Math - Others Questions

Prove the given identity csc sin 0 cos 0 cot 0 Choose the correct proof below OA csc 0 sin OB csc sin 0 OC csc sin 0 OD csc sin 0 1 sin 0 1 sin 0 1 sin 0 sin 0 sec 0 1 sin 0 sin 0 2 1 sin 0 sin 0 sin 1 sin 0 sin sin 1 sin sin 0 sin 2 1 sin 0 sin 2 Cos 0 sin 0 2 cos 0 cos 0 2 sin 0 2 COS 0 sin 0 cos 0 cot cos 0 cot 0 cos Ocot 0 cos 0 cot 0

Prove the given identity cot x secx csc x tan x Choose the correct proof below O A cot x sec X CSC X 1 COS X 1 cos x sin x O C sin x 2 1 cos x sin x cos X 2 sin X sin x cos x tan x cot x sec x csc x COS X sin X sin x cos x 2 1 cos X sin x cos X 2 sin x tan x OB O D cot x sec XCSC X COS X 1 1 sin x COS X sin x cos X sin x 2 1 Cos X sin x cos X 2 sin x tan x cot x sec Xcsc X COS X sin x 2 1 cos x sin x cos x 2 sin X sin x cos x tan x

verify the identity sin 0 sec 0 tan 0 Which of the following four statements verifies the identity O A sin 0 sec 0 sin 0 cos 0 OB sin 0 sec 0 OC sin 0 sec 0 sin 0 sin 0 COS 0 1 Cos 0 OD sin 8 sec 0 sec 0 1 COS 0 sin 0 sin 0 1 COS 0 COS 0 co 0 sin sin 0 tan 0 Cos 0 sin 0 Cos 0 tan 0 tan 0 tan 0

1 cost sin t Choose the sequence of steps below that verifies the identity A O B O C sin t 1 cost O D 1 cost 1 cost sin t sint 1 cost sin t 1 cost sin t 1 cost sin t 1 cost sin t 1 cost sin t 1 cost sin t 1 cost 1 cost 1 cost 1 cost 1 cost 1 cost 1 cost 1 cost 1 cos t sin t 1 cos t 1 cos t sin t 1 cost 1 cos t sin t cos t 1 cos t sin t 1 cos t sin t sin t 1 cost sin t sin t 1 cost sin t sin t 1 cost sin t sin t 1 cos t sin t 1 cost sint 1 cost sin t 1 cost sin t 1 cost

You may need to use the appropriate appendix table or technology to answer this question The Economic Policy Institute periodically issues reports on workers wages Suppose the institute reported that mean wages for male college graduates were 37 39 per hour and for female college graduates were 27 83 per hour in 2017 Assume the standard deviation for male graduates is 4 60 and for female graduates it is 4 10 Round your answers to four decimal places a What is the probability that a sample of 40 male graduates will provide a sample mean within 1 00 of the population mean 37 39 b What is the probability that a sample of 40 female graduates will provide a sample mean within 1 00 of the population mean 27 83 c In which of the preceding two cases part a or part b do we have a higher probability of obtaining a sample estimate within 1 00 of the population mean why O part b because the standard error is lower O part a because the standard error is lower O part b because the standard error is higher O part a because the standard error is higher d Calculate the amount that is 0 60 less than the population mean of 27 83 What is the probability that a sample of 130 female graduates will provide a sample mean less than this amount

If f x and g x are arbitrary polynomials of degree at most 1 then the mapping f g f 2 g 2 f 2 g 2 defines an inner product in P Use this inner product to find f g f g l and the angle afg between f x and g x for f x 4x 8 and g x 4x f g f g afg Note X radians

You may need to use the appropriate appendix table or technology to answer this question The Economic Policy Institute periodically issues reports on workers wages Suppose the institute reported that mean wages for male college graduates were 37 39 per hour and for female college graduates were 27 83 per hour in 2017 Assume the standard deviation for male graduates is 4 60 and for female graduates it is 4 10 Round your answers to four decimal places a What is the probability that a sample of 90 male graduates will provide a sample mean within 1 00 of the population mean 37 39 b What is the probability that a sample of 90 female graduates will provide a sample mean within 1 00 of the population mean 27 83 c In which of the preceding two cases part a or part b do we have a higher probability of obtaining a sample estimate within 1 00 of the population mean Why d Calculate the amount that is 0 60 less than the population mean of 27 83 What is the probability that a sample of 140 female graduates will provide a sample mean less than this amount Step 1 a What is the probability that a sample of 90 male graduates will provide a sample mean within 1 00 of the population mean 37 39 The population mean hourly wage for male graduates was given to be 37 39 with a standard deviation of 4 60 A sample from the population will not necessarily give these same values Let x represent the sample mean hourly wage for a group of 90 males To be within 1 00 of the population mean of 37 39 gives a range of hourly wages between 37 39 1 00 and 37 39 1 00 Therefore the desired probability that a sample mean of 90 males is within 1 00 of the population mean is x

Using the graph off shown below find three intervals on which f is one to one making each interval as large as possible Ay 6 3 3 A CID The intervals on which f is one to one are Simplify your answers 0 and c

d 2 5x 3y e ex 2x 3 1 3y

the ratio of carbon 14 to carbon 12 in a piece of wood discovered in a cave is R 1 915 Estimate the age of the piece of wood Round your answer to the nearest whole num x years old

On the first day of the fiscal year a company issues 45 000 8 six year installment notes that have annual payments of 9 734 T first note payment consists of 3 600 of interest and 6 134 of principal repayment a Journalize the entry to record the issuance of the installment notes If an amount box does not require an entry leave it blank Cash Notes Payable Feedback Check My Work 88 b Journalize the first annual note payment If an amount box does not require an entry leave it blank Interest Expense

12 Solve the following system of equations 4x 15y 17 x y 13 A 1 3 B 8 1 c 1 8 D 4 3

Multiply and simplify sec 8 cos 0 sin 0 tan 0 sec cos 0 sin 0 tan 0 Simplify your answer

Verify the identity tan x sec x 1 2 tan x 2 2 Which of the following four statements establishes the identity A tan x sec x tan x tan x 1 1 2 tan x B tan x sec x tan x 1 tan x 1 2tan x OC tan x sec x 1 1 2 tan x OD tan x sec x tan x 1 tan x 1 2 tan x

onometric Identities Prove the given identity sec xcsc x sin xsec x cos xcsc x Choose the correct proof below A sec xcsc x sin xsec x 1 1 cos x sin x 1 sin X sin x cos x cos 2 X sin x cos x cos x csc x OC sec xcsc x sin xsec x 1 1 cos x sin x 2 1 sin x sin x cos x sin x COS X sin x cos x cos xcsc X cos x Question 6 of 10 OB sec xcsc X sin xsec x 1 1 sin x cos x sin x sin x cos x 1 sin sin x cos x cos 2 X cos x cSC X This quiz 25 poi This question 3 OD sec xcsc x sin xsec x 1 1 cos x sin x sin x cos x 2 1 s n x sin x cos x COS cos x cos X CSC X

Prove the given identity 1 tan 0 cos 0 1 Which of the following shows the key steps in proving the identity OA 1 tan 20 cos2 0 sec 0 cos 0 2 OC 1 tan2 e cos 0 sin 0 1 csc 0 O B 1 tan 0 cos 0 cos 0 tan 0 cos 0 cos 0 sin 0 1 cos 0 cos 0 sin 20 2 cos 0 1 cos 0 sin 0 cos 0 sin 0 1 O D 1 tan 0 cos 0 cot 0 cos 0 1 cos 0 tan 20 cos 8 cos 8 1

lan s car gets 34 1 miles per gallon If gas cost lan 2 96 per gallon how much will it cost lan to go 750 miles Round your answer to the nearest penny Input only the number Do not input the dollar sign Example 78 50

4 Saving to open a business Madeline feels trapped in her current job and decides to save 75 000 over the next 7 yr to open up a Harley Davidson franchise To this end she invests 145 every week in an account paying 7 interest compounded weekly a Is this weekly amount sufficient to help her meet the 7 yr goal b If not find the minimum amount she needs to deposit each week that will enable her to meet this goal in 7 yr

Tx R8 11

6 3 8 5 10 7 88 85 toplam n n e iti ka t r

4 15 Use the Laplace transform to solve the initial value problem y y y U t 2 y 0 0 No credit for any other method

t 0 t 3 2 10 Express f t 0 3 t 5 in terms of unit step functions et t25

3 15 Use the Laplace transform to solve the initial value problem bo y y 1 y 0 0 y 0 0 No credit for any other method

A satellite camera takes a rectangle shaped picture The smallest region that can be photographed is a 3 km by 7 km rectangle As the camera zooms out the length I and width wa the rectangle increase at a rate of 2 km sec How long does it take for the area A to be at least 5 times its original size seconds Type an integer or a decimal rounded to the nearest hundredth as needed POLICIS

2 For each line described below is its slope positive negative zero or undefined Justify your answer a As x increases by 3 y decreases by 2 b The line has a negative x intercept and a negative y intercept c The line has a y intercept but does not have an x intercept

Find the value of a in the vector a b if b 36 and 39 is in Quadrant I

Let 3 3 and 8 4 Compute the dot product a b

6 24 32 k l s aralar nda asal ise k nin 20 den k k pozitif ka de eri vard r A 8 B 9 C 10 D 11 E 12

13 Match each equation with its graph Explain your strategy 1 a y x 3 c y 2x 3 Graph A 3 0 2 Graph C y 2 0 2 X 4 2 x b y 3x 2 d y 2x 3 Graph B y 2 0 2 Graph D y N 2

b cos 20 NII 2

12 For each graph below i Determine its slope and y intercept ii Write an equation that describes the graph iii Verify your equation a 6 4 2 2 0 2 N 4 y f x N X b 2 2 N 2 4 y y g x N X

6 4 11 For each equation identify the slope and y intercept of its graph then draw the graph a y 3x 4 3 b y x 2

Suppose a charity received a donation of 15 6 million If this represents 46 of the charity s donated funds what is the total amount of its donated funds Round your answer to the nearest million dollars million dollars X G

6 1 1 Determine the slope of each line a b 4 800 E 600 Distance m 0 y 400 y f x 200 0 X 2 For each line described below is its slope positive negative zero or undefined Justify your answer a As x increases by 3 y decreases by 2 b The line has a negative x intercept and a negative y intercept c The line has a y intercept but does not have an intercept 3 A line passes through A 3 1 For each slope given below y g x i Sketch the line through A with that slope ii Write the coordinates of three other points on the line b 14 a 1 4 Determine the slope of a line that passes through each pair of points What strategy did you use a B 6 8 and C 1 2 b D 3 7 and E 5 5 4 5 Gabrielle likes to jog and has a pedometer to measure how far she runs She checks her pedometer periodically and records its readings Gabrielle plotted these data on a grid Graph of Gabrielle s Run 2 5 800 2 320 0 y 6 Time min a What is the slope of the line and what does it represent b How is slope related to rate of change c Assume Gabrielle continues to run at the same rate i How far did Gabrielle jog in 4 min ii How long will it take Gabrielle to jog 1000 m 6 2 6 The slope of line FG is given What is the slope of a line that is i parallel to FG ii perpendicular to FG d 1 6 11 a 3 b c 8 7 The coordinates of two points on two lines are given Are the two lines parallel perpendicular or neither Justify your choice a H 3 3 J 1 7 and K 1 2 M 5 1 b N 4 2 P 1 7 and Q 2 5 R 4 1 8 Is quadrilateral STUV a parallelogram Justify your answer V 4 2 6 4 2 y T 9 Triangle ABC has vertices A 1 1 B 2 5 and C 6 3 Is AABC a right triangle Justify your answer 6 3 10 Sketch graphs to help explain what happens to the graph of y 3x 4 when a the coefficient of x increases by 1 each time until the coefficient is 6 b the constant term decreases by 1 each time until it is 4

5 The slope of line FG is given What is the slope of a line that is i parallel to FG ii perpendicular to FG 11 a 3 b d 1 8 6 UITO 5 c

6 1 1 Determine the slope of each line a b y 4 y f x 20 2 X y g x J 4 2 C y r X

4 Determine the slope of a line that passes through each pair of points What strategy did you use a B 6 8 and C 1 2 b D 3 7 and E 5 5

Which of the following are causes of the increased irrationality in our society Post modernism Relativism Polarization All of the above

Which of the following are objections to the technique of cost benefit analysis O Not all the factors to be considered are quantifiable O Long term forecasts of costs and benefits may turn out wrong O Prioritization in cost benefit analysis is not value free O All of the above

1 15 a Give the definition of the Laplace transform of a function f t defined for t 0 b Use this definition to calculate L f t for f t e t No credit for any other method

Find the exact value of tan 285

The extreme temperatures for each continent for a given year are listed in the data table Using a cubic model a location with a maximum temperature of 95 degrees Fahrenheit is predicted to have a minimum temperature of 86 degrees How reliable is this prediction Give at least two reasons to defend your answer Maximum Minimum F F Africa 136 11 Antarctical 59 129 Asia 129 90 Australia 128 9 Eurone 122 Continent 67

a b 26 a b 86 e itli inde a b ve a b asal say lard a api kact r

Solve the triangle b 4 c 6 and B 20 If a triangle exists find the ar Tri 2 9 07

rneks 3a 1 ile 4b 3 say lar aralar nda asald r 3a 1 240 4b 3 450 oldu una g re a b toplam ka t r

Solve the triangle a 9 b 7 and c 10 If a triangle exists find the area

In If it is known that sin a alue of sin a B 12 13 0 a 0 a that cos B 2 5 37 2 find the exact and that cos it rose to oulisy 5 2 202 nie 205 m 20 10

5 Find the exact value of each trigonometric expression a cos 70 cos 50 sin 70 sin 50 5 Cos 70 50 os 120 21 1 5 b cos 1 12 Cos os 2 233 1 12x 17 55 1 1 2 3 2 2 5 6 Find the exact value of tan 285 10

A B 18 oldu una g re bu e itli i sa layan ka tane A ikilisi vard r

4 5 oints 01 15 26 Minstrel Manufacturing uses a job order costing system During the month Minstrel purchased 198 000 of raw materials on credit issued materials to production of 195 000 of which 30 000 were indirect Minstrel incurred a factory payroll of 150 000 of which 40 000 was indirect labor Minstrel uses a predetermined overhead rate of 150 of direct labor cost The total manufacturing costs added during the period is Multiple Choice 540 000 470 000 440 000