Permutations and Combinations Questions and Answers

7 2 4x 14 10 4 2x 10 8 10 4 8x 11 12 13 5x 9 20 7 3x 12 4 x 10 2

1 10 x 3 4 2 x 4 5 Topic 3 Equations with variable on right 2 20 5x5 5 10 4 x 5 3 6 6x 12 6 3 x 2 1

Let p and q represent the following simple statements p The chair is broken q I work hard Write the symbolic statement p q in words Choose the correct sentence below OA If I do not work hard then the chair is broken OB The chair is broken if and only if I do not work hard OC If the chair is broken then I work hard OD If the chair is broken then I do not work hard

Let p and q represent the following simple statements p I get an A q I go to the gym Write the following compound statement in symbolic form I get an A or I do not go to the gym The symbolic form is

What type of function is f x 5 1 exponential growth exponential decay

1 4 12 4 10 4 7 10 6 10 4 3 Topic 1 Integer operations 2 10 3 5 5 8 8 106 11 4 2 3 2 6 8 8 9 20 5 12 4 8

3a 8 x 2 4a 10 4 2x 3b 12 2x 4 4b 6 3x 24

1a 10 4 2a 4x 12 3a 8 X 2 1b 6 8 Do Now 11 29 1c 4 6 2b 3x 4 11 3b 12 2x 4 1d 3 2 8 2

d 32 3 4 x 6 a 2 b 10 c 2 d 10 d 16 4 12 x 10 a 2 b 22 c 22 d 2

Listen I wish to have 12 000 in my account in 5 years to much money should I deposit now into my account earning 2 interest compounded quarterly Use one of the formulas below to solve the problem Future Value A P 1 1 xt Present Value P A 1 z nxt 13 258 75 10 860 75

Expand x 1 x 1 Simplify your answer

rigonometric Patios find an Find mZD D 47 E

Find the first term and the common difference 3 1 1 3 a d

Find the nth or general term for the geometric sequence 5 6 6 6 Which represents the nth term OA 6 1 1 OB 6 1 OC 6 1 OD 6 n 1

Find the sum of the first 53 terms of the arithmetic series 36 38 40 42 S53

Find m2V X 12 3 W mzv 12

Find mLX W 33

Find mZV V mZV Submit 3 26 W 3 13 X

Given vectors u and v find a 4u b 4u 7v c v 7u u 9 7 v 2 0 a 4u 36 28 b 4u 7v

If it exists find the inverse of the matrix A If it does not exist enter DNE 1 0 4 3 4 10 0 1 5 A

If possible find and enter the missing matrix If not possible enter DNE a 10 4 8 1 C d 01 missing matrix 2 4 4

Calculate each product below 7 3 4 a b 5 7 3 7 6 3 3 578 9 1 6 1 9 8

Simplify completely 12 X 7 O 12 X 7 x 7 x 3 O X 3 X 7 X 7 x 3 12x 36 x 4x 21 X 7 and find the restrictions on the variable

Evaluate each expression using the graphs of y f x and y g x shown below a gof 1 b gof 0 c fog 1 d fog 4 a gof 1 Simplify your answer y g x 6 d 13 y f x 8 10

Find mZX X Y mZX 2 3

Graph the circle x y 6 4 O A O G O B 10 Q O C 10 Q X Q O D IKD X

Solve the equation 2x 15 x 6 OA OB 7 OC 7 3 OD 3

f x O 4 2 co O x F R E O N C

The function f x x 5 is one to one Graph f as a solid line and f as a dashed line on the same axes 2 OA OD AY 12 12 12 Q G OB O E 12 12 GAM 12 Q Q E The function is its own inverse O C OF The function is not one to one

Calculate the binomial coefficient 11

asymptote s for the graph of h x 3x 27 x 4x Vertical Asymptote s Horizontal Asymptote s 3 pts

1 Let f x 6x 1 and g x Find f g x f g x fg x and H 1 f g x 6x 1 Simplify your answer fg x 1 X f g x 6x 1 Simplify your answer 1 X 6x 1 Simplify your answer x x 6x 1 Simplify your answer The domain of f g is 6 Type your answer in interval notation The domain off g is 8 in interval notation 4 x Give the domain of each

Use the given table to evaluate each expression in parts a through d if possible a f g 2 b f g 4 c fg 2 d 0 a f g 2 7 Simplify your answer b f g 4 8 Simplify your answer c fg 2 Simplify your answer X 2 0 2 4 J 0 7 10 14

Let f x 6x 1 and g x Find f g x f g x fg x and 1 f g x 6x 1 Simplify your answer X f g x 6x 1 fg x 1 X Simplify your answer 6x 1 Simplify your answer x Simplify your answer 4 x Give the domain of each www

5 x 5 y 3 49 6 x 5 y 3 49 7 x 5 y 3 49 8 x 5 y 3 49 5 Drag each graph above to the correct exercise number below 6 7 ON 8 below 27 C G G

Use the selected values of a linear function g x in the table and the equation h x shown below to evaluate goh 3 X 3 1 0 4 g x 5 1 1 9 h x x 2 O 22 O 21 O 14 O 15

Question 1 14 Simplify Assume that all variable exponents represent positive real numbers 2x 3 8x 2 27x 30 6x O 2x 6 3x 5 2x 6 3x 6x

1 B 9 Basics to Multiplying Rational Expressions Simplify each expression A 6b C 3 5 7b 8 9b 9b A 7 k 7 5 7k 5 k 6 C k 5 9 A 2v 56 81b 5 35v 45 A C v 3 4 n 3 49n 14 A 2 k 2 7k 5 2 k 8 k 2 B B b D 14v 18v n 1 6 n 2 B D 5 n 6 n 7 4 36 3a 7 21a 64a 35 3 a 1 k 1 4k k 7 k 8 21n 64n 20 9n 30n 5a a 6 a 10 6 v 2 v 9 100 9v B D 14a 10a 5a 45 B n 3 21n 8 9n D 2q 5 a 9 a 6 9a 2 4 6 2 6x A 9x 2x 4 5 r 6 r 2 10 6 8 10 A 6 3x 9 8 8 A C 0 A 10r r 2 r 6 r 5 7 x 4 5x 4 x 9 7n 6 18n 27n n 3 10n A B 7 D C n 9 n 2 10 30x90 6k k 3 9x 20 r 2 5 r 5 r 2 12k 60k 5k 22k 21 4 k 3 k 3 D B 1 10 r 9 D r 8 2n n 6 21n 18 B B D x 8 3x B D 10k 36k 70 4k 100 8 k 8 k 10 54k4 k 9 2 3n n 6 n 2 27n

y x Graph the hyperbola 25 49 1 Give the domain range center vertices foci and equations of the asymptotes for the figure 7 B Y 5x 5 c y x y x 7 OD x 5Y Graph the hyperbola y x 25 49 1 The domain is 0 00 Type your answer in interval notation The range is rin interval notation Choose the correct graph below C 1 8 More B O D Q

Graph the hyperbola x y 9 Give the domain range center vertices foci and equations of the asymptotes for the figure The hyperbola has a center at 0 0 Type an ordered pair The vertices are 3 0 3 0 Type ordered pairs Use a comma to separate answers as needed The foci are 3 2 0 3 2 0 Type ordered pairs Type an exact answer using radicals as needed Use a comma to separate answers as needed What are the equations of the asymptotes Choose the correct answer below OA y 3x OB x y O C x 3y OD y x

X Graph the hyperbola 25 49 equations of the asymptotes for the figure The hyperbola has a center at Type an ordered pair 1 Give the domain range center vertices foci and

25 16 1 Which graph is correct B 5 OC What are the foci of the ellipse 3 0 3 0 Type an ordered pair Round to the nearest integer as needed Use a comma to separate answers as needed What is the domain G nowor in interval notation Round to the nearest integer as needed Use a comma to separate answers as needed OD

State the domain of the rational expression X 2 x 4x 32 Select the correct answer below and if necessary fill in the answer box to complete your A XIX Use a comma to separate answers as needed B x x is any real number

9x y 225 The endpoints of the minor axis are 5 0 5 0 Use a comma to separate answers as needed Type an ordered pair using integers or fractions OA CHICK CAR The foci of the ellipse are 0 10 2 0 10 2 Simplify your answer Use a comma to separate answers as needed Type an ordered pair Type exact answers for each coordinate using radicals as needed Graph the ellipse Choose the correct graph below B The domain of the ellipse is Type your answer in interval notation Type an exact answer using radicals as needed OC Ay Q

Graph the given interval and then express the given interval as an inequality in terms of x 0 9 Choose the correct graph below O A O C 9 10 8 6 4 2 0 2 4 6 8 10 10 8 6 4 20 2 4 6 8 9 10 O B 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 6 6 8 9 9 10 8 10

17 10 12 x 18

Graph the given interval and then express the given interval as an inequality in terms of x 0 9 Choose the correct inequality OA x 9 B X 9 OC x 9

Question 1 10 points Which is the graph of y x 1 2 O 2 51 2 2 1 11 A 2 21

Graph the ellipse Identify the center vertices endpoints of the minor axis and foci 20x 560 7y The center is 0 0 Simplify your answer Type an ordered pair The vertices are Simplify your answer Type an ordered pair Type exact answers for each coordinate using radicals as needed Use a comma to separate answers as nee

Paired or not paired Decide whether each situation involves paired or not paired data Then select the correct program for constructing a CI to estimate the difference a The wait times for Caucasian Walmart customers ages 56 34 45 23 18 and 41 were recorded Then the wait times for non Caucasian Walmart customers ages 56 34 45 23 18 and 41 were recorded The data is Select an answer so we should use the program Select an answer b We take a random sample of 50 days and record Microsoft stock and Apple stock on those same days The data is Select on opow chou