Math - Others Questions

K Verify the identity secx secx sin x cos x Choose the sequence of steps below that verifies the identity O A OB O C O D 1 secx 1 sin x cos x cos x cos 2x secx secx sin x secx secx sin x secx 1 sin x secx secx sin x secx sin x 1 secx secx sin x 1 sin x cos x 1 cOS X 1 COS X cos x COS X cos x cos x

Express the given expression in its simplest form with only positive exponents 4z 2 Z 2 Question 5 of 2 3 Simplify your answer Type exponential notation with positive exponents

25y Question 3 of 20 Simplify by taking roots of the numerator and denominator Assume that all expressions under the radicals represent positive numbers 25y7 11 This test 65 poin This question 4 p

Question 3 of 20 This test 65 point s possible This question 4 point s possible Solve the following trignometric equation analytically and by use of a graphing calculator Compare the results Use values of x for 0 x 2x 12 sin 2x cos x sin x 0 GELEE Type an exact answer using x as needed Use a comma to separate answers as needed Use integers or fractions for any numbers in the expression Simplify your ans

Using DeMoivre s theorem find 4 2j 5 KIL This question 3 point s 4 25 cos cos isin 0 Simplify your answers Round to two decimal places as needed Type any angle measures in degrees Use angle measures greater than or equal to 0

3 Given the equation y 8 cos 7x 6 5 find a 5 pts the amplitude b 5 pts the period c 5 pts the horizontal shift and direction d 5 pts the midline

Listed below are two solutions for a service issue Work out the present costs for option 1 so you can compare it to option 2 Use a 5 interest rate Option 2 35 000 First Cost Maintenance Salvage Life Option 1 a 18 182 Ob 33 888 OC 36 356 O d 41 057 Option 1 15 000 1200 yr 100 3years 900yr 2000 6 years

5 Suppose sin x and 270 x 360 a 5 pts Use identities to find the exact value of sin b 5 pts Use identities to find the exact value of cos c 5 pts In what quadrant is the angle Explain your answer

Suppose cos x and 90 x 180 a 5 pts Use identities to find the exact value of sin 2x b 5 pts Use identities to find the exact value of cos 2x c 5 pts In what quadrant is the angle 2x Explain your answer

4 x 4 69 X non intogor or decimal rounded to four decimal pla

Suppose cos x and 90 x 180 a 5 pts Use identities to find the exact value of sin 2x b 5 pts Use identities to find the exact value of cos 2x c 5 pts In what quadrant is the angle 2x Explain your answer

4y 4y Question 20 of 20 Simplify by taking roots of the numerator and denominator Assume that all expressions under the radicals represent positive numbers 0 This test This quest FOLLO

Solve 9 x 2 83 XX Simplify your answer Type an integer or decimal rounded to four decimal places as needed

Solve the given equation log 2x 1 log x 3 1 X Type an integer or a decimal Round to two decimal places as needed Use a comma to separate answers as needed

Simplify 3 7 18 7 25 7 y1 4 3 4 y 1 4 3 7 18 18 7 25 7 1 4 3 4 y 1 4 Simplify your answer Use positive exponents only

Simplify 3a 2 302 2 0 3a Simplify your answer Use positive exponents only Use integers or fractions for any numbers in the expression

2 10 pts Solve the following triangle that is find A B and c Don t forget to show your work Round your answers to one decimal place B a 14 25 C b 7 PADLESEX LLEGE

Simplify by taking roots of the numerator and denominator Assume that all expressions under the radicals represent positive numbers 16y 10

Prove the given identity tan x sec xcsc x cot x Choose the correct proof below O A O C tan x sec xcsc x 1 sin x COS X sin x cos x cot x 2 1 sin x sin x cos x 2 COS X 1 cos x sin x tan x sec xcsc x sin x COS X sin x cos x 2 1 sin X sin x cos x 2 COS X cot x Question 7 of 20 www OB tan x sec xcsc x sin x COS X 2 1 sin x sin x cos x 2 COS x sin x cos x cot x OD tan x sec xcsc x 1 sin x cos x 1 sin x This te This qu sin x cos x 2 COS X sin x cos x cot x cos x sin

Verify the identity tanxesc x tanx cotx Choose the sequence of steps below that verifies the identity tanx csc x tanx tanx csc x 1 1 cotx tanx csc x tanx tanx csc x 1 O A OB cot x O C cotx tanx csc x tanx tan x 1 csc x 1 O D tanxesc x tanx c c x cotx 2x Question 12 of 20 cot x cotx cotx cotx cotx cotx

2x y 20x Type an exact answer using radicals as needed Question 8 of 20 Simplify Assume that no radicands were formed by raising negative quantities to even powers 2x y 20x

Verify the identity csct 1 cott O A Choose the sequence of steps below that verifies the identity OB O C O D cott csc1 1 csct 1 csct 1 cott cott csct 1 csct 1 cott cott csct 1 cott csct 1 cott csct 1 csc 1 1 CSC csct 1 cot csct 1 csct 1 csct 1 csct 1 csct 1 cott csct 1 csc 1 1 cott csct 1 csc 1 1 cott csct 1 csct 1 csct 1 csc t 1 cott csct 1 cott csct 1 cott cott csct 1 cot 1 cott cact 1 cot t cott csct 1 cot t cott csct 1 cott csct 1 cott csct 1 cott csct 1 cott csct 1

Prove the given identity sin x sec x cos x csc x sec xcsc X Choose the correct proof below OA sin xsec x cos xcsc x 1 sin x cOS X sin x cos x sin x cos x 1 sin x cos x sec xcsc x cos X sin x OC sin x sec x cos x csc x 1 cos x sin x cos x 1 sin x sin x cos x 2 sin x cos x 1 sec x csc x www OB sin x sec x cos xcsc x 1 sin x cos X sin x cos x 2 sin x cos x sin x cos x 1 sec x csc x OD sin x sec x cos x csc x 1 sin x cos X COS X 2 sin x cos x sin x cos X 1 sin x cos X sec x csc x

My company is currently buying an item for 54 We can make the same item internally for a labor cost of 17 a material cost of 11 and a tooling cost of 3 per part However I need to purchase a machine to do the job The machine will cost 450 000 and will require annual maintenance of 35 000 The machine will have a salvage value of 135 000 in seven years At 6 interest what is the break even point O a 1809 Ob 2207 OC 4327 O d 5904

Verify the identity sect 1 tant tant sect 1 Choose the sequence of steps below that verifies the identity O A B OC O D sect 1 sect 1 sect 1 tant tant sect 1 sect 1 sect 1 tant sect 1 tant sect 1 tant sect 1 tant sect 1 sect 1 sect 1 tant sect 1 sect 1 sec t 1 tant sect 1 sec t 1 tant sect 1 sec t 1 tant sect 1 tant sect 1 sect 1 sect 1 ec t 1 tant sect 1 tant sect 1 tan t tant sect 1 tan tant sect 1 tan t tant sect 1 tan t tant sect 1 tant sect 1 tant sect 1 tant sect 1 tan t sect 1

Verify the identity sin x sin x cot x csc x Choose the sequence of steps below that verifies the identity O A O B O C O D D sin x sin x cot x sinx 1 cot x sin x sinxcot x sinx 1 cot x sin x sin x cot2x 1 cot x csc x 1 csc x 1 CSC X 1 sinx sinx cot x sinx cot x 1 CSC X CSC X CSC X csc x csc x csc x csc x

Solve the given equation 0 9 2x Question 1 of 20 The solution s is are x Round to three decimal places as needed Use a comma to separate answers as needed

An engineer deposits 1500 per month into an account that pays interest at 6 per year compounded quarterly 4 times a year How much will be in the account at the end of 5years Assume no interperiod compounding 5 points O a 6 061 Ob 22 750 O c 88 978 Od 104 056

1 5 pts Solve the following trigonometric equation algebraically Give the exact solutions in the interval 0 27 Don t forget to show all of your work 2 cos x cosx 1 0

What is the present worth of the following at 6 interest Initial investment 125 000 Annual revenue 50 000 Annual expense 25 000 Salvage value after 8 years 22 000 a 44 048 Ob 294 048 c 44 048 Od 294 048

I am told that a house will cost 250 000 in 5 years because of a 6 rate of inflation What should the house cost toda O a 186 814 O b 197 455 O c 201 989 O d 222 765

A company had the following situation last year Gross sales 15 890 000 Expenses 11 700 000 They purchased a machine that cost 2 000 000 that they intend to depreciate over 5 years using MACRS what was their before tax income a 3 680 000 O b 3 790 000 O c 3 987 000 O d 4 190 000

A company had a before tax profit if 2 500 000 what was their after tax profit O a 850 000 Ob 1 250 000 O c 1 650 000 O d 2 000 000

Joe s shoe store had sales last year of 4 000 800 He had cost of goods sold of 1 800 700 He had nothing to depreciate what was his taxable income O a 1 800 700 O b 2 200 100 O c 4 000 800 O d 5 810 500

If the nominal rate is 9 annually compounded continuously what is the effective rate O a 9 O b 9 211 O c 9 417 O d 9 678

What is the break even in the following situation in terms of of pieces Fixed cost 4 000 000 Sales price 10 00 Variable cost 3 60 O a 575 000 Ob 625 000 O c 658 000 Od 695 000

Rubrics 01 marks for solving each question 01x 4 4 marks 5 1 P 1 12 18 6 iii f x 5x5 8 x 6x 6 marks ii f t iv i Question 6 Find x so that 06 Marks Rubrics 03 marks for solving each question 03 x 2 2014 8t t t f x 8x4 2x2 9 7x 9x5 3 4 log281 log 128 loga 4 loga x 4 7 2 t

Given that ZQ ZS and ZQRT STR prove that AQTR ASRT T Statement Q 25 ZQRT STR AUTREASRT S Given Reason Reflexive Property

Q13 Part B Solve the following polynomials and state if the operation is closed multiplication addition or subtraction a 3x2 2 2x 3 b 5x 2x 3 2x x 5 c 6x 5x 3x 2x 5x 7 4x 3x 2 Q14 Use the Graph Provided to determine What Type of Parallelogram TUNE is whe T 0 10 U 4 2 N 2 1 and E 6 7

The authors of a paper were interested in estimating the mean time that patients who broke a hip had to wait for surgery before and after the opening of a new hospital facility They reported that for a representative sample of 405 patients seen at this hospital before the new facility was opened the mean wait time for surgery was 31 1 hours and the standard deviation of wait times was 27 0 hours For a representative sample of 214 patients seen after the new facility was opened the mean wait time for surgery was 28 7 hours and the standard deviation of wait times was 16 2 hours USE SALT a Construct a 95 confidence interval for the mean wait time in hours of patients seen before the new facility was opened Enter your answer using interval notation Round your numerical values to three decimal places hr Interpret the previously found interval We are 95 confident that the true mean wait time of patients in this sample who were seen before the new facility was opened falls within this interval We can say that 95 of all patient wait times before the new facility was opened fall within this interval There is a 95 chance that the true mean wait time of patients in this sample who were seen before the new facility was opened falls within this interval We are 95 confident that the true mean wait time of patients seen before the new facility was opened falls within this interval There is a 95 chance that the true mean wait time of patients seen before the new facility was opened falls within this interval b Construct a 95 confidence interval for the mean wait time in hours of patients seen after the new facility was opened Enter your answer using interval notation Round your numerical values to three decimal places hr MY NOTES Interpret the previously found interval There is a 95 chance that the true mean wait time of patients in this sample who were seen after the new facility was opened falls within this interval We are 95 confident that the true mean wait time of patients in this sample who were seen after the new facility was opened falls within this interval We can say that 95 of all patient wait times after the new facility was opened fall within this interval We are 95 confident that the true mean wait time of patients seen after the new facility was opened falls within this interval There is a 95 chance that the true mean wait time of patients seen after the new facility was opened falls within this interval

The National Sleep Foundation surveyed representative samples of adults in six different countries to ask questions about sleeping habits Each person in a representative sample of 250 adults in each of these countries was asked how much sleep they get on a typical work night For the United States the sample mean was 391 minutes and for Mexico the sample mean was 426 minutes MY NOTES The report also gave data for representative samples of 250 adults in Canada and 250 adults in England The sample mean amount of sleep on a work night was 423 minutes for the Canada sample and 409 minutes for the England sample Suppose that the sample standard deviations were 34 minutes for the Canada sample and 43 minutes for the England sample USE SALT minutes PRACTICE ANOTHER a Construct a 95 confidence interval estimate of the difference in the mean amount of sleep in minutes on a work night for adults in Canada and adults in England Use Canada England Use technology to calculate your critical value Enter your answer using interval notation Round your numerical values to three decimal places Interpret the interval There is a 95 chance that the sample difference in the mean amount of sleep on a work night for adults studied in Canada and adults studied in England falls within this interval We are 95 confident that the true difference in the mean amount of sleep on a work night for adults in Canada and adults in England falls within this interval There is a 95 chance that the true difference in the mean amount of sleep on a work night for adults in Canada and adults in England falls directly in the middle of this interval We are 95 confident that the sample difference in the mean amount of sleep on a work night for the adults studied in Canada and adults studied in England falls within this interval There is a 95 chance that the sample difference in the mean amount of sleep on a work night for adults studied in Canada and adults studied in England falls directly in the middle of this interval 0 b Based on the confidence interval from part a would you conclude that there is evidence of a difference in the mean amount of sleep on a work night for the two countries Explain why or why not The confidence interval allows us contained in the confidence interval to conclude that there is evidence of a difference in the mean amount of sleep on a work night for the two countries because zero is not 0

Children with ADHD Do children diagnosed with attention deficit hyperactivity disorder ADHD have smaller brains than children without this condition This question was the topic of a research study Brain scans were completed for a representative sample of 152 children with ADHD and a representative sample of 139 children without ADHD Summary values for total cerebral volume in cubic milliliters are given in the following table USE SALT n ML3 152 Children without ADHD 139 1 104 7 Interpret the interval X S 1 058 5 116 3 111 7 MY NOTES Construct a 95 confidence interval estimate of the difference in mean brain volume in mL3 for children with and without ADHD Use With ADHD Without ADHD Use technology to calculate your critical value Enter your answer using interval notation Round your numerical values to two decimal places PRACTICE ANOTHER We are 95 confident that the true difference in mean brain volume for children with ADHD and the mean brain volume for children without ADHD falls within interval The bounds of the interval suggest the mean brain volume is higher for those without ADHD this

one is done for you Qu hora es 1 do the picture below and write what time it is in Spanish for each one The first 2 1 1152 13 2 Son las siete menos cuarto de la ma ana 3 45 Y

Head movement evaluations are important because disabled individuals may be able to operate communication aids using head motion A paper reported the accompanying data on neck rotation in degrees both in the clockwise direction CL and in the counterclockwise direction CO for 14 subjects For purposes of this exercise you can assume that the 14 subjects are representative of the population of adult Americans Subject 1 H CL CO 2 3 57 6 35 7 54 5 USE SALT 13 R 084 S 4 5 6 7 56 8 51 1 8 9 70 877 3 51 6 54 7 63 6 59 2 59 2 55 8 38 3 44 6 52 1 60 2 52 7 47 2 65 6 71 4 48 8 53 1 66 3 59 8 47 5 64 5 34 4 10 Find the test statistic Round your answer to two decimal places 11 12 13 14 Based on these data is it reasonable to conclude that mean neck rotation is greater in the clockwise direction than in the counterclockwise direction Carry out a hypothesis test using a significance level of a 0 01 Use for clockwise for counterclockwise and g M State the appropriate null and alternative hypotheses in degrees Enter for as needed Ho MY NOTES Use technology to find the P value Round your answer to four decimal places P value State the conclusion in the problem context We fail to reject Ho It is not reasonable to conclude that mean neck rotation is greater in the clockwise direction than in the counterclockwise direction We fall to reject Ho It is reasonable to conclude that mean neck rotation is greater in the clockwise direction than in the counterclockwise direction We reject Ho It is not reasonable to conclude that mean neck rotation is greater in the clockwise direction than in the counterclockwise direction rotation is greater in the clockwise direction than in the counterclockwise direction

A paper summarizes data from a study of food waste in the United States Data from a representative sample of adult Americans resulted in a mean food waste per day of 431 grams For purposes of this exercise assume that the sample size was 500 and that the sample standard deviation was 520 grams USE SALT Construct a 98 confidence interval for the mean food waste weight in grams for adult Americans Enter your answer using interval notation Round your answer to two decimal places Submit Answer MY NOTES grams Interpret the interval We are 98 confident that the mean food waste weight for adult Americans who were in the sample falls within this interval O There is a 98 chance that the true mean food waste weight for adult Americans falls within this interval There is a 98 chance that the mean food waste weight for adult Americans who were in the sample falls within this interval There is a 98 chance that the true mean food waste weight for adult Americans falls directly in the middle of this interval We are 98 confident that the true mean food waste weight for adult Americans falls within this interval

The amounts in millions of dollars grossed by movies in categories with PG PG 13 and R ratings we obtain the analysis of variance results from statistical software below Use a 0 05 significance level to test the claim that PG movies PG 13 movies and R movies have the same mean gross amount Amount Grosses By Movies Sum of df Squares Between Groups Within Groups Total 84801 867 255396 1 2 32 340198 0 34 Mean F Sig Squares 42400 933 5 313 010 7981 129 O We cannot come to any conclusions because the F distribution in this case is skewed to the right There is not sufficient evidence to warrant rejection of the claim that PG movies PG 13 movies and R movies have the same mean gross amount

Write the symbolic statement using words p We will go to the movies q It will rain on Saturday p q 1 We will not go to the movies if and only if it will not rain on Saturday 2 If we don t go to the movies then it will rain on Saturday 3 We will not go to the movies if and only if it will rain on Saturday 4 We will go to the movies if and only if it will not rain on Saturday

Use the formula to answer the question The price of your dream vacation home is 178 000 The cost of the home is financed with a 15 year fixed rate mortgage at 3 9 Use this information to find the amount of your monthly payment Round your answer to the nearest cent PMT 1 307 74 12 177 54 4 571 37 579 09 P 1 1 nxt

James and Susan wish to have 10 000 available for their wedding in 2 years How much money should they set aside now at 6 compounded monthly in order to reach their financial goal Use one of the formulas below to solve the problem Future Value A P 1 nxt Present Value P 5000 00 8871 86 9419 05 10 616 78 2 1 1 108

You want to have 120 000 in an account after 40 years for your retirement Your investment counselor suggests that you make regular monthly deposits into an annuity that pays 4 25 interest compounded monthly Find the amount that must be deposited monthly rounded to the nearest cent Periodic Deposit P 1 40 95 2 68 39 3 288 90 4 171 nxt 4 95 34