Complex numbers Questions and Answers

George secured an adjustable rate mortgage ARM loan to help finance the purchase of his home 5 years ago The amount of the loan was 400 000 for a term of 30 years with interest at the rate of 9 year compounded monthly Currently the interest rate for his ARM is 2 5 year compounded monthly and George s monthly payments are due to be reset What will be the new monthly payment Round your answer to the nearest cent

ow many different 9 letter words don t worry about whether they are in the dictionary can be formed using the letters in the word SEVENTEEN words

How many different license plates consist of 3 letters followed by 2 numbers te letters or digits are t license plates

3 Which graph below is a tree graph IN O X

A hoagie consists of a roll one type of meat one type of cheese and three different toppings If there are 5 kinds of rolls 5 kinds of meat 4 kinds of cheese and 9 toppings from which to choose how many different hoagies can be built hoagies

For the following questions use the graph of f x 5 x 61 10

Question 1 25 points Traveling Sales Person Graph TSP As a business person you need to visit each of the following cities once You need to start in Atlanta and end in Atlanta Use the Nearest Neighbor Algorithm to find one of the cheaper routes to visit each city and return home again 200 Trip Between Atlanta and Boston Atlanta and Chicago Atlanta and Denver Boston and Chicago Boston and Denver Chicago and Denver Cost 300 150 340 200 550 500 ATL BOS CHI DEN ATL CHICAGO 500 550 DENVER 5150 BOSTON 300 340 ATLANTA

Find 2 conecutive even integers such that the sum of the larger and twice the smaller is 62

15 For each number do the following Find all of the complex cube roots Write answers in polar form Graph each cube root in the complex plane b 64 c 1 3 d 2 3 2i a 8i

Find a formula for the volume of the box in terms of z V z 42 34z 72z Find the value for that will maximize the volume of the box Round your answer to three decimal places of cubic inches inches

Jeff Friedman was a section chief for an electric utility company After the numbers in one of his reports to the management of the utility didn t add up he was reassigned to the home economics department He interviewed 128 people in a suburban shopping center to discover some of their cooking habits He obtained the results shown to the right Should he be reassigned one more time Why or why not 60 use microwave ovens 64 use electric ranges 56 use gas ranges 23 use microwave ovens and electric ranges 25 use microwave ovens and gas ranges 5 use both gas and electric ranges 3 use all three 4 uses none of the three possible Select the correct choice below and if necessary fill in the answer box to complete your choice OA Yes he should be reassigned He says that he interviewed 128 people but the numbers in his report indicate that he actually interviewed error he should be reassigned people Since he mad OB No he should not be reassigned He says that he interviewed 128 people and the numbers in his report indicate that this is true Since he did not make an error he be reassigned

How many different 4 letter radio station call letters can be made if a the first letter must be G X P or L and no letter may be repeated b repeats are allowed but the first letter is G X P or L c the first letter is G X P or L there are no repeats and the last letter is R a If the first letter must be G X P or L and all the letters in the radio station call letters must be different then there are 4 letter radio station call letters b If the first letter must be G X P or L and letters can be repeated then there are radio station call letters c If the first letter must be G X P or L and the last letter must be R and all the letters in the radio station call letters must be different then there are 4 letter words

What is the Chromatic Number of a Planar Graph

To produce x units of a religious medal costs C x 13x 70 The revenue is R x 23x Both cost and revenue are in dollars a Find the break even quantity b Find the profit from 530 units c Find the number of units that must be produced for a profit of 100 a units is the break even quantity Type an integer b The profit for 530 units is C units make a profit of 100 Type an integer

is defined Through 3 8 and 12 7 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The slope is OB The slope is undefined Type an integer or a simplified fraction

Write a sample space for the following random experiment A month of the year is chosen for a fundraising event Choose the correct sample space below OA S January February Monday April May June July August Saturday October November December B S January February March April May June July August September October November December O C S Sunday Monday Tuesday Wednesday Thursday Friday Saturday OD S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 OE S January March April May June July August September October December

P 36 17 P 36 17 Use scientific notation Use the multiplication symbol in the math palette as needed Round to four decimal places as needed

Shade the Venn diagram for the set Cn B UA Use the graphing tool to shade the regions Click to enlarge graph A C B

Solve the problem using a system of equations in two variables Find two numbers whose sum is 19 and whose product is 70

2 f x log3 x 1 2 f x X Domain Range Asymptotes

3 Use change of base formula to evaluate the function log3 7 4 Evaluate 5 og 7343 g properties to expand these funcitons x y 1082 310ga x 1092 log2 5 6 log3 3 77 1086 1 log y c log6

x x is a whole number greater than 2 and less than 5 3 4 Choose the correct answer below OA The statement is false The whole numbers 3 and 4 are not the only members The set should include all numbers less than 5 and all numbers greater than 2 OB The statement is true The whole numbers 3 and 4 are the only members in the union of x x is a whole number greater than 2 and x x is a whole number less than OC The statement is false The list of whole numbers is incomplete There are other whole numbers between 2 and 5 OD The statement is true The whole numbers 3 and 4 are the only whole numbers greater than 2 and less than 5

Find an equation of the line in the form ax by c whose x intercept is 6 and y intercept is 3 where a b and c are integers with no factor common to all three and a 20 What is the slope of the line whose x intercept is 6 and y intercept is 3 OA The slope is Type an integer or a simplified fraction B The slope is undefined The equation of the line is Simplify your answer

Let A 6 6 4 7 Find 4A 4B 4A 4B and B 86 46

5 The diagonal of a rectangle is 25 in The width is 15 inches What in

T Insert C or to make the statement true 1 6 7 8 1 7 6 5 1 6 7 8 1 7 6 5

Find the values of the variables in the equation s 9 t 1 5 1 0 6 r Or

Let g x 6x 2 Find g 2 Type an integer or a fraction

Find an equation in slope intercept form for the line Through 4 4 and 1 6 The equation of the line is Simplify your answer Use integers or fractions for any numbers in the equation Type your answer in slope intercept form Do not factor

380 Determine if it is a square column or row matrix The matrix isx Choose the correct type of matrix O row matrix O square matrix Ocolumn matrix no special type

Write a linear cost function for the following situation Identify all variables used A ski resort charges a snowboard rental fee of 30 plus 5 50 per hour Identify all variables used Choose the correct answer below OA C t represents the cost for renting t snowboards OB C t represents the number of hours the snowboard was used after renting a snowboard for t dollars O C C t represents the cost of renting a snowboard for t hours OD C t represents the number of snowboards that can be rented for t dollars A linear cost function for the situation is C t 0 Use integers or decimals for any numbers in the expression

Find an equation for the given line in the form ax by c where a b and c are integers with no factor common to all three and a 0 Through 24 9 parallel to 3x 8y 11 The equation of the line in the form ax by c passing through 24 9 and parallel to 3x 8y 11 is Simplify your answer

The base of a triangle is 4 meters longer than the height of the triangle If the area of the triangle is 48 square meters what are the base and height of the triangle The height is The base is meters meters

The square of a negative number is 32 more than 4 times the negative number Find the number The number

Solve the equation p 4p 5 0 If there is a solution enter as an integer or reduced fraction If there are multiple solutions separate them using commas For no solutions click No solution No solution

Find the exact value of cos 90

Find the exact value of sin 330

A ladder leans against the side of a house The angle of elevation of the ladder is 66 when the bottom of the ladder is 7 ft from the side of the house How high is the top of the ladder from the ground Round your answer to the nearest tenth 66 7 ft X S

Factor the expression completely 4x 24x 20

Factor the expression completely 5y 5y 10y

Suppose 12 is raised to the second power like this 122 Which answers show the inverse operation There is more than one correct answer Select all that apply 12 2 O 121 12

Question 2 20 points Euler Circuits Paths Is the following statement True or False The graph has an EULER CIRCUIT TRUE FALSE B

Question 4 20 points Euler Circuits Paths Which of the following BEST describes an EULER PATH A path that goes through every VERTEX once and starts and ends at the same vertex A path that goes through every EDGE once and starts and ends at the same vertex A path that goes through every VERTEX once and starts and ends at different vertices A path that goes through every EDGE once and starts and ends at different vertices Question 5 20 points

Consider the following polynomial function f x x 6x 2x 18x 15 Step 3 of 4 Find the x intercept s at which f crosses the axis Express the intercept s as ordered pair s Answer 2 Points Select the number of x intercept s at which f crosses the axis Selecting an option will display any text boxes needed to complete your answer none 01 02 3 4

Hamilton Circuits Paths Which graph below has a Hamiltonian Circuit N B R 02 G to E W

Question 3 25 points Hamilton Circuits Paths Find a HAMILTONIAN PATH of the graph below A D B G E ABDFGHIJCE BAJIHGFECB JIHGFDBECJA H C J

he table gives a set of outcomes and their probabilities Let A be the event the outcome is divisor of 4 Let B be the event the outcome is prime Find P AIB Outcome 1 2 3 4 Probability 0 2 0 4 0 1 0 3

While visiting her grandparents Lucy found a box with a surprising number of spare keys Lucy figured that the color of the sticker on each key must indicate what the key was for When Lucy tested the keys she was surprised to find that this was not the case Front door of the house Back door of the house Car Blue sticker Green sticker 5 5 2 2 3 8 What is the probability that a randomly selected key opens the car given that the key is labeled with a blue sticker Simplify any fractions

For a statistics assignment Darrell looked at the relationship between hair color and eye color During lunch he recorded the eye color of each student he saw and whether the student had light or dark hair Blue eyes Brown eyes Other Light hair 2 4 10 Dark hair 6 8 14 What is the probability that a randomly selected student has brown eyes given that the student has dark hair Simplify any fractions

A toy store sells individual marbles in a variety of colors and sizes Big Small Red 3 6 Green 6 6 Purple 7 6 What is the probability that a randomly selected marble is purple given that the marble small Simplify any fractions