Permutations and Combinations Questions and Answers

ference between the squares of two numbers is 5 Three times the square of the first number increased by the square of the second number mbers are Ordered pairs Use a comma to separate answers

Perform each matrix row operation and write the new matrix 1 1 1 2 0 1 2 4 0 6 0 7 5 11 74 3 6 5 Complete the new matrix below 000 6R R3 7R R4 L

5 XXXX XXX X Mean 12 Median 7 Mode 14 Mean 14 Median 12 Mode 7 0 Mean 7 Median 14 Mode 12 10 X X 15 20 X XXXX X 25

18 To which number set s does the following number belong 0 Multiple answers may be correct Mark all correct answers integers counting or natural numbers rational numbers Oreal numbers whole numbers irrational numbers

Write the equation of the line slope 3 1 4 O y 3x 7 O y 3x 7 O y 3x 4 O y x 4 Check Find the slope of the line through the pair of points Input as fraction in simplest fo 2 3 and 1 5 m

Find the distance between the points on a number line 5 42 The

Find the absolute value 0 The absoluto

Find the absolute value 6 71 6 7 Simplify your answer Type an

Decide whether the statement is an example of the commutative associative identity inverse or distributive property 3 14 14 3 Choose the correct answer below OA inverse property OB commutative property OC identity property OD distributive property OE associative property

If N is the set of natural numbers W the set of whole numbers Z the set of integers Q the set of rational numbers I the set of irrational numbers and R the set of rea numbers then determine whether the following statement is true or false 3E Q 3 EQ O True False

10 9 L00 OA 8 1 OB 8 1 C 8 1 OD 1 8 7 Choose the correct interval 6 5 4 3 2 1 O 0 1 2 3

r graph shows the average annual spending per person on selected items in 2010 mbined spending on housing vehicles gas and health care was 13 762 The difference between spending on g and spending on vehicles gas was 3870 The difference between spending on housing and spending on care was 593 Find the average per person spending on housing vehicles gas and health care in 2010 L the average per person spending on housing in 2010 Annual Spending per 8000 7000 6000 Annual spending per person S 5000 4000 Housing P 3000 2000 1000 0

Name the irrational numbers from the list below A 14 B 0 C 42 D 9 08 E 2 1 F 100 G 22 H 15 1 1 3838838883 The irrational numbers are Type the corresponding letters separated by commas

Franklin rolls a pair of six sided fair dice with sides numbered 1 through 6 The probability that the sum of the numbers rolled is either even or a multiple of 5 is 4 is The probability that the sum of the numbers rolled is either a multiple

An arrow is shot straight up into the air The function H t 16t 176t 4 gives the height in feet of the arrow after t seconds Round answers to two decimal places as needed How long does it take for the arrow to reach its maximum height It takes Determine the maximum height of the arrow The maximum height of the arrow is How long does it take for the arrow to hit the ground It takes The arrow was seconds for the arrow to reach its maximum height Practical Domain Practical Range Identify the vertical intercept and interpret its meaning in a complete sentence Vertical Intercept feet seconds for the arrow to hit the ground t feet above the ground when it was shot H t seconds feet

Construct a 90 confidence interval of the popu x 240 n 300 Click here to view the table of critical values One or more of your responses is incorrect Recall that the confidence interval for a population proportion is equal to 1 P p za 2 n find the critical value Za 2 X where p Use technology or a table of critical values to n X

a Consider the following figure ABC is a right angle AB 10 inches BC 13 inches and AD 3 feet AD A Determine the exact values of the following in inches AC B In in Determine the surface area in square inchies and the volume in cubic inches of the figure Round your answers to one decimal place surface area In2

62 Each wallpaper border shown illustrates at least one and possibly all of the isometries in this sec tion For each border list all possible isometries that can take the design onto itself a b C d AN M NOT A 8 XX

2 Use the Laplace transform to solve the initial value problem y 4y g t vith and y 0 0 and y 0 0 g t ft if 0 t 1 1 if 1 t 00

Use a graphing utility to graph the two equations in the system in the same viewing rectangle Then use the intersection lea x y 5 x y 1 Use a graphing utility to graph the two equations in the system in the same viewing rectangle Choose the correct graph below O A H XE O B CE U O C All graphs are 10 10 by 10 10 Q 0 0 Q O D X

Use a system of linear equations to solve the following problem A new restaurant is to contain two seat tables and four seat tables Fire codes limit the restaurant s maximum occupancy to 60 customers If the owners have hired enough servers to handle 19 tables of customers how many of e table should they purchase Write a system of linear equations using the given information Choose correct answer below O A OB O C O D 2x 4y 60 x y 19 2x 4y 60 x y 19 x y 60 2x 4y 19 x y 60 2x 4y 19 C

Malik won the raffle at the zoo and gets to feed the dolphins The dolphin trainer gives Malik a bucket of fish to divide evenly among 3 dolphins Each dolphin gets 6 fish Which equation can you use to find the number of fish f in the bucket before Malik feeds the dolphins f 3 6 f 3 6 fish 1 1 6 3f 6 Solve this equation for f to find the number of fish in the bucket before Malik feeds the dolphins

B F E D Trapezium ABCD is similar to trapezium CEFB The ratio of the shaded to unshaded area is 3 1 Find the ratio of the areas of CEFB and AFED

olve the following optimization model using Excel Solver Upload the final excel fi in 2x 5xz 8zy s t 8x 16y 21z 400 3x 5y 8z 160 4z 5xy 600 ryz 0

survey was given to adult residents in a particular city It found that 27 of the residents regularly use public transportation and 75 of the residents have the ability drive 16 of the residents regularly use public transportation AND have the ability to drive Find the probability that an adult resident in this city regularly uses public transportation given that he or she has the ability to drive Round your answer to the nearest hundredth 0 21 O 0 59 0 11 0 36

For the given matrix and eigenvalue find an eigenvector corresponding to the eigenvalue A 60 16 A 10 1 6

Use transformations of the graph of f x 3 to graph the g x Be sure to graph and give the equation of the asymptote Use the graphs to determine the function s domain and range g x 5 3 Graph g x and its asymptote Graph the asymptote as a dashed line Use the graphing tool to graph the function Click to enlarge graph 0

Use properties of logarithms to expand Evaluate logarithmic expressions without using a calculator if possible log 2 log 2 8 x x 2 x 2

Find the exact value of sin tan Do not use a calculator

First rewrite and so that they have a common denominator 11 Then use or to order and 9 11 1 8 1 8 7 11 6 02 1 7 0 0 X 0 0 0 0 S

First rewrite 11 12 14 and so that they have 15 Then use or to order 5 II 14 15 12 V 14 15 11 12 14 15 12 www 2 and 14 15

The 1984 explosion at a nuclear lab sent about 1000 kilograms of a radioactive element into the atmosphere The function f x 1000 0 5 describes the amount f x in kilograms of a radioactive element remaining in the area x year after 1984 If even 100 kilograms of the radioactive element remains in the atmosphere the area is considered unsafe for human habitation Find f 40 and determine if the area will be safe for human habitation by 2024 f 40 Type an integer or a decimal rounded to the nearest tenth as needed 30 COLD

HUMIRA a recombinant human monoclonal antibody is available in a prefilled syringe containing 40 mg 0 8 mL of injection Calculate the concentration of drug on a mg ml basis Question 2 Mandatory 1 point A prefilled syringe contains 20 mg of drug in 2 mL of solution How many micrograms of drug would be administered by an injection of 0 5 mL of the solution A 500 micrograms B 5000 micrograms C 20000 micrograms A D 2000 micrograms

Find the leading coefficient of the following polynomial 6 3x 4x 6x 7x 3x5

lim x 0 cos 2x 1 x5 ex x 1

4 An obtuse triangle has sides 11 11 and 19 Then what is the smallest distance from the orthocenter to each vertex of the triangle

1 In Fig 6 17 i and ii DE BC Find EC in i and AD in ii 3 cm B AM AB 1 5 cm D i 1 cm E C B 7 2 cm ii Fig 6 17 2 E and F are points on the sides PQ and PR respectively of a APQR For each of the following cases state whether EF QR 1 PE 3 9 cm EQ 3 cm PF 3 6 cm and FR 2 4 cm ii PE 4 cm QE 4 5 cm PF 8 cm and RF 9 cm iii PQ 1 28 cm PR 2 56 cm PE 0 18 cm and PF 0 36 cm 3 In Fig 6 18 if LM CB and LN CD prove that AN AD 4 In Fig 6 19 DE AC and DF AE Prove that BF BE FE EC B 1 8 cm E M 5 4 cm C B F E D Fig 6 18 n

Which of the following can not be valid assignment of probabilities for outcomes of sample space S 0 0 03 04 05 06 0 Assignment a b c d e W W W3 W4 0 1 0 01 17 0 1 1 1 14 0 05 0 03 0 01 1 7 0 1 0 2 0 3 2 14 0 2 0 3 0 4 17 3 14 7 W5 4 14 7 0 5 W6 0 2 0 6 17 1 0 4 0 2 0 1 W7 0 6 0 7 5 6 14 14 1 7 0 3 15 14

f f x x find Answer 1 1 f 1 1 1 1

Evaluate the function h x x 4x 8 at the given values of the independent variable and simplify a h 3 b h 1 c h x d h 3a a h 3 b h 1 c h x d h 3a Simplify your answer Simplify your answer Simplify your answer Simplify your answer L

Find the domain of the function f x 4 4x What is the domain of f Type your answer in interval notation

2 A B C ABA BAB E N ABA BAB 1221 max ABC A 998 B 988 C 928 D 987 E 897 Where is c

ab cd EN ab d 185 ab c 111 ab cd A 1165 B 1185 C 1265 D 1295 E 1

Obtain all other zeroes of 3x 6x 2 10 5 if two of its zeroes are

f x x 2x x 2 a Use the leading coefficient test to determine the graph s end behavior Which statement describes the behavior a the ends of f x x 2x x 2 OA The graph rises to the left and to the right OB The graph falls to the left and to the right OC The graph falls to the left and rises to the right OD The graph rises to the left and falls to the right

Use the graphs of f and g to evaluate the composite function fog 5 10 8 B V 10 10 B y N 10

f First find f g f g fg and g f x 4x 3 g x x 8 Then determine the domain for each function f g x Simplify your answer

d the probability for the experiment of drawing two marbles at random witbout replacement from a bag containing ee green four yellow and four red marbles The marbles are different colors

f x 2x 2 5 use this function O 32 3 O 14 O 14 32 3 Question 5 05 Find the average rate of change over the interval 0 x 1

A history teacher gives a 16 question true false exam In how many ways can the test be answered if the possible answers are T or F or possibly to leave the answer blank ways