Algebra Questions

Rewrite the quadratic function in standard form f x 2x 6x f x Give the vertex x y

Simplify each of the following Enter the exact answers Enclose numerators and denominators in parentheses For example a b 1 a 729

You decide to purchase a car for 22 750 Assuming the sales tax is 5 5 of the purchase price find each of the following a What is the total cost including sales tax b If you make a down payment of 18 of the total cost find the down payment c Assuming you finance the remaining cost at an annual interest rate of 7 05 for 10 years find the monthly payment

4 10 points Use the Remainder Theorem and Synthetic Division to evaluate P c for P x 2x 21x 9x 200 at c 9 antanirions sie

Find the domain of the function Enter your answers as a comma separated list X 3 9 The domain of f x is all real numbers except x Find the vertical asymptotes and horizontal asymptotes of the function Enter your answers as comma separated lists of equation vertical asymptote s horizontal asymptote s

24 109 4 3x 2

MY NOT An article titled The Discipline of Business Experimentation provides several examples of randomized experiments in the context of making business decisions In one such experiment the retail Kohl s decided to test whether opening stores an hour later would lead to a significant decrease in sales The experiment involved 100 of the company s stores which were divided into two groups One group of stores opened an hour later than usual The other group continued with regular store hours The experiment did not find a meaningful difference in sales between the groups of stores Explain why it is important that the company use random assignment to create the two experimental groups If the groups were not randomly assigned Kohl s employees would be upset that they were not given fair treatment Random assignment allows the researcher to create groups that are equivalent This ensures that the experiment does not favor one experimental condition over another Business decisions should only be made after a randomized experiment has been conducted This is the only way to prove if opening the store earlier will be effective Random assignment allowed the researchers to use blinding and thus the employees were not aware of which experimental condition they were assigned to

As of 2011 the following are the ages at which a country s presidents were inaugurated 61 49 54 56 44 52 52 46 54 43 54 48 47 50 69 54 69 63 46 62 50 60 57 65 47 66 65 64 51 60 68 55 66 57 62 48 59 48 52 57 48 52 60 43 Construct a grouped frequency distribution for the data Use 41 45 for the first class and use the same width for each subsequent class Type the frequency value for each class Frequency Age 41 45 O

The accompanying figure shows the highway fuel consumption mi gal for two different models of car How is the graph misleading How could it be drawn so that it is not misleading Click the icon to view the figure How is the graph misleading OA The graph is misleading because it does not use a uniform scale for the vertical axis OB The graph is misleading because the vertical axis scale does not start at zero OC The graph is misleading because the fuel consumption for each car is given in different units OD The graph is misleading because the height of each bar is proportional to the fuel consumption for the two cars but the area of each bar is proportional to the square of each car s fuel consumption Fuel Consumption Data mi gal uel consumption mi gal X

The is found by adding all the data values and dividing by the total number of values Fill in the blank below The is found by adding all the data values and dividing by the total number of values

The heights of ten male students in inches in a college biology class are listed below Find the mean 72 72 71 67 67 72 76 72 73 68 72 OA 67 inches OB 68 inches OC 72 inches OD 71 inches

When an odd number of data values are arranged in order the Fill in the blank below When an odd number of data values are arranged in order the is the middle value is the middle value

12 HW 71 The commuting times in minutes of an employee for ten consecutive days are listed below Find the median commute 67 67 72 76 72 73 68 A 73 minutes B 72 minutes OC 67 minutes D 71 minutes Question 15 3 1 10 72 72 HW O

A questionnaire was given to students The first question asked was How stressed have you been in the last week on a scale of 0 to 10 with 0 being not stressed at all and 10 being as stressed as possible The responses are shown in the table CCEED a Which stress rating describes the greatest number of students out of 10 Type a whole number Part 1 of 2 O Points 0 of 1 Stress Rating Frequency e 6 4 0 1 2 3 4 5 6 7 8 9 10 5 17 11 10 11 26 35 18 16

Define and distinguish among mean median and mode Choose the correct description of the mean below SOCCE O A The mean is the middle value in a data set It can be strongly affected by outliers OB The mean is the most common value in a data set It can be strongly affected by outliers OC The mean is the most common value in a data set It is not affected by outliers D The mean is the middle value in a data set It is not affected by outliers OE The mean is the sum of all the values divided by the number of values It is not affected by outliers OF The mean is the sum of all the values divided by the number of values It can be strongly affected by outliers

Compute the range for the set of data 15 15 15 20 26 26 26 OA 20 4 OB 20 OC 11 OD 30 3

The graph to the right uses cylinders to represent barrels of oil consumed by two countries Does the graph distort the data or does it depict the data fairly Why or why not If the graph distorts the data construct a graph that depicts the data fairly Does the graph distort the data Why or why not 19 2 Daily Oil Consumption Millions of barrels 5 7 Country A Country B O A Yes because the graph incorrectly uses objects of volume to represent the data OB Yes because 3D objects always distort the data in graphs OC No because the proportions are accurate OD No because the graph is technically correct A

The February utility bills in dollars for ten residents of a large city are listed below Find the mode amount 71 67 67 72 76 72 73 68 72 72 OA 67 OB 72 OC 76 OD 73

12 HW If the maximum and minimum values in a data set are averaged the result is the Fill in the blank below If the maximum and minimum values in a data set are averaged the result is the median mode mean

A random sample of 30 college students is selected Each student is asked how much time he or she spent on homework during the previous week The following times in hours are obtained 16 20 21 25 16 15 24 17 20 25 20 17 23 24 21 22 15 19 16 24 22 19 20 21 15 17 20 17 19 23 Construct a frequency distribution for the data Type the frequency for each data value Hours Studied Freq

me graph shows the percentage change in a price index over 17 years In what year s of the years displayed was the change in the price index the greatest In what year s was the change in ice index the least How do actual prices in 1991 compare to those in 1990 Based on this graph what can you conclude about changes in prices during the period shown Click the icon to view the graph what year s of the years displayed was the change in the price index the greatest A 1992 B 1990 OC 2000 and 2005 OD 2002 Graph chart Percent change from previous year N WA i I I 2000 2002 2004 2006 U X

Next question Fill in the blank so that the resulting statement is true A sample obtained in such a way that every element in the population has an equal chance of being selected is called a an A sample obtained in such a way that every element in the population has an equal chance of being selected is called a an sample sample

Use the given table to evaluate each expression in parts a through d if possible a f g 2 b f g 4 d c fg 2 a f g 2 7 Simplify your answer b f g 4 8 Simplify your answer c fg 2 Simplify your answer X 2 0 2 4 f x 0 7 10 14

The campus of a college has plans to construct a rectangular parking lot on land bordered on one side by a highway There are 680 ft of fencing available to fence the other three sides Let x represent the length of each of the two parallel sides of fencing a Express the length of the remaining side to be fenced in terms of x b What are the restrictions on x c Determine a function A that represents the area of the parking lot in terms of x d Determine the values of x that will give an area between 20 000 and 40 000 ft e What dimensions will give a maximum area and what will this area be A for x between 32 52 ft and 75 66 ft or 259 34 ft and 307 48 ft B for x between 32 52 ft and 80 66 ft or 259 34 ft and 307 48 ft C for x between 32 52 ft and 75 66 ft or 264 34 ft and 307 48 ft D for x between 32 52 ft and 80 66 ft or 264 34 ft and 307 48 ft e The area is maximum when the width is feet and the length is Type whole numbers HH y values A Se such that A UTU Type whole numbers c The area of the parking lot in terms of x is A x x 680 2x Type an expression using x as the variable d For what values of x is the area between 20 000 and 40 000 feet X A

For the functions f x x 3 and g x 5x find the following a fog x and its domain b gof x and its domain a fog x 5x 3 Simplify your answer 3 The domain is Type your answer in interval notation b gof x Simplify your answer 8

Use the graph to evaluate each expression a f g 2 b f g 3 c fg 1 d 1 f g 2 3 f g 3 7 fg 1 0 Select the correct choice below and fill in any answer boxes within your choice A OB 1 Type an integer or a simplified fraction 1 is not defined 6 C 6 TO 2 7 tv X Q G

The population of Stuart can be modeled by the function P 169880 001019t where t is the number of years since 2020 Use the above function to answer the following questions What was the population of Stuart in 2020 In what year is the population of Stuart projected to reach 25 482 Round the solution to the nearest w number U

In chemistry pH is a scale used to specify how acidic or basic a water based solution is Acidic solutions have a lower pH while basic solutions have a higher pH At room temperature 77 F pure water is neither acidic nor basic and has a pH of 7 A room temperature solution with a pH greater than 7 is basic while a room temperature solution with pH less than 7 is acidic The pH of a solution is given by mol L Hint log where H is the concentration of hydrogen ions in the solution measured in moles per liter mol L Use this formula to address the following items The pH of beer is 4 What is the hydrogen ion concentration of beer ph mol L H The pH of bread is 5 5 What is the hydrogen ion concentration of bread H log log H One can use the propties of logarithms to prove why

C H 8 y 7 5 4 3 2 1 6 5 4 3 2 AB 1 2 3 4 5 6 7 8 9 6 D 1 2 3 4 X 5 Write the equation of a polynomial function that passes through A B C and D f x 4

Show that fog x is not equivalent to gof x for f x 9x and g x Find fog x fog x f g x fog x f 7x 9 fog x 9 7x 9 7 fog x Definition of composition Replace g x with its expression Use the definition of f x Simplify

For the functions f x x 3 and g x 5x find the following a fog x and its domain b gof x and its domain a fog x 5x 3 Simplify your answer The domain is Type your answer in interval notation

Use the given table to evaluate each expression in parts a through d if possible a f g 2 b f g 4 c fg 2 d 0 a f g 2 7 Simplify your answer b f g 4 Simplify your answer X 2 0 2 4

The compound interest formula is given by A P 1 5 where A is the accumulated amount after an initial investment of P dollars is invested for t years at annual interest rate r compounded in times per year Use the formula above to determine how long it will take an initial investment of 26 000 to quadruple if the account earns 6 interest per year compounded monthly Round the solution to two decimal places The account balance will quadruple after Use the formula above to determine how long it will take an initial investment of 26 000 to quadruple if the account earns 12 interest per year compounded monthly Round the solution to two decimal places The account balance will quadruple after years years

For the given equation and graph of the quadratic function do each of the following Complete parts a through e f x 2 x 8 2 a Give the domain and range The domain is 00 00 Type your answer in interval notation The range is 0 2 Type your answer in interval notation b Give the coordinates of the vertex The vertex is 8 2 Type an ordered pair c Give the equation of the axis of symmetry The axis of symmetry is x 8 d Find the y intercept s The y intercept s is are Type an ordered pair Use a comma to separate answers as needed AY 40 B

The compound interest formula is given by T nt A P 1 7 where A is the accumulated amount after an initial investment of P dollars is invested for t years at annual interest rate r compounded n times per year Use the formula above to determine how long it will take an initial investment of 12 250 to grow to 51 450 if the account earns 14 interest per year compounded daily Round the solution to two decimal places Assume there are 365 days in a year The account balance will reach 51 450 after years

f x Simplify your answer Use integers or fractions for any numbers in the expression www

Find the Maclaurin series for the given function 7 cos x What is the Maclaurin series of 7 cos x k 0 Type an expression using k and x as the variables

Let f x 7x 5 and g x 2x 7 Find f g x f g x fg x and 1 f g x Simplify your answer x Give the domain of each

Explain how you function could restrict the domain of f x 2 x 4 2 5 so that it is a one to one

Graph the quadratic function f x x 4x 7 Give the a vertex b axis c domain and d range a The vertex is 2 3 Type an ordered pair Use the graphing tool to graph the function b The axis is x 2 Type an equation c The domain is Type your answer in interval notation 20

Solve the following exponential equation Use logarithms to express the solution in its exact form In addition use a calculator to approximate the solution 4 91 The exact solution is given by U The approximate solution rounded to four decimal places is given by

Solve the following logarithmic equation In addition use a calculator to approximate the solution 7log z 11 The exact solution is given by Z The approximate solution rounded to four decimal places is given by

y 1 2 3 4 X 5 Write down the equation of a polynomial function with the following properties As x y As x y 8 The number of different real roots is 4 The y intercept is positive f x

Use the logarithm change of base formula to convert each of the following logarithms to the specified base Convert log 4 3 from base 14 to base 7 log 4 3w Convert log 3 5p6 from base 13 to base 10 log 5p 6 Convert log 2 92 from base 4 to base e Joga 2 92

For the quadratic function f x x 2 4 determine the largest open interval of the domain a over which the function is increasing and b over which the function is decrea a The largest open interval of the domain over which the function is increasing is Type your answer in interval notation

Solve the inequality ite the 5x 2 4x 7 x 3 0 Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is Simplify your answer Type your answer in interval notation Use integers or fractions for any numbers in the expression OB The solution is the empty set

For the given equation and graph of the quadratic function do each of the following Complete parts a through e f x 2 x 8 2 a Give the domain and range The domain is Type your answer in interval notation C 81 6 AY 10 6 h b 4 6 8 10

Use the properties of logarithms to condense the following logarithmic expression The solution should be a single logarithm with a coefficient of 1 Where possible evaluate logarithmic expressions log x log x 2 loga z loga z 2

Find a polynomial of least possible degree having the graph shown 0 1 5 f x Type your answer in factored form

se the properties of logarithms to expand the following logarithmic expression as much as possible Where ossible evaluate logarithmic expressions In