Questions

Determine whether the series 1 1 2 1 k2 k 1 is absolutely convergent conditionally con vergent or divergent 1 conditionally conver 2 absolutely converger 3 divergent

Collins Company is preparing its master budget for April Use the given estimates to determine the amounts necessary for each of the following requirements Estimates may be related to more than one requirement a What should total sales revenue be if territories A and B estimate sales of 10 000 and 16 000 units respectively and the unit selling price is 48 b If the beginning finished goods inventory is an estimated 2 000 units and the desired ending inventory is 3 000 units how many units should be produced 27 000 c What dollar amount of material should be purchased at 4 per pound if each unit of product requires 3 pounds and beginning and ending materials inventories should be 5 000 and 4 000 pounds respectively x d How much direct labor cost should be incurred if each unit produced requires 1 5 hours at an hourly rate of 17 e How much manufacturing overhead should be incurred if fixed manufacturing overhead is 55 000 and variable manufacturing overhead is 2 50 per direct labor hour

3 Let sin A with 180 A 270 and find 5 1 sin 2A 2 cos 2A

Estimate cos x2 da using a the Trapezoidal Rule and b the Midpoint Rule each with n 4 Give each answer correct to five decimal places a T 0 84549 b M 0 5373 c By looking at a sketch of the graph of the integrand determine for each estimate whether it overestimates underestimates or is the exact area 1 T Underestimate Overestimate 2 M4 d What can you conclude about the true value of the integral A TA cos x dx M4 B T4 C TA cos x2 dx and M4 cos x dx cos x dx and M4 f cos x dx D No conclusions can be drawn E MA cos x2 dx T

Prove each of the following identities 31 sin x cos x 1 sin 2x 32 cos xsin x cos x sin x cos 2x 1 cos 20 33 cos 2 sin 20 35 cot 1 cos 20 37 cosxsin x cos 2x 39 sin 303 sin 0 4 sin 0 41 2 csc 2x tan x cotx 34 sin 36 cos 20 1 cos 20 2 1 tan 0 1 tan 0 38 sin x cos x cos 2x 40 cos 304 cos 0 3 cos 42 2 cot 2x cot x tan x

For each independent situation below determine the missing amounts A B C D Beginnning inventory 6 000 x 2 000 X Produced 40 000 22 000 x 60 000 Available x x 26 000 69 000 Sold 45 000 33 000 X x Ending inventory x 10 000 11 000 3 000

Let cos x 5 cos 2x V10 with 270 x 360 and find

Let tan 0 with 0 in QI and find 9 sin 20 10 cos 20

Let csc t 5 with t in QII and find 13 cos 2t 14 sin 2t 17 Express cos 100 in terms of sin 50 15 sec 2t 16 csc

5 Show how you could set up and find the exact value of cos COS 57 COS 4 2 2 cos x cos COS 4 COS X TU 2 2 in two different ways

A researcher wishes to estimate with 95 confidence the population proportion of adults who think the president of their country can control the price of gasoline Her estimate must be accurate within 3 of the true proportion a No preliminary estimate is available Find the minimum sample size needed b Find the minimum sample size needed using a prior study that found that 34 of the respondents said they think their president can control the price of gasoline c Compare the results from parts a and b a What is the minimum sample size needed assuming that no prior information is available n Round up to the nearest whole number as needed b What is the minimum sample size needed using a prior study that found that 34 of the respondents said they think their president can control the price of gasoline n Round up to the nearest whole number as needed c How do the results from a and b compare OA Having an estimate of the population proportion reduces the minimum sample size needed B Having an estimate of the population proportion has no effect on the minimum sample size needed OC Having an estimate of the population proportion raises the minimum sample size needed

List all halfway points on the graph of y cot x on the interval 3 3 2 2 The points are Type an ordered pair Use a comma to separate answers as needed Simplify your answer Type an exact answer using it as needed Use integers or fractions for any numbers in t

Using V 9 mV and given the voltage across an inductor L 10 mH as shown in Fig P6 25 determine the waveform for the inductor current during the time t1 t t2 where t1 4 ms and t2 19 ms Assuming the solution looks like i t X t t1 2 Y t t1 C what is the initial condition of the current the constant C For your answer just put the magnitude of the initial value of the constant and in milliAmps there should only be a number in your answer D f MV V t1 t2 ms Figure P6 25

The following is a report from a BLS survey taker There were 70 people in the houses I visited 12 of them were children under the age of 16 25 people had full time jobs and 6 had part time jobs There were 10 retirees 5 full time homemakers 5 full time students over age 16 and 2 people who were disabled and cannot work The remaining people did not have jobs but all said they would like one 1 of these people had not looked actively for work for three months however Find the labor force the unemployment rate and the participation rate implied by the survey taker s report Labor force people Instructions Enter your responses rounded to two decimal places Unemployment rate Participation rate

George and John stranded together on an Island use clamshells for money Last year George caught 500 fish and 5 wild boars John grew 200 bunches of bananas In the two person economy that George and John set up fish sell for 1 clamshell each boars sell for 10 clamshells each and bananas go for 5 clamshells per bunch George paid John a total of 30 clamshells for helping him to dig bait for fishing and he also purchased five of John s mature banana trees for 30 clamshells each What Is the GDP of George s and John s Island in terms of clamshells Instructions Enter your response as whole number GDP clamshells

Given a capacitor of C 3 F calculate the current going through the capacitor during the interval t1 st st2 when the capacitor voltage is as described in Fig 6 12 Assume V1 10V V2 5V and t1 8 S and t2 13 S Note values might be different than the above problem v t V A V1 V2 O Figure P6 12 t2 t3 t1 1 ps

Given a capacitor of C 23 F calculate the current going through the capacitor during the interval t2 t t3 when the capacitor voltage is as described in Fig 6 12 Assume V1 9V V2 7V t2 90 s and t3 185 s Note The values might be different than the above problem v t V V1 V2 t2 t3 0 t1 t s Figure P6 12 Notes on entering solution Enter your solution in Amps Pay attention to the interval Enter your solution to 2 decimal points Do not include units in your answer ex 5A is entered as 5 00

Required information The following information applies to the questions displayed below In 2023 Elaine paid 2 000 of tuition and 680 for books for her dependent son to attend State University this past fall as a freshman Elaine files a joint return with her husband What is the maximum American opportunity tax credit that Elaine can claim for the tuition payment and books in each of the following alternative situations Note Leave no answer blank Enter zero if applicable b Elaine s AGI is 172 500 Note Round your intermediate calculations to the Nearest whole dollar amount American opportunity tax credit

Sketch the graph of the following between x CSC X 4 and x 4 Y

Use the formula in this example to determine the sample size n The estimated prevalence is 36 and the desired confidence level is 98 with a margin of error of 1 Round your answer to the nearest integer n

1 of 3 IS eBook Required information The following information applies to the questions displayed below In 2023 Juanita is married and files a joint tax return with her husband What is her tentative minimum tax in each of the following alternative circumstances Use Tax Rate Schedule Dividends and Capital Gains Tax Rates for reference Note Input all values as positive Leave no answer blank Enter zero if applicable a Her AMT base is 156 000 all ordinary income 1 AMT base Print Description ferences 2 Dividends taxed at preferential rate 3 Tax on dividends 4 AMT base taxed at regular AMT rates 5 Tax on AMT base taxed at 26 rate 6 Tax on AMT base taxed at 28 rate Tentative minimum tax Amount 156 000

2 Exam 4 f x 2x 5 g x 2x 2x 1 Find the value of fg 3

Alice is single and self employed in 2023 Her net business profit on her Schedule C for the year is 191 200 What are her self employment tax liability and additional Medicare tax liability for 2023 Note Round your final answers to the nearest whole dollar amount Leave no answer blank Enter zero if applicable Answer is not complete Self employment tax liability Additional medicare tax liability 0

Ook This year Paula and Simon married filing jointly estimate that their tax liability will be 221 000 Last year their total tax liability was 184 000 They estimate that their tax withholding from their employers will be 191 100 Required a Are Paula and Simon required to increase their withholdings or make estimated tax payments this year to avoid the underpayment penalty b By how much if any must Paula and Simon increase their withholding and or estimated tax payments for the year to avoid underpayment penalties int Complete this question by entering your answers in the tabs below ences Required A Required B By how much if any must Paula and Simon increase their withholding and or estimated tax payments for the year to avoid underpayment penalties

point Library Michigan Chap16Sec3 Q47 pg Let W be the solid half cone bounded by z x y z 1 and the yz plane with x 0 and let Let W be the solid half cone bounded by z x y z 4 and the xz plane with y 0 V For each of the following decide without calculating its value whether the integral is positive negative or zero a Jw x y2 dV is positive negative zero b Jw yzdV is positive negative zero c Jw Vx y2dV is positive negative zero

Required information The following information applies to the questions displayed below Lacy is a single taxpayer In 2023 her taxable income is 51 600 What is her tax liability in each of the following alternative situations Use Tax Rate Schedule Dividends and Capital Gains Tax Rates for reference Note Do not round intermediate calculations Round your answer to 2 decimal places a All of her income is salary from her employer Tax liability

Alice is single and self employed in 2023 Her net business profit on her Schedule C for the year is 191 200 What are her self employment tax liability and additional Medicare tax liability for 2023 Note Round your final answers to the nearest whole dollar amount Leave no answer blank Enter zero if applicable Self employment tax liability Additional medicare tax liability

Which of the following values are in the domain of th function graphed below Check all that apply A 2 B 2 C 1 D 5 5 5

Required information The following information applies to the questions displayed below Julie paid a day care center to watch her two year old son while she worked as a computer programmer for a local start up company What amount of child and dependent care credit can Julie claim in 2023 in each of the following alternative scenarios Use Exhibit 8 9 c Julie paid 4 100 to the day care center and her AGI is 24 900 all salary Child and dependent care credit

Given the function b x x 4 Find all of the following information algebraically Find the domain Give the domain using interval notation Find the vertical asymptotes Find the removable discontinuity Express as an ordered pair Find the horizontal intercept s Express as ordered pair s Find the vertical intercept Express as an ordered pair Find the horizontal or slant asymptote

Required information The following information applies to the questions displayed below Trey has two dependents his daughters ages 14 and 18 at year end Trey files a joint return with his spouse What amount of child tax credit either as a child or a qualifying dependent will Trey be able to claim in 2023 for his daughters under each of the following alternative situations Use Exhibit 8 8 c His AGI is 422 400 and his daughters are ages 10 and 12 Amount of child tax credit

2 Which of the following is a solution to the system of equations shown below A 2 2 B 15 5 C 5 0 D 3 1 2x 4y 10 y 8 3x

Let S and T be two sets defined as S 1 2 3 5 and T 2 4 6 7 8 9 10 Let f be a binary relation from S to T defined by the set of ordered pairs 1 Is fa function f 1 2 2 4 3 4 5 6 2 What is the domain of f codomain of f 3 What is the image of f 4 What is the image of 2 and the image of 3 5 What is the pre image of 2 6 Is this a one to one function

Required information The following information applies to the questions displayed below Steve s tentative minimum tax TMT for 2023 is 249 200 Note Leave no answer blank Enter zero if applicable b What is his AMT if his regular tax is 258 500 Alternative minimum tax

4 Composition of functions For each of the following pairs of functions f and g calculate go f and fog 1 f 1 2 3 4 5 6 and g 2 1 4 3 6 5 2 f x 2x 1 and g x 4x 5 for all x Z

a Consider the three following Hasse diagrams representing three poset relations RA RB and Rc a a b 3 4 b b C a 1 2 A B C 1 For each poset list all the ordered pairs that belong to the relation 2 For each relation provide all least minimal greatest and maximal elements b Which of the following posets are lattices Justify your work for the non lattices only 1 1 2 2 3 A B 3 2 3 3 D

5 Inverse functions Let f be a bijective function f RR defined by f x 4x 5 1 Find the inverse of f 2 Calculate f 1 of and fof 1 What do you notice

Type numbers in the boxes Part 1 5 points aby Part 2 5 points 10 points According to the website www collegedrinkingprevention gov About 25 percent of college students report academic consequences of their drinking including missing class falling behind doing poorly on exams or papers and receiving lower grades overall A statistics student is curious about drinking habits of students at his college He wants to estimate the mean number of alcoholic drinks consumed each week by students at his college He plans to use a 90 confidence interval He surveys a random sample of 56 students The sample mean is 3 94 alcoholic drinks per week The sample standard deviation is 3 43 drinks Construct the 90 confidence interval to estimate the average number of alcoholic drinks consumed each week by students at this college Your answer should be rounded to 2 decimal places

Estimating Mean SAT Math Score Part 1 5 points Part 2 5 points 10 points The SAT is the most widely used college admission exam Most community colleges do not require students to take this exam The mean SAT math score varies by state and by year so the value of u depends on the state and the year But let s assume that the shape and spread of the distribution of individual SAT math scores in each state is the same each year More specifically assume that individual SAT math scores consistently have a normal distribution with a standard deviation of 100 An educational researcher wants to estimate the mean SAT math score u for his state this year The researcher chooses a random sample of 618 exams in his state The sample mean for the test is 495 Find the 90 confidence interval to estimate the mean SAT math score in this state for this year Note The critical z value to use zc is 1 645 Your answer should be rounded to 3 decimal places

In the year 1984 an investment was worth 30200 In the year 1992 this investment was worth 39000 The value this investment is increasing at a rate of dollars

Is smoking during pregnancy associated with premature births To investigate this question researchers selected a random sample of 107 pregnant women who were smokers The average pregnancy length for this sample of smokers was 265 days From a large body of research it is known that length of human pregnancy has a standard deviation of 16 days The researchers assume that smoking does not affect the variability in pregnancy length Find the 90 confidence interval to estimate the length of pregnancy for women who smoke Note The critical z value to use ze is 1 645 Type numbers in the boxes Part 1 5 points Part 2 5 points 10 points Your answer should be rounded to 3 decimal places

A group of engineers developed a new design for a steel cable They need to estimate the amount of weight the cable can hold The weight limit will be reported on cable packaging The engineers take a random sample of 48 cables and apply weights to each of them until they break The 48 cables have a mean breaking weight of 773 lb The standard deviation of the breaking weight for the sample is 16 1 lb Find the 95 confidence interval to estimate the mean breaking weight for this type cable Type numbers in the box Part 1 5 points Part 2 5 points 10 points Your answer should be to 2 decimal places

a After listing the possible samples and finding the proportion of females in each sample use a table to describe the sampling distribution of the proportion of females Proportion of females Probability 1 0 16 6 0 5 16 9 16 Type integers or fractions b Find the mean of the sampling distribution Bound to two decimal places as needed

For each ordered pair determine whether it is a solution to 5x 4y 17 Is it a solution x y Yes No 3 8 2 9 O 6 2 O 7 1

K mple of grade point averages of statistics students and she calculates the mean of this sample Under what conditions can that sample mean be treated as a va from a population having a normal distribution Select all that apply A The researcher collects more than 30 samples B The sample has more than 30 grade point averages C If the population of statistics students has a normal distribution D If the population of grade point averages has a normal distribution

Create an application based problem that uses linear algebra to solve the unknown numbers in a linear system and make a eexplanation how you will solve it using the three different methods a Gaussian Gauss Jordan Elimination b Inverse Method c Cramer s Rule Your problems should have unique given parameters on your problem Dont use Ai for making problems solutions

At a raffle 10 000 tickets are sold at 5 each for three prizes valued at 4 800 1 200 and 400 What is the expected value of one ticket O 0 64 O 0 64

Find the equation in terms of a of the line through the points 2 6 and 3 9 Y

Use synthetic division to divide 3 X 2 2x x 2 by x 3 The quotient is The remainder is Use synthetic division to divide x 2x x 2 by x 3 1 2 1 2 The quotient is The remainder is

Given the coefficient matrix A for the following system of equations find 42 7x14x2 1 2x15x2 3 7 4 A 2 5 Ex 42 A2