Permutations and Combinations Questions and Answers

1 55 According to a poll 56 of voters support funding a new community center A surveyor randomly selects 75 voters and asks each voter if he or she is in favor of the center If being in favor of the center is a success what is the probability of a success for this binomial experiment O 0 34 0 44 0 56 O 0 75

What is the approximate degree measure of angle A in the triangle below A O 37 9 38 9 O 51 1 52 1 18 B 14 U

B Find the inverse of the function f x 3x 7 O f x 7 x 72 3 x 7 2 3 O x x 7 3 2

Chris is studying the growth of a particular type of plant He is testing the effects of three growth factors lighting age and temperature Here are the levels he s testing for each Growth factor Levels Lighting Low Medium High Age 1 month 2 months 3 months 4 months 5 months Temperature 20 C 22 C 24 C 26 C He wants to find the number of ways of combining one level from each of the growth factors How many ways are there

A tax rate schedule is given in the table If x equals taxable income and y equals the tax due construct a function y f x for the tax schedule f x 0 1x If taxable income is over But not over x D x D 15 132 50 0 33 x 74 300 0 7 550 30 650 74 300 74 300 7 550 30 650 The tax is this amount 0 00 755 00 4 220 00 15 132 50 If 0 x 7 550 if 7 550 x 30 650 if 30 650 x 74 300 fx 74 300 Plus this 10 15 25 33 Of the excess over 7 550 30 650 74 300

To make 1 as the leading coefficient multiply Equation 2 by and Equation 3 by y Z 7 Eq 1 Eq 3y 2 5 2 72 21 Eq 3 Write the equivalent system with the resultant Equation 2 and Equation 3 x y z y z 1 Eq 1 Eq 2 Eq 3

A cube is called colored if each of its faces is colored by one of three given colors Two colorings are considered to be the same if there is a rotation of the cube carrying one coloring to the other Prove that there exist exactly 57 different colorings of the cube

7Q Given that x 2 is a zero of P x x x 16x 20 find all other zeros of P x by using long division

Triangle Similarity State if the triangles in each pair are similar I complete the similarity statement If it helps sl 1 D C 96 ARCD B 96 W

7 n 2 n 3 2 44 8 3x 7 4 x 2x 5 2 3

Inequality 0 x 3 0 x 4 2 x 5 x 1 12 2 x 3 or x 2 0 Graph 3 Interval Notation 0 4 2

he largest set on which the funtion f x y x y x y is continuous is A x y x y x B x y x y x C the whole xy plane D x y x y E x y x y x

Homework Unit 7 MATH 0307 14 1 2 solving systems by grap Solve the system of linear equations by graphing x y 1 x y 3 Use the graphing tool to graph the system AXED Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution of the system is Type an ordered pair OB There are infinitely many solutions x y x y 1 or x y x y 3 OC There is no solution or Question 4 4 1 25 Part 2 of 2 A Ay HW Score 50 3 O Points 0 of 1

Consider the following 1 f x 2x x y 3 0 2 5 2 0 1 5 1 0 0 5 1 y 2x 2 3 dx 3 4 5 6 a Write the integral that describes the area of the shaded region 6 C X b Find the area Give an exact answer Do not round

17 g x x 3x f x 4x 1 Find g f x 19 g n 2n 2 f n n 5 Find g f 1

You are asked to explain what 18 means Which of the following explanations is true 18 means the number that multiplies itself 6 times to equal 18 18 means to multiply 18 18 18 18 18 18 18 means to divide 18 by 6 18 means to find of 18 D

Solve the system of linear equations by graphing x y 2 x y 2 Use the graphing tool to graph the system Click to enlarge graph Question 2 of 10 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution of the system is 10 8 b 10 2 This test This quest 6

60 5 40 5 2 5 of the following graph 20v5 4n 5 6Gn 5 Bn 5 2n 120 510 5160 5 O a f x 2 cos x 1 Ob f x 2 cos x 1 Oc f x 2 cos x 1 Od f x 2 cos x 1

In AKLM the measure of M 90 KM 9 ML 40 and LK 41 What ratio represents the cosecant of ZL 40 L M 41 2

If U V are ideals of R let U V u vjuEU VEV Prove that U V is also an ideal

Pentagon ABCDE can be mapped to pentagon A B C D E by a rotation 90 counterclockwis about the origin followed by a translation A 10 9 8 7 6 5 4 3 2 1 B 104Y 9 8 7 6 5 4 3 A 2 C op 27 1 1 2 23 4 5 6 1 8 9 10 E Rotation x y 70 E D D Write the functions that describe the rotation and translation C 1 2 3 4 5 6 7 8 9 10 B X

104 Express the following quotient in simplest form without the use of negative exponents 8xy 4xy

Question 1 1 point Graph the function Label the vertex and axis of symmetry h x x 1 O a Ob Oc O d 8 4 1 0 8 8 4 X MA 2 4 8 B HO 6 24 MD 1 12 4 x 0 2 0 1 x 0 N w 4 6 8 6 6 X 6 6 On 6 X 1 0 T

Job SKETCH THE GRAPH of f x TAN 2x 2TT 3 2 SHOW ALL STEPS DIS CUSSED IN CLASS SUCH AS THE GENERAL FORM OF ZEROSIVERTICAL ASYMPTOTES SAMPLE TABLES OF ZEROS AND VERTICAL ASYMPTOTES ETC

8 A GRAPH of Y cosx cos3x SIN2X IS GIVEN FIND THE 13 X INTERCEPTS THAT ARE IN THE INTERVAL 271 27 HINT GROUP THE FIRST infhife TWO TERMS AND USE A SUM TO PRODUCT FORMULA

Find the limit L Then use the e 6 definition to prove that the limit is L lim F 241

dP The solution to the population model 3P with initial condition Po 2 is dt O 3e t O 2e t O None of the others O 3e 2t 22e 2e 3t

The order of the differential equation is 10 7 2 None of the others y 2 6y5 sin x

1 Consider the graph below Find the betweenness of the following edges a AB b BC C DE A F E D

Perform the indicated operation Write the answer in scientific notation 3 6 10 14 9x10 1 3 6 10 14 11

Use the graph of the following function f x to find f 0 10 BB 2 4 4 B Q 2

se the graphing tool to graph the equation Use the intercepts when drawing the line If only one intercept exists use it d another point to draw the line pe the equation using function notation Simplify your answer 6 4 2 2

Consider the linear transformation Tao a x a x a a ao a a x If u 2 x 3x B 1 x 1 x 1 and C 1 x x what is T Pg u A B C D 4 4x 4 8x 4 4x 8 4x

Given the formula T 8w 2wz solve for z Make sure to use appropriate parenthesis When simplifying keep T positive and leave the answe N 0 Solve the systems of linear equations using the substit 23 y x 20 20x60y 117 1 1 4 O 1 4 3 7

Solve the quadratic equation by factoring then se all possible answers You may check your solution graphing it x x 42 0 More than one answer may be correct mark all 6 6 7 1 7

a Find the volume by integration and b sketch the solid of integration To sketch p 6 cos use a table of values and sketch on the yz plane Then think about rotation 2 2 6 cos p SS S 1 p sin p dp do do 0

d the maximum and minimum values and a vector where each occurs of the quadratic form subject to the constraint Z 7x 6x x 1 The constrained maximum of occurs when x1 x and the constrained minimum of occurs when x1 x2

Suppose H x 6x 9 Find two functions and g such that fog x H x Neither function can be the identity function There may be more than one correct answer 0 0 8 0 0 0 X CIC

A For any sets P and Q show that PQ P UQ 2 For any sets X and Y show that X Y XO 3 How many 5 person teams contain at lea mon

Here is a graph of y a x represented with a solid curve and a set of data dots on the graph D X ALONS HAI Occur to meye Write an expression for the Data set function b x in terms of a x detted data set

2 Is the set A x 0 r 3 4 open in R2 Justify your answer

A farmer has 80 meters of fencing to use to enclose a rectangula 1 Let I represent the length of the rectangular garden in meters and let A represent the area of the rectangular garden in square meters a Write a formula that expresses A in terms of L A Preview b What is the maximum area of the garden It may help to use a graphing calculator square meters Preview c What is the length and width of the garden that produces the maximum area Length Width W meters Preview meters Preview Length Width d If the farmer instead had 270 meters of fencing to enclose the garden what garden length and garden width will produce a garden with the maximum area meters Preview meters Preview

In ARST ZR 63 ZT 90 RS 23 and ST 10 4 Which ratios are correct 23 RT O csc 63 O csc 27 O csc 27 csc 63 RT 23 E 23 RT RT 23 sec 63 sec 27 sec 27 sec 63 23 10 4 and cot27 10 4 23 3 and Cot63 23 10 4 and cot63 10 4 23 and cot27 0 a 10 4 RT 10 4 RT RT 10 4 RT 10 4

A circle has a radius of 5 ft and an arc of length 7 ft is made by the intersection of the circle with a central angle V equation gives the measure of the central angle q O e 5 O 8 5 O 8 7 5 O 8 7 5

Given the following information determine the value of x 3T u 3x 7 v 5x x and u v 10x

A research study asked 2892 homeowners how many bedrooms were in their homes The results are shown in the table below What is the probability that a homeowner chosen at random has 3 bedrooms Number of Bedrooms Number of Homeowners 2 or less 3 4 5 or more 0000 d about 24 about 27 about 38 about 11 318 1099 781 694

The student body of 60 students wants to elect a president vice president secretary and treasurer Combination 487 635 O Permutation 23 406 480 O Combination 3 901 080 O Permutation 11 703 240 Question 6 State if each scenario involves a permutation or a combination Calculate the number of possibilities Five out of 15 students will ride in a car instead of a van O Combination 9 009 Permutation 360 360 1 pts

Simplify the given expression 7t u 5t u 8t u 7t u

1 Simplify the given expression 4ry 1x y

4 Simplify the following polynomial 3a b ab 8ab 9ab 8 O 3a b 8ab 8ab 8 O 3a b 8ab 10ab 8 O 11a b 8ab 8 O 11a b 10ab 8