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mathematics
linear algebra

Questions and Answers of Linear Algebra

Danny just answered a help-wanted ad. The ad states that the job pays $27K annually. What would Danny's monthly salary be if he gets this job?
Becky is looking for a new job as an account executive. She responds to a classified ad for a position that pays 34.5K. What would Becky's weekly salary be to the nearest cent, if she gets this job?
The Rockville Employment Agency just placed Howard Jacobson in a job as a junior pharmacist. The job pays $51.2K. The agency fee is equal to 40% of the first three weeks' pay.a. What is Howard's
Maple Place Garage is posting five job listings with the online service from Example 4. a. How much is each posting?b. How much less does Maple Place pay per posting compared to the price for one
Roger wants to have 400 copies of his resume printed. His local print shop charges $21.50 for the first 200 copies and $10 for every 100 additional copies. a. How much will the 400 copies cost,
Pat earns $575 per week at her new job. Express her annual salary using the K abbreviation found in classified ads?
Interpret the quote in the context of what you learned about jobs and salaries?
Last year Nancy's annul salary was x dollars. This year she received a raise of y dollars per year. She is paid semimonthly.a. Express her semimonthly salary last year algebraically.b. Express her
Lynn regularly works a 40-hour week and earns $9 per hour. She receives time and a half pay for each hour of overtime she works.a. What was her regular gross pay?b. What was her hourly overtime
Tom earns $12.50 per hour at the Yankee Bowling Alley. He regularly works 40 hours per week. He is paid time and a half for each hour of overtime work. Last week he worked 42 hours. What was his
Pedro works 35 regular hours per week at the Meadow Deli. His hours over 35 are considered overtime. He earns $9.20 per hour and receives time and a half pay for each hour of overtime he works. Last
Michael earns $10 per hour. He regularly works 40 hours per week. How many overtime hours would he have to work in a week for his overtime pay to be greater than his regular gross pay?
Jim worked 40 regular hours last week, plus 8 overtime hours at the time and a half rate. His gross pay was $1,248.a. What was his hourly rate?b. What was his hourly overtime rate?
Julianne works as a waitress. She earns $5.90 per hour plus tips. a. Today she worked x hours. Express her pay for these hours algebraically.b. She served nine tables. The total bill for these nine
Mike works at Cheesecake King. He earns $11 per hour as a busboy.The waiters he helps give him 25% of their tipsa. If Mike worked 6 hours today, how much did he earn, without tips?b. The waiters Mike
Gary earns 42,990 per year. He is paid weekly. He currently has a $456-per month car loan payment, and he pays $1,277 per year for auto insurance. Is one week's paycheck enough to pay for his monthly
The following spreadsheet can be used to compute total weekly pay, given the hours, hourly rate, and overtime rate.a. Write the formula to compute the regular gross pay in cell D2.b. Write the
Marty is working with a math problem that defies insulting. He is going to pay his gardener for the entire month of July. He will pay the gardener every day. On the first day, he will pay the
John's weekly salary is $478.25. His employer is changing the pay period to semimonthly.a. What is John's annual salary?b. What will John's semimonthly salary be to the nearest cent?
Ralph earns $72,000 annually as an architect and is paid semimonthly. Alice also earns $72,000 but she is paid biweekly.a. How many more checks does Alice receive in a year when compared to Ralph?b.
Last year Beth's annual salary was $38,350. This year she received a promotion and now earns $46,462 annually. She is paid biweekly.a. What was her biweekly salary last year?b. What is Beth's
Alanna is a stockbroker. She receives a commission based on the value of the trades she makes.a. If Alanna earns $50 for sales of $1,000, what is her percent of commission?b. If she earns x dollars
Barb works in a local factory. She receives 92 cents for each of the first 100 units she produces and $1.01 for each unit over 100. Yesterday, she produced 120 units. How much did Barb earn?
Bill works for the Stuff-It Mailing Service. He receives 25 cents for each document he puts together and prepares for mailing. Last week, Bill prepared 2,000 documents for mailing for a local
Audrey works in a factory. She receives a salary of $8 per hour and piecework pay of 12 cents per unit produced. Last week she worked 38 hours and produced 755 units. a. What was her piecework pay?b.
Anton picks corn at a local farm. He is paid 80 cents per bushel for the first 50 bushels, 90 cents per bushel for the next 50 bushels, and $0.95 per bushel for all bushels picked over 100. Express
Rock musician Donny West is paid 15% on his CD sales and tour video sales. Last year, he sold one million CDs and 550,000 videos. The CDs were sold to music stores for $5 each and the videos for $6
Arielle receives a piecework rate of 10 cents per unit from the Wiggy Factory. Her production record for last week was affected by a machinery breakdown on Tuesday. Her production results were:
Janice is a travel agent. She receives a 7% commission based on the value of the trips she books. Today she spent five hours arranging a $3,300 cruise for a newlywed couple.a. How much commission did
Appel's Music Store pays its sales staff a commission of 9.5% of the first $1,000 in sales and 15.5% of the balance of sales. Alex, the store's drum expert, received $1,234.25 in commission last
Salespersons at the Kings Park Auto Giant are paid a commission, c(p), based on the profit, p. The following piecewise function gives the commission rules.a. If the profit is $1,500, what is the
McCormack Chrysler pays their sales staff by commission. They are paid a percent of the profit the dealership makes on the car. If the profit is $500 or less, the commission rate is 17%. If the
Aileen is a salesperson at Lopez Sporting Goods. She is paid a monthly commission on all Little League uniforms she sells. She receives 10% of her first $2,000 in sales and 12% of the balance of her
Oscar sells Internet access subscriptions by telephone. He receives 12% of the first $1,000 and 15% on the balance over $1,000. Last month he sold $7,500 worth of Internet access subscriptions. What
How can the quote be interpreted in light of what you have learned?
The spreadsheet calculates a yearly pension. Users enter the pension percentage as a percent in cell B1, the number of years worked in cell B2, and the last four working years' salaries in cells
Natalia worked in an automobile plant. She lost her job when the plant relocated to another state. She applied for unemployment compensation. In her state, the amount is calculated by taking 55% of
In Rodger's state, unemployment compensation is calculated by finding the total of the quarterly wages of two consecutive quarters and dividing by 26. The weekly unemployment is 65% of that amount.
Roberto's employer offers a sliding paid vacation. When he started work, he was given three paid days of vacation. For each six-month period he stays at the job, his vacation is increased by two
When Lisa started at her current job, her employer gave her two days of paid vacation time with a promise of three additional paid vacation days for each year she remains with the company to a maxi-
When Lou started his current job, his employer told him that he would receive two vacation days for each full year he worked. Let x represent the number of years he has worked for the company and y
When George started his current job, his employer told him that at the end of the first year, he would receive two vacation days. After each year worked, his number of vacation days would double up
At Richardson Manufacturing Company, there are two factors that determine the cost of health care. If an employee makes less than $55,000 per year, he pays $40 per month for individual coverage and
Eddie is a plant manager at North Salem Construction Company. He has been employed there for 20 years and will be retiring at the end of this year. His pension is calculated on the average of his
As part of their employee benefits, all workers at Middletown Electronics receive a pension that is calculated by multiplying the number of years worked times 1.65% of the average of their three
Keesha earned x dollars per month in 2006, where x < $5,600.a. Did she earn more or less than the maximum taxable income for 2006? b. Express her Social Security tax for the year algebraically.c.
A politician is listening to y a proposal for a new Social Security tax plan. The graph is shown. The two parts of the graph are disconnected where x = 100,000. Explain why this would be an unfair
In a year when the maximum income for Social Security was $106,800, Bart worked at two jobs. In one job he earned $99,112. In his second job, he earned $56,222. Both of his employers took out Social
An All-Star baseball player earning $25,000,000 per year plays 162 games per year. If you divide the salary by the number of games, does that baseball player reach this year's maximum taxable income
The table on the right gives a historical look at Social Security tax before there was a separate Medicare tax. Find the maximum you could pay into Social Security for each year.
In 1990, Jerry's gross pay was $78,000.a. What was his monthly gross pay?b. In what month did Jerry hit the maximum taxable Social Security income?c. How much Social Security tax did Jerry pay in
In 1978, Dawn earned $48,000.a. What was her monthly gross pay?b. In what month did Dawn reach the maximum taxable Social Security income?c. How much Social Security tax did Dawn pay in February?d.
In 1991, Social Security and Medicare taxes were itemized separately on paycheck stubs and tax forms for the first time. The table on the right gives a historical look at Social Security and Medicare
Express the 1993 Social Security tax function as a piecewise function t(x), where x is the annual income. Graph the function. What are the coordinates of the cusps on the graph?
Graph the Social Security tax function for 1992. What are the coordinates of the cusp? On the same axes, graph the Medicare function?
Josephine is looking for a new part-time job as a plumber. She responds to a classified ad for a position that pays 44.5K. What would her weekly salary be to the nearest cent if she gets this job?
Anton works at First National Bank. His employer offers him a pension retirement plan which will be 1.45% of his average salary for the last five years of employment for every year worked. Anton is
In 2008, the Social Security percentage was 6.2% for the first $102,000 earned. The Medicare percentage was 1.45% of your entire salary. Darby made $143,000 in 2008. a. Write the combined taxes, y,
The percentages at the turn of the 21st century are shown in the table. Ray worked at the same job for those three years making $80,400 without any increase in salary.a. Calculate his Social Security
In many states, the weekly unemployment compensation is a certain percentage of the 26-week average for the two highest-salaried quarters. A quarter is three consecutive months. In the spreadsheet
Frank got a new job through the Valley Employment Service. The job pays $51K per year, and the agency fee is equal to 35% of one month's pay. How much must Frank pay the agency?
Derek is placing a seven-line classified job for an assistant. The following piecewise function gives the price of an x-line ad.Find the difference between the cost of a 6-line ad and the cost of a
Carole worked her 40 regular hours last week plus 5 overtime hours at the time and a half rate. Her gross pay was $451.25. What was her hourly rate?
Tania earns $13.50 per hour at the Glendale Florist. She regularly works 40 hours per week. She is paid time and a half for each hour of overtime work. Last week she worked 43 hours. What was her
Patrick earns x dollars per hour for his regular 40 hours per week. He also works three hours overtime each week, at a time and a half rate. Express his annual salary algebraically?
The Price King Auto Mall pays their sales staff by commission. They are paid a percent of the profit the dealership makes on each sold car. If the profit is $900 or less, the commission rate is 18%.
Calculate the tax for each of the taxable incomes of a head of house- hold taxpayer.a. $400,000b. $108,962c. $201,102d. $106,000
Let w represent the tax for any taxable income t on the interval 182,400 < t ≤ 357,700. a. Calculate the lowest tax on this interval.b. Calculate the highest tax on this interval.c. Given the
Calculate the tax using the computation worksheet for a head of household taxpayer with a taxable income of $115,700?
Using the tax schedule from Exercise 6, calculate the tax for the person in Exercise 14.
Use Schedule Z from Exercise 6 to calculate the tax for the tax- payer in Exercise 17. Show working.
Determine the tax for each filling status and taxable income amounta. Single $57,723b. Head of household $60,950c. Married filling jointly $63,999d. Married filling separately $57,521
Use Schedule Z from Exercise 6 to calculate the tax for the tax- payer in Exercise 17.
Given a taxable income amount, express the tax table line that would be used in compound inequality notation.a. i = $63,124b. i = $57,333
Given the taxable income amount, express the table line that would be used in interval notation.a. i = $57,555b. i = $63,411c. i = $57,333d. i = $63,301
Given the filing status and the tax, identify the taxable income interval that was used to determine the tax.a. Head of household $9,406b. Single $12,275c. Single $11,538 d. married filing jointly
Schedule Z - If your filling status is Head of householdCalculate the tax for each taxable income of a head of household.a. $400,000b. $10,954c. $108,962d. $201,102
For what taxable income would a taxpayer have to pay $5,975.00 in taxes? Explain your reasoning?
According to the tax schedule, Rich has to pay $25,000 in taxes. What is Rich's taxable income?
Kelly's taxable income is $110,000. Approximately what percent of her taxable income is her tax?
You are given this portion of a tax schedule from a pervious year for single taxpayers with income over $71,950.a. Model each of the three rows as a simplified equation in y = mx + b form.b. Create
Examine the following tax computation worksheet. Let x represent the taxable income and y represent the tax.a. Let Y1 represent the graphing calculator function for taxable incomes on the interval
Examine this tax schedule. Let x represent the taxable income and y represent the tax.a. What is the calculator keystroke sequence for an equation that models the tax on the interval over 32,550 but
Use the graph of a piecewise function with three equations.a. A taxpayer has a taxable income of $39,800. What is her tax?b. A taxpayer will owe $21,197. What is his taxable income?c. What is the
Many people claim that once they are married, they pay more taxes than they did before they were married. Many call this a marriage penalty. Could this be true?Suppose that Alli and DeWitt are
There are six taxable income intervals in this chart. Let x represent any taxable income. Express those intervals in tax schedule notation, interval notation, and compound inequality?
Let y represent the tax and x represent the taxable income of a single taxpayer.a. Use the tax schedule to write three equations in y = mx + b form for values of x that are greater than or equal to
Write a piecewise function to represent the tax f(x) for the first three taxable income intervals in the schedule for a married taxpayer who is filling separately.
Use the 2000 tax schedule for a married taxpayer filing jointly. Write an equation in y = mx + b form for a tax- able income in the interval over $105,950 but not over $161,450?
Use the 2006 tax schedule for a married taxpayer filing a married taxpayer filling jointly. Write the piecewise function for the tax intervals?
In 1998, a single taxpayer used this tax schedule. Let x represent the single tax- payer's taxable income and y represent that taxpayer's tax. Express the tax schedule as a piecewise function.
Use the tax computation worksheet for a head of household taxpayer's taxable income and y represent the tax. Express each line of the worksheet as a linear equation in y = mx + b form. Use interval
How can the quote be interpreted in light of what you have learned? Discuss.
Joe makes an hourly wage of $8.10. For hours worked over 40, he is paid at a rate of $12.15 per hour. Last week, Joe worked 45 hours.a. What is Joe's gross pay for this pay period?b. What is Joe's
Leslie works for Blanck Corporation. His annual salary is $57,285.50. a. What is Leslie's annual Social Security deduction?b. What is Leslie's annual Medicare deduction?c. Leslie is paid every other
Let A represent the number of the paycheck for the year. For example, if the paycheck was the fifth of the year, A is 5. Let B represent the biweekly gross pay. Let C represent the biweekly union
Complete the missing entries in the following pay stub.a. As indicated in the paycheck number box, this is the 18th pay- check of the year. Determine the current gross pay.b. What is the Social
How can the quote be interpreted in light of what you have learned? Discuss in detail.
Betsy and Rich Crosmour are married with two children. Rich is a chef and Betsy is a designer. This information was reported on their W-2 forms. Betsy and Rich received $1,287.43 in interest on bank
Mukul is a teacher at Rockland School and he runs a tennis shop called Racket's Rackets. He and his wife Nikki have combined bank interest of $1,011. Nikki made $850 in tips last year. If they get a

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