 6
College Calculus
Indefinite Integration
The series Ratio Test Op series Test Root Test 4k 5k 4 k2k O Geometric Series Test O Comparison Test Divergence Test Alternating Series Test Select an answer according to the choose the method you used
College Algebra
Complex numbers
s autosave question2981466 12 able shows the socks that are in your sock drawer You randomly choose one sock put it on your left foot then choose another Socks in a drawer White Black Green Blue Yellow a Find the probability of the compound event of choosing a black sock and then a green sock Enter your probability as a fraction 1 30 X Describe the likelihood O The event is likely The event is unlikely b Find the probability of the compound event of choosing a blue sock and then a yellow sock Enter your probability as a fraction X 3 80 Describe the likelihood
College Statistics
Statistics
the times to test the claim that the mean of all such wait times is more than 30 minutes the accompanying Excel display is obtained Test the given claim by using the display provided from Excel Use a 0 05 significance level iClick the icon to view the Excel display Identify the null and alternative hypotheses Ho Hy Type integers or decimals Do not round Excel Display Difference 3 t Observed value 0 967 t Critical value 1 686 X
College Calculus
Limits & Continuity
9 5 4 3 2 1 5 4 3 4 2 4 4 2 3 4 TU 5 1 4 Identify the function whose graph appears above f x
College Algebra
Complex numbers
AS Four jars of coins each contain 144 coins The theoretical probability of randomly drawing a quarter is given in simplified form Find the number of quarters in each jar a 1 1 48 3 b 11 10 6 24 3 c 1 10 72 8 d 2 3 quarters per jar quarters per jar X quarters per jar quarters per jar
College Algebra
Permutations and Combinations
How many three digit numbers can be formed under each condition a None of the digits can be 4 648 X three digit numbers b The leading digit is one of the digits 0 through 4 500 three digit numbers
College Algebra
Quadratic equations
There are three 20 bills five 10 bills eight 5 bills and four 1 bills in your wallet You select one bill at random What is the expected value for this experiment 7 75
High School Geometry
Vectors
Multiplication Theorem a How many ways are there to make a list of two different letters among those that appear in COAT b How many ways are there to make a list of two different letters among those that appear in MATHEMATICS c How many ways are there to make a list of two different letters where the first is a vowel and the second is a consonant among those that appear in COAT d How many ways are there to make a list of two different letters where the first is a vowel and the second is a consonant among those that anneer in MATHEMATICS
College Algebra
Quadratic equations
The bar graph shows the results of spinning a spinner 60 times Find the experimental probability of each event Enter your probabilities as fractions Spinning a Spinner 16 Times spun 642086420 14 12 10 1 2 3 4 5 Number spun a Spinning a 4 13 100 b Spinning an even number 11 30 Spinning a number greater than 2
College Statistics
Probability
A credit card company claims that the mean credit card debt for individuals is greater than 4 900 You want to test this claim You find that a random sample of 37 cardholders has a mean credit card balance of 5 046 and a standard deviation of 650 At a 0 01 can you support the claim Complete parts a through e below Assume the population is normally distributed What is are the critical value s to to 2 435 Use a comma to separate answers as needed Round to three decimal places as needed Determine the rejection region s Select the correct choice below and fill in the answer box es within your choice Round to three decimal places as needed OA t C t B t and t D t 2 435 c Find the standardized test statistic t t 1 37 Round to two decimal places as needed d Decide whether to reject or fail to reject the null hypothesis A Reject Ho because the test statistic is not in the rejection region B Fail to reject Ho because the test statistic is not in the rejection region C Fail to reject Ho because the test statistic is in the rejection region OD Reject Ho because the test statistic is in the rejection region e Interpret the decision in the context of the original claim OA At the 1 level of significance there is not sufficient evidence to support the claim that the mean credit card debt is greater than 4 900 OB At the 1 level of significance there is sufficient evidence to support the claim that the mean credit card debt is less than 4 900 OC At the 1 level of significance there is not sufficient evidence to support the claim that the mean credit card debt is less than 4 900 OD At the 1 level of significance there is sufficient evidence to support the claim that the mean credit card debt is greater than 4 900
College Math - Others
Mathematical Induction
8 Your parents give you 700 to spend on books and supplies for this semester Your math book is 114 your biology book is 132 your biology lab book is 50 your English books are 142 and your drama book is 44 After you buy your books how much is left for supplies 9 Which property is represented by the following equation 23 7 2 23 7 2 Associative property of addition b Commutative property of addition c Distributive property of multiplication over addition d Additive inverse and additive identity A 10 The endpoints of a diameter of a circle C on the Cartesian plane are 5 2 and 0 2 Find the circumference of the circle C 11 The scores for your math tests are 88 81 97 97 83 78 85 95 79 82 What is your average score 12 Write 30 as the product of two odd numbers and one even number each of which is greater than 1 13 On a scavenger hunt you are supposed to cover an area on a map represented by a 2 cm by 5 cm rectangle to find clues for your hunt If the scale drawing on the map is 1 cm equals 20 feet what is the area in square feet you are supposed to cover 14 Find the answer to the following 13 5x3 3x6 2 12 15 True or False a a a xa 0 b a a a a 0 c axa axa 1 d aa xa 0
College Calculus
Definite Integrals
According to the formal definition of the definite integral if the function f x is continuous on the interval a b then f x dx f x dx lim 100 where Ax interval 3 and the value of x is in the
College Algebra
Permutations and Combinations
Use the appropriate formula to calculate each permutation or combination a P 18 4 b C 9 4 c P 100 2 d C 7 4
College Calculus
Indefinite Integration
Compute the given integral 10 cos sin x dr
College Algebra
Complex numbers
ASK YOUR TEACHER A college calculus class consists of 26 females and 14 males There are 8 biology majors 18 mathematics majors and 14 computer science majors If a student is chosen at random what is the probability that the student is a male Enter your probability as a fraction What is the probability that the student is a mathematics major Enter your probability as a fraction Nood Holm2
College Statistics
Statistics
A research center claims that more than 31 of employees in a certain country have changed jobs in the past four years In a random sample of 140 people from that country 49 have changed jobs in the past four years At a 0 10 is there enough evidence to support the center s claim Complete parts a through d below a Identify the claim and state Ho and Ha Identify the claim in this scenario Select the correct choice below and fill in the answer box to complete your choice Type an integer or a decimal Do not round OA The percentage of employees in the country who have changed jobs in the past four years is not OB At most C years of employees in the country have changed jobs in the past four of employees in the country have changed jobs in the past fouryears OD More than years of employees in the country have changed jobs in the past four