Sequences & Series Questions and Answers

The daily earnings of an employee who works on a commission basis are given by the following probability distribution Find the employee s expected earnings 0 Probability 07 25 50 75 100 125 150 12 17 14 28 18 04 1

Solve each equation Round your answers to the nearest tenth 17 e 77 18 10 64 19 5e 38 20 4 10 22

7 log 3x log 8 2 9 In 8 In x 7 2 11 In 10 In x 7 5 13 log 8 log 4x 9 3 46535 8 10 In 4 In 4x 5 12 log x 10 log 5 1 14 In 2x 6 In 7 4

21 61 5 9 in 232 5 M 4 In 52 5 4 M 0 039 23 8 10 46 25 esp 10 5 52 27 5 102 9 1 54 22 8 Tog 10x 5 6 x p 6 log 84 X 6 621 24 e 4 8 31 26 10 4 2 93 28 9e5 7 10 18

3 In 9 In x 6 4 ela x 6 4 9x y c 54 9 54 9 X c 54 9 In 5 In x 3 4 4 log x 4 log 2 2 6 log 5 log x 2 2

What is the expected value for the binomial distribution below Successes Probability 0 1 3125 1 4 625 2 32 625 3 128 625 4 256 625 5 1024 3125

9 53 Identify the statements below as sometimes true always true or never true a 1419 b x 1 a c 57 2 shoots the rocket off into the air The rocket s path is represented by the equation y 10x 130x 400 9 54 Robbie builds model rockets One day he sets up a rocket backs away from the launch pad and then where y is the height in meters off the ground and x is the horizontal distance in meters from Robbie d 3x 5 2 e 61 61 f 61 6 Robbie s rocket What do the x intercepts tell you Use either the Zero Product Property or the Quadratic Formula to find the x intercepts of the path of b When Robbie s rocket lands how far is it from the launch pad 9 55 For each parabola graphed below visually estimate the x intercepts Then use the Quadratic Form confirm your estimates ay x 5x 3 N b y x 2x 6 W

Elle is weight lifting and trying to determine how much weight to use for a particular exercise Her coach tells her to stay within 15 pounds of the weight she used last week If Elle used 75 pounds for this exercise last week select an absolute value inequality to represent this scenario Ox 75 15 Ox 75 15 O 75 15 x 75 x 15

Describe the graph using the choices from the drop down menus 1 0 8 6 The graph is Select Select S k 1 0 CO 6 4 2 2 4 6 8 10 2 4 8 10 and represents a relationship that is a

Describe the transformation of y 5 x as it relates to the parent graph y x Vertical Stretch O Horizontal Stretch O Vertical Compression

For x y groups 4 different practices is made a b c d to test the nereden groups whether there is a difference X Y a 150 90 b 30 20 C 30 10 d 90 80 X 0 05

What is the approximate value of x Round to the nearest tenth X O 3 1 cm 3 9 cm 4 6 cm 5 4 cm 6 cm y 50 D

Stage 0 How many dots are in stage 21 Stage 1 For which stage are there 100 dots Stage 2 Stage 3

Suppose the length of voicemails in seconds is normally distributed with a mean of 40 seconds and standard deviation of 10 seconds Find the probability that a given voicemail is between 20 and 50 seconds 10 20 30 99 7 95 68 40 50 60 70 P Enter

Tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours Find the probability that a randomly selected light bulb will last between 750 and 900 hours 99 7 95 68 525 600 675 750 825 900 975 P Enter

Weekly wages at a certain factory are normally distributed with a mean of 400 and a standard deviation of 50 Find the probability that a worker selected at random makes between 350 and 450 99 7 95 68 250 300 350 400 450 500 550 P Enter

Diego and Elena found two new dot patterns shown below Stage 0 Patterns D is Patterns E is linear Dot Pattern D Stage 1 Stage 2 because the pattern is because the pattern is quadratic exponential Stage 3 adding 3 Stage 0 subtracting 3 Dot Pattern E Stage 1 multinting by 3 Stage 2 Stage 3 dividing by 3

Here is Takeshi s work determining a third point on the graph of an exponential function h x Explain why the work is incorrect X 4 5 h x 34 2 25 2 25 2 6 59 4 6 59 4 is also on the graph h x

D A Which of the of the following following graphs represents the inequalities 5x 5 5 B on 21 Points 1 OA OB 5 4 3 2 1 5 4 3 2 1 0 1 5 4 3 2 1 0 5 4 3 2 1 0 0 1 1 2 2 2 1 2 3 3 3 3

1 B Determine or whether C be a cyclic group with order 6 is a normal subgroup of dihedral group D Find the elements of quotient group De ci

Identify the principle or rule of counting Suppose that a procedure can be broken down into a sequence of two tasks If there are n ways to do the first task and for each of these ways of doing the first task there are m ways to do the second task then there are nm ways to do the procedure If a task can be done either in one of n ways or in one of m ways where none of the set of n ways is the same as any of the set of m ways then there are n m ways to do the task A The product rule B Generalized pigeonhole principle C Pigeonhole principle D The sum rule E Principle of inclusion exclusion If a task can be done in either n ways or m ways then the number of ways to do the task is n m minus the number of ways to do the task that are common to the two different ways If k is a positive integer and k 1 or more objects are placed into k boxes then there is at least one box containing two or more of the objects

Solve the equation for the indicated variable Assume all variables are nonze s d v for v

Determine whether each equation is an identity a conditional equation or a contradiction Give the solution set 7x 3 2 3x 2 1 Is the equation a conditional equation an identity or a contradiction OA contradiction OB identity OC conditional equation Select the correct choice below and fill in any answer boxes present in your choice OA The solution set is Type an integer or a fraction Use a comma to separate answers as needed OB The solution is all real numbers C The solution is the empty

Perform the indicated operations 9 3i 6 i 9 3i 6 i Simplify your answer Type your answer in the form a b

the line segment indicated Find the measure of the line segment indicated Find GW 7 Find GW W 6r 3 10 G 8 12

A winery has a vat with two pipes leading to it The inlet pipe can fill the vat in 6 hours while the outlet pipe can empty it in 10 hours How long will it take to fill the vat if both pipes are left open It will take hours Simplify your answer Do not round

Two families visited an amusement park The first family bought 2 hot dogs and 3 bottles of waters which totaled 18 The second family bought 4 hot dogs and 2 bottles of waters which totaled 28 How much did one hot dog cost O 2 O 4 O 5

Convert from Fahrenheit F to Celsius C Use the conversion formula C A city recorded a temperature of 105 F Convert the temperature to Celsius The answer is C integer decimal Round to the nearest tenth 9 C

What is the restriction on the domain of g x x 4 a x 2 2 b x 4 c x 2 d x 2 for 2 2 and x

Dr Steve needs to calculate how long it will take his 64 gram sample of a radioactive substance to decay to 27 grams The substance decreases at a rate of 25 every hour Fill in the values of A b and c to write the equation Dr Steve should use to find t the number of hours it will take for the substance to decay to c grams Enter the correct answer in the box

The solution s to 8 sin x 10 sin x 7 for 0 x 2 is are O a 7 626 O b 0 7 2 7T c 6 Od 1 2 1 2 7 49 H

Write the expression as a logarithm of a single quantity 2 log 5log x 1 a Ob O c d log log log log 5 x 1 25 x 1 3 25 J x 1 3 25 x 1 21 3

Express as a single logarithm and simplify 1 3 log425 log45 a log430 b log45 Oc 1 O d 1 9log4 5

00 Determine the positive intervals of the following equation a 2 x 0 and x 0 b 2 x 0 and x 2 c 2 x 0 d x 2 f x 3x 15 4x 1 x x 3 4x

Find the standard deviation o of the data 22 34 7 27 25 X 23 Variance 79 6 12 Round to the nearest tenth Standard Desviation

Find the variance of the data 22 34 7 27 25 X 23 Variance Variance Enter

Find the standard deviation o of the data 147 141 120 124 128 x 132 Variance 2 106 0 Round to the nearest tenth Standard Deviation Enter

Find the mean X of the data 147 141 120 124 128 X Mean

rday I went to the store and I bought a journal 54 I gave the cashier a dollar bill How much money should I get back Show your work below and be sure to label your answer 100 50 50 50 4 44 2 Write down two combinations of coins that I could get back as my change and how many coins you used to get to that amount Then put a check mark next to the combination of coins that is most efficient Most Efficient a Amount of Coins Used Combination of Coins

Listen When the following polynomial division is performed what is the remainder 4x53x 4x 1 x 1 a 2 b 0 c 12

A polynomial division is performed and the result is given as f x g x h x 1 x The portion of this statement that is the remainder is a f x b g x Oc h x d 1 x

When the polynomial f x is divided by x 2 the remainder is 3 What would be the remainder if 2 f x 7 were to be divided by x 2 a 1 b 4 c 1

or the given functions f and g complete parts a h For parts a d also find the domain 2x 5 8x 5x 2 5x 2 g x f x a Find f g x f g x Simplify your answer

f 3 lim f x X 3 lim F x X 3 Jim f x x 3 1 Points DETAILS Math 110 Course Resources Limits Continuity Course Packet on limits Limits Continuity Course Packet on computing limits algebraically Let f x X 16 3 if x 2 8 if x 2 x2 6x 14 if x 2 Determine each of the following values If an answer does not exist enter DNE 2 lim f x X 2

10 If n A 4 n B 7 and n C 10 what is the least number of elements that each of th follow sets could have a AUC b An B c C B

3 An astronaut drops a rock off the edge of a cliff on the Moon The distance d t in meters the rock travels after t seconds can be modeled by the function d t 0 8t What is the average speed in meters per second of the rock between 5 and 10 seconds after it was dropped 1 12 2 20 3 60

1 Determine what type of relationship linear quadratic exponential or neither exists in each case Justify your answer A C X 1 2 3 4 5 x Y 64 B 96 144 216 Y 9 72 324 48 7 28 6 12 Diff 1 Diff B D x 0 2 3 X 2 4 y 23 6 7 8 10 15 1 49 Y 1000 1100 1210 1331 1 Diff 1 Diff

A nurse has two solutions that contain different concentrations of a certain medication One is a 20 concentration and the other is a 5 concentration How many cubic centimeters of each should he mix to obtain 10 cc of a 8 solution 20 concentration solution CC 5 concentration solution CC

Using data from 2014 and projected to 2019 the percentage of people in the world who are Internet users can be described by p 2 14x 32 2 where x is the number of years after 2010 a Find the slope m and the p intercept of the graph of this linear function slope p intercept b Interpret the meaning of the slope as a rate of change The world population with Internet service does not change each year O The world population with Internet service is increasing by an additional m percentage points each year The world population with Internet service is increasing by multiplying m percent each year The world population with Internet service is decreasing by multiplying 1 m percent each year The world population with Internet service is decreasing by m percentage points each year c Write a sentence that interprets the meaning of the p intercept The p intercept shows the percentage of people in the world who were Internet users in 2014 O The p intercept shows the percentage of people in the world who were Internet users in 2010 O The p intercept shows the percentage of people in the world who will be using the Internet after 2019 The p intercept gives a prediction the of the percent rise in users during the first five years The p intercept shows the percentage of people in the world who were Internet users in 1990

where x is the number of years after 1990 a Find the slope m and the p intercept of the graph of this equation slope p intercept b Write a sentence that interprets the meaning of the slope as a rate of change O The U S population with Internet service is increasing by an additional m percentage points each year The U S population with Internet service does not change each year c Graph the function with x representing the years from 1990 and p representing the percent from 50 P 100r 90 2000 and projected to 2025 the percent p of the U S population that uses the Internet can be described by p 1 19x 58 0 P 100r 80 70 The U S population with Internet service is decreasing by multiplying 1 m percent each year The U S population with Internet service is decreasing by m percentage points each year The U S population with Internet service is increasing by multiplying m percent each year 60 0 10 20 30 40 X DO 90 80 70 60 0 10 20 30 40 MY NOTES