Algebra 4 Name Final Exam Review Per

Algebra 4 Name _____________________________________ Final Exam Review Per ___________ Module 10 Find the inverse. Confirm the inverse relationship using composition. Graph the function and its inverse. 1. f(x) = 5x2 2. f(x) = (x + 3)2 3. f(x) = 6x2 - 4 Find the inverse of each cubic function. Confirm the inverse relationship using composition. Graph the function and its inverse. 4. f(x) = -4x3 5. f(x) = x3 + 7 6. f(x) = 2x3 – 5 7. The function m(r) = 31r3 models the mass in grams of a spherical zinc ball as a function of the ball’s radius in centimeters. Write the inverse model to represent the radius r in cm of a spherical zinc ball as a function of the ball’s mass m in g. 8. The function A = s2 gives the area, A, of a square with sides of length s. Express s as a function of A. Use your function to find the length of a square whose area is 121 square units. Show your work.

Algebra 4 Name _____________________________________ Final Exam Review Per ___________

Describe the transformations of g(x) from the parent function f(x) = x . Graph each function, and identify its

domain and range.

9. 32

1)( xxg 10. 624)( xxg

Use the description to write the square root function g.

11. The parent function f(x) = x is compressed vertically by a factor of 4

1, reflected across the x-axis, and

translated 6 units up.

12. The parent function f(x) = x is translated 8 units left, reflected across the y-axis, and stretched

horizontally by a factor of 3. Graph each cube root function. Include three key points on your graph. Describe the transformations of the

parent function, f(x) = 3 x .

13. 3 32)( xxg 14. 41)( 3 xxg

Write an equation, g(x), for the transformation equation described.

15. The graph of the function f(x) = 3 x is translated 7 units to the left and 3 units up.

16. The graph of the function f(x) = 3 x is vertically stretched by a factor of 3, translated 2 units to the right,

and then reflected across the x-axis.

Algebra 4 Name _____________________________________ Final Exam Review Per ___________ Write the equation of the cube root function shown on the graph. 17. 18.

Module 11 Write each expression in radical form. Simplify numerical expressions when possible.

1. 3

2

216 2. 3

4

n 3. 2

1

36x

4. 21

349v 5. 23

316x 6. 31

581r

Write each expression by using rational exponents. Simplify numerical expressions when possible.

7. 34 b 8. 46a 9. 43

5ab

10. 56y 11. 25 3t 12. 9 1816

Simplify each expression. Assume all variables are positive.

13. 2

23

21

21

yxx 14.

31

3

125

x


15. 4

1

12

8

n

m 16. 3

73

233 xx

17. 23 98x 18. 3 632

188 yx

Solve each equation.

19. 452 xx 20. 413 x

21. 1032 x 22. 64 21x

23. 10165 41x 24. 4763 x

25. 632 xx 26. 18113 x

Algebra 4 Name _____________________________________ Final Exam Review Per ___________ Module 12 Write an explicit and a recursive rule for each sequence. 1.

2.

3.

4.

5.

6.

7.

n 0 1 2 3 4 …

f(n) 23 21 19 17 15 …

n 1 2 3 4 5

f(n) -15 -19 -23 -27 -31

n 0 1 2 3 4

f(n) 4 24 144 864 5184

n 1 2 3 4 5 …

f(n) 3 12 48 192 768 …

n 1 2 3 4 5 …

f(n) 15 23 31 39 47 …

n 0 1 2 3 4

f(n) 3 -15 75 -375 1875

n 0 1 2 3 4

f(n) -3.4 -2.1 -0.8 0.5 1.8

Algebra 4 Name _____________________________________ Final Exam Review Per ___________ 8.

9.

10.

11.

12.

13. A recursive rule for an arithmetic sequence is f(1) = -8, f(n) = f(n-1) – 6.5 for n ≥ 2. Write an explicit rule for this sequence.

14. A recursive rule for a geometric sequence is f(1) = 3

2, f(n) = f(n-1)∙8 for n ≥ 2. Write an explicit rule for this

sequence.

n 1 2 3 4 5

f(n) 9 27 81 243 729

n 0 1 2 3 4

f(n) -3 -6 -12 -24 -48

n 1 2 3 4 5

f(n) -32 -42 -52 -62 -72

n 1 2 3 4 5

f(n) -34 -14 6 26 46

n 1 2 3 4 5 …

f(n) 72 36 18 9 4.5 …


15. Given the explicit rule 14.010)(

nnf for n ≥ 1, write the recursive rule.

16. Given the explicit rule f(n) = -37 + 3n for n ≥ 1, write a recursive rule for this sequence. Problems 17-21, write an explicit rule that models the situation. Use your model to answer the question asked. 17. Edgar is getting better at math. On his first quiz he scored 57 points, then he scores 61 and 65 on his next two quizzes. If his scores continued to increase at the same rate, what will be his score on his 9th quiz? Show all work. 18. Suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 85% of its previous height. How high will the ball rebound after its third bounce? Round to the nearest tenth. 19. Viola makes gift baskets for Valentine’s Day. She has 13 baskets left over from last year, and she plans to make 12 more each day. If there are 15 work days until the day she begins to sell the baskets, how many baskets will she have to sell? 20. In a certain region, the number of highway accidents increased by 20% over a four year period. How many accidents were there in 2006 if there were 5120 in 2002? Hint: When the percent increases, you want the original 100% plus the additional 20%. 21. A house worth $350,000 when purchased was worth $335,000 after the first year and $320,000 after the second year. If the economy does not pick up and this trend continues, what will be the value of the house after 6 years.


Module 13

Graph each function. On your graph, include points to indicate the ordered

pairs for x 1, 0, 1, and 2.

1. ( ) 0.75(2)xf x 2. 1( ) 6(3)xf x

Solve.

3. Odette has two investments that she purchased at the same time.

Investment 1 cost $10,000 and earns 4% interest each year.

Investment 2 cost $8000 and earns 6% interest each year.

a. Write exponential growth functions

that could be used to find v1(t) and v2(t), _________________________________

the values of the investments after t years. _________________________________

b. Find the value of each investment after 5 years.

Explain why the difference between their values, ____________________________

which was initially $2000, is now less. ____________________________

4. If A is deposited in a bank account at r% annual interest, compounded

annually, its value at the end of n years V(n) can be found using the formula

( ) 1 .100

nr

V n A

Suppose that $5000 is invested in an account paying

4% interest. Find its value after 10 years.

________________________________________________________________________________________

Solve.

5. The annual sales for a fast food restaurant are $650,000 and are increasing at a

rate of 4% per year. Write the function f(n) that expresses the annual sales after

n years. Then find the annual sales after 5 years.

________________________________________________________________________________________


6. Starting with 25 members, a club doubled its membership every year. Write

the function f(n) that expresses the number of members in the club after n

years. Then find the number of members after 6 years.

________________________________________________________________________________________

7. During a certain period of time, about 70 northern sea otters had an annual

growth rate of 18%. Write the function f(n) that expresses the population of

sea otters after n years. Then find the population of sea otters after 4 years. ________________________________________________________________________________

Graph each function. On your graph, include points to indicate the ordered

pairs for x 1, 0, 1, and 2.

8. ( ) 5(0.4) 1xf x 9. 1( ) 15(0.3) 20xf x

Solve.

10. The half-life of a radioactive substance is the average amount of time it takes

for half of its atoms to decay. Suppose you started with 200 grams

of a substance with a half-life of 3 minutes. How many minutes have passed

if 25 grams now remain? Explain your reasoning.

________________________________________________________________________________________

________________________________________________________________________________________

11. Colleen’s office equipment is depreciating at a rate of 9% per year. She paid

$24,500 for it in 2009. Write the function f(n) that expresses the value of the

equipment after n years. What will the equipment be worth in 2015 to the

nearest hundred dollars? ________________________________________________________________________________


12. If a basketball is bounced from a height of 15 feet, the function

f(x) 15(0.75)x gives the height of the ball in feet of each bounce, where x is the bounce number.

What will be the height of the 5th bounce? Round to the nearest tenth of a foot.

________________________________________________________________________________________

13. The value of a company’s equipment is $25,000 and decreases at a rate of

15% per year. Write the function, f(n), that expresses the value of the

equipment after n years. Then find the value of the equipment in year eight. ________________________________________________________________________________

Given the function of the form keaxg hx )( ,

a. Identify a, h, and k.

b. Identify and plot the reference points.

c. Draw the graph.

d. State the domain and range in set notation.

14. 31

( ) 45

xg x e 15. 2( ) 4 6xg x e 16. 5( ) 0.75 2.5xg x e

a. _________________ a. _________________ a. _________________

b. _________________ b. _________________ b. _________________

c. c.

c.

d. _________________ d. _________________ d. _________________

Solve.

17. When interest is compounded continuously, the amount A in an account after t

years is found using the formula ,rtA Pe where P is the amount of principal and r

is the annual interest rate. Ariana has a choice of two investments that are both compounded continuously. She can invest $12,000 at 5% for 8 years, or she can invest $9000 at 6.5% for 7 years. Which investment will result in the greater amount of interest earned?

_________________________________________________________________________________

Algebra 4 Name _____________________________________ Final Exam Review Per ___________ 18. When interest is compounded continuously, the amount A in an account after t

years is found using the formula ,rtA Pe where P is the amount of principal and r

is the annual interest rate.

a. Use the formula to compute the balance of an investment that had a

principal amount of $4500 and earned 5% interest for 6 years.

____________________________________________________________________________________

b. What is the amount of interest earned in the investment? ____________________________________________________________________________

For each investment described, (a) write an exponential growth model that

represents the value of the account at any time t, and (b) use a graphing

calculator to solve for t for the given value.

19. The principal amount, $16,550, earns 2.89%

interest compounded annually. How long will it

take for the account’s value to surpass $75,250?

a. ______________________________________

b. ______________________________________


interest compounded semiannually. How long will

it take for the account’s value to surpass $150,000?

a. ______________________________________

b. ______________________________________


interest compounded continuously. How long will

it take for the account’s value to reach $300,000?

a. ______________________________________

b. ______________________________________


Module 14 Determine whether f is an exponential function of x. If so, find the constant

ratio.

1. 2.

________________________________________ ________________________________________

3. 4.

________________________________________ ________________________________________

Use exponential regression to find a function that models the data.

5. 6.

________________________________________ ________________________________________

7. 8.

________________________________________ ________________________________________

Solve.

9. a. Use exponential regression to find a function that models this data.

Time (min) 1 3 6 8 10

Bacteria 413 575 945 1316 1832

____________________________________

b. When will the number of bacteria reach 2500? ____________________________________

c. How many bacteria will exist after 1 hour? ____________________________________

x 1 0 1 2 3

f (x) 3.28 8.4 14.8 22.8 32.8

x 1 0 1 2 3

f (x) 3.5 7 14 21 28

x 1 0 1 2 3

f (x) 8

3 4 6 9

27

2

x 1 0 1 2 3

f (x) 243

4

81

2 27 18 12

x 1 2 3 4 5

f (x) 9.3 21.8 50.8 118.6 276.6

x 2 4 6 8 10

f (x) 413.2 45.5 4.9 0.6 0.1

x 1 2 3 4 5

f (x) 11.3 8.4 6.3 4.7 3.6

x 2 4 6 8 10

f (x) 14.2 21.3 33.9 57.2 99.8


A pot of boiling water is allowed to cool for 50 minutes. The table below

shows the temperature of the water as it cools. Use the table for the

problems that follow. Round all answers to the nearest thousandth.

Temperature of Water (y), in degrees Celsius,

after cooling for x minutes

x 0 5 10 15 20 25 30 35 40 45 50

y 100 75 57 44 34 26 21 17 14 11 10

10. Use a graphing calculator to find a linear regression

equation for this data.

______________________________________________________

11. Graph the linear model along with the data. Does it

seem like the model is a good fit for the data?

______________________________________________________

12. Use a graphing calculator to find a quadratic regression

equation for this data.

______________________________________________________

13. Graph the quadratic model along with the data. Does it

seem like the model is a good fit for the data?

______________________________________________________

14. Use a graphing calculator to find an exponential

regression equation for this data.

______________________________________________________

15. Graph the exponential model along with the data. Does

it seem like the model is a good fit for the data?

______________________________________________________

16. Use each regression model to estimate the temperature of the water after 55

minutes. Which estimation seems the most likely?

____________________________________________________________________________________________________


Module 15

Write each exponential equation in logarithmic form.

1. 203 8000 2. 114 14,641 3. ab c

________________________ ________________________ ________________________

Write each logarithmic equation in exponential form.

4. log10 10,000,000 7 5. log6 216 3 6. logp q r

________________________ ________________________ ________________________

Evaluate each expression without using a calculator.

7. log 1 8. log 10,000 9. log 1000

________________________ ________________________ ________________________

10. log5 3125 11. log15 1 12. log4 256

________________________ ________________________ ________________________

Use the given x-values to graph each function. Then graph its inverse. Write an

equation for the inverse function and describe its domain and range.

13. f (x) 0.1x; x 1, 0, 1, 2 14. 5

( )2

x

f x

; x 3, 2, 1, 0, 1, 2, 3

________________________________________ ________________________________________

Solve.

15. The acidity level, or pH, of a liquid is given by the formula 1

pH log ,[H ]

where

[H] is the concentration (in moles per liter) of hydrogen ions in the liquid. The

hydrogen ion concentration in moles per liter of a certain solvent is 0.00794.

a. Write a logarithmic equation for the pH of the solvent. ____________________

b. What is the pH of the solvent? ____________________


Graph each function. Find the asymptote. Tell how the graph is

transformed from the graph of the parent function.

16. f (x) 2.5log2 (x 7) 3 17. f (x) 0.8 ln (x 1.5) 2

________________________________________ ________________________________________

Write each transformed function.

18. The function f(x) log9 (x 4) is translated 4 units right and 1 unit

down and vertically stretched by a factor of 7. ____________________

19. The function f(x) 3 ln (2x 8) is vertically stretched by a factor of 3,

translated 7 units up, and reflected across the x-axis. ____________________

20. The function f(x) log (5 x) 2 is translated 6 units left, vertically

compressed by a factor of 1

3, and reflected across the x-axis. ____________________

21. The function f(x) 8log7 x 5 is compressed vertically by a factor of

0.5, translated right 1 unit, and reflected across the x-axis. ____________________

22. What transformations does the function f (x) ln (x 1) 2 undergo

to become the function g(x) ln (x 1)? ____________________

Solve.

23. The function A(t) Pe rt is used to calculate the balance, A, of an investment

where the interest is compounded continuously at an annual rate, r, over t

years. Find the inverse of the formula. Then use it to determine the amount

of time it will take a $27,650 investment at 3.95% to reach a balance of

$50,000.

________________________________________________________________________________________


Module 16

Express as a single logarithm. Simplify, if possible.

1. log6 12 log6 18 2. log3 81 log3 27 3. log4 128 log4 8

________________________ ________________________ ________________________


________________________ ________________________ ________________________


________________________ ________________________ ________________________

10. log8 80 log8 51.2 11. log7 13.3 log7 1.9 12. log10 125 log10 80

________________________ ________________________ ________________________

Evaluate. Round to the nearest hundredth.

13. log8 86 14. 2log 82x

15. log2 165

________________________ ________________________ ________________________

16. log3 3(2x 1) 17. log4 16(x 1) 18. 5log 175

________________________ ________________________ ________________________

19. log3 52 20.

2

5

1log

125

21.

3

6 4

1log

6

________________________ ________________________ ________________________

22. log4 202 23. log9 274 24. log2 10

________________________ ________________________ ________________________

Solve.

25. Carmen has a painting presently valued at $5000. An art dealer told her the

painting would appreciate at a rate of 6% per year. In how many years will

the painting be worth $8000?

a. Write a logarithmic expression representing the situation. _________________________

b. Simplify your expression. How many years will it take? _________________________


Solve each equation by graphing. If necessary, round to the nearest

thousandth.

26. 0.5 9 0.2 73xe 27. 79 5.5 51xe

________________________________________ ________________________________________

Solve each equation algebraically. If necessary, round to the nearest

thousandth.

28. 3 616 8x x 29. 2 33 4 78xe 30. 1 212 20x

________________________ ________________________ ________________________

31. 2 49 27x x 32. 0.5 2 5256 64x x 33. 2 33216 36x

x

________________________ ________________________ ________________________

34.

31

279

x

35.

5

218

16

x

36.

8 22 25

5 4

x

________________________ ________________________ ________________________

37. 8 10

7 10 9 4x

38. 4

3 10 4 91x

39. 8 110 3 70xe

________________________ ________________________ ________________________

Solve.

40. Lorena deposited $9000 into an account that earns 4.25% interest each

year.

a. Write an equation for the amount, A, in the

account after t years. ____________________________________

b. In how many years will her account exceed

$20,000? ____________________________________

c. If she waits for 50 years, how much will be in her

account? ____________________________________

Algebra 4 Name _____________________________________ Final Exam Review Per ___________ Module 17

Draw an angle with the given measure in standard position.

1. 550 2. 645 3. 715

Find the measures of a positive angle and a negative angle that are

coterminal with each given angle.

4. 400 5. 360 6. 1010

________________________ ________________________ ________________________

7. 567 8. 164 9. 358

________________________ ________________________ ________________________

Convert each measure from degrees to radians or from radians to degrees.

10. 3

2

11. 450 12.

5

18

________________________ ________________________ ________________________

13. 200 14. 7

4

15.

11

6

________________________ ________________________ ________________________

Find the measure of the reference angle for each given angle.

16. 580 17. 15

4

18. 375

________________________ ________________________ ________________________

19. 18

13 20. 705 21.

22

9

________________________ ________________________ ________________________


Find the exact value of each trigonometric function.

22. cos 870 23. sin 19

6

24. sin 240o

________________________ ________________________ ________________________

25. tan 945 26. cos 23

4

27. tan

13

6

________________________ ________________________ ________________________

Use a calculator to evaluate each trigonometric function. Round to four

decimal places.

28. sin 840 29. tan 19

18

30. sin

341

60

________________________ ________________________ ________________________

Solve. Assume each circle is centered at 0.

31. Find the exact coordinates of the point on a circle of radius 7.25 at an angle

of 315.

________________________________________________________________________________________

32. Find the exact coordinates of the point on a circle of radius 5 at an angle of

5.

3

________________________________________________________________________________________


Using f (x) sin x or f (x) cos x as a guide, graph each function. Identify

the amplitude, period, and x-intercepts.

1. 2. ( ) sin2

q x x

________________________________________ ________________________________________

Using f (x) cos x or f (x) sin x as a guide, graph each function. Identify

the amplitude and period.

3. h(x) = -5sin(4x) 4. q(x) 2 cos(2x)

________________________________________ ________________________________________


Write the function shown in the graph in the form

1sin .y a x

b

5.

6.

________________________________ ____________________________________

Write the function rule for the transformed tangent function shown. Use the

form ( ) tanx

f x ab

.

7.

8.

________________________________________ ________________________________________

For each rule given for a transformed tangent function, find the asymptotes and reference

points for one cycle. Then graph the function.

9. 5

tan4 3

xf x

10. )25.0tan(2)( xxf

Asymptotes: ______________________ Asymptotes: ______________________

Reference Points: __________________ Reference Points: _________________


For each rule given, identify the indicated points or features for one cycle.

Then graph the function.

11. 33

2cos2)(

xxf

Starting point: __________________

Ending point: __________________

Middle point: __________________

1st Midline point: __________________

2nd midline point: __________________

12. 4)(3tan5)( xxf

Asymptotes: ___________________

Center point: ___________________

Halfway point 1: ___________________

Halfway point 2: ___________________

Write a function rule for the indicated trigonometric function.

13. Write a sine function for the graph.


For Problems 17, the universal set consists of the natural numbers from 1 20. For each description, write a statement in set notation.

1. Set P _____________________________________

2. Set T _____________________________________

3. Set F _____________________________________

4. number of elements in set P _____________________________________

5. intersection of sets P and T _____________________________________

6. union of sets T and F _____________________________________

7. complement of set P _____________________________________

Use the sets above to solve Problems 810.

8. Explain why the intersection of all three sets,

P, T, and F, is the empty set.

________________________________________

________________________________________

9. What numbers are in neither P, T, nor F?

________________________________________

10. Create a Venn diagram of these sets.

For Problems 1115, use the sets defined above and your Venn diagram to

find the probabilities. Write each probability statement in set notation, and

give the probabilities in simplest form.

11. probability that a number in the universal set is a multiple of 3

________________________________________

12. probability that a number in the universal set is not a multiple of 3

________________________________________

13. What is P(T) P(Tc)? _____________________________________

14. probability that a number in the universal set is a multiple of both 3 and 5

_____________________________________

15. probability that a number in the universal set is prime or a multiple of 5

_____________________________________

Set U: integers from 120

Set P: prime numbers

Set T: multiples of 3

Set F: multiples of 5


Solve each equation by graphing. If necessary, round to the nearest

thousandth.

1. 0.5 9 0.2 73xe 2. 79 5.5 51xe

________________________________________ ________________________________________

Solve each equation algebraically. If necessary, round to the nearest

thousandth.

3. 3 616 8x x 4. 2 33 4 78xe 5. 1 212 20x

________________________ ________________________ ________________________

6. 2 49 27x x 7. 0.5 2 5256 64x x 8. 2 33216 36x

x

________________________ ________________________ ________________________

9.

31

279

x

10.

5

218

16

x

11.

8 22 25

5 4

x

________________________ ________________________ ________________________

12. 8 10

7 10 9 4x

13. 4

3 10 4 91x

14. 8 110 3 70xe

________________________ ________________________ ________________________

Solve.

15. Lorena deposited $9000 into an account that earns 4.25% interest each

year.

a. Write an equation for the amount, A, in the

account after t years. ____________________________________

b. In how many years will her account exceed

$20,000? ____________________________________

c. If she waits for 50 years, how much will be in her

account? ____________________________________


Use the scenario in the box for Problems 16–18. Tell

whether the events are mutually exclusive (ME) or

overlapping (O), and give the probability of each.

16. drawing an odd number or a multiple of 7 __________ P ___________

17. drawing an even number or a perfect square __________ P ___________

18. drawing a prime number greater than 10 or a multiple of 5 __________ P ___________

Use the table and description of the experiment

for Problems 19-21. Express probabilities as

fractions and as decimals to the nearest hundredth.

19. If a volunteer is chosen randomly, what is the probability that

this person receives the highest dose of the drug per day? __________________

20. If a volunteer is chosen randomly, what is the probability that

this person receives more than 150 milligrams per day? __________________

21. If a volunteer is chosen randomly, what is the probability that this

person does not receive 200 milligrams per day? __________________

Use the scenario in the box for Problems 22 and 23.

Express probabilities as decimals.

22. What is the probability that a student in the class

has blonde hair and blue eyes? ___________

23. What is the probability that a student in the class

has blonde hair and brown eyes? ___________

Find the probabilities for Problems 24 and 25.

24. A student is collecting a population of laboratory mice to be used in an

experiment. He finds that of the 236 mice in the lab, 173 mice are

female and 99 have pink eyes. Just 10 of the pink-eyed mice are male

What is the probability that a mouse is female or has pink eyes? __________________

25. A group of 4 friends buys a CD of 12 computer screen savers. Each

friend will pick 1 screen saver to use on their computer. What is

the probability that at least 2 of the friends will choose the

same screen saver for their computer? __________________

Group Volunteers Daily

Amount (mg)

A 353 150

B 467 200

C 310 250

A drug company is testing the side effects of

different doses of a new drug on three different

groups of volunteers.

Mr. Rodney has 28 students in his

class. Six students have blonde hair,

10 have blue eyes, and 5 have brown

eyes. The blonde-haired students

make up 1

5 of the blue-eyed students

and 3

5 of the brown-eyed students.

Cards numbered 1–25 are placed in

a bag and one is drawn at random.


Use the table to find the probabilities in Problems 1–4. Write your answer

as a percentage rounded to an integer.

The table shows the results of a poll of randomly selected high school students. They

were asked if they think smartphones should be allowed in class.

9th

Graders

10th

Graders

11th

Graders

12th

Graders Total

Yes 0.15 0.16 0.19 0.18 0.68

No 0.12 0.11 0.05 0.04 0.32

Total 0.27 0.27 0.24 0.22 1

1. What is the probability that a 9th or 2. What is the probability that an 11th or

10th grader answered yes? 12th grader answered no?

________________________________________ ________________________________________

3. What is the probability that a 9th or 4. What is the probability that a 10th or

11th grader answered yes? 12th grader answered no?

________________________________________ ________________________________________

Solve.

5. Sarah asked 30 randomly selected students at

her high school whether they were planning to

go to college and whether they were planning

to move out of their parents' or guardians'

homes right after high school. The results are

summarized in the table.

Which is more likely, that a student planning to go to college is also planning to move out, or that

a student planning to move out is also planning to go to college? Justify your response with

conditional probabilities.

________________________________________________________________________________________

Go to College

Move

Out

Yes No Total

Yes 12 9 21

No 8 1 9

Documents

Algebra 4 Name Final Exam Review Per