Permutations and Combinations Questions and Answers

Given f x 4x and g x 3x 1 find the following expressions a fog 4 b gof 2 c fof 1 d gog 0 a fog 4 b gof 2 c fof 1 d gog 0 Simplify your answer Simplify your answer Simplify your answer Simplify your answer 4

d Square Root 9 6X 10 123 125 X e Exponential Gro

1 point Compute the Laplace transform us t te u t f you don t got thic in 2 trioc YOU Can got a hint

State whether the system of equations is independent inconsistent or dependent

The following data set represents the dollar amounts of donations collected at the entrance to a free museum during one hour Donation Amount 1 5 10 15 600 Frequency 1 5 3 1 1 Is the median a reasonably good measure of central tendency for this data set What if the outlier were removed from consideration Select the correct answer below The median is a good measure regardless of whether the outlier is included The median is a very poor measure regardless of whether the outlier is included The median is a good measure when the outlier is included but it would be a very poor measure if the outlier were removed from consideration The median is a very poor measure when the outlier is included but it would be a good measure if the outlier were

Assume that 80 houses are present in the form of a grid consisting of 10 columns and 8 rows If a loud speaker is placed just before the first row which sampling method works the best to select a sample of houses if we want to get an estimate of the average loudness measured in decibels near all the 80 houses Select the correct answer below Simple Random Sampling Stratified Sampling using the rows of the houses as strata Cluster Sampling using the rows of the houses as clusters Convenience Sampling

Use algebraic tests to test y 9 for symmetry with respect to x axis y axis and origin

a Determine the volume of the solid obtained by rotating the region bounded by y x 1 2 and y about y axis Determine the volume of the solid obtained by rotating the region bounded by y x 1 x 5 and x axis about x axis using both disk method and shell method

Given the functions f and g below find f g 1 Provide your answer below f x x 6x 3 g x 2x 3

An account is opened with an initial deposit of 100 and earns 3 0 interest compounded monthly What will the account be worth in 25 years Round your answer to the nearest dollar Provide your answer below

Question content area top Part 1 The lawyer for a credit union member has sent a cheque for 3738 86 in full settlement of the member s loan balance including simple interest at 6 1 2 for 5 months How much of the payment is interest

20 Let x 3x 9 and g x x 2 a Find the composite function fog x and simplify Show work b Find fog 3 Show work

When we estimate distances from velocity data it is sometimes necessary to use times to t t2 t3 that are not equally spaced We can still estimate distances using the time periods Ati ti ti 1 For example a space shuttle was launched on a mission the purpose of which was to install a new motor in a satellite The table provided gives the velocity data for the shut etween liftoff and the jettisoning of the solid rocket boosters Use these data to estimate the height h above Earth s surface of the space shuttle 62 seconds after liftoff Give the upper approximation available from the data 48623 X ft Event Launch Begin roll maneuver End roll maneuver Throttle to 89 Throttle to 67 Throttle to 104 Maximum dynamic pressure Solid rocket booster separation Time s Velocity ft s 0 10 15 20 32 59 62 125 0 180 319 442 742 1100 1430 4052

McDonalds wanted to find out the favorite sandwich of teen agers from the ages of 15 18 They elease a questionnaire to 3 local high schools and ask them to respond with whether or not they ked the Big Mac Fish Sandwich or Chicken They calculated the results to decide which andwich to market to the area O Experimental None of the answer choices Survey

O A 9 x 3 C 7 x 3 B O D 2 X Which x values make the ordered pair x 5 a solution of the system of inequalities represented by the graph below B 3 x 2 D 3 x 7 7502

How many solutions does the given system have y 3x 1 6x 2y 2 A one solution B two solutions C infinite solutions D no solution COA B Do

What is the solution to this system 0 0 0 O 1 0 O 0 5 1 3 0 wwwww www X www

Which of the following equations has no solution in the set of real numbers A x x 1 0 B x 1 0 C x 2 1 0 D x x 1 0

Find the equation in standard form of a circle containing points by substitution and elimination methods 1 2 5 2 2 1

For the following polynomial function completely Use the Conjugate Roots Theorem if Swer f x applicable f x x 6x 31x 36

f 3 Need Help Submit Answer 0 83 Points f x Read It DETAILS 6 9 3 SPRECALC7 2 8 034 4 7 A table of values for a one to one function is given Find the indicated value 0

2 Solve the following polynomial f x 6x 3 19x 2 11x equation 6 0

14 Find an equation for the line which passes through the origin and is perpendicular to 2x 3y 2

If angle A 170 what is the radian measure of A Enter an exact fraction that contains the symbol Provide your answer below

Change to radical form 7 3 C 7 3 Type an exact answer using radicals as needed Nex C

Solve for x by writing the equation in exponential form log3 x 2 X

Use a calculator to evaluate the expression Round your answer to four decimal places 31 2

Consider the following function on the given domain s x x 1 5 x2 1 Step 2 of 2 Find the domain of the inverse function s x Express your answer as an inequality Answer

On the graph below draw the Horizontal Asymptote and write the equation for the horizontal asymptote underneath 5 4 3 Two copies of the same Rational Function are shown below f x for 5 4 3 2 1 20 3 x 1 3 Clear All Draw Horizontal Asymptote On graph below draw the the Vertical Asymptote and write the equation for the Vertical Asymptote underneath est be 7 5 4 3 2 4 2 3 1 x Clear All Draw 3 C Vertical Asymptote on

possible College students are randomly selected and arranged in groups of three The random variable x is the number in the group who say that they take one or more online courses Determine whether a probability distribution is given If a probability distribution is given find its mean and standard deviation If a probability distribution is not given identify the requirements that are not satisfied Does the table show a probability distribution Select all that apply A Yes the table shows a probability distribution B No the sum of all the probabilities is not equal to 1 C No not every probability is between 0 and 1 inclusive D No the random variable x is categorical instead of numerical E No the numerical values of the random variable x are not associated with probabilities OA Find the mean of the random variable x Select the correct choice below and if necessary fill in the answer box to complete your choice P students Round to one decimal place as needed OB The table does not show a probability distribution www OA students X P x 0 0 106 1 0 359 2 0 394 3 0 141 Find the standard deviation of the random variable x Select the correct choice below and if necessary fill in the answer box to complete your choice Round to one decimal place as needed OB The table does not show a probability distribution

Write the first ten terms of the sequence defined by an 9n I a1 a a3 24 a5 11 26 a7 as 11 11 11 ag a10 11

Fuppose that follows a chi square distribution with 16 degrees of freedom se the ALEKS calculator to answer the following a Compute P 13 x 24 Round your answer to at least three decimal places P 13 x 24 b Find such that P x k 0 1 Round your answer to at least two decimal places k 0

0 1 pt 2 Details Find the degree leading coefficients and the maximum number of real zeros of the polynomial 2 f x x 3x5 5 4x4 Degree Leading Coefficient

Find a polynomial of degree 3 with real coefficients and zeros of 3 1 and 4 for which f 2 30 f x Simplify your answer Do not factor

Suppose 32 cars start at a car race In how many ways can the top 3 cars finish the race The number of different top three finishes possible for this race of 32 cars is Use integers for any number in the expression

Suppose Aaron is going to build a playlist that contains 10 songs In how many ways can Aaron arrange the 10 songs on the playlist Aaron can arrange the 10 songs on the playlist in different ways

6x 5 Use the Quotient Rule of Logarithms to write an expanded expression equivalent to In OX Make sure to use parenthesis around your logarithm functions log x y X 4 1 Note When entering natural log in your answer enter lowercase LN as In There is no natural log button on the Alta keyboard Provido

30 Identify the number that needs to be added to both sides of the equation 2 14x 15 to complete the square O 49 35 42 O 28

19 Solve the following equation by graphing 12 4 Find the solution algebraically to verify your graph Find the solution and any values for that make the graph undefined Solution no solution undefined values for a O Solution x 48 undefined values for x x Solution x 24 undefined values for x x x O Solution x 48 undefined values for x x x 12 12 x 0 12 x 0 12

9 What is Sn of the geometric series with a 78125 r and n 7 O 52514 O 52510 O 52476 O 52505 O52487 O None of these are correct E

Find an equation for a polynomial of degree 7 with the following properties 1 zeros at x 7 x 14 and x 9 2 f 0 7 3 f x 0 only on the interval 00 14 Enter an expression

Factor out the greatest common factor 4a b3 8a b3 4a b 20a4b 4a b 8a b 4a b 20a4b

Subtract the polynomials as indicated 7m 9m m 2 3 3m 8m 3 4 7m 9m m 2 3 3m 8m 3 4 Simplify your answer Use integers or decimals for any number in the expression

Let f x b where 0 b 1 Match each characteristic of the graph off to the correct response Drag and drop options on the right hand side and submit For keyboard navigation SHOW MORE Domain Range X intercept y intercept Increasing or decreasing Equation of Asymptote III E x 0 III 0 00 Decreasing Increasing 00 00 y 0 0 1 1 0 X X X

2 Consider the diagram below Given LUN and RAN are secant lines and point N is a point exterior of circle O R a Prove that ZLNR R LR UA N 10 marksl

8 9 10 Write the equation of the graph poned 2

Modern Geometry Show that AB bisects the angle PBQ Use Angle Bisector Theorem External Show that P D AB bisects the angle PBQ

Find the weight of the path CDGAFE The weight of the path is A 3 F 2 1 3 4 B E E 5 7 6 4

8 Find cos a B given cos a 45 sin B 3 2 a 90 180 and BE 270 360

0 6 0 2 0 2 A Markov chain has transition matrix 0 1 0 4 0 3 0 3 0 4 0 5 Which one of the following is the probability of moving from state 1 to state 2 in two steps O 0 19 O 0 2 0 28 O 0 1