Permutations and Combinations Questions and Answers

the volume of this rectangular prism is 4 320 cubic yards What is the value of q

Determine the growth constant k then find all solutions of the given differential equation y 1 2y k The solutions to the equation have the form y t

Shade the Venn diagram for the set B nC UA Use the graphing tool to shade the regions Click to enlarge graph SITE C 09 B

The force F in pounds on a person s back when he or she bends over at an angle from an upright position is modeled by 0 6W sin 0 90 sin 129 where W represents the person s weight in pounds a Simplify the model F b Use a graphing utility to graph the model where W 125 and 0 0 90 At what angle in degrees is the force maximized 6 0 At what angle in degrees is the force minimized 0 foo

5 T Condense each expression to a single logarithm log a 2 17 2log c 19 3 log a 12log b 21 3 logg 12 5log 11 23 30log u 6log v 18 6log 3 20 5logg 11 log 2 2 logg 5 3 22 4log x 6log y 24 2log 10 3 log 3

Expand each logarithm 9 log 11 log 13 log 6 15 log 5 12 7 10 log 02019 Kuta Softwa re LLC All rights reserve 1 Made with Infin 12 log x y z G 14 log 3 16 log s a b s

Expand each logarithm 9 log 11 log O u 13 log 20 19 Kuta Softwa re LLC All rights TODO O B 15 log 5 12 7 10 log y 12 log x y 24 reserve 1 Made with Infinite A 14 log a b s 16 log xy4

rights reserved 2 log 64 4 log 3 1 243 Date

8 3 Problem Set Evaluate each expression 1 log 343 3 log 5 1 125

Select one Which sentence describes the relationship between the graphs of y x and y x 3 O The graph of y x 3 is translated 3 units up from y x a De O O O The graph of y x 3 is translated 3 units down from y x The graph of y x 3 2 is translated to the left 3 units of y x The graph of y x 3 is translated to the right 3 units of y x

You roll a normal 6 sided die What is the probability of rolling a number less than 6 Enter your answer in reduced fraction form Example 1 2

Perform the indicated operation h a a 5a g a 4a 1 Find hog a O4a 20a 1 16a 28a 6 4a 20a 1 O 4a 12a 5

1 Rewrite the following equation into STANDARD form Then identify the y intercept y 2x 4 x 7 Equation y intercept 3 Rewrite the following equation into STANDARD form Then identify the y intercept y x 5 9 2 Rewrite the following equation into STANDARD form Then identify the y intercept y 3x 8 Equation y intercept 4 Rewrite the following equation into STANDARD form Then identify the y intercept 2 y 2 x 7 19

Find the radius of convergence of The radius of convergence is Type an exact answer in terms of e 2k X 3k k

The management of a firm wishes to check on the opinions of its workers Before the workers are interviewed they are divided into various categories Define events E F and G shown Complete parts a through 1 E Worker is on the day shift F Worker has worked more than 4 years G Worker contributes to a voluntary retirement plan a Describe the event E in words Choose the correct answer below OA The worker is on the night shift OB The worker is on neither the night shift nor the day shift C The worker is on the day shift D The worker is on the night shift and the day shift b Describe the event EnF in words nit q OA The worker is on the night shift and has worked for less than 4 years OB The worker is on the day shift or has worked for more than 4 years or both OC The worker is on the night shift or has worked for less than 4 years or both On The worker is on the day shift and has worked for more than 4 years

What is the probability that the marble is not yellow Simplify your answer Type an integer or a fraction If a marble is drawn at random find the proba

A marble is selected at random from a jar containing 5 red marbles 4 yellow marbles and 3 green marbles What is the probability that the marble is red What is the probability that the marble is red ww TH

X x 5 2x to be approximated numerically in the interval 2 3 Which of the following is true O 1 We need at least 14 iterations of the bisection method to approximat root correct to 10 4 2 Applying Newton s method with

The temperature of the wa Choose the correct answ

The scatter plot shows the relationship between birth year t and the life expectancy L in years for a certain country Life Expectancy years 80 30 L 20 40 60 80 Years after 1900 100 t Do the data on the scatter plot suggest a linear association If so what is a function that represents the line of best fit A Yes L t 39 67t 0 37 B Yes L t 0 24t 74 33 Yes L t 0 37t 39 67 DNo the data on the scatter plot do not suggest a linear association

3 Use the Venn diagram to represent each set in roster form 3 S 19 2 10 12 6 13 16 a ANB UC 77 B 8

Simplify 2 32 10 2 3 9 30 19 0000

5 Perform the indicated composition f x x g x x Find g f x and state the domain Then evaluate g fC

Find P Junior Girl Hint P A and B P B Classroom of Students Boys Girls Freshman 4 4 8 Sophomore 5 7 12 Junior 2 Senior 1 35 45 12 18 Reduce your fraction to lowest terms

Find P Senior Girl Hint P A and B P B Classroom of Students Boys Girls Freshman 4 48 Sophomore S 7 12 Junior 2 35 Senior 1 45 12 18 Reduce your fraction to lowest terms Enter the number that belongs in the green box Ente 10

Boys Girls P A B Freshmen 3 7 P ANB P B Sophomores Juniors 1 P Girl Senior 5 557 Seniors 2

C One milliliter of liquid has the equival

Establishing a sole proprietorship generally requires the owner to get a charter from the state governmen True or False True False

A spool of thread OA genus 0 B genus 2 O C genus 1 O D genus 3

A bag contains 6 white marbles and 4 black marbles A marble is drawn from the bag and then a second marble is drawn without replacing the first one What is the probability of drawing a white marble on the first draw and another white marble on the second draw 1 2

Write an explicit formula that represents the sequence defined by the following recursive formula a 2 and an an 1 6

Write the following number in the form a bi 0 3 a 0 0 3i b 0 0 3i 2 c 0 3 Oi d 0 3 Oi Chap 1 HW Write the following number in the form a bi a 2 Oi b 0 2i C 2 2i

A bag contains 42 red 45 green 20 yellow and 32 purple candies You pick one candy at random Find the probability that it is not yellow Simplify your answer completely P not yellow

for all values of a in simplest form a 11 6

Find Find the interest rate required for a deposit of 7 300 to grow to 40 000 in 18 years if the interest is compounded continually

find the interest rate required for a deposit of 6 000 to grow to 15 000 in 20 years if the interest is compounded continually

you divide A by BC it is the same as D divided by E What is the value of lect one a b C ACDE EC AE CD d A C T E

Which of the following is a possible first step in solving X2 y2 16 and Y 2X 1 Select one O a Multiply Y 2X 1 by 16 O b Substitute 2X 1 for Y in the first equation O c Substitute 2X 1 for X in the first equation O d Divide X2 y 16 by two

Let E and be two events of an experiment with sample space S Suppose P F 0 6 P F 0 3 and PF 0 1 Compute the values below a PEUF 07 b P E 04 c 07 m

A restaurant offers the following limited lunch menu Main Courses Vegetables Turkey Spaghetti Meatloaf Shrimp Hamburger Broccoli Carrots Potatoes Beverages Coffee Tea Milk Soda Desserts Ice Cream Brownies If one item is selected from each of the four groups in how many ways can a meal be ordered There are ways a meal can be ordered

Given that sin 17 9 8 69 cos and tan 9 17 8 1 find csc a sec a and cot a CSC sec cot Simplify your answers including any radicals Use integers or fractions for any numbers in the F

Solve the following system using elimination 4x 3y 27 4x 4y 8 5 5 1 5 3 5 no solution Question 4 25 points Kim Smart was given the following system of equations and told that she must solve this problem by using the elimination method Which of the following would indicate to her teacher that she understands this process 3x 7y 10 15x 7 2y Multiply the first equation by 2 and the second equation by 3 Put the second equation in standard form and then add both equations Put the second equation in standard form then multiply the top equation by 2 and bottom equation by 7 Since this problem has two variables it can not be solved

For what values of x is the inequality 6x 22 10 true Ox 2 0x 0x22 Question 3 25 points For what values of x is the inequality 6x 20 2x true 0 100 O Ox s Ox s Question 4 25 points Solve the following inequality for y 3 9 Ox 3 Ox 2

What is the domain of f z log z 2 The domain is

Rewrite the following in logarithmic form 1 a 4 1 b 10 C 4 c e 6

Evaluate the following logarithm Round your answer to three decimal places In 23

3 Solve a i n 2 b i 2 3 91 1330 ii n 2 ii 2 3 351 680

Find the logarithm login 10 000 000

Use a calculator for questions 1 4 Evaluate the following logarithm Round your answer to three decimal places log 47

Multiply using the FOIL method 2 y 3 8y 1