Permutations and Combinations Questions and Answers

A plane is flying at an elevation of 21000 feet It is within sight of the airport and the pilot finds that the angle of depression to the airport is 26 Find the distance between the plane and the airport Find the distance between a point on the ground directly below the plane and the airport

Find the vertex of y x 6x 6 using the vertex formula Step 1 Find the x coordinate of the vertex For any parabola y Az Bz C the x coordinate of the vertex will always be t Using this formula what is the x coordinate of the vertex for the parabola y x 6x 6 Step 2 Find the y coordinate of the vertex lue the vertey of the serab

4x y 1 What is the slope of this line What is the y intercept of this line

K Expand 3x 4y What is the expansion Simplify your answer

Z

5 6 5 4 3 2 1 Ty 2 3 4 5 2 3 6 1 2 3 4 5 16 What are the coordinates of the circle s center What is the radius of the circle r Given the circle write the equation of the circle in standard form

Find the exact value of the logarithm without using a calculator log 28 log8 8

Find the exact value of the logarithm without using a calculator log 12144

Problem 7 Which of the following statements are always true for vectors in R i If u vxw 4 then w vx u 4 ii 5u v u 6v 31 u xv iii If u is orthogonal to v and w then u is also orthogonal to w v v u A all of them B iii only C i and iii only D i only E none of them F ii only G ii and iii only H i and ii only

In an arithmetic sequence a17 a Simplify your answer 59 and 230 12 49 Find a and d Write the first 5 terms of the sequence

Simplify each difference 2 3n 6 3n 4n 7 7m A n 4n 12 6m B n 4 14 6m C n 4n 12 4n 13 D Simplify each sum 4 2x 5 6 2x A 1 C 1 5x B 1 x D 3 5x 3 5 3 6 5 2n 4 5 8n A 10m 7n 5 B 10m 8n 5 C 10n 2n 5 D 10m 2 5 2x 6x 3x x A 7x x C 8 x B 15x x D 14x 17

Divide 2 2 2 3 A B C D 3 2 3 10 5 3 5 15 8 4 2 2 2 3 6 2 5 5 25 2 15 5 6 45 21 2 2 3 4 2 2

Simplify mn 2 2n4 m n O O O O 2m n4 2 4n m 4n8m 4 6 n 8m6

Ise a matrix equati 28 x y 3 2x y 6

62 of the freshmen like both rap and classical but don t like jazz 29 of the freshmen like both rap and jazz but don t like classical 56 of the freshmen like classical but like neither rap nor jazz 117 of the freshmen like jazz but like neither rap nor classical 47 of the freshmen like rap but like neither classical nor jazz 572 of the freshmen like at least one of these three types of music rap classical jazz Construct a Venn diagram illustrating these results Then answer the question All freshmen in the survey Like rap 297 7 Like classical How many of the freshmen don t like jazz freshmen X 3

7 41n 2214n 71 n 54 76 A 41n n 1 2 B 41n n 2 C 41n 71 n 54 D 41n 1 n 54 70 n 54 71 n 54 8 8 66x 2912x x 3036 96 x 41 A x 30x 29 B x 30x 35 C x 30x 33 D x 30x 32 96 x 39 96 x 37 96 x 36 96 x

5 32x x 30 x4 18x x 6 6 6 5 x 6 6 A x 5x 2x 5 B x 5x 4x 3 x 6 6 C x 5x 2x 6 D x 5x 4x 3 x 6 1 x 6 6 b 3b 3 b 3 1 A b b b 3 B b b 2 C b b 3 3 b 3 D 6 2 b 3 7 b 3

Synthetic Division Divide 1 3 2v v 2 v 6 A v v 3 2 v 4 2 v B v v C v v 3 3 D v 2 v 2 2 2n 3n 2 n 1 1 A 2n n 1 n 1 3 B 2n n 2 C 2n n n 3 D 2n n 3 n 1 3 n 1 3 n 1

Synthetic Division Divide 1 3 2v v 2 v 6 A v 3 2 v 4 2 v B v v C v v 3 3 D v 2 v

5r2 8 43

6x 480

2x 3y 4 x 2y 3

18x 81 0

Construct a truth table for the given statement qV p Fill in the truth table P T F q T P qv p

Find the x intercepts of the polynomial function State whether the graph crosses the x axis or touches the x axis and turns around at each interce f x 4x x OA 0 crosses the x axis 4 crosses the x axis 4 crosses the x axis OB 0 touches the x axis and turns around 4 crosses the x axis 4 crosses the x axis OC 0 touches the x axis and turns around 4 touches the x axis and turns around D O touches the x axis and turns around 4 crosses the x axis

oblem 8 Let V be the set of all ordered pairs of real numbers with u 0 Consider the following addition and scalar multiplication operations on u and v v v u v U v 2 6u v ku ku1 ku Use the above operations for the following parts a Compute u v for u 6 2 and v 4 7 b If the set V satisfies Axiom 4 of a vector space the existence of a zero vector what would be the zero vector c If u 3 8 what would be the negative of the vector u referred to in Axiom 5 of a vector space Don t forget to use your answer to part b here

Change the exponential statement to an equivalent statement involving a logarit ex 19

Numbered disks are placed in a box and one disk is selected at random If there are 6 red disks numbered 1 through 6 and 2 yellow disks numbered 7 through 8 find the probability of selecting a red disk given that an odd numbered disk is selected 34 1 1 30 00

O You are dealt one card from a standard 52 card deck Find the probability of being dealt a picture card 3 13 1 S 3 52 3 26

You are dealt one card from a 52 card deck Find the probability that you are not dealt a 4 09 10 12 13 1 10

You randomly select one card from a 52 card deck Find the probability of selecting a black ten or a black queen 1 26 12 1 13 13

A single six sided die is rolled twice The 36 equally likely outcomes are shown below Find the probability of getting two numbers whose sum is 5 Second Roll First Roll OOOHH 1 1 12 3 1 6 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 2 1 36 4 1 9

Find all of the real solutions to the following equation Write your answers in order from least to greatest 5x x 4x X X X

Use the given display to find the mean Round to the nearest tenth if necessary A 10 11 12 13 14 15 Score Frequency 13 5 4 12 5 12 6 12 4

A researcher records the number of employees of each of the IT companies in th town of Westmoore The results are summarized in the table Number of Employees 0 749 750 1499 1500 2249 2250 2999 3000 3749 Find the class width 750 749 5 5 Number of IT Companies 30 24 6 5 5

Find the exact value of the real number y if it exists Do not use a calculator y tan 3 Select the correct choice and fill in any answer boxes in your choice below O A y tan 3 Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the express 1 OB tan 3 does not exist

Let A 14 19 a a13 b a31 19 10 11 6 c a a22 13 3 15 Find the following matrix entri FI A

b 3x 2 3 1 4 6 81y x

Describe the transformations and give the equation for the graph 10 PPA K 111 8 6 8 A 2 AIXS OA It is the graph of f x x shrunken vertically by a factor of 9 and translated 5 units down The equation is y xl 5 OB It is the graph of f x x stretched vertically by a factor of 9 and translated 5 units down The equation is y 9 x 5 OC It is the graph of f x x shrunken vertically by a factor of 9 and translated 5 units down The equation is y 9 x 5 OD It is the graph of f x x stretched vertically by a factor of 9 and translated 5 units down The equation is y x 5

Give a rule for the piecewise defined function Then give the domain and range OA O C f x 5 if x 2 6 if x 22 Domain 5 6 Range 0 00 5 if x 2 6 if x 2 Domain 00 00 Range 5 6 f x 81 B O D f x 4 f x 5 ifx 2 6 if x 2 Domain 5 6 Range 0 00 5 if x 2 6 if x 2 Domain 00 00 Range 5 6 X

Determine whether the equation has a graph that is symmetric with respect to the y axis the x axis the origin or none of these y x 4 x 2 OA x axis only OB x axis y axis origin OC y axis only OD none of these ALLEN

Does the relation shown below define a function 8 2 8 8 0 6 6 3 7 4 O No Yes

18 k 9 k 5

Write your solutions on a separate sheet of paper Estimate 250 as an integral power of 10 1

Approximate the following number using a calculator 133e 025 9 0025 91

5 4 15 3 7 15n 10n 3 6 20x 20x 8 18a 4 3a

3 18 3 2

B A x C x D 5 x x 2 6 12x 8x 16 9 3x x 8 2 2x 3x x 1 9 2x 4 3x 5 A 6x 22x 20 B 6x 20 C 6x 2x 20 D 6x 2x 20 1 11 2p 5p 3 5p 2 A 56p 4p 4p 8 B 10p 21p 5p 6 C 7p 31p 16p 20 D 10p 19p p 35 8 10 8 6a 7 2a 7 A 12a 56a 49 B 12a 49 C 12a 28a 49 D 12a 56a 49 10 7v 7v 2 7v 3 A 16v 20v 58v 16 B 25v 55v 34v 16 C 49v 28v 7v 6 D 56v 11v 12v 9 12 12 A B C D P p 5p 85p 10 3 18 3 5p 10 3 3 5 10 18 3 15p 107p 18 5 2 3P P 0 22

2 Are 6b and 6b3 like terms Why or why not 3 Are 5ab and 4ac like terms Why or why not 4 Are 5 and 10 like terms Why or why not

27 10 1 9x 6 x 10 29 3 10b 10 5 b 2 28 5 2n 4 2 n 3 30 7 n 3 8 1 8n