Permutations and Combinations Questions and Answers

the amplitude of a cosine curve is 2 and the period is with no phase shif the function that describes this curve f x 2 cos x f x 2 cos 2x f x 2 cos f x 2 cos x

Which equation is represented in the graph below C y 2 sin 4x y 3 sin 2x y 2 sin 3x Dy 3 sinx 1 M TC TY T 2T X

X x A 15 B 9 C x D yan interviewed 24 students to see whether they collected sports cards and whether they participated in sports The table shows his data ow many of the students interviewed do not collect sports cards 10 Sports Card Collecting and Sports Participation Does Not Participate in Sports 3 14 Collects Sports Cards Does Not Collect Sports Cards Participates in Sports 6 X 7

Based on the definition of x x x x x A B C D E independence which statements are correct P A 0 61 P B 0 27 P A and B 0 88 Events A and B are not independent P A 0 44 P B 0 42 P A and B 0 86 Events A and B are independent P A 0 64 P B 0 78 P A and B 0 4992 Events A and B are independent P A 0 43 P B 0 30 P A and B 0 129 Events A and B are not independent P A 0 42 P B 0 42 P A and B 0 84 Events A and B are not independent

4x Henry tosses a coin and it comes up Heads three times in a row What is the probability that the next toss will also be a Head 4x x A 0 0625 B 0 25 C 1 D 0 5

x x A B C Which statements when combined describe a sequence of transformations that exhibits the similarity between AQRS and AQ R S D E A dilation centered at the origin by a scale factor of 3 10 A dilation centered at the origin by a scale factor of 3 A translation x y x 5 y 8 A translation x y x 5 y 8 A translation x y x 8 y 5 Q R 0 6 10 O

Consider the two triangles shown Which statements are correct A B C The triangles are similar ZC 42 44 Side B 5 D Side D 6 a 44 42 7 P B 57 12 C 78 46 D 28 3 57 12

Answer 2023 Hawkes Learning A 7 8 7 18 Selecting the check box will replace the entered answer value s with the check box value Entering the dimensions of a matrix will display any boxes necessary to create the matrix X 9 6 63 6 B 7 8 Not Possible tv MacBook Pro Keypad Keyboard Shortcuts A Submit Answer P

Given the following sets of ordered pairs determine which of the following is not a function Set A 0 1 2 5 3 7 4 9 Set B 1 1 2 2 3 3 4 4 Set C 1 5 2 7 2 11 5 3 Set D 0 2 3 2 5 9 7 3

a 1 r or y a 1 r State the growth or decay rate and t T 28 y a 4 1 6 4 za 1 4 grow 30 y a 0 25 9 4 a l o decay 32 y a 22 3t 34 y a 36 REASONING You deposit 2200 into each of three separate bank accounts that pay 3 annual interest Interest is compounded quarterly in Account 1 monthly in Account 2 and daily in Account 3 How much interest does each account earn after 6 years

Find the equation 1 D y cos x 75 A y cos x 2 B y cos x 2 C y cos x

7 EXPAND the logarithm completely SIMPLIFY if possible 5 log 3 2 log 8a 6 8 logs 2x 1 log mn

8 For a given area of a triangle the base varies inversely as its height When the height is 10 in the base is 5 in Find the base if the height is increased to 20 in

the expression See Example 1 2 e4 e 8 8e12x 5 Se7x 4 9 3 22e10 6 4e 2

URE In Exercises 13 16 match the function with its graph Explain your reasoning 14 y 2 15 y 4e 0 5x 39 0 4 2 C D 8 6 y 4 0 0 75 2 Y 2 6 AYA 4 1 2 04 2 16 y 0 75e 2 4x 1 7 39 0 1 Y 2 4x

Eleven runners will compete in a race Trophies will be awarded to the first and second place finishers Does this represent a permutation or a combination computation How many ways can the runners finish in first and second place type your answer

the chart to answer the following questions in decimals format to the nearest 100th 1 2 3 m 5 6 1 1 1 2 1 3 1 4 1 5 1 6 1 2 1 2 2 2 5 2 6 2 3 1 3 2 3 3 3 4 3 5 3 6 3 4 1 4 2 4 6 1 6 2 6 3 6 4 6 5 6 6 6 5 1 5 2 5 3 5 4 4 4 5 5 4 5 5 6 5 6 4 a 3pts What is the probability of rolling a sum of 7 on the two numbered cubes b 3pts What is the probability of rolling a sum of 4 on the two numbered cubes c 3pts What is the probability of rolling a sum of 10 on the two numbered cubes

Find the range and standard deviation for the set of values 25 19 5 21 18 22 17 10 7 OA range 20 standard deviation 6 62 OB range 20 standard deviation 6 91 OC range 16 standard deviation 6 91 OD range 16 standard deviation 6 62

Find the mean median mode and range of the data set daily temperature in degrees Celsius 24 24 25 27 31 32 38 39 A mean 24 median 30 mode 29 range 16 OB mean 29 median 30 mode 24 range 15 OC mean 30 median 29 mode 24 range 15 OD mean 30 median 24 mode 29 range 16

4 324 1 1 2 3 4 Determine the period 4 8 12 16 20 24 28 Ent

3 The table to the right shows the average diameter of a pupil in a person s eye as he or grows older What is the average rate of change in millimeters per year of a person pupil diameter from age 20 to age 80 1 2 4 2 0 04 3 2 4 4 0 04 Age years 20 30 40 50 60 70 80 Average Pupil Diameter mm 4 7 4 3 3 9 3 5 3 1 2 7 2 3

A population of fruit flies grows exponentially At the beginning of the experiment the population size is 400 After 27 hours the population size is 473 a Find the doubling time for this population of fruit flies Round your answer to the nearest tenth of an hour hours Pe b After how many hours will the population size reach 570 Round your answer to the nearest tenth of an hour

2 1 10 AAAA MAYAMAN 1 Determine the period 2 12 14 Enter

u 0 0 v 6 5 a Find u v u V Sketch the resultant vector 10 5 V U V y 10 5 5 10 u 5 10 X 10

In a poll 60 of the people polled answered yes to the question Are you in favor of the death penalty for a person convicted of murder The margin of error in the poll was 3 and the estimate was made with 96 confidence At least how many people were surveyed The minimum number of surveyed people was Round up to the nearest integer

5 Describe the similarities and differences between finding the slope of a linear equation from a graph that has x and y scales that are 1 1 and from a graph that has x and y scales that are not 1 1 say your x scale is 2 4 6 and your y scale is 100 200 300 for each tick mark or square

Kiera picks a marble at random puts it back and then picks another marble at random Are these two events dependent or independent dependent independent

8 What is the equation of the line shown on the graph 1 6 4 2 6 4 2 O N 2 Ay 0 5x 6 By 2x 6 y 6x 0 5 Dy 6x 2 X x 2

B3 B4 B 2 Select one O a B13 3 O b B19 3 O c B4 3 Od B2 3

squares are ect one a rectangles b triangles c congruent d circles

The tangent ratio is the same as Select one O a hypotenuse over opposite O b opposite over adjacent O c adjacent over hypotenuse O d opposite over hypotenuse

2 Which equation is represented by the graph below A y 2 sin 2x 1 By 2 sin x y 2 cos 2x 1 Dy 2 cos x MA 2x X

9 h 6 450 days 2 A 500 term deposit earns interest at 5 per year How much interest is earned in 2 years 3 Determine the total interest earned on a 1000 regular interest CSB at annually with a term of 10 years 1 per year His

ectors have two components which are elect one O a magnitude and measure O b magnitude and force O c measure and weight O d direction and magnitude

Evaluate the indicated function where f x x2 3x 2 and g x 3x 6 fg 3

If you expand the binomial 8 24 what coefficient is in front of the 2 term

2 Shaun eats six egg whites a day with a protein content of 21 6 grams Calculate his protein intake if he consumes 9 egg whites a day Assume the number of eggs varies directly with the amount of protein 3 A group of 49 hikers registered for an 8 day trekking trip The organizers arranged food to last for the entire trip A few last minute registrations saw more hikers join the expedition As a result the food lasted only for 7 days if the number of hikers varies inversely with food then how many hikers in all went trekking 4 An airplane travels at a speed of 582 miles per hour to reach its destination in 4 hours Assume speed varies inversely with time Determine the duration of the flight if the airplane travels at a speed of 388 miles per hour 5 Seacausus Stadium has seating capacity for 25 000 spectators the stadium has 25 exits and can be vacated in 20 minutes The time to exit the stadiu

The two parallel lines are cut by a third line in the figure to the right Find the angles marked What is 4 a 4a D L

f x Answer 2 Points if x 2 if 2 x 5 4 x 4 if x 5 log x 5 if x 5 Evaluate this function at x 2 Write the exact answer Do not round If the answer is undefined writ Und as your answer f 2 Keyp Keyboard Short

Rhoda is saving up money for a down payment on a condominium She currently has 2571 but knows she can get a loan at a lower interest rate if she can put down 3308 If she invests the 2571 in an account that earns 4 9 annually compounded monthly how long will it take Rhoda to accumulate the 3308 Round your answer to two decimal places if necessary AnswerHow to enter your answer opens in new window 2 Points years Keypad Keyboard Shortcuts

rev A biologist conducted a six month field study of a small plot of land The following table shows the population of a species of meadow mouse during that time Month x 0 1 2 3 4 5 Answer 2 Points 6 Population f x 6 7 10 17 26 33 37 A Copy Data Use the regression commands on a graphing utility to find the exponential function of best fit for the mouse population over the six months Write your answer in the form f x a b and round a and b to three decimal places if necessary Note that using different graphing utilities may yield different results Keypad Keyboard Shortcuts

ev approximation rounded to four decimal places If there is no solution indicate No Solution In x 2 In x 4 ln x 1 AnswerHow to enter your answer opens in new window 2 Points Keypad Keyboard Shortcuts If you wish to enter log or In you must use the keypad If there is more than one solution separate your answers with a comma Selecting a radio button will replace the entered answer value s with the radio button value If the radio button is not selected the entered answer is used X No Solution Smy Next

5 Find the exact value of the following expression You do not need to rationalize nor simplify the radical expressions cot a B Suppose angles a and are given such that a arccos and B arcsin

You rent a jet ski at the beach The cost for the jet ski is 60 plus 6 per hour to cover the cost of gas You can only rent the jet ski for a maximum of 5 hours Part A Create a graph that represents the linear relationship between the price y and the number of hours you can rent the jet ski x Line TUU 90 80 70 60 T 50 40 30 y Move Undo Redo x Reset Part B What is an appropriate range for the given situation H0 90 sys 6 96 60 72 102 78 8 84 S

Find all angles O deg C 360 deg that satisfy the equation below to the nearest tenth of a degree if necessary 5cosC sqrt 5 0

Find the midpoint of the line segment from 2 9 to 4 9 Midpoint Give your answer as a point with coordinates given as integers or reduced fractions

Which statement is correct about the function g x e 9 10 A The y intercept of g x is 0 1 B The graph of g x has no x intercept The range of g x is y 10 D The domain of g x is x 9

Alec rolls two number cubes at the same time If he rolls 60 times predict how many times the product of the two numbers would be greater than 20

Two cards are drawn at random from an ordinary deck of 52 cards Find the probability that the 2 card hand contains no more than 1 two How many ways can a hand with no more than 1 two be drawn ways Type a whole number example Get more help Clear all Check

10 8 6 4 0 2 1 1 2 4 the points 1 1 and 7 6 Round decimals to the nearest tenth 6 7 6 8 10 X