Complex numbers Questions and Answers

Given the graph of y f x below solve for f x 3 Enter multiple values as a list separated by comm s H 5 4 3 2

Solve X 2x 4 42 x8 07 07 O 0 77 O 2x 7 x 2

Given the following piecewise function evaluate f 3 f x Provide your answer below 3 8x 2 9x 5 x 3 x 3

Find the value h 7 where his defined below Provide your answer below h 7 h t 4t 4

The following table represents the result of a synthetic division 3 4 2 3 2 2 4 12 1 1 2 6 15 21 Use x as the variable Part 0 3 Part 1 of 3 a Identify the divisor The divisor is

Given y1 cos x 2 answer the following questions a Amplitude and period b Horizontal Phase shift value and direction if applica c Vertical shift value and direction if applicable d Graph this function over a one period interval

20 You are a talk show host on a morning radio talk show You want to find out what people s opinions are on immigration You asked people to call in and give their opinion Do you think that you would get a representative sample A Yes Everyone has the same chance to call in and give their opinion OB Yes People from all walks of life will call in and give their opinion O C No Only the people who really care strongly about immigration one way or the other will take the time to call in No People who listen to morning talk shows do not know anything about immigration D

Solve x 6x 5x 42 0 Show your work

18 Issara deposits 2000 into an account that pays 3 05 interest compounded continuously How much will she have in her account in 5 years O A 2324 18 B 6185 82 O C O D 9190 29 2329 48 47

16 Using the same scenario as the one from Questions 12 The University of Minnesota annually collects data from their graduate students to measure their experience in graduate school Which sampling method would provide a random sample that represents the graduate student population at the University of Minnesota O A B Survey every other student that exits the engineering building Survey all of the graduate students in the Research Methods in Education course C Survey all of the graduate students in the graduate student lounge in the middle of the day D Send an email to all of the graduate students at the University of Minnesota asking them to participate in a survey Follow up nonrespondents with a phone survey

Choose all of the following statements that apply to the graph o f x 3x x 5 x 2 A B D E F G The degree is 6 It has a negative orientation It has 6 distinct different x intercepts The range is all real numbers It passes through the origin 0 0 2 0 is one of the roots The y intercept is 0 500

3 Rynn wants to know if people in their town consume movies more often in theaters or at home They want to use a survey and create a representative sample of people to answer their research question Which of the following questions would be the least biased A Since movie theaters are full of germs do you watch movies more often at home OB Do you watch movies more often in a theater or at home C Do you agree that theaters are better places to watch movies or would you rather watch them at home D Because movies are expensive do you watch them more often in the theater or at home

Which of the following is equivalent to log4 6 log4 2x 6y O A log4 x y6 2log4x6log4y B 2log4x 6log4y

1 0 Note You can click on the graph to obtain a larger version in a new browser window The graphs of the function f given in blue and g given in red are plotted above Suppose that u x f x g x and v x f x g x Find each of the following u 1 1

point For each angle below determine the quadrant in which the terminal side of the angle is found and find the corresponding references le 11m is found in quadrant 4 1 0 2 0 is found in quadrant 3 19 3 0 10 is found in quadrant 3 40 2 is found in quadrant 2 and pv3 pi 4 and and pv6 and o 4 mark Enter t for quadrant 1 2 for quadrant II 3 for quadrant III and 4 for quadrant IV

Suppose a small company employs 23 people The owner of the company would like to select 4 employees to work on a special project How many such groups of size 4 are possible 8855 O212520 0 19

Find the future value and interest earned if 8704 56 is invested for 9 years at 5 compounded a semiannually and b continuously w a The future value when interest is compounded semiannually is approximately Type an integer or decimal rounded to the nearest hundredth as needed The interest earned is approximately Type an integer or decimal rounded to the nearest hundredth as needed b The future value when interest is compounded continuously is approximately Type an integer or decimal rounded to the nearest hundredth as needed The interest earned is approximately Type an integer or decimal rounded to the nearest hundredth as needed

5 Jaylen wants to save 54 000 for a down payment on a home How much will he need to invest in an ccount with 8 2 APR compounding daily in order to reach his goal in 5 years

Use the half angle identities to find tan and 0 x 2 NOTE Enter the exact fully simplified answer tan if sec x 65

Use the data below to determine the exponential regression for the population of snakes on a farm relative to the population of rats Round the values in the regression equation to two decimals Then estimate the number of rats wher snake population is 75 snakes Round your answer to the nearest whole number Snakes Rats 1 20 40 60 80 100 5 12 32 45 61

Question If the exponential model f x Provide your answer below 14 5 is written with the base e it will take the form Anek What is An and what is k

Factor out the greatest comm 3 45y 75y

Factor out the greatest common factor Then determine if the polynomial is a perfect square trinomial If it is factor it 2p 44p 8 The polynomial is not a perfect square trinomial O The polynomial is a perfect square trinomial The complete factorization of 2p 4p 8 is 9 X

Rewrite the exponential model f x 6 13 using base e given that b 0 and b eln b Provide your answer below

QUESTION 15 1 POINT Sung Lee invests 3 000 at age 18 He hopes the investment will be worth 9 000 when he turns 30 If the interest compounds continuously approximately what rate of growth will he need to achieve his goal Round to the nearest tenth of a percent Provide your answer below

For the following bonds find a the cost of the bond b annual interest and c the annual yield 1 Source GC Inc JFF LLC GIT ECE CO Face Value of Bond 10 000 1 000 10 000 5 000 Quoted Price Cost of Interest Bond Rate 70 25 a 96 00 a a a 104 00 104 375 3 00 2 50 5 25 4 75 Annual Annual Yield Interest b b b b C C C C 2 Barry Severes purchased a 25 000 Baltic Ridge School District bond at a quoted price of 105 7 The bond pays annual interest at a rate of 3 7 3 Lloyd Zion purchased an ITT 80 000 corporate bond at a quoted price of 96 622 The bond pays annual int

Solve 37 3 5 for x Provide your answer below

What value of a makes the equation 2 6 PAARNE 64 9 true

A pride of lions is growing at a rate of 0 5 per year compounded continuously If the growth rate continues how many years will it take for the size of the pride to reach 275 of its current size Round your answer up to the nearest whole number and do not include units Provide your answer belour

Find the angle 0 in degrees between u and v u 3 1 6 v 3 9 4 0 Ex 1 234

The probability of an event is a negative number

Solve the system by using any met x 11 2 y 2 121 x y 2

Pa gutter is to be made of aluminum sheets that are 28 inches wide by tuming up the edges 90 See the ustration a What depth will provide maximum cross sectional area and hence allow the most water to flow b What depths will allow at least 66 square inches of water to flow a The depth that will provide the maximum cross sectional area is inches b The depths between in and in wil allow at least 66 square inches of water to flow

In the picture below the distance between gridlines is 2 inches Image Description

14 13 Theorem The following are three equivalent conditions for a subgroup H of a group G to be a normal subgroup of G 1 2 ghg g Hg H for all g G C H for all ge G and he H

Change the function y 3 0 5 to a function with base e Select the correct answer below Oy 0 5e ln 3 x O y 3e ln 0 5 Oy 3e0 52 Oy 0 5e

Consider the following h x a State the domain of the function O all real numbers x except x 12 O all real numbers x except x 2 O all real numbers x except x 2 O all real numbers x all real numbers x except x 14 b Identify all intercepts If an answer does not exist enter DNE 0 0 x intercept 4 y intercept asymptotes hole x y c Find any vertical or horizontal asymptotes or holes Enter the asymptotes as a comma separated list of equations If an x 2 2 y 1 x y 0 0 x y DNE d Plot additional solution points as needed to sketch the graph of the rational function y 10

Find the solution of the following polynomial inequality Express your answer in interval notation x x 8 x5 0

Nicholas hopes to earn 1300 in interest in 4 years time from 13 000 that he has available to invest To decide if it s feasible to do this by investing in an account that compounds quarterly he needs to determine the annual interest rate such an account would have to offer for him to meet his goal What would the annual rate of interest have to be Round to two decimal places Interest formulas

The displacement of a mass suspended by a spring is modeled by the function h t 12 sin 97t Where h t is measured in centimeters and t is measured in seconds Find the Amplitude Period Frequency cm seconds Hz

Use the graph to the right to factor f x Assume that all zeros are integers f x 2x 2x Determine the leading coefficient of f x The leading coefficient of f x is 10

If 3 000 00 is deposited into a savings account with continuous compounding wi an annual interest rate of 4 how long will it take for this amount to reach 12 000 00 Round to the nearest tenth

Given that f x 8x 1 and g x 6x 8 determine each of the following Make sure to fully simplify your answer a fog x b go f x c fof x d go g x

Make box and whisker plots for the given data 1 17 29 32 9 30 14 8 39 11 32 23 Minimum Q Q Maximum Q

Find a b a b 4a a 6 7 a b D 5b 4a 5b and e b 3 0 0000

x 3 60 12 30 45 x x 5 12 60 3x 5 3x x x 6 x 3 3x 4 3x 2x 8 1 already reduced to lowest terms 1 x 2 2 3 x 2 4 x 2 5 1 x 2 6 5 7 1 7

Consider the DE 1 yexy dx 2y xe y dy 0 then The DE is Fx Hence F x y and g y therfore the general solution of the DE is

consider the vector space of real polynomial say V P t Determine whether or not W is a subspace of V where a W consists of all polynomials with integral coefficients b w consists of all polynomials with degree 5 and the zero polynomial

Find the solution to 38 3 5 Provide your answer below X

Give an exact answer Do not include in your answer Sorry that s incorrect Try again 1 I e e 2