Questions

TT 10 Put the following in order from least to greatest sec 3 cot T CSC tan T

1 If tan 0 2 4 find cot 0

4 Evaluate a CSC b cos c tan 315 5TT 3 e sec 37 f fi cot 7 3 d 5TT 6 5 sin

2 Explain what is meant by the statement sec A 3 in terms of the sides of a right triangle

Solve the equation 3a a l 4 2a 8a a 3 4a 3 The solution set is 010

5 Complete the table to indicate for which angles between 0 and 27 each of the six trig ratios are undefined sin 0 cos 0 tan 0 csc 0 sec cot 0 is undefined when 0 N A

5T 7 5t 7 Type your answer in radians Type an exact answer using as needed Use integers or fractions for any numbers in the e The reference angle for is

Write the following expression in terms of its cofunction K COS 3 The expression in terms of its cofunction is Type an exact answer in terms of Simplify your answer

For what value s of between 0 and 27 does sec 0 2 3

Complete the table with exact trigonometric function values Do not use a calculator 0 225 sin 0 2 2 sin 0 2 COS COS tan 0 1 tan 0 cot 0 1 cot 0 sec sec CSC 2 CSC 0 1 225 2 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

Solve by completing the square and applying the square root property Express the solution set in exact simplest form 4m 2 28m 3 0 The solution set is 0 16 3

olve the Inequality and write the solution set in Interval notation if possible Write numbers as simplified fractions or Integers 8 4x 19 5 The solution set is DO 0 0 Innl

3 In which quadrant s is csc 0 0

Solve by completing the square and applying the square root property Express the solution set in exact simplest form 2y y 2 6 3y

comes to playing basketball and tall people are more efficient because they can ch the basket easily allowing for more points per game as well as more rebounds and blocked shots If you watch National Basketball Association NBA games regularly you certainly notice that many players are quite tall We will explore the distribution of NBA player heights using a sample of players active in the 2019 2020 season by making a histogram of HEIGHT INCHES with bins stating at 68 inches and bin width of 2 inches We will then determine the z scores for players who are 71 inches 5 11 and b 84 inches 7 0 The dataset consists of the NBA player s name team and height measured in inches for players active in the 2019 2020 season Aaron Gordon Player Aaron Holiday Adam Mokoka Abdel Nader Admiral Schofield WAS Z Variable symmetric Numerical Variable Team Height Inches ORL Data value a x x S IND LUSE SALT OKC Import the dataset into SALT for analyzing Data value b x x CHI After you have clicked the tab for your selected topic and read the problem answer the questions below a Use SALT to summarize the data and fill in the following table rounding values to four decimal places as needed Data value a is N 80 529 73 77 77 77 b Create a histogram with Starting Point and Bin Class Width values asked for The distribution for this variable is mound shaped and is Mean 78 393 Our sample s minimum value is not Standard Deviation 3 4505 c Determine the relative standing for the two data values of interest using the z score formula appropriate for samples Round your answers to two decimal places standard deviations below Median 78 Find the data value with a z score of 3 rounded to two decimal places x 2 5 X Minimum Value standard deviations above to determine the number of standard deviations each data value is away from the mean Find the data value with a z score of 3 rounded to two decimal places X Z S X 69 the mean whereas data value b is the mean Remember to take the absolute value of the z scort maximum is histogram in SALT it can be observed that almost all A Maximum Value 89 d Most data points are within three standard deviations of the mean In other words most observations will have a score that is larger than 3 and less than 3 at least roughly further than 3 standard deviations below the mean Our sample s further than 3 standard deviations above the mean Upon further inspection of the observations would have a z score between 3 and

Find the exact value of csc CSC T IN Simplify your answer including any radicals Use integers or fractions for any numbers in

Calculate the derivative of the following function dy dx 13 y 5x 4

1 cot 0 sin 0 1 Which of the following shows the key steps in establishing the identity OA 1 cot20 sin 0 sin 0 cot 0 sin 0 sin 0 cos 0 1 OB sin 0 O C O D 1 cot20 sin 0 csc 0 sin 0 sin 20 1 cot 0 sin 0 cos 0 sec cos 0 0 1 ec 0 1 cot20 sin 0 tan 0 sin 0 sin 20 S 1 cot 0 sin 0 1 cos 20 sin 20 cos 0 1 2 sin 0 in 0 sin 0 1

Make an appropriate substitution and solve the equation 2 7 2 7 72 0 The solution set is 3

2 pints Manny a calendar year taxpayer uses the cash method of accounting for his sole proprietorship In late December he performed 42 000 of legal services for a client Manny typically requires his clients to pay his bills immediately upon receipt Assume Manny s marginal tax rate is 37 percent this year and next year and that he can earn an after tax rate of return of 7 percent on his investments Required a What is the after tax income if Manny sends his client the bill in December b What is the after tax income if Manny sends his client the bill in January Use Exhibit 3 1 Note Round your answer to the nearest whole dollar amount c Based on requirements a and b should Manny send his client the bill in December or January Complete this question by entering your answers in the tabs below Required A Required B Answer is complete but not entirely correct Required C What is the after tax income if Manny sends his client the bill in December

Reaction time is the amount of time it takes to respond to a stimulus and for automobile drivers it is an important factor in staying safe while on the road by avoiding rear end collisions Reaction times vary from driver to driver and tend to be longer than one might think A recent study determined that the time for an in traffic driver to react to a brake signal from standard brake lights can be modeled with a normal distribution having mean value 1 24 seconds and standard deviation of 0 45 seconds If we let X denote reaction time for automobile drivers use the appropriate Normal Distribution to determine each of the following 1 What is the probability that a driver has a reaction time less than 0 6 seconds 2 Approximately what proportion of drivers have a reaction time more than 2 5 seconds 3 Within what limits centered about the mean would you expect driver reaction times to lie with 95 probability What are the z scores for these limits 4 What is the reaction time for which only 1 of drivers have a shorter reaction time What is its z score 5 What is the reaction time for which only about 5 of drivers have a longer reaction time What is its z score 4 X 6 Approximately what proportion of drivers have a reaction time within three standard deviations of the mean After you have clicked the tab for your selected topic and read the problem answer the questions below a To model the random variable X defined by the selected scenario use the Normal Distribution with mean 1 24 and standard deviation 0 45 USE SALT b Determine each of the following values rounded to four decimal places 1 2 3 The smaller value is The larger value is 5 X Z score with a corresponding z score of with a corresponding z score of

Consider the position function s t 7 sin 3t that describes a block bouncing vertically on a spring Complete the following table with the appropriate average velocities Then make a conjecture about the value of the instantaneous velocity at t 2 Time Interval Average Velocity T 2 Time Interval Complete the following table 2 T 2 2 T T 2 2 0 1 0 1 Average Velocity Round to five decimal places as needed T T 2 2 EIN EN 2 2 T The value of the instantaneous velocity at t Round to the nearest integer as needed 2 is 0 01 0 01 T B EN 2 2 T 2 2 0 001 0 001 T 2 2 KIN T T 2 2 0 0001 0 0001

Solve 2 34 32 6 2y 22 0 2 3

Make an appropriate substitution and solve the equation 9x 3 3 9x 3 108 0 The solution set is 0 0

Find exact values or expressions for the six trigonometric functions of angle A Do not use a calculator sin A cos A tan A Tuno csc A sec A cot A gore or simplified fractions A 45 53 28

Let f x be the number in thousands of computers sold when the price is x hundred dollars per computer Interpret the statements f 18 60 and f 18 4 Then estimate the number of computers sold if the price is set at 1850 per computer What does f 18 60 imply OA 60 000 computers are sold when the price is set at 180 B When the price per computer is 6000 for every 100 price increase the sales increase by 18 000 computers OC When the price per computer is 1800 for every 100 price increase the sales increase by 60 000 computers O D 60 000 computers are sold when the price is set at 1800

Let f x 1 x a Make two tables one showing values of f for x 0 01 0 001 0 0001 and 0 00001 and one showing values of f for x 0 01 0 001 0 0001 and 0 00001 1 b Estimate the value of lim 1 x X 0 1 c What mathematical constant does lim 1 x appear to equal x 0 Round to five decimal places as needed X 0 01 0 001 0 0001 f x Complete the following table of values of f for negative x values Round to five decimal places as needed X 0 01 0 001 0 0001 f x b An estimate for the value of the limit is Round to five decimal places as needed 0 00001 OA 2 OD e 1 OG 2 1 0 00001 1 c What mathematical constant does lim 1 x appear to equal X 0 OB e OE e 1 OH 1 II OC 2 1 OF OL x 1

Problems 47 through 54 refer to the diagram below Y A B y TE A 31 find Angle FCE C F T D y X E 52 If Angle ACE is 51 find F

Suppose that a linear system has fewer equations than variables What can you determine about the solution set of the system

Tawana owns and operates a sole proprietorship and has a 37 percent marginal tax rate She provides her son Jonathon 17 000 a year for college expenses Jonathon works as a pizza delivery person every fall and has a marginal tax rate of 15 percent Required a What could Tawana do to reduce her family tax burden b How much pretax income does it currently take Tawana to generate the 17 000 after taxes given to Jonathon c If Jonathon worked for his mother s sole proprietorship what salary would she have to pay him to generate 17 000 after taxes ignoring any Social Security Medicare or self employment tax issues d How much money would the strategy in part c save Complete this question by entering your answers in the tabs below Required A Required B Answer is not complete Required C Required D How much money would the strategy in part c save

Write the expression in terms of i and simplify 7 35 11

in pounds lbs We will treat a subset of this dataset as a representative sample of realized values for our random variable The first five rows of the data look like this Weight in lbs 4 9 12 0 9 2 9 5 6 1 Import the dataset into SALT for analyzing After you have clicked the tab for your selected topic and read the problem answer the questions below a Create a histogram in SALT to determine if the distribution of our sample is mound shaped and symmetric with no outliers When a data s distribution is mound shaped and at least roughly symmetric with no outliers a normal distribution can be used to model the variable s behavior USE SALT Since the histogram for our sample is mound shaped and is O at least roughly symmetric with no outliers the normal distribution can be used to approximate the behavior for this random variable b Locate the sample mean and standard deviation for our variable Round your answers to four decimal places X X S c Draw the normal distribution with a mean of x and a standard deviation of s on SALT s Distribution Calculators page Round your answers to two decimal places The random variable value that is predicted to be one standard deviation above the mean is The random variable value that is predicted to be two standard deviations below the mean is The random variable that is predicted to have a z score of 3 00 is X x x x d Use the Probability and Z Score sections on the left panel and radio buttons on the right panel to answer the following questions Remember to convert the percentage to a proportion before entering the value into SALT Round your answers to four decimal places Approximately 2 8 of values for our random variable are predicted to be larger than what value Approximately 90 of values for our random variable are expected predicted to be centered around the mean with a lower value of X and an upper value of The Z scores for these two values are Z X and z e How well is the normal distribution modeling the random variable represented by our sample data Use SALT s data filters and Descriptive Statistics page to answer the following questions In part d you found the boundary values where the normal model predicts the middle 90 of data values are located Use the filters on the Dataset page to filter out observations that are outside of this range then return to the Descriptive Statistics page to locate the number of sample values within this region There are sample values within this region Remove the filter and return to the Descriptive Statistics page There are values in the entire sample Use these two counts to determine the actual proportion of sample values within this region Rounded to three decimal places the proportion of sample values within this middle region is How different are the actual and predicted proportions Subtract the predicted proportion from the actual proportion and take the absolute value of the result to determine how different they are Calculate the following quantity difference in proportions actual proportion predicted proportion Also in part d you found the boundary value that the normal model predicts 2 8 of values are larger than Enter this value into SALT s data filter and determine the number of sample values that meet this criteria There are sample values within this region Use this count and the size of the sample to determine the actual proportion of sample values within this region Rounded to three decimal places the proportion of sample values within this region is How different are the actual and predicted proportions Subtract the predicted proportion from the actual proportion and take the absolute value of the result to determine how different they are Calculate the following quantity difference in proportions actual proportion predicted proportion

Write the expression in terms of i and simplify 9 81 i 10

Write the expression in terms of i and simplify 28 i

in pounds lbs We will treat a subset of this dataset as a representative sample of realized values for our random variable The first five rows of the data look like this Weight in lbs 4 9 12 0 9 2 9 5 6 1 Import the dataset into SALT for analyzing After you have clicked the tab for your selected topic and read the problem answer the questions below a Create a histogram in SALT to determine if the distribution of our sample is mound shaped and symmetric with no outliers When a data s distribution is mound shaped and at least roughly symmetric with no outliers a normal distribution can be used to model the variable s behavior USE SALT Since the histogram for our sample is mound shaped and is O at least roughly symmetric with no outliers the normal distribution can be used to approximate the behavior for this random variable b Locate the sample mean and standard deviation for our variable Round your answers to four decimal places X X S c Draw the normal distribution with a mean of x and a standard deviation of s on SALT s Distribution Calculators page Round your answers to two decimal places The random variable value that is predicted to be one standard deviation above the mean is The random variable value that is predicted to be two standard deviations below the mean is The random variable that is predicted to have a z score of 3 00 is X x x x d Use the Probability and Z Score sections on the left panel and radio buttons on the right panel to answer the following questions Remember to convert the percentage to a proportion before entering the value into SALT Round your answers to four decimal places Approximately 2 8 of values for our random variable are predicted to be larger than what value Approximately 90 of values for our random variable are expected predicted to be centered around the mean with a lower value of X and an upper value of The Z scores for these two values are Z X and z e How well is the normal distribution modeling the random variable represented by our sample data Use SALT s data filters and Descriptive Statistics page to answer the following questions In part d you found the boundary values where the normal model predicts the middle 90 of data values are located Use the filters on the Dataset page to filter out observations that are outside of this range then return to the Descriptive Statistics page to locate the number of sample values within this region There are sample values within this region Remove the filter and return to the Descriptive Statistics page There are values in the entire sample Use these two counts to determine the actual proportion of sample values within this region Rounded to three decimal places the proportion of sample values within this middle region is How different are the actual and predicted proportions Subtract the predicted proportion from the actual proportion and take the absolute value of the result to determine how different they are Calculate the following quantity difference in proportions actual proportion predicted proportion Also in part d you found the boundary value that the normal model predicts 2 8 of values are larger than Enter this value into SALT s data filter and determine the number of sample values that meet this criteria There are sample values within this region Use this count and the size of the sample to determine the actual proportion of sample values within this region Rounded to three decimal places the proportion of sample values within this region is How different are the actual and predicted proportions Subtract the predicted proportion from the actual proportion and take the absolute value of the result to determine how different they are Calculate the following quantity difference in proportions actual proportion predicted proportion

Find the slope of the secant line in red 510 to br p 09 ind 10 0 4 3 1 The slope of the secant line is 00 Undefined

Write the expression in terms of i and simplify 225 0 i

1 ok int rint erences Hui is currently considering investing in municipal bonds that earn 8 40 percent interest or in taxable bonds issued by the Coca Cola Company that pay 11 20 percent Required a If Hui s tax rate is 22 percent which bond should he choose b Which bond should he choose if his tax rate is 32 percent c At what tax rate would he be indifferent between the bonds d What strategy is this decision based upon Complete this question by entering your answers in the tabs below Required A Required B Required C Required D If Hui s tax rate is 22 percent which bond should he choose

Use the graph of g in the figure to evaluate the function or analyze the limit a g 1 b lim g x c lim g x X 1 X 1 e g 3 f lim g x h g 4 k lim g x X 4 d lim g x X 1 g lim g x x 3 j lim g x x 4 X 3 i lim g x X 4 a Select the correct answer below and if necessary fill in the answer box within your choice A g 1 Type an integer or a decimal OB The value g 1 does not exist because g is not defined at x 1 b Select the correct answer below and if necessary fill in the answer box within your choice OA lim g x X 1 OB The limit does not exist because g is not defined for all x sufficiently close to 1 with x 1 c Select the correct answer below and if necessary fill in the answer box within your choice Type an integer or a decimal F OA lim g x Type an integer or a decimal X 1 OB The limit does not exist because g is not defined for all x sufficiently close to 1 with x 1 AY 3 0 yag

Assume lim f x 10 lim g x 8 and lim h x 6 Compute the following limit and state the limit laws used to justify the computations X 9 X 9 X 9 f x lim x 99 x h x f x x 99 x h x Simplify your answer State the limit law s used to justify the computation Select all that apply lim A Difference B Quotient C Root D Sum E Power F Product G Constant Multiple D

The graph off in the figure has vertical asymptotes at x 1 and x 5 Analyze the following limits a lim f x b lim f x x 1 X 1 e lim f x d lim f x x 5 X 5 Ay 10 c lim f x X 1 f lim f x X 5 Q Q a Select the correct choice and if necessary fill in the answer box to complete your choice OA lim f x x 1 OB The limit does not exist and is neither co nor co b Select the correct choice and if necessary fill in the answer box to complete your choice OA lim f x X 1 OB The limit does not exist and is neither oo nor co c Select the correct choice and if necessary fill in the answer box to complete your choice 4 A lim f x X 1 OB The limit does not exist and is neither oo nor co d Select the correct choice and if necessary fill in the answer box to complete your choice OA lim f x X 5 OB The limit does not exist and is neither co nor 00 e Select the correct choice and if necessary fill in the answer box to complete your choice QA lim f x

A sequence is an infinite ordered list of numbers that is often defined by a function For example the sequence 2 4 6 8 is specified by the function f n 2n where n 1 2 3 The limit of such a sequence is lim f n provided the limit exists All the nx limit laws for limits at infinity may be applied to limits of sequences Find the limit of the following sequence or state that the limit does not exist 1 4 1 16 5 12 16 17 2 19 4 7 which is defined by f n n 15 for n 1 2 3 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The limit of the sequence is B The limit does not exist and is neither o nor 00

rmine a value of the g x x 3x 3x if x 1 ax 4 if x 1 ant a for wh X 1 g x exists and state the value of the limi possible Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA The limit exists for a With that value for a lim g x X 1 OB There is no value of a for which lim g x exists X 1

1 cos 3x Hint What to do with that 1 cos 3x Maybe use conjugates Or maybe x if you rearrange one of the half angle formulas from Week 1 you get 2 sin 0 1 cos 20 could that help Actually either of these ideas will work so choose one d lim 20

Determine the value of the constant a for which the function f x is continuous at 4 x 6x 8 X 4 a if x 4 if x 4 The function f x is continuous at 4 when a Type an integer or a fraction O

Given the following functions find each f x x 3x 4 g x x 4 f g x f g x f g x

In problems 29 32 use the information given in the diagrams to find angle A 43 44 45 A 4 20 6 8 30 A 4 46 A 3 10 2 45 A 2

What is the missing angle in radians Verify the following identities 1 CSCX tan T 2 secx sin x tan x csc x 2 2 tan x CSC CSCX cos x cot x Bec x

Q4 1 1 Point We want to remove Land bubble up from H and L to K What color does H become red black double black negative red Save Answer Last saved on Jan 29 at 12 58 PM Q4 2 1 Point What color does K become red black double black negative red Save Answer Last saved on Jan 29 at 12 59 PM Q4 3 1 Point After the double black elimination shown at the beginning of thi question what is the parent of L J H G Q4 4 1 Point Now let s remove L Is the result a valid red black tree Yes No Save Answer

Given the following figure 31 y 47 If h 12 find x and y 49 If y 10 find x and h r 43 h 48 If x 20 find h and y 50 If y 15 find r