Algebra Questions

Find the missing number in the proportion 4 X 7 28

Find the missing number in the proportion 5 25 x 20

Solve for t t 8 36 6 t Type Type an integer or a simplified fra

6 A survey of 120 twelfth graders finds that 36 were carrying more than 15 on the day of the survey What is the margin of error Round to the nearest whole percent Use the margin of error to complete the following An interval that will likely include the proportion of students in the population of twelfth graders who carry more than 15 is to

Which statement is true about interpretation of individual rights O The Supreme Court avoids prior cases when analyzing the Bill of Rights O Congress is the final authority on how to analyze and apply the Bill of Rights O Rights under the Constitution are a matter of ongoing legal and civic debate There is only one way to interpret each individual right in the Constitution

56x 81 ware LLC All right 13 K 13 f x x 4x 3x reserved 64 Made with Infinite Algebra 2

How did the Fourteenth Amendment become significant in certain Supreme Court decisions O This amendment limited rights for all citizens excluding land owning citizens O The due process clause addresses certain rights given to the states and not to the people O The due process clause prohibits states from depriving citizens of their natural rights O This amendment establishes that individual rights do not apply in certain state laws

1 What is the appropriate choice for u when solving the equation 2 Choose the correct answer below O A OB u 2 OD U 2 X OC u X 1 2 1 5 3 0 X

Consider the following function k x 2 Step 2 of 2 Find the length of the individual line segments of this function Then find the positive vertical separation between each line segment Simplify your answer Answer Enable Zoom Pan Keypa Keyboard Shortc

equation that is quadratic in form is solved by a substitution u x 7 and it has solutions u the values of x that solve the original equation e values of x that solve the original equation are 3 and u 2 What

A high school art teacher conducts a survey on whether or not students would be interested in an after school art club The teacher knows that it would be too time consuming to survey all 632 students in the high school so she decides to ask the 32 students currently in her classroom One of the students states that this survey cannot be used to make an inference about the entire high school Which of the following statements best justifies the student s interpretation of the survey A The survey sample was too small B A cafeteria worker should have conducted the survey C The survey method was flawed since the sample was not random D An observational study should have been used

Solve y 6 8 y 6 7 0 y 6 8 y 6 7 0 2 u 8u 7 0 Let u y 6 Step 2 Solve the equation au bu c 0 To solve the equation factor the left side of the equation u 8u 7 0 u 1 u 7 0 Use the Zero Product Property to finish solving for u u 1 u 7 0 u 1 0 u 7 0

4 Suppose that the weights of 4800 registered female Labrador retrievers in the United States are distributed normally with a mean of 62 5 lb and a standard deviation of 2 5 lb What percent of the Labrador retrievers weigh less than 65 lb A 34 B 50 C 84 D 99 7

Scores on the SAT are normally distributed The mean SAT score in 2022 was a 1050 with a standard deviation of 150 What is the percentile score of a student who received a scaled score of 1050 A 95th percentile B 84th percentile C 68th percentile D 50th percentile

5 A high school principal wants to rate student experience on the school bus He stops the first fifteen students who come into the school one morning and asks them to rate their school bus experience on a scale of 1 worst to 10 best Is the principal s method of surveying students valid A Yes it is valid because it was a scaled rating B Yes it is valid since the students were chosen randomly C No it is invalid because the bus driver should have conducted the survey D No it is invalid since the students were chosen by convenience

2 The annual salaries of all employees at a financial company are normally distributed with a mean of 34 000 and a standard deviation of 4 000 What is the z score of a company employee who makes an annual salary of 42 000 A 2 B 1 C 1 D 2

For the equation p 1 11 p 1 24 0 determine the appropriate substitution and write the equation in the form au bu c 0 The appropriate substitution is u The equation with substitution is

Convert the following number bases a AE91 to octal 624 to decimal b QUESTION B2 10 Marks A survey of machine shop reveals the following 44 employees can run on a lathe A B C D E a b c information about its emplo 49 employees can run the milling machine 56 employees can operate a punch press 27 employees run a lathe and milling machine 19 employees can run a milling machine and operate a punch 24 employees can run a lathe and operate a press punch 10 employees can operate all three machines 9 employees cannot operate any of these three machines Let L number of employees who can run on a lathe M number of employees who can run a milling machine P number of employees who can operate a punch press Draw a Venn Diagram to represent the situation above Determine the number of people employed at the machine shop Find LUM P 1 2n 1 2 1 2x 2x 4 1 4x 4x QUESTION B3 10 Marks Given the following functions f x 1 2x g x x 3

Solve y 6 8 y 6 7 0 Step by Step Solution Step 1 Determine the appropriate substitution and write the equation in the form au Let uay 6 y 6 8 y 6 7 0 8 1 7 0

An equation that is quadratic in form is solved by a substitution u x 6 and it has solutions u 3 and u 5 What are the values of x that solve the original equation The values of x that solve the original equation are Type integers or a simplified fractions Use a comma to separate answers as needed

Use the rational zeros theorem to list all possible rational zeros of the following g x 7x 7x 5x 9x 8 Be sure that no value in your list appears more than once 0

About the sequence x kezt we have the following a x 1 EB x b for each 1 to b t b 1 x MKk k 1 te t b t b k20 c x keZ is uniformly Cauchy on t b t b verification of these properties is left for the reader We consider the uniform limit of the sequence x to 6 1 8 B xo b which is given by x t lim x 1 11 b t b b Thus x t lim x ff s x s ds 60 x 60 de lim ff s x s ds x lim f s x s ds Finally the validity of this integral equation has the following two implications 1 x f f s lim x s ds x ff s x s ds E 00 Thus the function 1x 1 satisfying the integral equation x 1 x f f s x s ds for all t t b t b 2 X t x f s x s ds x 0 x dt S dt 0 ff s x s ds f t X t This now proves that the curve X 1 8 4 89 thus obtained is a solution of the initial value problem

of the six trigonometric functions for if 7 12 is a point on the terminal side of 8 Reduce fractions and simplify radicals Do not use decimals Answers for the six trigonometric values cos 8 sin 0 tan 0 Remember decimals are NOT allowed sec 0 csc 0 cot 0

and simplify radicals Do not use decimals A Convert 2490 to radians B Convert to degrees 47 3 C Determine the exact value of tan 20 3 237 ust be given in exact form Redu

Find the equation of the quadratic function f whose graph is shown below 4 1 3 4 10 12 f x

Fall 2023 Math 108 Section Due Wednesday September 27 at 6 00 PM Multiple Choice For each question there is one correct answer Indicate your choice by circling the letter If no letter is circled credit may not be given even if your work is correct Determine the value of sin 0 3 4 A sin 0 D sin 0 A N 16 cos 23 4 sin 23 4 16 B Determine a trigonometric expression for N D N B sin 0 1 E sin 0 4 16 A N 23 4 B N E N cos 23 4 16 16 sin 23 4 C sin 0 C N 16 cos 23 4

4 7 Determine the exact value of sec 0 if is in Quadrant IV and tan 0 6 6 A sec 0 85 85 B sec 0 85 7 C sec 0 85 D sec 0 85 6 85 E sec 0 6

asked on this document not on other notebook paper If you are asked to use a graph draw the graph accurately and clearly indicate the graphing window Explanations should be given in complete sentences 1 A business will be selling smartwatches for the upcoming year The current price of 600 yields 6000 smartwatches sold They estimate that for each 1 increase in price the number of smartwatches sold decreases by 12 Let x represent the price of a smartwatch A Determine a formula for the linear function relating the price x and quantity v of smartwatches sold Consider writing two points price quantity first B Write a simplified quadratic function representing the revenue C Algebraically determine the price x that maximizes revenue DO NOT find the y value of the vertex Include units with your answer

A lighthouse is located at the edge of a cliff near the ocean To measure the height of the light sightings are taken 2400 meters from the base of the cliff If the angle of elevation from the ground to the top of the cliff is 3 94 and the angle of elevation from the ground to the top of the lighthouse is 5 71 what is the height of the lighthouse Round your answer to two decimal places and include units 5 71 2400 meters h 3 94 2400 meters 2400 meters Show how you found the height of the lighthouse below Make sure you round your answer to 2 decimal places and include units

A ball is thrown from a height of 65 meters with an initial downward velocity of 10 m s The ball s height h in meters after t seconds is given by the following h 65 101 57 How long after the ball is thrown does it hit the ground Round your answer s to the nearest hundredth If there is more than one answer use the or button ground seconds or X

generate by selling x purses can be modeled by the function R x 3x 1920x and the total annual cost associated with producing these purses is given by C x 270x 143 000 A Determine a formula for the profit function and simplify your formula completely B Use the profit function to determine the number of purses x that should be sold to maximize profit Include units with your answer C Use the profit function to determine the maximum profit Include units with your answer

Multiple Choice For each question there is one correct answer Indicate your choice by circling the letter If no letter is circled credit may not be given even if your work is correct Determine the exact solutions to the equation x 8x 11 0 A x 4 5 B x 8 5 D x 8 3 3 E x 4 3 3 3 C x 4 6 3

Determine a formula for the quadratic function in vertex form that has its vertex at 7 4 and passes through the point 9 20 A y x 7 4 B y 4 x 9 20 C y 4 x 7 4 D y x 9 20 E y 4 x 7 4

Use the ALEKS graphing calculator to find the x intercept s and vertex for the quadratic function f x 4x 2x 3 Round to the nearest hundredth if necessary If there is more than one x intercept separate them with commas If applicable click on None 0 x intercept s 0 0 None

6 5 4 3 2 S N 65 3 2 1 51 67 hut 1 2 3 42 Write an equation for the graph above f x est 16

The length of a rectangle is 10 yd less than three times the width and the area of the rectangle is 77 yd Find the dimensions of the rectangle Length yd Width d 010 X

The length of a rectangle is 5 m more than twice the width and the area of the rectangle is 63 m Find the dimensions of the rectangle

Find the equation of the line Use exact numbers y x 9 8 7 6 5 4 3 2 1866 9 7 2345 6 5 4 3 2 1 Y ST 4 78 6 7 8 9 O 1 2 3 4 5 6 7 8 9

Use exact numbers y x 9 8 7 6 5 4 3 2 9 876 6 6 SK 5 4 3 2 14 23 Y 2 8788 3 4 5 6 7 8 9 HE 1 2 3 4 5 6 7 8 9

in a triangle one leg measures 14 km and the other leg measures 48 km what is the length of the hypotenuse

question Use the Mathematician s Plan to answer each question Show all work and attempt every 1 Determine the coordinates of each point below E 10 9 0 A 70 6 5 B 2 2 3 4 5 6 y 8 G H 2 State the coordinates of each of the points below YA A 7 6 B 5 C 4 3 D 2 E 1 F A 7 6 5 4 3 2 1 0 2 3 40 5 6 7 F 1 E 2 3 B 4 A B C D E F G H 1 5 6 D 7 x

5 If f x 2x 3 g x x x 21 find x when a f x 7 b g x

5 Distance miles 0 10 9 8 765 3 1 3 ate 2 3 19 Gulliver s Travels 4 5 6 Time hours 7 endent 8 9 10 read as 711 The function d represents Gulliver s distance from home after t hours 1 Use the graph to evaluate the function at each value Explain what each means in terms of the problem a d 2 4 b d 5 11 c d 2 9 4 d d 10 2 Calculate the value of t that makes each equation true Explain what each means in terms the problem a d t 2 c d t 4 b d t 5 d d t 0

Put the function P 7 1 2 in the form P Poekt NOTE Round your answer to four decimal places if required P

A turbo prop plane flying with the wind flew 1400 mi in 5 h Flying against the wind the plane required 7 h to travel the same distance Find the rate of the wind and the rate of the plane in calm air

F The position of a particle moving along a coordinate line is s 25 4t with s in meters and t in seconds Find the rate of change of the particle s position at t 6 sec The rate of change of the particle s position at t 6 sec is Type an integer or a simplified fraction m sec CL

Given s t 2t 4t where s t is in feet and t is in seconds find each of the following a v t b a t c The velocity and acceleration when t 2 sec a v t b a t c When t 2 sec the velocity is Simplify your answer When t 2 sec the acceleration is

Lena invested 400 in a fund for 3 years and was paid simple interest The total interest that she received on the investment was 36 As a percentage what was the annual interest rate of her investment If necessary refer to the list of financial formulas n

To be able to take her dream vacation Kaitlin decides to save for 3 years She opens a savings account with 800 The account pays simple interest a annual rate of 4 She doesn t make any more deposits Answer the following questions If necessary refer to the list of financial formulas a How much total interest will Kaitlin earn b What will the total amount in the account be including interest X

Use the quadratic formula to solve the equation 2x x 1 TER The solution set is Type an exact answer using radicals as needed Type your answer in the form a bi Use a comma to sep answers as needed