Questions

14 Select the appropriate substitution that would Simplify the evalution of the integral I since 0 1 COS 0 do A non B u COSCO C U COS 0 E u 1 cos 0 b u sincol

Drag the tiles to the correct boxes to complete the pairs Not all tiles will be used C B 90 5 3 Match the trigonometric ratios with their values based on the triangle shown in the diagram sin D cos Cx tan D sin C sin D x cos D tan Cx tan D 22 310 199

S 7 Find the integral x dx using substitution The resulting integral is 1 x2 Anone B S4 du C f1 zdu b f4 zdu E Sth ou Sz 2u 20 2 4 42 1 2 4 421782 Ou ax du

2 The appropriate substitution for the integral S cos 6 x Sin x dx is and the resulting integral is A U COSCX1 C none B Ul sin x D u cos MECOSX A U COSA S4 1 105t du 48 46 A U cos x Ju u du coscx Su urdu B u sin x Su u du C none 4 COSX e Sinx dx 48 46 E U sin x su uo du 46 48 du S46 1 cos x du

5 Find the integral 8x 1 dx x 3 x 2 A 8 n X 31 n 1x 2 C B 51n x 31 3 n x 21 C c In 1x 31 3 n 1x 21 C b none 15 Jx x 3 x 2x 1230x 63 6 E 3 n 1x 31 5 n x 21 C 51n1X 31 31n1x 2 C

V 6 Evaluate the integral 2 I sec x tan x dx

12 Evaluate the indefinite integral S 8 04 18 972 9 C 15 2

bers use the assumed values and only 1 section Otherwise the math will not work 75 lb L K H A B C D E F 4 ft 4 ft 4 ft 4 ft 4 ft 4 ft 3 15 lb 55 lb 25 lb 35 lb 6 ft

43 Use integration by parts to evaluate the integral S x e 4 x d x e4ex C 4 Sxe 4xdn xe 4x feux dx xe 4x 4 4n

M For each of the indefinite integrals below choose which of the following substitution would be most helpful in evaluating the integral enter the appropriate A x 7tan o 16 7 sino C x 7seco C B 1 SX 1 5 x 2 dx 2 5 x2 440x 49642 A 3 S 1491213 4 x 49 512x 51x2 dr A

Simplify Express your answer as a single fraction in simplest form P 2p 12p 24 4p 8

The number of hits on a certain website follows a Poisson distribution with a mean rate of 3 per minute Part A Define a function for calculating the probability of poisson distribution def poisson manual x lmbd Define poisson distribution based on x and lambda You can assume that x is a non negative intege You may want to use following functions math e math factorial Inputs x x lambda Lmbd Output prob I

Simplify Express your answer as a single fraction in simplest form b 5b b 2

Simplify Express your answer as a single fraction in simplest form a 9 a 10

Consider the data set represented by the dot plot 500 1000 Which word best describes the red data point Outlier Absolute Deviation Unbalanced Third quartile 1500

1 Find the area of the cross section of the rectangular prism shown below Round all calculations to the nearest tenth 11 cm 8 cm 15 am Note The figure is not drawn to scale a 187 cm b 139 7 cm c165 cm d 255 cm

125 lb H 75 lb G FL A B C ID 4 ft 4ft 4 ft 4 ft 4ft 90 lb 4 ft EI

PART 7 METAPHASE II for 2n 4

a Homologous Chromosomes Before Replication b Homologous Chromosomes After Replication c Diploid Somatic Cell 2n 4 after DNA Replication PART 2 MEIOSIS PREPARATION a A cell 2n 4 at Metaphase 1 of Meiosis b How do you indicate homologous pairs of chromosomes Where did this organism get each member of a homologous pair of chromosomes ART 3 MEIOSIS 2n 10 complete on separate pieces of paper and attach to lab results

3 M 3 0 N 5 2 O 3 4 P 1 2 MN slope MN OP slope OP MP slope MP NO slope NO

Find the zeros of the function f x x 7x 7 Round values to the nearest hundredth if necessary Answer Attempt 1 out of 2

Find M14 and M33 for matrix A 96 00 1 2 00 A 8 66 9 5 3 M14 12 M33 40

Find the first derivitative example g 1 1 x 2

21 4 Describe two groups of microbes at the vents along with their metabolic activities that facilitate symbiosis and or genera metabolism in these communities How do these organisms interact with the biogeochemistry at the vents and in the deep ocean Ch 21 How does the structure of the host and microbe impact functionality of the symbiosis

2 2x 2 3 dx x 3x

J 2 Improper integrels edx x4 2

Question Find the zeros of the function f 2x 16 8x 31 Round values to the nearest hundredth if necessary Answer Attempts out of 2

Question Watch Vide Show Exam Using the rational root theorem list out all possible candidate rational roots of f x 5x 222 3r 23 Express your answer as integers or as fractions in simplest form Use co to separate

Question Given 0 simplify 25x10 completely Answer Attempt 1 out of 2

4 A ballon being filled at rate of rct liters per sec Starting with a volume of o liters at time t 0 What is an expression that represents the volume of the ballon after 2 min in liters 2 A S r of 120 of B So randt C fire rus of E none

Consider the following recursive function fun x y What is the value of fun 4 3 int fun int x int y if x O return y return fun x 1 x y O 10 O 11 O 12

Which do you think is most deadly A Ground shaking B Liquefaction C Fire D Tsunami E Landslides

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