Permutations and Combinations Questions and Answers

Practice 1 If y 12x 10 what is the value of y when x is equal to 4

Graph the image of square ABCD after a dilation with a scale factor of 3 centered at the origin 10 8 6 D 4 104 8 6 4 12 63

Exit Ticket 12 5 1 13x4 2y 11 what is the value of x if y 3 A 3 B 3 C 4 D 7 2 If 2x 4 10 3x what is the value of x a 1 2 b 1 2 c 2 8 d 6 3 If 2 2x 4 x 7 12 what is the value of x a 9 b 1 c 1 d 13 3 4 If 2 3x 6y 5x 10y 6 what is the value of 3x 5 if y 4 A 14 B 37 C 94 D 277

Simplify each expression 3v 5 5v 36v 36 1 A B C D 3 A B 4 2k 8k 10 C 6v 6 5v 36v 39v 4 v 6 5v 6 5v 36v 40v 3 v 6 5v 6 D 5v 36v 39v 5 v 6 5v 6 4v 4v v 6 5v 6 13 4k k 2 k 5 13 k 3k 2 k 5 3k 12k 15k 2 k 1 k 5 6k 24k 29k 4 2 k 1 k 5 2 4 2 5 5 m 5 2m 2 A B C D 4 A B C 25 2m 8m 5 m 5 5m 1 2m 30m 60m 30m 3m 45 3m 16m m 3 D 12m 12 5 m 5 15m 15 2 m 1 m 5 3 2m m 10 2 m 3 m 4 25m 1 20m 40m 30m m 1 12m 4m 5 5 3m 1 44 3m 16m m 2 m 3 m 4

4 4i 3 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in the form a bi 2

Find the given power and write the answer in rectangular notation cos 90 isin 90 6 cos 90 isin 90 0 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in the form a bl

0 3 23 y 2 3x 5 D y 5x 2 What is the equation of the line 6B y 2x 5 y 5x 23 Dec 6 8 56 US O

7 2x 3y 5x 3 16 3x 6x A C 9 A 5n 5n n 4 n 5 B C D 11 A B 3 5 3 8r r 5 2 r 2 C D 5n 4 2n 3 10n 45n n 5 n 4 7n 2 n 1 2n 1 5 2 2n 3 B 3 7r 3r 1 3 8r D 3r 1 29r 12 7r 2 x 5 r 2 17r 6 41 r 5 r 2 8 3x 3x 5yx 2 5x 8 10 12 8 A v 2 B C D 10 A B C 12 4 2x D 2v 4 3 A B C D 7v 2v 4 3 v 2 8v 8 v 3 v 2 10v 8 3 v 2 8v 11 v 3 v 2 5 2x x 3 10x 17 2x 2x x 3 7x 17 x 2x x 3 9 2x 4 x 4x 17 2x x 3 5 5x 5 x 5x 2 x 6 17x 20 2x 3 x 5 35 7x 2x 3 x 5 x 6 25x 10x x x 6 5x 2 5 r 6 5x 2

Adding Rational Expressions Simplify each expression x 2y x 3y 9x 9x2 A 3 B C D A 2x 2y B C D A 2x 5y 9x 3x 5y 9x 2x 8xy 6y 81x4 B D 5xy 6y 81x4 3y 3x 2x x 2y 2yx y 3x 3 5 2 5 yx 3xy x 2 2x x 2 3y 2y 3x 10x 3y y x 5 15 6x 10x 15x 6y 10y 2x 3 2y 5 4 6 2 2 A C 6 A 3x 4 2 C A b 1 B 3b 2b 3 6b 3b 2b 4 6b 3b D 5a 3b x 9 x 2x x 3 66 2 2x 6 X 2 2x 3 b 2 a 4b Sab 3b 6a 4b b 3 5ba 5a 4b b 3 5ba 3a 5b b a B D 2b 3 b 2b 3 2b 2 b 2b 3 B D 3b a 25a b 3a 12b 15b a 6 x 2x x 3 3x 9x 2 2 x 3

w 2 If log3 325 x 4 Alog3x Blog3z Clog3 w D find A B C D

Calculate the binomial coefficient 15C14

Calculate the binomial coefficient 11C6

Evaluate the expression 15 13 2 15 13 2 Simplify your answer Type an integer or a fraction

Subtract and simplify your answer Do not add spaces in your answer 3 3 3y 15 5y 25 Numerator a Denominator b

etermine intervals on which the function is increasing decreasing and constant On what intervals is the function increasing OA 6 1 OB 3 9 OC 6 1 and 6 9 OD 9 6 and 3 9 On what interval the function decreasing On what interval is the function constant 4 10 40 10

Find the indicated term for the binomial expression 7th term 8 3x y The 7th term is

Use the graph to find the following a f 2 b the domain c any x values for which f x 1 d the range f 2 What is the domain Select the correct choice below and if necessary fill in the answer box es to complete your choice OA x1xs OB x1 x OC x1x OD x1x E The domain is all real numbers 10 8 8 10 8 4 Ay

Simplify each expression b 5 2b 12b 16 1 A 3 b 5 2b b 4 7 2 b 9 24k 16k 3k 1 14b 20b 146 48b 40 6 b 5 b 3 B D b 3 b 1 b 4 27k 18k 27k 9k Find each product 5 7p 3 6p 1 A 16p 64p 64 B 42p 25p 3 C 16p 64p 64 2 4 6 2 40n 56n 35n 49 5n 38n 48 5n 8 4 8n 7 n 6 A B 70m n 9 n 5 C n 6 D 10n n 4 7m 4 49m 28 14m 28 12m 24 6 6k 1 7k 2 A 42k 19k 2 B 4k 16k 12 C 42k 2 5k 2

Which graph is sketched to the right A g x x 1 x 2 x 3 B g x x 1 x 2 x 3 C g x x 3 x 2 x 1

Given the graph below determine whether each statement is true or false Statement 3 is a zero of the function 2 is a zero of the function 1 is a zero of the function 0 is a zero of the function 1 is a zero of the function True False 0000

How is the graph of g x x 3 related to the graph of f x x A The graph of g x is a translation of the graph of f x right 3 units and a reflection across the y axis B The graph of g x is a translation of the graph of f x down 3 units and a reflection across the x axis C The graph of g x is a translation of the graph of f x right 3 units and a reflection across the x axis

How is the graph of g x x 1 related to the graph of f x x A The graph of g x is a translation of the graph of f x down 1 unit B The graph of g x is a translation of the graph of f x up 1 unit C The graph of g x is a translation of the graph of f x right 1 unit

How is the graph of g x 2x related to the graph of f x x

Find the mean for the following group of data items 150 90 120 90 110 The meen is Type an integer or a decimal

A single die is rolled twice The 36 equally likely outcomes are shown to the right Find the probability of getting two numbers whose sum is 6 First Roll Second Roll A 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6 The probability of getting two numbers whose sum is 6 is Type an integer or a simplified fraction 0 www TAPUSTEN

Write the equation of the graph shown below in factored form 5 f x x 2 x 1 x 3 f x x 2 x 1 x 3 f x x 2 x 1 x 3 f x x 2 x 1 x 31 5 0 5

Which of the following describes the function x 1 O The degree of the function is even so the ends of the graph continue in opposite directions Because the leading coefficient is positive the left side of the graph continues down the coordinate plane and the right side continues upward O The degree of the function is even so the ends of the graph continue in the same direction Because the leading coefficient is negative the left side of the graph continues down the coordinate plane and the right side also continues downward O The degree of the function is even so the ends of the graph continue in opposite directions Because the leading coefficient is negative the left side of the graph continues up the coordinate plane and the right side continues downward O The degree of the function is even so the ends of the graph continue in the same direction Because the leading coefficient is positive the left side of the graph continues up the coordinate plane and the right side also continues upward

Construct a truth table for the given statement 9 p q Fill in the truth table P T T F F q T F T LL F q 9 P 9 P q

Step 2 This is a binomial experiment with n 18 trials Let a success be that a student withdraws from the course It is given that 15 of students withdraw Recall the method used to find the probability of an event given a percentage given percentage 100 probability Thus the probability p a student withdraws from the course is as follows given percentage 100 probability p 100 For 2 or fewer students to withdraw from the course means that exactly Select dents withdraw Therefore x will be Select The probability of each x value is f x so the probability that 2 or fewer students withdraw from the course will be 0 1 or 2 2 1 or 2 0 or 1 Submit Skip you cannot come back

1 4 4x 12 4 20 10 5x Topic 6 Mixture 2 20 5 3x 5 10 2 2x 3 10 5 3x 6 16 8 4x

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