Permutations and Combinations Questions and Answers

Write this number as a whole number or a decimal 9 76 10

Write this number as a whole number or a decimal 9 x 10 6

Rewrite the expression with a positive exponent and simplify If it is not a whole number write as a fraction not as a decimal Simplify 5 1 Simplify 5 3 10

16 In simplest radical form 80 is equivalent to a 16 5 c 4 5 17 Simplify the following radical 150 a 5 15 c 5 6 00 b 21 20 d 8 5 b 5 2 d 15 5

V99 a 3 11 c 2 3 3 160 a 20 8 c 2 3 b 9 d 11 Ob 4 1 d 8

Consider the following functions Step 1 of 4 Find f g 2 Answer How to enter your answer opens in new window f x x and g x x 3 f g 2

Find the standard deviation o of the data 87 94 103 84 112 90 X 95 Variance 94 o Round to the nearest tenth

7 Explain why astronomers have deduced that galaxies contain a large quantity of Dark Matter

5 Where in our Milky Way galaxy are the oldest stars found What does this tell us about the formation of the galaxy

Consider the Step 2 of 2 Find the domain for Answer x f x x 8 and g x 4x x Express your answer in interval notation Domain

Find the indefinite integral 204 1 x dx x4

Solve the logarithmic equation Be sure to reject any value of x that is not in the domain of the original logarithmic expressions Give an exact answer log 4x log 4 3x 1 1 Rewrite the given equation without logarithms Do not solve for x

Find u v vv u b u 0 2 5 3 v 0 5 4 4 a u V V V IC u d uv v and u e u 5v SV

Complete the square for the expression x 8x That is find real numbers A and B such that x 8x A x B Answer exactly A Preview B Preview

moving surface of the object is twice the speed Show Transcribed Text of the object find the function of the velocity

ich of the following is the equation of a parabola ect one a X Y 32 b x y 3 Y x 3 C d XY 3

Find three consecutive integers such that four times the first plus two tim he second is equal to four times the third Select one O a 3 4 5 O b 3 2 1 O c 4 5 6 O d 3 5 7

3 If one of the roots of the polynomial equation x4x 7x 13x 6 0 is 1 find the other roots and

A probability model for a particular experiment is a probability distribution that predicts the relative frequency of each outcome if the experiment is performed a large number of times Just as we occasionally refer to relative frequency as estimated probability we occasionally refer to modeled probability as theoretical probability Examples 1 Fair Coin Model See Example 2 above Flip a fair coin and observe the side that faces up Because we expect that heads is as likely to come up as tails we model this experiment with the probability distribution specified by SS H T P H 5 P T 5 2 Unfair Coin Model See Example 3 above Take SS H T P H 2 P T 8 We can think of this distribution as a model for the experiment of flipping an unfair coin that is four times as likely to land with tails uppermost than heads 3 Fair Die Model Roll a fair die and observe the uppermost number Because we expect to roll each specific number one sixth of the time we model the experiment with the probability distribution specified by S 1 2 3 4 5 6 P 1 1 6 P 2 1 6 P 6 1 6 4 Two Dice Model Roll a pair of fair dice recall that there are a total of 36 outcomes if the dice are distinguishable Then an appropriate model of the experiment has S 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 with each outcome being assigned a probability of 1 36 5 Look at the preceding example and take E to be the event that the sum of the numbers that face up is 3 so E 1 2 2 1 QBy the properties of probability distributions P E Check Hint Clear

Probability Quiz 1 Name L 1 Six papers are placed in a bag with names written on them The names are Lin Mai Mai Noah Priya and Priya If one name is chosen at random what is the probability that it is Lin a 1 4 b 1 6 1 2 d 1 3 6000 2 2 A student picks a random letter from the word car meow a How many outcomes are in the sample space 3x5 b What is the sample space andom letter from the word c What is the probability that an c is chosen d What is the probability that a m is chosen e What is the probability that a c and a m are chosen 3 Select all of the words for which the probability of selecting the letter a AREA 6 ACID C ANGRY APPEASED e AARDVARK andom is 1 4 R 4 What is the probability of the spinner landing on the section labeled Y a 1 8 b 1 5 c 1 4 d 1 2

12 The table shows data from a science fair experiment that studied the average growth rate of 20 samples of fungus at 70 degrees Fahrenheit and 20 samples of fungus at 80 degrees Fahrenheit a b 70 degrees 80 degrees 3 above average growth rate average growth rate below average growth rate 12 5 11 1 02 What is the probability that a sample selected at random had an above average growth rate What is the probability that a sample at 70 degrees selected at random had an above average growth rate c What is the probability that a sample selected at random was at 80 degrees d What is the probability that a sample with average growth rate selected a random was at 80 degrees

A group of college students were asked about their TV watching habits Of those surveyed 30 students watch The Walking Dead 21 watch The Blacklist and 27 watch Game of Thrones Additionally 11 watch The Walking Dead and The Blacklist 17 watch The Walking Dead and Game of Thrones and 13 watch The Blacklist and Game of Thrones There are 9 students who watch all three shows How many students surveyed watched at least one of the shows

Question 29 2 points Solve the 3 Variable System of Equations 2x 5y 3z 10 3x y 4z 8 Sx 2y 7z 12 In the answer blank below just provide the numeric value of x in the solution only put a single number in the blank

OP x 3 x 2 4 Question 7 2 points Rewrite the exponential equation as a logarithm e 8 O In x 8 x ln 8 O log x e log 8 e Question 8 2 points Loquation

Which statement is true about the function f x 7 The function is ODD because x x The function is EVEN because x f x O The function is ODD because x 1 The function is EVEN because x x

Consider the functions x 2 g x 3x 5 Which is the correct function below for h x given that h x f g x h x 15x 1 h x 15x 23 k x 8x 3 h x 8x 3

Male and female high school students reported how many hours they worked each week in summer jobs The data is represented in the following box plots Males 0 HC t 10 H Females 20 30 Identify any values of data that might affect the statistical measures of spread and center O a Ob Oc Od The females worked more than the males and the female Q3 equals the top of the range The spread and center are skewed due to the fourth quartile missing with the females There is a significant outlier at the low end for the females The males have a high outlier and the females have a low outlier

Add and simplify 2 72 2 22 24 72 36 2 22 24 Enter the numerator and denominator separately in the boxes below If the denominator is 1 enter the number 1 Do not leave either box blank Answer

Divide using synthetic division 5x5 12x4 7x x x 48 x 3 OA 5x4 3x 2x 5x 15 OB 5x4 3x 2x 6x 15 OC 5x 3x 2x 5x 14 OD 5x4 3x 2x 6x 15 6 X 3 12 x 3 6 x 3 12 X 3

Solve the following logarithmic equation Be sure to reject any value of x that is not in the domain of the original logarithmic expression Give the exact answer Then use a calculator to obtain a decimal approximation correct to two decimal places for the solution 8 5Inx 7 Rewrite the given equation without logarithms

A credit balance in the Cash Short and Over account represents a shortage of cash and would be treated as an expens True or False

Determine whether the function has an inverse function If it does find the inverse function Include domain and range f x x 2

Find the inverse function of f x 9x 9 O x 9 9 O g x 9x 9 g x g x g x x 9 9 x 9 g x x 9

Find f g x f x x 3x f 8Xx x 3x f 8Xx x 3x f g x x 3x 4 x f g x x 3 g x 4 x 0 0 f 8Xx 3

Use the information contained in the figure to determine the values of the six trigonometric functions of 0 Write the exact answers and simplify Do not round Answer 3 7 0 9 Keypad Keyboa ortcuts

Add in the indicated base 1245 445 1245 445 223

Use the graph to the right to complete the following For the graph tick marks along the axes represent one unit each a Determine the x intercepts if any b Determine the y intercepts if any a What is are the x intercept s Select the correct choice below and if necessary fill in the answer box to complete your choice O A The x intercept s is are Type an integer or a simplified fraction Use a comma to separate answers as needed OB There is no x intercept b What is are the y intercept s Select the correct choice below and if necessary fill in the answer box to complete your choice O A The y intercept s is are 1 Type an integer or a simplified fraction Use a comma to separate answers as needed B There is no y intercept 32545 C 8 84 21 Ay V 8 10 O

transcript A rectangular athletic field is twice as long as it is wide If the perimeter of the athletic field is 216 yards what are its dimensions The width is yards

Write the Mayan numeral as a Hindu Arabic numeral 0 21 2 3 4 5 6 13 14 15 16 The equivalent Hindu Arabic numeral is 17 8 18 9 19 A

Question 1 of 9 Step 1 of 1 0 9 Correct Simplify the expression using the properties of exponents Expand any numerical portion of your answer and only include positive exponents x5 x4 X Key

y 2x 9x 4 Convert the Form to Form Standard intercept Please

Part A Answers Only 1 Mark Each 14K Write the simplified answer in the box provided Include units where appropriate 1 Is the function f x x x 1 even odd or neither 2 What is the degree of the function g x 2x 2x 1 x 1 3 State the remainder when f x 2x x 1 is divided by x 1 4 For the function g x 2x 3 x 2 1 state a the vertical asymptote b the horizontal asymptote c the x intercept d the y intercept

The functions f and g are defined as f x x 4 g x x 7 f a Find the domain of f g f g f g fg ff g b Find f g x f g x fg x ff x 1 x Simplify your answer 9 and 9 1 x and f g x x 4 x 7 Simplify your answer fg x x x 7 4 x 7 Simplify your answer ff x x 8x 16 Simplify your answer G x

A table for f z is shown below X f x 2 1 0 4 2 2 X h x A table for h z is shown below 1 2 3 0 2 1 0 5 1 3 Based on the table h x Of t 1 Of x 1 O f x 1 Of x 1 1 4 2 1

Find all real values of x such that fix 0

9 Question Stem Consider the lines L and L defined by Sol For a fixed constant 2 let C be the locus of a point P such that the product of the distance of P from L and the distance of P from L is 2 The line y 2x 1 meets C at two points R and S where the distance between R and S is 270 Let the perpendicular bisector of RS meet C at two distinct points R and S Let D be the square of the distance between R and S The value of 22 is 9 L x 2 y 1 0 and L x 2 y 1 0 x 2 Locus C x 2 y 1 x 2 y 1 y 1 3 2 2x 2 y 1 372 for intersection with y 2x 1 2x 2x 32 2x 37 taking ve sign

tion 5 Unsaved 2 15 In the Metro Atlanta area how many phone numbers are possible using the area code 404 The restrictions for the phone company are listed below The first digit of the phone number cannot be numbers 0 4 The second number cannot be a zero The third and fourth numbers cannot be a zero or one The fifth number cannot be a zero one or two How many phone number are possible using the area code 404 a 2016000 phone numbers Ob 3000 phone numbers Oc 20160 phone numbers d 30 phone numbers

17 20 23 18 29 21 24 26 27 Question 26 Unsaved 30 mental ability So the researcher has groups of participants complete a few puzzles She times the group and grades their performance Then waits an hour and has them complete similar puzzles and again records their time and performance She experiments by playing different types of music during the second testing to see if their improvement is more significant with certain types of music How would you describe the type of music she plays O a Independent Variable Treatment Variable Ob Confounding Variable Dependent Variable Interact Vario 00000

According to the Henderson s equation pOH pK log bisa NH4 2SO4 NH OH ele DOUG 2 4 7 log 4 7 pH 14 pOH 14 4 7 9 3 Its given that the final volume is 500 mL and this final volume was arrived when 50 mL of 1 M Na2SO4 was added to unknown Ba solution 2 2 So we can interpret the volume of unknown Ba solution as 450 mL i e 450mL 50mL 500mL Ba 2 BaSO4 solution solution From thi we can calculate the concentration of SO2 ion in the solution via DA Na2SO4 solution M V M V 1x 50 M x 500 as 1M Na SO4 is taken into consideration 1 M 0 1 M nongo and

K Researchers conducted trials to investigate the effects of color on creativity Subjects with a red background were asked to think of creative uses for a brick other subjects with a blue background were given the same task Responses were scored by a panel of judges and results from scores of creativity are given in the accompanying table Higher scores correspond to more creativity The researchers make the claim that blue enhances performance on a creative task Assume that the two samples are independent simple random samples selected from normally distributed populations and do not assume that the population standard deviations are equal Complete parts a and b Click the icon to view the summary statistics a Use a 0 01 significance level to test the claim that blue enhances performance on a creative task What are the null and alternative hypotheses OA Ho H1 H2 H H H O C Ho H122 H H H The test statistic t is Round to two decimal places as needed The P value is Round to three decimal places as needed State the conclusion for the test O B Ho Hi H2 H H H2 O D Ho H H2 H Hy H possible O A Reject the null hypothesis There is sufficient evidence to support the claim that blue enhances performance on a creative task OB Reject the null hypothesis There is not sufficient evidence to support the claim that blue enhances performance on a creative task OC Fail to reject the null hypothesis There is not sufficient evidence to support the claim that blue enhances performance on a creative task D Fail to reject the null hypothesis There is sufficient evidence to support the claim that blue enhances performance on a creative task b Construct the confidence interval suitable for testing the claim in part a What is it about the confidence interval that results in the same conclusion from part a H H Round to hun decimal nlarge as needed