Questions

Problem 2 Find an explicit formula for the nth term an of each of the following sequences a 2 6 10 14 18 22 26 30 34 b 3 9 27 81 243 729 2187

Mary and Pat are getting divorced and decide to split the house and their savings using the method of Sealed Bids Each person will make a confidential bid to the attorney and if they present the highest bid for an item they will own it but will have to pay the other person their fair share of the cash value of the item Neither Mary nor Pat will know what the other bid Here are the results the attorney gathered House Bid Cash Mary Pat 280 000 1 000 220 000 80 000 I According to Pat what should be his perceived fair share cash value amount to the nearest dollar

2 20 points How much will be in a retirement savings account at Chase Bank 15 years from now if you deposit 8 000 now and 10 000 seven years from now The account earns interest at a rate of 6 per year compounded monthly

5 30 points Starting in 2024 the regional government offices health departments and public libraries in the city of Boulder Colorado will adopt a 9 hour day 4 day workweek from the beginning of June through the end of October The shortened workweek will affect 30 of the city s 8000 employees and will save 55 000 per month for those 5 months due to decreased electricity water and maintenance costs If this work schedule persists for the next 15 years what is the future value of the savings at the end of that period i e end of year 2039 Assume an interest rate of 0 6 per month

Use the Table of Integrals to evaluate the integral S x4e6x dx

Evaluate the integral 18 e2x

Evaluate the integral

Evaluate the integral 2 x 8 x

Note You can get full credit for this problem by just entering the final answer to the last question correctly The initial questions are meant as hints toward allow you the opportunity to get partial credit Consider the indefinite integral 63 8x2 45 45 x4 9x2 Then the integrand has partial fractions decomposition da where a b C d Integrating term by term we obtain that 6x3 8x2 45x 45 24 9x2 da a 22 78 b cx d x 9

Write out the form of the partial fraction decomposition of the function Q de 12 3 5x x 6x 9 dx Determine the numerical values of the coefficients A and B where BA and A B 5x x2 6x 9 A B denominator denominator

Use the Table of Integrals to evaluate the integral 6 eVe2x 1dx

Use the table of in Integrals in the back of your textbook to evaluate the integral 10 4x 4x2 dx

Make a substitution to express the integrand as a rational function and then evaluate the integral COS 4 sin x 5 sin dx

Which of the following is the correct form of the partial fraction decomposition of x 1 x3 x Ax B C A I x 1 Ax B Ca D B 2 x 1 A Bx C C A D x 1 B x 1

Split into partial fractions 64 64 2

190 10 300 y asinibx f C 180 1 30 360 4 acos bx d

5 A savings account balance is compounded continuously If the interest rate is 2 6 per year and the current balance is 1 685 00 what will the balance be 12 8 years from now 6 A savings account balance is compounded continuously If the interest rate is 3 7 per year and the current balance is 1 412 00 what will the balance be 10 5 years from now 7 A savings account balance is compounded continuously If the interest rate is 3 9 per year and the current balance is 1 553 00 what will the balance be 5 9 years from now 8 A savings account balance is compounded continuously If the interest rate is 2 2 per year and the current balance is 1 530 00 what will the balance be 7 5 years from now 9 A savings account balance is compounded continuously If the interest rate is 2 per year and the current balance is 1 919 00 what will the balance be 19 now years A 1 908 16 B 2 806 12 C 1 795 92 D 3 339 28 from 10 A savings account balance is compounded continuously If the interest rate is 4 per year and the current balance is 1 717 00 what will the balance be 13 years from now A 2 945 80 B 2 888 04 C 3 841 09 D 2 830 28

05 05 MC A table of data is given x f x 2 71 1 13 03 1 0 6 2 0 1 Which exponential model best represents the data Of x 3 1 2 x Of x 2 0 3 x Of x 2 3 x Of x 3 0 2

estion 1 Multiple Choice Worth 2 points 05 05 MC Which graph models the function f x 4 2 0 7 6 5 4 3 2 1 O 3 2 3 2 3 4 3 2 1 2 5 6 O 3 7 6 5 4 2 2 3 4 3 2 1 2 2 3 4 5 6 7

aluate the integral x3 11

Note You can get full credit for this problem by just entering the final answer to the last question correctly The initial questions are meant as hints towar allow you the opportunity to get partial credit Consider the indefinite integral 22 x 4 x 5 dx Then the integrand has partial fractions decomposition where a b C Integrating term by term we obtain that 22 dx x 4 x 5 2 a b 01 x 4 x 5 C x 5

150 yasin x 2 380 b 120 yacos x d 360

f x Delta Airlines quotes a flight time of 3 hours 4 minutes for a particular flight Suppose we believe that actual flight times are uniformly distributed between 3 hours and 3 hours 16 minutes a Show the graph of the probability density function for flight time Rx 16 19 1 16 Ax 36 16 100 16 39 3 16 8 16 16 1 8 16 X 172 180 188 196 Flight Time in Minutes 172 180 188 196 172 180 188 196 172 Flight Time in Minutes Flight Time in Minutes 180 Flight Time in Minutes 188 196 16 12 b What is the probability that the flight will be no more than 4 minutes late 0 25 x c What is the probability that the flight will be more than 8 minutes late 0 5 X d What is the expected flight time in minutes 188 min

Evaluate the integral 3 2

Solve the triangle shown to the right b 4

Type your answers in all of the blanks and submit X X N Fill in the blank with the simplified expression Use to denote an exponent a f x 7x 1 f x write your response here b f x x 4x f x write your response here c f x 2x3 5x f x Write your response here

The graph of f is given State the numbers at which f is not differentiable X x smaller value larger value y 2 0 2 13

Use the sum to product identities to rewrite the following expression in terms containing only first powers of tangent Answer sin9x sin5x cos9x cos5x

Derivative Test to find the max an min of the function on the interva 3 given a f x x 9xb 2 f x x x 2

graph one full cucle of y csc 3x 3 3

Use the binomial series or any other method to find the Maclaurin series for b a 1 n 1 x2n 2n 2 n 1 x2n 1 2n 1 n 0 8 d 1 1 n 0 n 0 f x 1 8 1 2 x2 n 2n 1 e 1 n 0 8 x n c 1 12n 1 2n n x2n 2n 1 n 0

Find the domain of the function f x x 1 13 8x 2x Answer in interval notation

You may need to use the appropriate appendix table or technology to answer this question The number of adults in the United States who smoke has declined greatly In 2005 more than 20 of adults in the United States smoked but this declined to about 12 5 in 2020 Consider a group of 220 adul surveyed in the year 2020 and use the normal approximation of the binomial distribution to answer the questions below a What is the expected number of adults who smoke adults b What is the probability that fewer than 25 smoke Round your answer to four decimal places c What is the probability that from 30 to 35 smoke Round your answer to four decimal places d What is the probability that 45 or more smoke Round your answer to four decimal places

What are your null and alternate hypotheses ull Hypotheses ants will not gravitate more towards high sugar foods than they will towards low gar ods ternative Hypotheses ants will gravitate more towards high sugar foods than they will low sugar ods What is your prediction rediction that ants will gravitate more towards high Sugar food than low sugar food due to their eference for energy rich source When an ant discovers a sugar source it employs multiple strategies to communicate this finding to its nestmates One such strategy involves the release of chemical signals known as pheromones along its foraging path These pheromones serve as a trail marker guiding other ants from the colony to the food source As more ants follow the pheromone trail and reach the sugar source they contribute to the reinforcement of the trail by depositing additional pheromones This positive feedback loop strengthens the trail making it increasingly attractive to other ants and effectively creating a gravitational pull towards the sugar source The intensity of this gravitational pull depends on factors such as the concentration of pheromones the distance to the sugar source and the size of the ant colony In addition to pheromone trails ants possess highly sensitive chemosensory receptors that enable them to detect and respond to minute concentrations of sugar molecules in their environment This ability allows ants to locate sugar sources even in the absence of a pheromone trail further enhancing their foraging efficiency Moreover environmental factors such as temperature humidity and competition from other organisms can influence the strength and direction of the gravitational pull towards sugar In conclusion the phenomenon of gravitation in ants towards different levels of sugar is a multifaceted process driven by chemical communication sensory perception and environmental cues Through the coordinated efforts of individual foragers and the collective behavior of the colony ants are able to efficiently locate and exploit sugar resources ensuring their survival and reproductive success

HER PRACTICE AN Suppose an electric vehicle manufacturing company estimates that a driver who commutes 50 miles per day in a particular vehicle will require a nightly charge time of around 1 hour and 30 minutes 90 minutes recharge the vehicle s battery Assume that the actual recharging time required is uniformly distributed between 70 and 110 minutes a Give a mathematical expression for the probability density function of battery recharging time for this scenario f x 70 x 110 elsewhere b What is the probability that the recharge time will be less than 101 minutes c What is the probability that the recharge time required is at least 79 minutes Round your answer to four decimal places d What is the probability that the recharge time required is between 75 and 105 minutes

You may need to use the appropriate appendix table or technology to answer this question A binomial probability distribution has p 0 20 and n 100 a What are the mean and standard deviation mean standard deviation b Is this situation one in which binomial probabilities can be approximated by the normal probability distribution Explain Yes because np 5 and n 1 p 5 Yes because n 30 No because np 25 and n 1 p 5 Yes because np 5 and n 1 p 5 No because np 5 and n 1 p 5 c What is the probability of exactly 25 successes Use the normal approximation of the binomial distribution to answer this question Round your answer to four decimal places d What is the probability of 18 to 22 successes Use the normal approximation of the binomial distribution to answer this question Round your answer to four decimal places e What is the probability of 12 or fewer successes Use the normal approximation of the binomial distribution to answer this question Round your answer to four decimal place

If a spherical tank 6 m in diameter can be filled with a liquid for 450 find the cost to fill a tank 24 m in diamete The cost to fill the 24 m tank is

Find the derivative of f x cos x 4

Determine the different possibilities for the numbers of positive negative and nonreal complex zeros for the following function 3 2 f x 4x 3x 4x 7 What is the possible number of positive real zeros of this function

Compute the value of the discriminant and give the humb teal solutions of the quadratic 2 ocuation 7x 3x 3

List all points on the graph of y tanx 5 on the interval 37 that have a 2 y coordinate of 3

b Solve the equation sin 4x sin 2x the identity sin a sin 3 2 sin a Mala of the f 0 on the interval 0 27 Begin by applying a b cos az 2 COS 2 al the

1 20 points What is the maximum loan amount that Bank of America can provide to an investor given that the investor plans to repay the loan by selling 10 apartment units priced at 250 000 each in 3 years Assume the bank applies a nominal annual interest rate of 12 compounded quarterly

The accompanying table lists probabilities for the corresponding numbers of unlicensed software packages What is the random variable what are its possible values and are its values numerical Number of unlicensed software packages x 0 P x 0 125 1 0 375 2 0 375 3 0 125 Choose the correct answer below OA The random variable is x which is the number of unlicensed software packages The possible values of x are 0 1 2 and 3 The values of the random value x are not numerical OB The random variable is P x which is the probability of a number of unlicensed software packages The possible values of P x are 0 125 and 0 375 The values of the random value P x are not numerical OC The random variable is P x which is the probability of a number of unlicensed software packages The possible values of P x are 0 125 and 0 375 The values of the random value P x are numerical OD The random variable is x which is the number of unlicensed software packages The possible values of x are 0 1 2 and 3 The values of the random value x are numerical

The 2004 General Social Survey asked a random sample of 977 adult Americans how often they feel rushed with three options to choose from always sometimes and never We are interested in testing whether one third of all Americans would answer always Step 1 The parameter is Select Step 2 The null hypothesis is H0 Select alternative hypothesis is Ha Select Step 3 The technical conditions Select The satisfied The sample result is that 304 of the 977 people responded always Step 4 The test statistic is Select Step 5 The p value is Select Step 6 At the 05 significance level we Select

Saved Help Save Exit Submit A student set up an experiment to show the effect of light color on photosynthesis in Elodea plants She filled two test tubes with distilled water and placed a piece of Elodea in each of the tubes She added a drop of phenol red which turns red in a basic solution and yellow in an acidic solution She blew in each tube before placing the volumeters on the top of the tube Why did she blow into the tube Multiple Choice to add oxygen to the tube to add carbon dioxide to the tube to add carbohydrates to the tube to add sodium bicarbonate to the tube i

s quiz assignment 7 Saved Help If a solution is undergoing a reaction where CO2 is being used as a reactant what color is the phenol red containing solution shifting towa Multiple Choice colorless red green pink yellow

The organelle where photosynthesis occurs is the Multiple Choice chlorophyll chloroplast mitochondria nucleus lysosome

What would you expect to happen if you compare the rate of photosynthesis in bright white light and in darkness Multiple Choice O The rate of photosynthesis will not be affected by bright white light or darkness The rate of photosynthesis will be less under bright white light than in darkness The rate of photosynthesis will start slowly under bright white light and then increase in darkness The rate of photosynthesis will remain constant in bright white light and darkness The rate of photosynthesis will be greater in bright white light than in darkness

Which of the following correctly summarize the overall process of photosynthesis Check all that apply Check All That Apply CO2 2H2O hv CH2O H2O O2 Water is absorbed by plant roots and combines with carbon dioxide in the leaves in the presence of sunlight to produce glucose and oxygen gas 6CO2 12 H2O hv C6H12O6 602 6 H2O CO2 H2O hv CH206 O2 H2O C6H12O6 6026CO2 C6H12O6 6 H2O