Quadratic equations Questions and Answers

Find the length of the side c in the triangle ABC where a 3 b 3 and LACB 120 zao bas 120 ble han DE

26 In the formula A t Agekt A is the amount of radioactive material remaining from an initial amount Ao at a given time t and k is a negative constant determined by the nature of the material A certain radioactive isotope decays at a rate of 0 3 annually Determine the half life of this isotope to the nearest year

Which binomial is a factor of the following expression 2x 2 x 1

2 Identify the roots of the function Roots BONUS Sketch the quadratic below y x2 5x 14

zeros include x 1 with multiplicity 2 and x 3 2i

1 Given f x x 5x 6 what are the x intercepts of f x Show all work a 2 0 and 3 0 b 0 0 and 6 0 c 0 2 and 0 3 d 2 0 and 3 0

Graph the system of linear inequalities Ps 1

The population of a particular city is increasing at a rate proportional to its size It follows the function P t 1 ke0 08t where k is a constant and t is the time in years If the current population is 22 000 in how many years is the population expected to be 55 000 Round to the nearest year

Solve the equation for 0 x 2 pi 10 cotx 10 000 0

Ompany that sold fish for an aquarium had a special one weekend on tetras and angel fish The store sold a total of 110 of those types of fish over the weekend The tetras each sold for 0 40 and the angel fish each sold for 1 20 They made a total of 80 in selling those fish Which system of equations best represents this situation if t the number of tetras and a the number of angel fish O O O 110 04 80 80 1 2 110 0 4f 1 2a 110 80a 04 110 110 12 80 O of a 110 0 4 1 2a 80

Which graphed system of equations below has no solution O O O O 64 3 2 1 1 54 321 5 4 3 2 2 3 2 1 19 6 2 TA 2 2 11 7 2 J 1 2 3 1 2 A 2 3 2 3 G 3 4 5

Rewrite the repeating number as a fraction 18 181818 O O 1836 101 181 9 200

Determine S29 for an arithmetic series given a1 7 and 70 329 077 O490 1116 5 There is not enough information

What is the area of the rhombus 8 4 2 1 2 7 4 4 S

In the figure below m2 99 Find m 1 m3 and m 2 4 1 2 4 3 m 21 m 23 m 24 99

There were 45 people in the group that received a new medicine to treat the flu If the treatment group is normally distributed and population standard deviation is known to be 5 hours 5 This group had the flu for an average of 49 hours Construct a 99 confidence interval estimating the actual population mean number of days 000 47 08 S S 50 92 48 25 49 75 40 50 36 12 SS61 88 P

Given the same sample statistics which level of confidence will produce the narrowest confidence interval 75 85 90 95

A goblet contains 2 red marbles 6 green marbles and 4 blue marbles If we choose a marble then another marble without putting the first one back in the goblet what is the probability that the first marble will be green and the second will be green as well

Use the central limit theorem if possible For a sample of n 64 find the probability of a sample mean being between 29 and 32 given 30 and a 16 The population is uniformly distributed Hint First determine use those values to find z and o 0 0747 0 4672 0 5328 and Distribution of the Sample Means 26 13 6 28 34 1 34 1 30 32 13 6 34

The length of pregnancies are normally distributed with a mean of 268 days 268 and a standard deviation of 15 days 15 A group of 36 pregnant women n 36 were in a parenting class together What is the probability that the average pregnancy for the women lasted longer than 270 days 21 2 28 8 55 2 78 8

A restaurant noted what type of food its customers ordered last week Here are the results Burger Fries 30 40 10 20 Find the probability that a randomly chosen customer ordered a burger given that they ordered fries P burger fries

Captain Ben has a ship the H M S Crimson Lynx The ship is five furlongs from the dread pirate Luis and his merciless band of thieves 2 If his ship hasn t already been hit Captain Ben has probability of hitting 3 the pirate ship If his ship has been hit Captain Ben will always miss 1 If his ship hasn t already been hit dread pirate Luis has probability of hitting the Captain s ship If his ship has been hit dread pirate Luis will always miss If the Captain and the pirate each shoot once and the pirate shoots first what is the probability that the pirate hits the Captain s ship but the Captain misses

In a class of 7 there are 5 students who forgot their lunch If the teacher chooses 2 students what is the probability that neither o them forgot their lunch

Researchers surveyed one hundred students on which superpower they would most like to have The two way table below displays data for the sample of students who responded to the survey Superpower Male Female TOTAL 30 10 40 44 16 100 Fly Invisibility Other TOTAL 12 10 52 32 6 48 Find the probability that the student was male given the student chose to fly as their superpower P male fly

Isabella built a time travel machine but she can t control the destination of her trip Each time she uses the machine she has a 0 25 probability of traveling to a time before she was born During the first year of testing Isabella uses her machine 5 times Assuming that each trip is equally likely to travel before Isabella was born what is the probability that at least one trip will travel before Isabella was born Round your answer to the nearest hundredth P at least one before she s born

A website offers a coupon to 50 of its visitors selected at random each day Yasemin visits the website for 4 days What is the probability that Yasemin will not be offered a coupon on at least one of the days she visits the website Round your answer to the nearest hundredth P at least one day without coupon

When Julia is writing a first draft there is 0 7 probability that there will be no spelling mistakes on a page One day Julia writes a first draft that is 4 pages long Assuming that Julia is equally likely to have a spelling mistake on each of the 4 pages what is the probability that she will have no spelling mistakes on at least one of them Round your answer to the nearest hundredth P at least one without mistakes

There are 300 students in a twelfth grade high school class 120 of these students have at least one sister and 100 have at least one brother Out o the students that have at least one brother there are 40 who have at least one sister and one brother Let A be the event that a randomly selected student in the class has a sister and B be the event that the student has a brother Based on this information answer the following questions What is P A the probability that the student has a sister What is P B the probability that the student has a brother What is P A and B the probability that the student has a sister and a brother What is P AB the conditional probability that the student has a sister given that he or she has a brother Is P A B P A Are the events A and B independent Choose all answers that apply Yes P A B P A No P AB P A Yes events A and B are independent events No events A and B are not independent events

Captain Emily has a ship the H M S Crimson Lynx The ship is five furlongs from the dread pirate Umaima and her merciless band of thieves 3 5 of If her ship hasn t already been hit Captain Emily has probability hitting the pirate ship If her ship has been hit Captain Emily will always miss 1 If her ship hasn t already been hit dread pirate Umaima has probability of hitting the Captain s ship If her ship has been hit dread pirate Umaima will always miss If the Captain and the pirate each shoot once and the pirate shoots first what is the probability that the pirate misses the Captain s ship but the Captain hits

When Hiroto is writing there is 0 92 probability that there will be no spelling mistakes on a page One day Hiroto writes an essay that is 11 pages long Assuming that Hiroto is equally likely to have a spelling mistake on each of the 11 pages what is the probability that he will have a spelling mistake on at least one of the pages Round your answer to the nearest tenth P at least one mistake

s favorite colors are red and green He has 1 red shirt 1 green shirt 1 red hat 1 green scarf 1 red pair of pants and 1 green pair of pants Bilal selects one of these garments at random Let A be the event that he selects a green garment and let B be the event that he chooses a scarf Which of the following statements are true Choose all answers that apply A P A B P A the conditional probability that Bilal selects a green garment given that he has chosen a scarf is equal to the probability that Bilal selects a green garment B P B A P B the conditional probability that Bilal selects a scarf given that he has chosen a green garment is equal to the probability that Bilal selects a scarf Events A and B are independent events The outcomes of events A and B are dependent on each other EP A and B P A P B the probability that Bilal selects a garment that is green and is a scarf is equal to the probability that Bilal selects a green garment multiplied by the probability that he selects a scarf

Solve each equation Show your reasoning put your final answers in the table Show your work in the sketch OR take a picture of your paper work and upload it in the textbox below Equations x 8 2x 5 0 x 13x 40 0 x 6x 20 7 Solution s

Suppose that Eitan rolls a fair six sided die and a fair four sided die simultaneously Let A be the event that the sum of the dice is 8 and B be the event that Eitan rolls doubles Using the sample space of possible outcomes below answer each of the following questions What is P A the probability that the sum of the dice is 8 What is P B the probability that Eitan rolls doubles What is P A and B the probability that the sum of the dice is 8 and Eitan rolls doubles Are events A and B independent Choose 1 answer Yes events A and B are independent events No events A and B are not independent events APARA BARABA 8 6 88 6 88 3

2 Solve 3x 6x by rewriting the equation Show your reasoning use the sketch option or upload a picture of your work in the textbox upload work for 2 if needed

A rancher has a square cow pen with side length x He decides to change the shape of the pen to a rectangle while still using the same amount of fencing materials The equation x 10 x 10 300 represents the relationship of the new side lengths in feet of the pen and its area in square feet 1 If 300 represents the area of the new cow pen what do the expressions x 10 and x 10 each represent 2 Find x the original side length in feet of the square pen Show your reasoning 1 the expression x 10 represents the expression x 10 represents 2 x feet I know this is correct because Submit

Each expression is given in standar Rewrite it in factored form If it cannot be rewritten in factored form write cannot be done use paper pencil to rewrite the expression Put your final answer only in the table Original Equation 900 p 18p 40 2 3t 10 9 16x 1 Factored Form

Select all the expressions that could be equivalent to x bx 36 where bis negative 2 Select all that apply x 3 x 12 x 2 x 18 x 13 x 3 x 4 x 9 x 9 x 4

Select all equations that have two solutions Select all that apply 2 x 16 4x 0 x 16 2 3x 2 14 x 1 24 x 8 x 8 0

f x x e 2 s tx5 16x 0 O There is not enough information to find the maximiser O x 2 x 2

The bearing from City A to City B is N 49 E The bearing from City B to City C is S 41 E An automobile driven at 65 mph takes 1 4 hours to drive from City A to City B and takes 1 2 hours to drive from City B to City C Find the distance from City A to City C Neglect the curvature of the earth The distance from City A to City C is approximately Round to the nearest mile as needed miles

The average age of a student at Central High School is 16 5 years old 16 5 with a standard deviation of 1 5 a 1 5 If samples of size 9 n 9 were taken from the population what would be the standard deviation of the sample means a 0 5 1 0 1 5 2 0

If the standard deviation of a population is 4 a 4 what happens to the standard deviation of the sample means a as the sample size n increases a decreases o increases Nothing happens to 07 5

et sin a 2 7 and sin 3 with n 2 a n 3n 2 Evaluate the following a sin a B b cos 2a c tan a B d sin e tan B

What is the required rolls of tape 150 ft per roll and pounds of joint compound to tape and bed the interior finish wall The building is 100 0 feet by 55 0 long and 14 tall walls 10 rolls and 542 lb s 11 rolls and 239 lb s 52 rolls and 542 lb s 45 rolls and 500 lb s

What are the equations of the horizontal and vertical asymptotes of y 1 horizontal asymptote vertical asymptote

Rewrite the logarithmic expression as a single logarithm with the same base Simplify any fractions log 2 log 9

1 What is the equation of the horizontal asymptote of y X 1 MA 8

ook at the graph 10 5 10 L 5 7 X 10 MAY What are the equations of the horizontal and vertical asym horizontal asymptote

Which graph below shows a normal distribution O oll

A study determined that the average student who graduates takes 58 months to graduate from college with a bachelor s degree and a standard deviation of 10 months The distribution was approximately normal What percentage of college graduates will take longer than 4 years 48 months 13 08 15 9 47 7 84 1 97 7 341N AU 34 15 13 06