Permutations and Combinations Questions and Answers

14 Given f x 3 2x and g x 2x 1 a 5 Find f g b 2 What is the domain off g c 2 Find

Multiply the radical expression 10p 3p

Simplify the radical Assume all variables are greater than or equal to zero 125x 64 3 9 3 125x 64

Two neighbors Wilma and Betty each have a swimming pool Both Wilma s and Betty s pools hold 8000 gallons of water If Wilma s garden hose fills at a rate of 650 gallons per hour while Betty s garden hose fills at a rate of 500 gallons per hour how much longer does it take Betty to fill her pool than Wilma It takes Betty hours minutes longer to fill her pool than Wilma

The number of tropical fish that an aquarium can hold depends on the volume of the fish tank The interior dimensions of the fish tank below are 60 cm 50 cm and 50 cm Each fish requires 10 000 cubic centimeters of water How many tropical fish will this fish tank hold

10 Circadian rhythms are biological processes that oscillate with a period of approximately 24 h That is a circadian rhythm is an internal daily biological clock Blood pressure appears to follow such a rhythm For a certain individual the average resting blood pressure varies from a maximum of 100 mmHg at 2 00 p m to a minimum of 80 mmHg at 2 00 a m Find a sine function of that models the blood pressure at time t measured in hours from midnight Graphthe function over two periods

Solve the following by FACTORING and using the ZERO PRODUCT PROPERTY 3x 36x 60 0 In the blank list only the smaller of the 2 solutions just the number only

What is the GCF of the expression below that could be use to rewrite the polynomial in factored form 24p 30p 3p op 24p 6p3

3 Matt wanted to play his favorite card game with 8 total people If each player received 7 cards to start at least how many cards c would Matt need to start with

Evaluate g x x 2 h x 2x 4 Find goh 7 A 98 B D 194 62 C

Simplify each and state the excluded values 1 2 1 A B D 3 v v 2 9 v v 4 v 3 v 1 C 6v 16 A v 8 D v 1 v 1 v 8 1 2 9 4 8x 24 x 12x 27 x 4 6 1 8 2 2 5 x 2 8 B 9 3 x 9 x 9 8 x 9 x 1 3 5 1 2 4 2 24a 8a 2 40a 48a A B C D 4 A B C 2a 7 3a 5 5a 6 9b 21 9b 6 D 3a 1 a 5 a 10 3a 1 5a 6 b 6 b 3 3b 7 UNI 2 b 9 0 0 3 3b 2 3 b 9 7 10 5 5 3 1 3 9 7

A local realtor sold 5 houses this quarter The prices of the houses were 85 000 127 500 197 000 240 000 750 000 Find the mean and the median Explain which is a better measure of the average for this situatio and why you think so This question must be answered in 2 4 complete sentences

a g i for such that 0 0 360 sin 0 0 5 sin 0 80 17 12 2 OF US Sin sin 0 3 2 cos 30 150 sin 0 1 tan 0 undef b tan 9 Tan 36 d tan 0 3 60 f cos 0 0 45 h 7 2 cos 0 0 J cos 0 11 123 Q 60

Solve the following system of equations There is a unique solution which should be entered as the ordered triplet x y z 2x 5y z 25 4x 4z 24 6x 15y3z 27

9 a For each line write an equation in slope point form i P 2 4 4 4 2 0 2 4 4 20 P 4 2 y f x N X y y h x 2 ii iv y g x 2 6 0 2 y 2 0 y y k x N X P 1 2 b Write each equation in part a in slope intercept form then determine the P 3 3 X

5 An einem Berufskolleg sind 60 der Sch ler weiblich und 40 m nnlich Von den Sch lerinnen rauchen 30 unter den m nnlichen Sch lern liegt die Quote bei 25 Wahrscheinlichkeit dass jemand der raucht weiblich ist a Wie gro ist die b Wie gro ist die Wahrscheinlichkeit dass jemand der nicht raucht weiblich ist C Wie viel Prozent aller Sch lerinnen und Sch ler rauchen 6 In einem Industrieunternehmen sind 95 der Produktion fehlerfrei In der Endkon trolle werden 90 der defekten Produkte aussortiert jedoch auch 5 der funktions f higen Teile a Formulieren Sie den Sachverhalt unter Benutzung von bedingten Wahrscheinlich keiten b Stellen Sie den Sachverhalt mit einer Vierfeldertafel dar c Wie hoch ist die Wahrscheinlichkeit dass ein verkauftes Produkt fehlerhaft d Wie hoch ist die Wahrscheinlichkeit dass ein aussortiertes Produkt fehlerfrei ist

4 For each equation identify the slope of the line it represents and the coordinates of a point on the line a y 5 4 x 1 b y 7 3 x 8 c y 11 x 15 d y 5 x 2 4 e y 6 x 3 8 f y 21 x 16

10 Solve the following logarithmic equation log 12t 4 1

8 Solve the following exponential equation Use logarithms to express the solution in its exact form In addition use a calculator to approximate the solution 7 8 775 The exact solution is given by

2 Solve the following exponential equation e72 6 e If multiple solutions exist enter solutions using a comma separated list

3 Use the properties of logarithms to condense the following logarithmic expression solution should be a single logarithm with a coefficient of 1 Where possible evaluate logarithmic expressions log 5 25 log 5 9

7 Without using a calculator find the exact value of the following expression in reduced form log 8 logo 001 log1 log12144

1 Find the area of the triangle using the formula A bh and then verify that Heron s formula gives the same result 1 bh Use the formula A 2b The area is 48 Use Heron s formula The area is C 10 16 10

Find the standard form of the equation of the parabola with the given characteristics Vertex 7 6 directrix x 14

1 At the end of each year Carl and Linda Munson will deposit 2100 into a 401k retirement account Find the amount they will have accumulated in 10 years if funds earn 8 per year 2 Every six months Paul Sewell puts 1400 into an account paying 10

Determine the due date of the loan using the exact time if the loan is made on the given date for the given number of days April 8 for 270 days Click the icon to view a table of the number of the day of the year for each date due date of the loan is www

arry and Sally can both produce fish and fruit Sally can produce 1 kg of fish in 4 hours and 1 kg of fruit in 5 hours Harry can produce 1 kg of fish in 5 hours and 1 kg of fruit in 2 hours Each person wants to have 4 kgs of fish and 6 kgs of fruit per week Each person works for 20 hours a week Who has a comparative advantage in fish Who has a Comparative advantage in fruit O Sally Sally O Harry Sally O Sally Harry O No one Sally O Harry Harry

The birth of a baby is considered to be premature if the baby is born before 37 weeks of pregnancy have been completed According to a study 10 of babies born in the United States in a par year were premature Suppose that a random sample of 57 babies born in the U S in this year will be selected The proportion of the babies who were premature p will be calculated a What are the mean and standard deviation of the sampling distribution of p Round your standard deviation to four decimal places mean standard deviation b Is the sampling distribution of p approximately normal Explain The sampling distribution of p is not approximately normal because n 1 p is at least 10 O The sampling distribution of p is not approximately normal because np is less than 10 The sampling distribution of p is not approximately normal because n 1 p is less than 10 O The sampling distribution of p is approximately normal because np and n 1 p are both less than 10 The sampling distribution of p is approximately normal because n and n 1 p are both at least 10 c What is the smallest value of n for which the sampling distribution of p would be approximately normal n MY N Submit Answer

a Find the center radius form of the equation of the circle with center 4 2 and radius 5 b Graph the circle SACHCICH a The center radius form of the equation of the circle is Type an equation 15 12 9 6 B 15 12 Q 6 13 B Ay

Write in logarithmic form 5 25 What is the equivalent logarithmic form log Simplify your answers Type integers or fraction

Match the logarithm in Column I with its value in Column II Remember that log ax is the exponent to which a must be raised in order to obtain x 2 1 a log 2 16 b log 31 c log 100 1 d log 2 2 e log e 1 f log 1 28 B www

For the function f x 6x 7 determine whether f x is one to one If so a write an equation for the inverse function in the form y f x b graph f and f on the same axes and c give the domain and the range of f and f If the function is not one to one say so 1 a Write an equation for the inverse function in the form y f x Select the correct choice below and if necessary fill in any answer boxes to complete your choice O A The function f x is one to one and f x Simplify your answer OB The function is not one to one b Choose the correct graph off and f below O A O B Q www OA The domain of f is and the range of fis OC O D The function f x is not one to one c Give the domain and range of f and f Begin by finding the domain and range of f Select the correct choice below and if necessary fill in any answer boxes to complete your choice

Use the definition of inverses to determine whether f and g are inverses f x 2x 8 g x 4 Are the f and g inverses of each other O No OYes

Without using a calculator find the exact value of the following expression in reduced form log 1 log 0 0001 logs 25 log53 75

Rewrite the following logarithmic equation in exponential form Then solve the logarithmic equation log v 5 3 Rewrite the following logarithmic equation in exponential form log4 v 5 3 is equivalent to

Graph the function f x log 1 2 x 3 1 Use the graphing tool to graph the equation Click to enlarge graph Ay

Determine the remaining sides and angles of the triangle ABC A 26 36 B 26 48 c 10 68 m C 127 16 a 5 95 m Round to the nearest hundredth as needed Question 7 7 1 Part 3 of 3 b m Round to the nearest hundredth as needed

a Expand and factor the expression z x 2 24 Enter the factored form below help formulas b Solve the equation z x 2 24 If there is more than one correct answer enter your answers as a comma separated list If there are no ans enter NONE help numbers

Find the value log 542 log 391 log 542 log 391 Round to four decimal places as needed

Rationalize the denominator 15 60 15

Rationalize the denominator Assume that the variable is positive 5 2x 3

Multiply and simplify Assume all variables are greater than or equal to zero 5x 3 30x 5x 3 V30x

Use a proportion to solve the problem below 41 of 78 is what

3 2x a 86 b C

Solve the logarithmic equation log 20 x 5 1 log 20 X 6 Determine the equation to be solved after removing the logarithm Type an equation Do not simplify

Write the expression as a sum and or difference of logarithms Express powers as factors log 2 8x log 2 8x Type an exact answer in simplified form

A nonlinear system is given along with the graphs of both equations in the system Verify that the points of intersection specified on the graph are solutions of the system by substituting directly into both equations Substitute the coordinates of the point 2 1 into the left side of the first equation x y 0 6 5 4 3 2 1 4 3 3 6 5 5 x y 5 116

Find the area of the triangle ABC a 10 2 m b 5 2m C 15 9 What is the area of the triangle 2 Points 0 of 1 m Simplify your answer Type an integer or decimal rounded to the nearest tenth as needed

Determine the remaining sides and angles of the triangle ABC A 26 36 B 26 48 c 10 68 m C

Brian is 15 years old and Jeremy is 22 years old In how many years will Jeremy be 7 years older than three times Brian s age now