Algebra Questions

Suppose that bacteria growth is modelled by the DE given in the notes Suppose that the number of bacteria is observed to double after 10 days and the estimated carrying capacity is 14 times the initial population What is the estimated population as a multiple of the initial population after 27 days For example an answer of 3 5 would indicate a population 3 5 times the initial population Give the answer accurate to 2 decimal places number

6 Scientists use the following formula when examining skeletal remains H 66 4 2 26 H represents a person s height and f is the length of the person s femur bone length The equation has a margin of error of 3 42 centimeters All changes sa a You are on an archeological dig and need to calculate the height of some of the remains You have found several femur bones In order to determine the heights we need to first solve the given formula for H b The femur bones measure 40 6 cm 39 cm and 48 2 cm Find the height of each person c Find the height of each person in feet note 2 54 cm 1 inch d Using the margin of error create an absolute value inequality to represent the range of the height for each individual

out of the microwave and has an initial temperature of 198 F The drink is placed on the counter in a room whose temperature is 73 F After 7 minutes the temperature of the hot chocolate has dropped to 150 F a Find the function T t which gives the temperature of the hot chocolate in degrees Fahrenheit t minutes after the hot chocolate was removed from the microwave T t 73 125e 0 069t Not quite 113 82 F b Estimate the temperature of the hot chocolate 16 minutes after the drink was removed from the microwave Round to two decimal places That s not it Preview T t 73 125e 0 069t oF F Preview 113 82 F c Estimate the number of minutes after removal from the microwave for the temperature of the hot chocolate to reach 91 F Round to two decimal plago

According to one source the world population can be modeled using the function P t 6 17e0 012t where P t is the world population in billions of people and t is the number of years after January 1st 2000 a Predict the year during which the world population is expected to reach 10 3 billion people year 2043 Not equivalent b Predict the world population on January 1st 2060 Round to the nearest person population 13000000000 I Preview 2043 people Preview 13 000 000 000 people

Situation 3 You are trying to a build doghouse for your adorable Pomeranian The dimensions of the base of the doghouse will be needed Determine the length and width of your doghouse The roof of the house is a triangle with two sides that are the same length Decide the height of the roof

Under ideal conditions a certain bacteria population is known to double every 4 hours Suppose there are initially 800 bacteria a Find the number of bacteria after 12 hours bacteria b Find the function P t which gives the number of bacteria after t hours P t bacteria c Estimate the number of bacteria after 17 hours Round your answer to the nearest whole number bacteria

are 22 grams of the isotope a Find the function P t which gives the number of grams of the isotope after t days P t 22 1 2 t 7 Correct Good Job 9 30 b Estimate the number of grams of the isotope after 12 days Round to two decimal places 20 grams Not quite grams Preview P t 22 grams c Estimate the number of days it will take for the isotope to reach 3 grams Round to two decimal places days Preview 9 30 grams Preview 20 days

A steep mountain is inclined 75 from the horizontal and rises to a height of 3350 ft above the surrounding plain A cable car is to be installed running from a point 850 ft from the base of the mountain to the top of the mountain The shortest length of cable ft Round the final answer to 2 decimal places You can round the distance from the top of the mountain to its base to 5 3 additional decimal places or use the Ans feature on your calculator uestion Help Video Moccago instructor Bort to foru cum

According to one source the world population can be modeled using the function P t 6 17e0 012 where P t is the world population in billions of people and t is the number of years after January 1st 2000 a Predict the year during which the world population is expected to reach 10 3 billion people b Predict the world population on January 1st 2060 Round to the nearest person population people

wolves and 7 years later the population was 3000 wolves a Find the function P t which gives the population of wolves t years after day one P t 1600 Not quite po 2 t 3 b Estimate the number of wolves 14 years after day one Round your answer to the nearest wolf That s not it wolves 16127 wolves Preview P t 1600 wolves c Estimate the number of years it will take to reach a population of 4300 wolves Round to two decimal places years Preview p o 2 wolves Preview 16 127 years

Force X has a magnitude of 1250 pounds and Force Y has a magnitude of 1470 pounds They act on a single point at n angle of 75 to each other Find the magnitude of the equilibrant and the angle between the equilibrant and the 250 pound force What is the magnitude of the equilibrant Round to the nearest tenth pounds

Laboratory tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours Find the probability that a randomly selected light bulb will last between 600 and 750 hours 21

Find an orthogonal matrix A where the first row is a multiple of 1 2 2 A

Apply Cramer s rule to solve the following equations x 3y 6z 2 3x y z 9 X 4y 2z 7 Select one O a X 1 y 2 z 1 O b X 2 y 2 z 1 Oc X 2 y 1 z 0 5 O d X 1 y 2 z 0 5

Prove that every positive rational number can be expressed uniquely as a finite sum of the form a a2 2 az 3 where an are integers such that An n

Find a basis for S for the subspace S 1 1 5 S span 11

Roger has found a home to be purchase for 112 057 and has agreed to pay 10 down Find the amount of Roger s down payment Find the amount of money that Roger would need to borrow through a mortgage in order to purchase the home If Roger found a 30 year mortgage with a 5 6 APR What would Roger s monthly payment be Round your answer to the nearest cent

8 Find a the square roots of z 1 2 b the cube roots of z 1 j

What is the accumulated value of periodic deposits of 50 at the beginning of every month for 18 years if the interest rate is 2 58 compounded monthly

31 7 2k 8 10 8k 4 32 3 8r 6 7 r

buy a total of 50 turkey burgers and veggie burgers You spend 90 total paying 2 per veggie burger and 1 50 per turkey burger ermine the number of veggie burgers x and turkey burgers y that were purchased You MUST 1 Write a system of equations 2 Show your work to solve the system if you use DESMOS remember to use the buttons in the top right to zoom out until you see the equations then label the solution before you take a screenshot 3 Explain your answer in the context of the problem Answer the question how many veggie burgers and how many turkey burgers did you buy in a complete sentence 15

an agreement should get the same answer If you alsa A travel company uses a quadratic function to model the profit in dollars that it expects to earn from selling tickets to a river cruise at x dollars per person Determine the average rate of change for the interval 20 x 60 Partner A 1800 1700 1600 1500 1400 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100 Profit 100 200 Partner A Number of Widgets 0 20 40 20 60 40 80 Cost 800 Cost of Ticket Together What does the average rate of change from 20 x 60 represent 700 800 60 1100 20 1600 100 Partner B Partner B The table and graph shown below model the daily production costs in y dollars of x widgets Determine the average rate of change for the interval 20 80 from the given representation Cost 2000 1800 1600 1400 1200 1000 800 600 400 200 Cost per ticket 20 10 20 30 Together What does the average rate of change from 1 3 represent 40 50 60 40 60 Number of Widgets Profit 80 0 700 1200 1500 1600 1500 100

Partner A Use the equations above to determine the key features of the graph X Intercepts Vertex Domain 2 2 Partner B Check the work from Partner A If you agree with the values in the table use the values to sketch a graph of the quadratic function 4 Y Intercept Now pass the paper to partner C End Behavior Range Partner C Use the Desmos Graphing Calculator to check Partne A and B s work Then answer the following question What is the average rate of change for the interval 0 2 Now pass the paper back partner A to review the finc work

Let g x 2 3x 4 x 1 x 3 be a polynomial function 1 Sketch a graph of the polynomial HTT X

Let f cos x and g sin x Which of the following lie in the space spanned by fand g a cos 2x b 3 x c 1 d sin x e 0 O a c e O a b c d e O a d O a c d O d

A doctor prescribes 26 milligrams of a therapeutic drug that is absorbed by the body in such a way that the drug reduces by 30 each hour a Find the function P t which gives the number of milligrams of the drug after t hours P t e 0 3t That s not it 0 39 b Estimate the amount of drug after 14 hours Round to two decimal places milligrams Not quite 7 20 milligrams Preview P t 0 3t milligrams c Estimate the number of hours it will take for the drug amount to reach 3 milligrams Round to two decimal places hours Preview 0 39 milligrams Preview 7 20 hours

A cup of hot chocolate is taken out of the microwave and has an initial temperature of 198 F The drink is placed on the counter in a room whose temperature is 73 F After 7 minutes the temperature of the hot chocolate has dropped to 150 F a Find the function T t which gives the temperature of the hot chocolate in degrees Fahrenheit t minutes after the hot chocolate was removed from the microwave T t OF b Estimate the temperature of the hot chocolate 16 minutes after the drink was removed from the microwave Round to two decimal places c Estimate the number of minutes after removal from the microwave for the temperature of the hot chocolate to reach 91 F Round to two decimal places

8 6x6 9 7x Date x 2 x 7 5 11 8b 6 7b 4 his true true false n has 1 2v 3v 8 ns have infinite solutions or no solutions ed his c Maria solved her got equation and got 8 8 16 16 This equation is ve This equation is ve true false true false This equation has x 6 5x 3x 1 5 3r 7r 7 b Mario solved his equation and got This equation has lutions infite selvtors

Solve each equation 2 3n 2n 6n 6 6b 11 1 8b x 15 2x 7 2

der ideal conditions a certain bacteria population is known to double every 3 hours Suppose there are initially 200 bacteria a Find the number of bacteria after 9 hours 1599 29 Not equivalent P t b Find the function P t which gives the number of bacteria after t hours 200e 0 231t That s not it A bacterial 16112 bacteria Preview 1599 29 bacteria bacteria P t 200e0 231t c Estimate the number of bacteria after 19 hours Round your answer to the nearest whole number Preview bacteria Preview 16 112 bacteria

The logistic function below models the population of fish in a pond as a function of time in weeks since fish were first introduced into the pond P t 780 1 19e 0 08 a Find the number of fish that were first introduced into the pond fish b Predict the number of fish in the pond 17 weeks after they were first introduced Round to the nearest fish fish c Predict when the the population will reach 530 fish Round to two decimal places weeks d Determine the maximum number of fish that can be sustained by the pond

A newly discovered isotope has a half life of 7 5 days Initially there are 10 grams of the isotope a Find the function P t which gives the number of grams of the isotope after t days P t grams b Estimate the number of grams of the isotope after 11 days Round to two decimal places grams c Estimate the number of days it will take for the isotope to reach 4 grams Round to two decimal places

Under ideal conditions a certain bacteria population is known to double every 3 hours Suppose there are initially 200 bacteria a Find the number of bacteria after 9 hours bacteria b Find the function P t which gives the number of bacteria after t hours P t bacteria c Estimate the number of bacteria after 19 hours Round your answer to the nearest whole number

A doctor prescribes 26 milligrams of a therapeutic drug that is absorbed by the body in such a way that the drug reduces by 30 each hour a Find the function P t which gives the number of milligrams of the drug after t hours P t milligrams b Estimate the amount of drug after 14 hours Round to two decimal places milligrams c Estimate the number of hours it will take for the drug amount to reach 3 milligrams Round to two decimal places

Use n 2 partitions to find an upper sum for the region under the graph of y 4x 6 above the x axis and between x 9 and x 15 The upper sum for this region is

On day one the population of gray wolves in Montana was 2100 wolves and 7 years later the population was 3000 wolves a Find the function P t which gives the population of wolves t years after day one P t wolves b Estimate the number of wolves 14 years after day one Round your answer to the nearest wolf wolves c Estimate the number of years it will take to reach a population of 4300 wolves Round to two decimal places

According to one source the world population can be modeled using the function P t 6 17e0 0123t where P t is the world population in billions of people and t is the number of years after January 1st 2000 a Predict the year during which the world population is expected to reach 10 6 billion people year b Predict the world population on January 1st 2052 Round to the nearest person population people

18 k 9 k 5

18 k 9 k 5

The following graph depicts the area between the x axis and a functions curve You can zoom in and out using the scroll on the mouse You can move the graph by clicking in an empty space and dragging n 6 12 Show Right Endpt Sum Show LeftEndpt Sum Show Actual Area 2 19 O A 2 C 6 8 10 What is the smallest value of n 1 for which the left endpoint sum differs from the exact area by at most 0 2

17 2 v 5 10v 18 k 9 k

Find the distance between u MAN 0 H 3 The distance between u and z is 6 and z 5 1 7

b x 4 10 2x 10 x 3

4x3 8x2 4x 42 x 3

4x3 8x2 4x 42 x 3

1 3 2x 4 2 8 2x

Write your solutions on a separate sheet of paper Estimate 250 as an integral power of 10 no calculator

iv g x ex 10 9 8 Domain Range x intercept y intercept Horizontal Increasing Degreasing G

oints Among all unit vectors u X Y in R find the one for which the sum x 8y 7z is minimal 2

9 10 1 6n 11 10 1 4v 13 4 8 3 10n 15 9 2 9 8n 10 5 6k 6 12 10 5k 6 14 9 5 3 6x 16 8 9 8n 10