Sequences & Series Questions and Answers

10 For each of the following graphs determine the zeros and state each zero s multiplicity 4 Marks

All else being equal if you cut the sample size in half how does this affect the margin of error when using the sample t make a statistical inference about the mean of the normally distributed population from which it was drawn ME Z S 17 O The margin of error is multiplied by 0 5 O The margin of error is multiplied by 2 The margin of error is multiplied by 0 5 O The margin of error is multiplied by 2

2 Show that the vector x 7 7 7 7 R5 is in the subspace spanned by 2 1 2 by expressing x as a linear combination of v and v 6 57 AM

c Table of Data Consider the function represented by the following data table Temp 125 120 115 Or consider the associated scatter plot graph 110 105 100 t Date in June 1990 F t Daily High Temp F 109 113 114 113 113 113 120 122 118 118 Rule 20 Input values Output values 19 20 21 22 23 24 25 26 27 28 22 24 26 28 What questions might this data help you to answer bed at Rockhurst University Mathematics Department 2009 day in June

e function f x 1 3x 36x 261x 553 below models the number of discharges from the military f x of active duty gay service members under the do k don t tell policy x years after 1994 Complete parts a and b Number of Discharges 1400 900 400 0 4 f 4 0 f 0 4 Years after 1994 10 Q a Find the slope of the secant line from x 0 to X 4 The slope of the secant line is Round to the nearest whole number as needed

Let A 3100 000 1 2 4 8 0 3 5 003 a 3 marks The eigenvalues of A are 2 and X 3 Find a basis for the eigenspace E of A associated to the eigenvalue X 2 and a basis of the eigenspace E of A associated to the eigenvalue A 3 A basis for the eigenspace Eis BE 481 A basis for the eigenspace Es is b 2 marks State the algebraic multiplicity and the geometric multiplicity of each eigenvalue of A Algebraic multiplicity of A 2 alg 2 Geometric multiplicity of A 2 geo 2 Algebraic multiplicity of A 3 alg 3 Geometric multiplicity of 3 geo 3 Hint compute the characteristic polynomial CA A of A

Find the domain of the function 1 8 X 10 X 8 f x What is the domain of f OA 0 8 U 8 10 U 10 00 OB 0 10 U 10 00 OC 0 0 U 0 00 OD 00 00

2 8 8 8 1 4 Determine whether or not the vectors v linearly independent 1 2 7 in R are

4 A 3 LAJ 2 1 1 2 h 8 T 4 37 8 2 37 2 Above is a graph of the sinusoidal function State the function s formula in terms of x Be sure to PREVIEW your answer before submitting

Useful formulas and identities sin 0 cos2 0 1 sin a B sina cos sin cos a cos a B cosa cos sin a sin f sin 20 2 sin cos cos 20 cos 0 sin 0

Employee Anja Raz Natalie Mic Paul What is the variance for the data Variance 5 O 118 35 O132 32 14 006 X X Weekly Salary 245 300 325 465 100 2 X27 2 7 1 Xn X 2

Select one 9 Which of the following is the graph of a function of x 4 X th

Use the graph to find the following Q Ly a the domain of f b the range of f c the x intercepts d the y intercept e intervals on which f is increasing f intervals on which f is decreasing g intervals on which f is constant h the number at which f has a relative minimum i the relative minimum of f j f 5 k The values of x for which f x 3 1 Is f even odd or neither a What is the domain of f 0 00 Type your answer in interval notation b What is the range of f 4 00 Type your answer in interval notation c What are the zeros of the function The left zero of the function is 3 and the right zero is 7 d What is the y intercept The y intercept of the function is 21 e Over what interval is f increasing 5 00 Type your answer in interval notation f Over what interval is f decreasing Type your answer in interval notation

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nd the orthogonal projection of v ojv v 13 B 9 onto the subspace V of R spanned by 20 4 and 0

When three sets are related there are many more possible relationships among the sets Some of the possibilities are shown below 00 b 1 B Animals Vegetables Minerals Puppies Dogs Animals g Match each list of items below with one of the diagrams above The sizes of the circles do not represent the relative sizes of the sets Flies Ladybugs Insects Soccer Players Athletes Soccer Ball O d O h 000

Determine the shaded area The shaded area is 13 yo 14 yd 20 yd 15 yd G

110 7 X Find the measure of side X

Required information Appendix 10B The Baby Clothing Company makes and sells a single product called a New bodysuit and employs a standard costing system The following standards have been established for one unit of New bodysuit Direct Materials Direct Labour There were no inventories of any kind on August 1 During August the following events occurred Purchased 14 000 board metres at the total cost of 22 000 Used 10 300 board metres to produce 2 100 New bodysuits Used 1 400 hours of direct labour time at a total cost of 18 060 Standard Quantity or Standard Cost per New Hours bodysuit 8 00 5 board metre 0 7 hours 8 40 Appendix 10B To record the purchase of direct materials the general ledger would include what entry to the Materials Price Variance account Multiple Choice 1 500 credit

Multiply 81 x X Select the correct choice below and fill in any answer boxes within your choice O A x 9x X X 90 OB x 9x X x x 90 Simplify your answer Use a comma to separate answers as needed x 81 x 81 x 9x x x 90 no numbers must be excluded 1

We have seen before that money deposited into an account with continuous interest follows the A Pert formula However this required strict conditions that the money cannot be withdrawn or added to throughout the term of the investment A more complicated model that allows for deposits withdraws is A t P Kert K where K is the constant amount deposited x o or withdrawn xo each year Problem You just retired to find your retirement savings account has reached 1 000 000 The savings account has a rate of 3 7 compounded continuously Your lifestyle requires you to live off 45 000 each year to be comfortable A How long will your retirement savings account last note your K value should be negative because it is withdrawn from the principal balance Number years ground to the nearest whole number B If at retirement age you are 65 years old how old will you be when the money runs out Number years old round to the nearest dollar

20 10 40 30 20 10 10 20 b The above graph representing the exponential decay curve for the radioisotope was sketched using mathematical software If we wished to find the slope of the graph at time t 10 hours what mathematical process would we use

Find the quotient using long division 12a 6a 2a 9 4a 2

while A simple random sample of size n is drawn from a normally distributed population and the mean of the sample is X the standard deviation is s What is the 90 confidence interval for the population mean Use the table below to help you answer the question Confidence Level Ox OX 0 90 s n OX z score 1 645 s n X 1 96 s n 2 58 s 90 1 645 95 1 96 99 2 58

Precalculus 1 y f x 2 y f x 4 3 y 2f x 4 y f x 4 5 y f x 3 6 y f x 1 7 y f 2x Use the graph off to sketch each graph 6 4 10 5 4 2 y 10 5 6 4 5 4 2 10

for an minimize subject to x1 x x 2x x x 1 x x 0

Question 37 Given that c 3 and a 28 find the values of a and b to the nearest tenths b a a C Note The picture isn t drawn to scale

Simplify Write the answer using positive exponents OB For any numbers a and any integers m and n an Use b X A 5 X c For any numbers a and b and any integer n b OD For any numbers a and b and any integer n ab a b 4 a bn 5 4 5 to start simplifying the expression y4 5 4 y Simplify the exponents x 4 C 5 5 am n an bn b 0

Each student listed in the table has taken 3 math tests Find the score each student needs on the next test in order to have an 80 average ame Bill Phil Will Test 1 78 68 72 91 Test 2 78 79 82 64 Test 3 78 74 82 76

Use the graph of f to determine each of the following a the domain of f b the range of f c the zero s of f d f 4 5 e the intervals on which f is increasing f the intervals on which f is decreasing g the values for which f x 0 h any relative maxima or minima i the value s of x for which f x 3 j Is f 1 positive or negative a The domain of f is 1 Type your answer in interval notation b The range of f is 3 Type your answer in interval notation c The zero s of f are 5 and 1 Ay OA d f 4 5 1 e The interval on which f is increasing is 2 Type your answer in interval notation f The interval on which f is decreasing is 2 1 Type your answer in interval notation g Which interval or union of intervals represents the values for which f x 0 Select the correct choice below and fill in the answer boxes to complete your JU B D JU JU F

I 329 B XX85 0 C D Angle ADB 32 also equals Angle ACB And Angle ACB also equals Angle XCB So in triangle BXC we know Angle BXC 85 and Angle XCB What is the measurement for Angle CRX

1 Find all f such that f xy f x y xy for all x and y

What are the coordinates of the midpoint of the line segment whose end points are 2 6 and 10 4

Use the graph shown to the right to find each of the following a the x intercept s and b the zero s of the function 6 2 6 41 2 2 4 6 2 X O a The x intercept s is are Type an ordered pair Use a comma to separate answers as ne

Write the quotient in its simplest form 8 32 8 Select an answer and submit For keyboard navigation use the up down arrow keys to select an answer 23 b P 1 4 2 2 2 1 4 2 2 2 5

When a college started an aviation program the administration agreed to predict enrollments using a straight line method If the enrollment during the first year was 13 and the enrollmen during the fifth year was 27 find the rate of growth per year the slope of the line See the illustration Enrollment 27 13 FLY WITH US The enrollment is growing by ENROLL IN THE AVIATION PROGRAM Years students per year

Given A 2 2 1 44 and 4 4 2 What is A

19 18 17 16 15 14 13 12 11 10 8 7 54 3 n FE 10 q The curve above is the graph of a sinusoidal function It goes through the points 9 0 and 5 0 Find a sinusoidal function that matches the given graph If needed you can enter T 3 1416 as pi in your answer otherwise use at least 3 decimal digits

blank The graph of x c is a n The graph of x c is a n line with x intercept line with x intercept

Cost of Gasoline In September 2016 the cost of gasoline in Berlin was around 1 23 euros per liter What would the equivalent cost be in U S dollars per gallon 1 U S dollar 1 gallon 0 896 euros 3 785 liters

Use summation notation to write the series 1 2048 1 12 1 4 118 The summation notation for the series is Simplify your answer

Miguel wrote the predicted and residual values for a data set using the line of best fit y 1 82x 4 3 He left out two of the values X 1 2 3 4 Given 2 3 0 9 1 1 3 1 Predicted 2 48 0 66 a 2 98 Residual 0 18 0 24 0 06 b Which represents the missing values of a and b O a 1 16 and b 0 12 O a 1 16 and b 0 12 O a 0 5 and b 6 08 O a 0 5 and b 6 08

Analyze the graph of the given function a4a 12 3a 12 For this function which of the following do NOT exist Hole Maximum or Minimum Value Intervals of decrease

Select all properties that are true of the given rational function graph five 0 2 2 As x f x 2 The domain of the function is x x 2 0 H H O

Which type of function best models the data in the table below X 2 4 6 8 00 10 O inverse variation O linear O logarithmic O quadratic y 4 2 1 3 1 45 5

3 5 Naturalists find that populations of some kinds of predatory animals vary periodically with time Assume that the population of foxes in a certain forest varies sinusoidaly with time A minimum number of 400 foxes appeared at t 2 years The next maximum 600 foxes occurred at t 3 75 years The function to model this situation is f t 100 cos 1 1000 900 800 700 600 500 400 300 200 100 100 Round answers to the hundredths 2 What to a dad 4 5 After 3 75 years when is the population 550 for the first time answer to nearest tenth Lor 1 75 6 After 3 75 years When is the population 550 for the second time answer to nearest tenth t 3 75 500 is below 7 8 9 10 11 years round years round 12

shows the number of student members in school clubs School Clubs Number of Students 80 70 60 50 40 30 20 10 0 Art Chess Astronomy Robotics French Type of Club Which club has twice as many student members as the robotics club A French club

Provide your answer below Move Parabola 10 9 8 7 6 5 4 3 2 TU 9 8 7 6 5 4 3 2 1 1 Q N 1 2 Undo 3 4 5 Redo x Reset 6 7 8 00 9 1

Which value for the two classes is the same Class B Class A OA IQR OB Q2 OC Q1 D 03

Find the present value of 80 000 due in 2 years at the given rate of interest Use a 365 day year Round your answer to the nearest cent 3 year compounded monthly A