Algebra Questions

Click the following link to view nominal GDP data from FRED Then use that data to answer the following questions Real time data provided by Federal Reserve Economic Data FRED Federal Reserve Bank of Saint Louis For this exercise you will need to enter data from FRED for nominal gross domestic product GDP The following table gives the GDP deflator for the second quarter of 2023 and 2022 Using data from FRED enter the values for nominal GDP Series ID GDP for the two periods shown as 2023 04 01 and 2022 04 01 in FRED Enter your responses exactly as they appear in FRED Period 2023 Q2 GDP Deflator 131 52 Value bil

ind the domains of the given functions Remember that a domain is a set f x x b f x 21 x x c f x 1 flo flor 3y fl f a x 6 1 x x 1 1 x

Show that the map RCX given by exp ix is a group homomorphism Determine its image and kernel

Consider the following a Evaluate 1 b Evaluate f 1 c Solve for f x 3 d Solve for f x 3 7 TI X 7 6 5 4 3 2 1 2 3 4 5 6 7 y 4 6 5 T 3 2 book 2 LE 1 3 LE In 6 7

Solve 13 22 cosx 8 sin x 0 x 2 3

8 Use Laplace Transform to solve o t 2 cos t 7 7 dt e for o t Sho 0 all work Note Let s o t 20 points

f sin x 3 5 x 3 2 and sec y 13 12 3 3 2 y 2 3 find the exact value of cos x y

ou are in a submarine tracking a ship that is not changing direction or speed Its first position on the radar is 9 113 After one minute the ship is at 8 5 94 What is the equation of the position of the ship in rectangular coordinates In polar coordinates what will be its position after 4 min In polar coordinates what will be its position after 7 min

15 GID 2nd choice 3rd choice 4th choice B D C A vs B Votes where A is preferred to B Votes where B is preferred to A A vs C Votes where A is preferred to C Votes where C is preferred to A A vs D Votes where A is preferred to D Votes where D is preferred to A B vs C Votes where B is preferred to C Votes where C is preferred to B Find the winner of the election using the Pairwise Comparison method For each comparison enter the number of times each candidate was preferred to the other Tally the results Points for A Points for B Points for C Points for D A D B C B vs D Votes where B is preferred to D Votes where D is preferred to B Who is the winner OA OB OC C vs D Votes where C is preferred to D Votes where D is preferred to C C A D A B C B A D A B D

Find the centroid of the area of the composite shape shown below Find BOTH x and y values but input y 1 ft 6 ft 3 ft 2 f

and alternative hypothesis are as follows Ho p 0 02 Ha p 0 02 Suppose the manager inspects 120 products and finds that 3 are faulty What is the value of the z statistic Please round your standard error to five decimal places for calculations and round your answer to two decimal places O z 0 03 z 0 65 O z 0 39 O z 0 01 Question 6 A manufacturer must ensure that the rate f faulty products is less than 0 02 Suppose we do a hypothesis test with a significance level of 0 05 Symbolically the null and alternative hypothesis are as follows Ho p 0 02 H p 0 02 Suppose the manager inspects 120 products and finds that 3 are faulty A researcher gives a p value of 0 652 in her analysis Which of the following definitions is the correct definition of p value The population proportion The sample proportion O The probability of rejecting a true null hypothesis diste 3 pts of 100 IE the true faultymto in 0 02

Rewrite the fraction with 36 as the denominator

If the following represent a model for the height in feet of a tree after x years what is the growth factor f x 8 1 62 0 62 0 38 1 62 0 8 Question 4 25 points After purchasing a home for 160 000 the homeowner noticed the suggested value of her house was depreciating going down each year by 5 for at least the 6 years she lived there Year 1 Year 0 160 000 152 000 130 321 106 147 111 734 Year 2 144 400 If this trend continues how much will the house be worth in 8 years to the nearest dollar 05 700 Year 8

Which function below has the greatest average rate of change from x 0 to x 5 1 Asymptote y 0 Asymptote yad 6 Asymptate y Asymptote y 4 7

Given the function x 3 4x determine the average rate of change from x 1 to x 2 O 0 2

The function h x 4 is graphed at the right What is the range of the function h x shown Range h x 4 Range h x 4 Range h x 2 Range ALL REALS A Asymptote y 4 M M 24 4 w h x 4

Consider the function m x 2 4 Determine the y intercept for the function m x 0 4 2 0 3 0 0 3 Question 8 10 points Consider the function g x 3x 1 Determine the asymptote for the function g x Oy 0 y 1 Oy 2 y 2 x 3

The function f x x 6x 9x 3 is graphed at the right What is the complete set of interval s of increase for the function f x 00 3 u 1 00 3 1 1 3 O 00 00 N 4 N 3 f x x 6x2 9x 3

Sarah Pinski started creating the following pattern in steps aj represents 1 triangle tile a a2 27 40 9 2 represents 3 triangle tiles 1 594 323 4 782 969 a3 If Sarah continues this pattern how many triangle tiles will be needed for the 14th step a

Given that the sequence is geometric a10 78 732 i e the 10 term is 78 732 and the common ratio is 3 find a i e the 1st term 091 3 9 4 091 78 9 12 Question 5 20 points Consider the first six terms of this sequence 5 7 11 19 35 67 Which equation below explicitly defines the sequence 9 2n 3 9 3 2 9 3 2a 1 3n 2 a

Question 1 20 points Given that the sequence common difference is 5 find a24 i e the 24th term 2 119 24 124 a24 460 24 480 is arithmetic a 4 i e the first term is 4 and th

Find all distinct eigenvalues of A Then find the basic eigenvectors of A corresponding to each eigenvalue For each eigenvalue specify the number of basic eigenvectors corresponding to that eigenvalue then enter the eigenvalue followed by the basic eigenvectors corresponding hat eigenvalue 4 6 8 3 4 Number of distinct eigenvalues 1 Number of Vectors 1

5 4 1 x 3 x 3 3 x 4 x 4 xs 3 7 x 2 3 x 0 xz0 2 2 T 6 3x 3 x 0 0 x 4 x 4 1 3 2 1 3 5 1 3 2 1 2 AM Ky

3 Generate two additional pairs of values that belong in each proportional relationship Lemonade I cups Lemon Juice j cups Number of Days d 0 5 1 5 1 3 2 2 3 334 Number of Hours h 4 1 12 36 24 72 10 5 114 Writing Equations from Tables Use table 1 to write an equation to show how the number of hours h relates to the number of days d

If f x 67 1 what is the value of f 2 to the nearest ten thousandth if necessary

3 Homework 1 5 To write and graph linear piecewise functions Graph or write the following piecewise functions x 3 x 2 x 2 1 2x 2x 5 x 3 15 x 3 y x 3 x 0 x 0 2 1 Period

shown to the right Find the distance AB across the pond to measure the distance across a pond The distances AC and BC are The distance AB across the pond is about yd Type an integer or decimal rounded to the nearest tenth as needed 43 yd 21 yd

Find the length of a www Type an exact answer using radicals as needed a 201

Add Simplify by removing a factor of 1 when possible 5z 2 3z 2 3z 18 6 2 3z 12z 9 The sum is Type your answer in factored form if factorable

Suppose that X N 1 2 X N 4 3 and Cov X X 1 Let and X X X In a matrix form find 7 A Y 14 Y 2 1 Y AX a the mean of Y b the variance covariance matrix of Y Show your working c obtain the eigenvalues and eigenvectors for Cy the variance covarian matrix of Y Show your working d hence using your answer to c show your working illustrating the va lidity of Singular Value Decomposition SVD for Car

You should be able to answer this question after studying Unit 12 a Find all roots to the following equation in Cartesian form 28 3 i b Express 2 in Cartesian form to 4 decimal places Hint The rules for logarithm on page 273 of Book A still apply to complex numbers

Solve the following equation for x 5 3 22 MA LAUN SHARE CON 3 8 5

Solve the following equation for 2 16 Ox 1 x 2 A Ox 4 Ox 8 F

Given g x is a transformation of the graph f x determine which of the below correctly describe q x Asymptote y 0 34 3 2 1 1 9 C f x 4 34 g x 32 x 3 1 g x x 1 3 q x 32 x 3 1 O g x 1 2 x 1 3 Asymptote y 1 54 2 1 1 9 x

Given h x is a transformation of the graph f x 2 determine which of the below correctly describe h x H 3 2 1 2 Asymptote y 0 12343 h x 2 x h x 2 x h x 2 x Oh x 2x 1 Asymptote y 3 h x

Given t x is a transformation of the graph f x 2 determine which of the below correctly describe t x f x 2x 3 2 1 1 Asymptote y 0 2 3 4 t x 2 x 1 3 Ot x 2 x 1 3 t x 2 x 1 3 t x 2 x 1 3 t x 2 13 Asymptote y 3

Review If the linear function is of the form g x mx b and the following points are on the function 4 3 and 6 2 which function correctly describes g x g x 2x 5 8 x x 1 8 x x 5 g x 2x 5 Question 2 14 4 points Review Below is a table of a partial set of values of the linear function x h x 1 1 1 2 5 6 1 If the function is of the form h x mx b what is the value of the parameter b 0 E 4 0 2 8 10

54 3 Or P 5x OY 5x Ov 2 Ov y Review What is the equation of the following parabola in vertex form T n 3 5 CURGE XA MEDIANGLE HOSINGE SZENIE C JODE PUBE Pente

Review What is the equation of the following parabola in vertex for 4 3 2 1 O 6 ev 1 y 3x y 3x Or 2 O N 23

A boat moves in the direction of a lighthouse whose windows are located 50 m apart above sea level From a window in the lighthouse you can see at 02 45 p m the boat at an angle of 7 8 below the horizontal plane At 3 p m is the corresponding angle 42 4 How fast is the boat traveling Answer in km h

a Given the complex numbers z 1 5 3 i and w 0 5 0 75i find the moduli and principal arguments of zu and answer in 3 decimal places b Solve the equation 25 24 4 4 0 and plot the solutions in the complex plane w giving your

Review The graph of the linear function x is shown below If the function is of the form h x mx b what must be true of the parameter m m 0 O m 0 Om m2 0 Question 2 14 4 points Review If the parent function is f x mx b what is the value of the parameter b fo the line passing through the points 4 0 and 0 2 2 h x 4 2

Starting from the group N 1 12 construct a chain of distinct normal subgroups of at least 5 elements that is find 5 groups N N N3 N4 N5 in such a way that each is a normal subgroup of the next

graph to determine the domain and range of the function E A domain xx 1 x 1 range yly 0 B domain all real numbers range all real numbers OC domain xx 1 x 1 range all roal numbers OD domain all real numbers range yly 1 y 1

The circle shown above has center point 0 Chord AC is perpendicular to radius OD and intersects OD at point B Line segment OB has a length 8 and line segment BD has length 9 What is the length of chord AC A 2 145 B 30 C 24 2 D 34

Insert appropriate 13 2 1 71 3 2x6 symbol or into the box 3 2 1 2 3 1 X 22x32 2 4 6 2 4 2 2 1 314

3x 2x1 c x 6x 5x e 4x 1 b 7x 14x d x 2x 11 f NH 3x

Q2 Condense the following expression to a single complicated logarithm ONLY 1 2 5 log 3x 1 log 4y m

3 a Find each of the trig ratios Leave your answers as reduced fractions P 30 11 H n 24 40 Z 25 m nz Q b Sketch AABC with ZC as the right angle If cos B 15 then find sin B and tan B Leave your answers as a fraction 17 4 a Find the missing side or angle Leave your answers exact and approximate to the nearest whole number 1 X xx sin Q 17 m cos Q 15 m tan Q sin B tan B b The angle of elevation from a ship to the top of a 35 meter lighthouse at the water s edge measure 28 To the nearest meter how far is the ship from the shore Provide a sketch in your work

Ashley manages the team of drivers of a delivery company Each year the 75 drivers need to be allocated to five distribution centers The allocations are done according to each center s projected number of deliveries The numbers of deliveries are shown in the table below Use Webster s method to allocate the drivers to the distribution centers You may use the apportionment tool to help you To do this turn ON the apportionment tool enter a divisor and click on Compute You will then see the quota the lower quota the rounded quota to the nearest whole number and the upper quota for each distribution center You may also click on active cells to fill in the bottom row Apportionment Tool ON Divisor Distribution center Number of deliveries Quota Lower quota Rounded quota Upper quota Pigeon Crest 64 819 Laguna 42 040 Compute Del Mar 69 390 Blackwoods 93 870 C Rio Seco 122 131 Total 392 250 27 U DI E 2