Complex numbers Questions and Answers

Find the mean median and mode of the data set 15 16 21 23 25 25 25 39 OA mean 23 6 median 25 mode 24 OB mean 24 6 median 24 mode 25 23 6 mode 25 OD mean 23 6 median 24 mode 25 OC mean 24 median

Two commonly used measures of variance are OA range and standard deviation OB mode and median OC range and mean OD standard deviation and median

Write an equation that illustrates each of the following a The product of two irrational numbers is irrational b The product of two irrational numbers is rational

What is f g x f x x 8x g x x 3x 2 Write your answer as a polynomial or a rational function in simplest form

Find the values of all the trigonometric functions from the given information csc t 3 2 3 2 t 2

Find sin tand cost for the given value of t t 55 4

A community theater uses the function p d 4d 200d 100 to model the profit in dollars expected in a weekend when the tickets to a comedy show are priced at d dollars each 1 Write and solve an equation to find out the prices at which the theater would earn 1 500 in profit from the comedy show each weekend Show your reasoning 2 At what price would the theater make the maximum profit and what is that maximum profit Show your reasoning 7

Select all expressions that are squares of line expressions 2 0x x 6x 36 2 2 7x 4 Select all that apply 2d 8 2d 8 p 6p 9 2 x 36 9x 36

5 7 A 3 4 T 9 5 H 1 10 ISOSCELES TRAPEZOID A 5 1 B 0 3 C 2 5 and D 3 3

Find the zeros of the equation z5 32 0 and draw the zeros in the complex plane

F Find the equation of the image of the line y x 5 when the reflection line is the x axis

A construction crew is lengthening a road that originally measured 41 miles The crew is adding one mile to the road each day The length L in miles after days of construction is given by the following function L d 41 d What is the length of the road after 27 days miles

Carlos received a 15 00 gift card for a photo center He used it to buy prints that cost 9 cents each The remaining balance B in dollars on the card after buying x prints is given by the following function B x 15 00 0 09 x What is the remaining balance on the card if Carlos bought 15 prints dollars X

Keiko has two coupons for a chair Coupon A 15 off of a 45 chair Coupon B 4 rebate on a 45 chair Choose the coupon that gives the lower price Then fill in the blank with the correct value Coupon A gives the lower price The price with coupon A is less than the price with coupon B Coupon B gives the lower price The price with coupon B is less than the price with coupon A

Evaluate log 1 1000 Reminder When a logarithm is written log without an explicit base it refers to the common logarithm log10 log 1 1000 A log A Olog No solution

Write this number as a whole number or a decimal 8 7 x 10 6

Divide the following and write answer in scientific notation Use an asterisk for the multiplication symbol 3 84 x 108 1 6 1048

Find the vertex of the following quadratic equations without using the graphing calculators 1 y 4 x 2 3 2 y x 5 2 3 f x x 5

7 Simplify the expression 2 2 3 3 4 A 3 1 1 0 4 7 1 10 B

i 3i Select one O a i O b 4i 3 O c 4i 3 O d 7i

valt 6 Medhi invested 10 000 in treasury bills for 90 days 139 32 in interest What rate of interest did the bills earn 7 Sam invested 800 at 6 5 per year and received 25 64 interest on maturity How many days did Sam hold his investment 8 Suppose you are working with simple interest If you double the length of time of an investment do you double the interest earned Justify your answer with a full explanation TL 162 12 41 s sp cat 4pmaddy L 4659 4paddy9 COSS S 10757

Which equation is represented by the graph below A y 2 cos 3x By 2 sin 3x 2T 3 2TT y 2 cos Dy 2 sin 3 x x 2 1 2 17 0 27

ne sine ratio is the same as lect one O a O b O c O d hypotenuse over opposite opposite over adjacent adjacent over hypotenuse opposite over hypotenuse

X is the equation of a n Select one O a parabola O b ellipse O c line O d hyperbola

There are 1 368 grams of CS What is the mass of the carbon if the atomic weight of C is 12 and the atomic weight of S is 32 Select one O a 513 g O b 256 5 g O c 216 g O d 373 g

Given A 2X 3Y Z 11 and B 3X Y 2Z 4 what would ensure that adding the two equations will eliminate z Select one O a Multiply equation B by 3 O b Multiply equation A by 1 and equation B by 2 O c Multiply both equations by 2 O d Multiply equation A by 2

in terms of one of the variables Leave all fractional answers in fraction form Answer 2023 Hawkes Learning Selecting an option will display any text boxes needed to complete your answer O Only One Solution O Inconsistent System 13 3 x 3y 13 3x 9y 39 lations If the system is dependent express the solutio MAY 14 x m BOE BEE Dependent System M x ER Ke Keyboard She Submit Answ tv S JOVE

If there is a 10 chance that the moon will be in the Seventh House and Jupiter will also align with Mars and a 25 chance that Jupiter will align with Mars then what is the probability that the Moon is the Seventh House given that Jupiter aligns with Mars ere take M The Moon is in the Seventh House J Jupiter aligns with Mars P M J P MJ P J 10 4 25 There is a 40 chance that you will study for the exam and earn the highest grade in the class and a 50 chance that you will earn the highest grade in the class The probability that you will study for the exam given that you earn the highest grade in the class is Check Clear Free Hint Cast two dice one red and one green and add the numbers facing up Let E The green die shows 6 F The sum is 9 Q P E F Check Clear Help

Here is a table showing fictitious trial results of a new acne medication Condition Improved No Change Condition Worse Total Used Medication 1100 300 300 1700 This kind of table is sometimes referred to in statistics as a cross tabulation or contingency table Calculate the following Q The probability that a participant s condition got worse regardless of treatment is Check Clear Help Note You can enter all answers as fractions QIf we knew beforehand that the participant used the medication then the probability that their condition got worse is Used Placebo 500 100 700 1300 Total 1600 400 1000 3000

When treated with antibiotic 97 of all the dolphins are cured of an ear infection if a group of 40 dolphins are treated with antibiotics how many cured dolphins should be expected

Let r be given by 1 5 llowing graph 1 0 5 Q 5 0 5 0 5 Show Transcribed Text 1 5 2 what s the f 1 where are the turning point of f x

You were asked to perform the following division and write the quotient in trigonometric form 3i 6 5i Finally we use the formula for the quotient of complex numbers in trigonometric form 3 cos 4 71 isin 4 71 61 cos 0 69 isin 0 69 3 61 cos 4 71 0 69 isin 4 71 0 69 Simplify this expression to obtain the trigonometric form of the quotient Write the magnitude in exact form Write the argument in radians and round it to two de places if necessary

Evaluate the function at the given value of the independent variable Simplify the results If an answer is undefined enter UNDEFINED 3 P x x f x f 12 x 12 33 3 x 12 x 3 x

Solve the following 5 problems 1 What is the sum of the first four terms of the sequence a 5 an an 1 3

2 2i find 25 Write an exact answer in polar form wit Given the complex number z 1 0 2TT

Debra is adding water to a swimming pool at a constant rate The table below shows the amount of water in the pool after different amount me Time minutes 12 16 8 Water gallons 153 197 241 nswer the following questions 20 285 a How much water was already in the pool when Debra started adding water gallons per minute gallons b Choose the statement that best describes how the time and the amount of water in the pool are related Then give the value requested As time increases the amount of water in the pool decreases At what rate is the amount of water in the pool decreasing O As time increases the amount of water in the pool increases At what rate is the amount of water in the pool increasing 8 08 G

erence and area of the adjacent circle Use the key for The circumference of the circle is approximately Type an integer or decimal rounded to the nearest t www

The Venn diagram here shows the cardinality of each set Use this to find the cardinality of the given set A B

Find the missing quantities for the following circle Use the key for Radius Circumference Radius Type an inter Diameter 10 4 m 1

14 Find the PERIMETER and AREA of the triangle in the diagram below A 5 BORS C 3 2

Plot the product of the complex numbers on the plane below Answer 2 cos 210 isin 210 3 cos 90 isin 90 E Keyboard Points can be moved by dragging or using the arrow keys If using the arrow keys note that the right left arrow will increase decrease the radius and the up down will increase decrease the angle Enable Zoom Pan

You need to buy some chicken for dinner tonight You found an ad showing that the store across town has it on sale for 3 19 a pound which is cheaper than your usual neighborhood store which sells it for 3 39 a pound Is it worth the extra drive First determine what information you need to answer this question then click here to display that info along with other info How much chicken will you be buying 7 pounds How far away are the two stores My neighborhood store is 2 5 miles away and takes about 8 minutes The store across town is 8 5 miles away and takes about 21 minutes What kind of mileage does your car get It averages about 22 miles per gallon in the city How many gallons does your car hold About 16 gallons How much is gas About 3 68 gallon right now Going to the further store is cheaper O Going to the close store is cheaper The cheaper option saves you

Use Descartes Rule of Signs to state the number of possible positive and negative real zeros of the polynomial function Enter your answers as a comma separated list P x 9x3 x2 21x 17

Tyler ordered a pat toepee 14137 fe 1077ft 3534 fe O 3375 fe or an authentic 30 foot diameter American Indian teepee that stands 15 feet tall when assembled What is the volume of them

Let x y z be non zero vectors and suppose w If z 4x 3y then w 8 x 6 y 4x 3y z Using the calculation above mark the statements below that must be true A Span w x Span w x y B Span w z Span w x z C Span w x z Span y z D Span w y z Span w z E Span w y z Span w y

Given that f x sinx g x cos x and h x tan x evaluate the given function The point ox 3 on the circle x 7 also lies on the terminal side of an angle a in quadrant The point on the circle x22 1 also lies on the terminal side of an angle in quadrant 1 34 2x oc Carre OB 4 5 OD 4 5

Decompose v into two vectors v and v2 where v is parallel to w and v2 is orthogonal to w v i 5j w 21 j 14 OA 1 5 7 11 28 i 51 V25 5 5 13 O B V 1 1 V2 21 14 7 2 OC V1 5 5l 25 314 18 5 14 7 9 OD V1 5 5 V2 5 5 18

Identify the function family to which g belongs 2 g is a n 1 5 y function

2 If y varies directly as x and y 24 when x 6 find y when x 7 3 If y varies inversely as x and y 10 when x 28 find y when x 35 4 If y varies inversely as Vx and y 10 when x 25 find y when x 100 6 If y varies jointly as x and z and y 240 when x 12 and z 10 find y when x 6 and z 8 7 If y varies directly as x and inversely as z and y 20 when x 12 and z 3 find y when x 7 and z 5 8 If y varies directly as x and inversely as z and y 4 when x 12 and z 3 find y when x 7 and z 5

2 A landscaper wants 100 pounds of grass seed mixture that is 45 of type A seed and 55 of type B He has a mixture that is 10 type A and one that is 60 type A How much of each should he use to make the desired mixture