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Lesson 3 Mar 11 2010
The document defines net worth as the difference between total assets and total liabilities. Assets are things owned that have value, while liabilities are amounts owed. Assets can be liquid, semi-liquid, or non-liquid depending on how easily they can be converted to cash. Debts can be short-term, usually under 12 months, or long-term like mortgages. The document uses Krista's financial information, including home value, investments, bank account, credit card and vehicle debts, to calculate her net worth.
Lesson 1 Oct 26
The federal government spends trillions of dollars each year, with around $4 trillion spent in 2019. Most of the government's revenue comes from individual and corporate income taxes, as well as payroll taxes that fund programs like Social Security and Medicare. The government also borrows money by issuing Treasury bonds and bills to help fund its spending.
Correlation May 14 2009
The document discusses different types of correlations: positive correlation, where two variables increase together or decrease together; negative correlation, where one variable increases as the other decreases; and zero correlation, where there is no relationship between the variables. It provides examples of years of education and income showing positive correlation, while grade point average and time spent watching TV show negative correlation. The correlation coefficient r indicates the strength of correlations, with values between 0 and 1 for positive correlations, between 0 and -1 for negative correlations, and close to 0 for zero correlation.
Lesson 8 Nov 27 09
The document discusses linear approximation and finding zeros using Newton's method. It provides the formula for calculating the equation of the tangent line near a given point using the value and derivative of the function at that point. As an example, it calculates the tangent line approximation of the function y = -4x^2 + 6x + 9 near x = 2. It also gives the general formula for performing one iteration of Newton's method to find zeros of a function.
Algebra Project Period 4
Algebra is a branch of mathematics that studies structure, relations, and quantities. The quadratic formula provides a method for solving quadratic equations of the form ax^2 + bx + c = 0 by using the coefficients a, b, and c. There are three main methods for solving quadratic equations: factoring, completing the square, and using the quadratic formula.
Statement And Demand For Taxes
This document discusses property taxes, which include municipal taxes and education taxes. Municipal taxes have a general municipal tax and local improvement taxes. Education taxes include provincial education taxes and school division taxes. The document provides an example of calculating the annual municipal and education taxes for a property owner named Andre Herbert based on his property's assessed value, tax rates, and other details. His total annual property taxes are calculated to be $3,287.51.
Foreign Exchange March 20
The document discusses foreign exchange rates and customs duties when importing goods into Canada from other countries. It provides examples of calculating costs of purchasing foreign currency and importing items. Foreign exchange rates have a buying rate and selling rate, with the difference earned by the bank. When importing goods, costs include converting currency, paying applicable customs duties and taxes, and GST. Personal exemptions apply to goods travelers bring into Canada depending on trip length.
Mar2 09 House Insurance
The document discusses the key factors that determine the cost of homeowners insurance. It lists five main factors: 1) replacement cost of buildings, contents, and liability coverage, 2) location and proximity to fire services, 3) type of coverage (comprehensive or standard), 4) deductible amount, and 5) available discounts for claims history, security systems, and age. It then provides examples of calculating insurance premiums for different policy scenarios.
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Lesson 3 Mar 11 2010
The document defines net worth as the difference between total assets and total liabilities. Assets are things owned that have value, while liabilities are amounts owed. Assets can be liquid, semi-liquid, or non-liquid depending on how easily they can be converted to cash. Debts can be short-term, usually under 12 months, or long-term like mortgages. The document uses Krista's financial information, including home value, investments, bank account, credit card and vehicle debts, to calculate her net worth.
Lesson 1 Oct 26
The federal government spends trillions of dollars each year, with around $4 trillion spent in 2019. Most of the government's revenue comes from individual and corporate income taxes, as well as payroll taxes that fund programs like Social Security and Medicare. The government also borrows money by issuing Treasury bonds and bills to help fund its spending.
Correlation May 14 2009
The document discusses different types of correlations: positive correlation, where two variables increase together or decrease together; negative correlation, where one variable increases as the other decreases; and zero correlation, where there is no relationship between the variables. It provides examples of years of education and income showing positive correlation, while grade point average and time spent watching TV show negative correlation. The correlation coefficient r indicates the strength of correlations, with values between 0 and 1 for positive correlations, between 0 and -1 for negative correlations, and close to 0 for zero correlation.
Lesson 8 Nov 27 09
The document discusses linear approximation and finding zeros using Newton's method. It provides the formula for calculating the equation of the tangent line near a given point using the value and derivative of the function at that point. As an example, it calculates the tangent line approximation of the function y = -4x^2 + 6x + 9 near x = 2. It also gives the general formula for performing one iteration of Newton's method to find zeros of a function.
Algebra Project Period 4
Algebra is a branch of mathematics that studies structure, relations, and quantities. The quadratic formula provides a method for solving quadratic equations of the form ax^2 + bx + c = 0 by using the coefficients a, b, and c. There are three main methods for solving quadratic equations: factoring, completing the square, and using the quadratic formula.
Statement And Demand For Taxes
This document discusses property taxes, which include municipal taxes and education taxes. Municipal taxes have a general municipal tax and local improvement taxes. Education taxes include provincial education taxes and school division taxes. The document provides an example of calculating the annual municipal and education taxes for a property owner named Andre Herbert based on his property's assessed value, tax rates, and other details. His total annual property taxes are calculated to be $3,287.51.
Foreign Exchange March 20
The document discusses foreign exchange rates and customs duties when importing goods into Canada from other countries. It provides examples of calculating costs of purchasing foreign currency and importing items. Foreign exchange rates have a buying rate and selling rate, with the difference earned by the bank. When importing goods, costs include converting currency, paying applicable customs duties and taxes, and GST. Personal exemptions apply to goods travelers bring into Canada depending on trip length.
Mar2 09 House Insurance
The document discusses the key factors that determine the cost of homeowners insurance. It lists five main factors: 1) replacement cost of buildings, contents, and liability coverage, 2) location and proximity to fire services, 3) type of coverage (comprehensive or standard), 4) deductible amount, and 5) available discounts for claims history, security systems, and age. It then provides examples of calculating insurance premiums for different policy scenarios.
Logatithms 0918
The document discusses properties of logarithms, including formulas for logb(MN), logb(M/N), and logbMr. It also covers the change of base formula and provides an example of approximating log5 7. The document then presents a word problem about modeling population growth over time for Ottawa, asking the reader to write a function for the population as a function of years and calculate how many years it will take for Ottawa's population to reach 3 million people, growing at 3% per year.
Doug's Truck project
The document summarizes work done over two summers to restore a truck cab. It describes picking up the cab in Detroit to replace the original, taking out the old cab, sandblasting and priming the cab and frame, doing bodywork like installing a new floor, and finally lifting the restored cab onto the frame.
Feb112009
This document discusses how to invest in stocks and provides examples of calculating costs for purchasing stocks and profits or losses from stock transactions. It explains that Louis wants to buy 500 shares of Manitoba Telecom and calculates his total cost including a 2% broker fee. It also gives an example of Mary purchasing then selling shares of Astral Media, calculating her profit/loss while factoring in 3% broker commissions for each transaction.
Invest review
Rem purchased 1000 shares of Wartel stock at $7.50 per share with a 7% commission. Six months later, Rem sold the shares at $8.50 per share with another 7% commission. Rem's total gain or loss from the transaction needs to be calculated. Registered savings plans offer advantages like tax-deferred growth that Marlon should consider for his $50 monthly investment goal. GICs have low risk but also low returns, while stocks have higher risk and potential returns. A 3% commission applies to purchasing 300 shares worth $12.48 each. Appropriate financial goals differ by age, such as saving for emergencies for a 20-year-old and retirement for a 50-year
04 Probability Mar8
This document contains 15 probability and counting problems involving scenarios like choosing meal combinations, generating random numbers, arranging letters, and determining routes. It asks the reader to find theoretical probabilities, count outcomes, and calculate the number of possibilities that satisfy given constraints.
01 Probability Mar2
The document describes two probability experiments: spinning a die 30 times and recording results to calculate the probability of landing on 5, and spinning a spinner 20 times to calculate the probability of landing on red. It asks the reader to conduct the experiments, record their results, and compare the experimental probabilities to the theoretical probabilities of 1/6 for the die and the spinner's designated probability for each color section.
Quadratic Functions
This document provides information about graphing parabolas on a graphing calculator. It discusses the key parts of a parabola graph like the vertex, axis of symmetry, zeros, and y-intercept. It explains how to input equations into the graphing calculator and use functions to find the vertex, zeros, and maximum or minimum points. The document also covers how changing variables in the standard parabola equation affects the shape, direction, and location of the graphed parabola. Some examples of word problems involving parabolas are presented as well.
Perm And Comb Review Answers
This document contains a permutation and combination review test with multiple choice, short answer, and long answer questions. The test covers topics like permutations of letters, binomial expansions, and arrangements of identical objects on a shelf. It provides questions without answers to assess understanding of fundamental permutation and combination concepts.
Imaginary Mar 16 09
A rectangular piece of cardboard had its length and width determined by cutting out 3 cm by 3 cm squares from each corner and folding up the sides to form an open box with a volume of 450 cm3. An equation was needed to calculate the original length and width of the cardboard based on this information.
Quadratic Lesson 5feb12
The document provides instructions to multiply out several quadratic expressions, including (x+1)2, (x+2)2, (x+3)2, (x-1)2, (x-2)2, (x-3)2. It then gives examples of converting quadratic equations into the standard form of y = ax2 + bx + c, including converting y = x2 + 4x - 5, y = 3x2 - 12x + 16, and y = -2x2 - 5x + 3. It concludes by stating it is now time for Exercise 5.
Lesson 4 Apr 8 2010
Dave needs a new computer for university costing $3,294 before taxes. Financing is available at 18.99% compounded monthly over 48, 36, or 24 months. The monthly payments and total paid are calculated for each term. Daniel can also lease the same computer for $106.92/month over 48 months, $132.32/month over 36 months, or $182.88/month over 24 months. The document then provides information about leasing, including what costs make up monthly lease payments and details that would be in a lease agreement.
Lesson 2 Apr 6 2010
The document discusses various interest rates and compounding periods for investments, savings accounts, and credit cards, and uses calculations to determine future values, effective interest rates, and the best investment options based on interest rates and compounding frequencies. Formulas like the Rule of 72 are presented for estimating doubling times given interest rates.
Lesson 3 Apr 7 2010
The monthly payments and total amount paid will increase as the loan term decreases from 48 months to 36 months to 24 months due to the interest being applied over a shorter period of time.
Lesson 1 Apr5 2010
The document defines key terms and concepts related to circles and their equations. It explains that a circle consists of points equidistant from a fixed center point, and defines the radius as the distance from the center to any point on the circle. It provides the standard equation for a circle with center at the origin, and notes that the standard form includes variables h and k to indicate the center coordinates and r for the radius. It also describes a second form for the circle equation that can be converted to standard form by completing the square.
Lesson 1 Apr 5 2010
This document discusses personal finance concepts like the time value of money and compound interest. It provides the basic formulas for calculating future value (FV), present value (PV), interest rate (I%), number of periods (N), principal (P), payments (PMT), periodic interest rate (r), number of compounding periods per year (n), and time (t). The document works through examples of using these formulas to calculate things like how much money you will have after investing a principal amount over a period of time at a given interest rate.
Pretest
The document contains 6 math problems: 1) Find the value of k that gives equal roots of the quadratic equation f(x)=x^2 + 4x + k. 2) Determine the nature of the roots of the quadratic equation 13x^2 - 15x = 4. 3) Solve the equation x - 3 = 2 for x. 4) Find the quadratic equation with integer coefficients given the roots 3 + 9i and 10. 5) Solve the equation x + 8 = 10x - 81 for x. 6) Solve the equation x/3 = 6 - 2x for x.
Lesson 03 Appsof Integrals Mar23
This document discusses using the shell method to calculate volumes of solids generated by revolving regions between functions around axes. It provides examples of revolving the function f(x)=x^2 around the x-axis and y-axis, and revolving the region between f(x)=0.5x^2-2x+4 and g(x)=4+4x-x^2 around both the x-axis and y-axis. Instructions are given to use the shell method to find each volume.
Lesson 08 Mar 23
Absolute value refers to the distance from zero on the number line. There are two values, -2 and 2, that have an absolute value of 2. Absolute value can never be negative because distance cannot be negative. The document provides examples of using absolute value to solve equations.
Lesson 07 Mar 20
This document discusses solving rational equations by finding the least common denominator, combining like terms, and then solving the resulting equation for the variable. It contains an exercise with questions 1, 6, and 7 about solving rational equations.
Vectors 03 Mar 20
This document provides instructions and problems for solving vector problems by drawing scale diagrams, adding vectors using the triangle method, and calculating distances and directions from starting points. Specifically, it asks the reader to: 1) draw scale diagrams of vectors for a person walking 13 blocks E15°S and a boat headed 300° at 45 km/h; 2) add the vectors using the triangle method; and 3) solve problems involving distances and directions for a man walking in different directions and a jogger moving north and east over time.
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Logatithms 0918
The document discusses properties of logarithms, including formulas for logb(MN), logb(M/N), and logbMr. It also covers the change of base formula and provides an example of approximating log5 7. The document then presents a word problem about modeling population growth over time for Ottawa, asking the reader to write a function for the population as a function of years and calculate how many years it will take for Ottawa's population to reach 3 million people, growing at 3% per year.
Doug's Truck project
The document summarizes work done over two summers to restore a truck cab. It describes picking up the cab in Detroit to replace the original, taking out the old cab, sandblasting and priming the cab and frame, doing bodywork like installing a new floor, and finally lifting the restored cab onto the frame.
Feb112009
This document discusses how to invest in stocks and provides examples of calculating costs for purchasing stocks and profits or losses from stock transactions. It explains that Louis wants to buy 500 shares of Manitoba Telecom and calculates his total cost including a 2% broker fee. It also gives an example of Mary purchasing then selling shares of Astral Media, calculating her profit/loss while factoring in 3% broker commissions for each transaction.
Invest review
Rem purchased 1000 shares of Wartel stock at $7.50 per share with a 7% commission. Six months later, Rem sold the shares at $8.50 per share with another 7% commission. Rem's total gain or loss from the transaction needs to be calculated. Registered savings plans offer advantages like tax-deferred growth that Marlon should consider for his $50 monthly investment goal. GICs have low risk but also low returns, while stocks have higher risk and potential returns. A 3% commission applies to purchasing 300 shares worth $12.48 each. Appropriate financial goals differ by age, such as saving for emergencies for a 20-year-old and retirement for a 50-year
04 Probability Mar8
This document contains 15 probability and counting problems involving scenarios like choosing meal combinations, generating random numbers, arranging letters, and determining routes. It asks the reader to find theoretical probabilities, count outcomes, and calculate the number of possibilities that satisfy given constraints.
01 Probability Mar2
The document describes two probability experiments: spinning a die 30 times and recording results to calculate the probability of landing on 5, and spinning a spinner 20 times to calculate the probability of landing on red. It asks the reader to conduct the experiments, record their results, and compare the experimental probabilities to the theoretical probabilities of 1/6 for the die and the spinner's designated probability for each color section.
Quadratic Functions
This document provides information about graphing parabolas on a graphing calculator. It discusses the key parts of a parabola graph like the vertex, axis of symmetry, zeros, and y-intercept. It explains how to input equations into the graphing calculator and use functions to find the vertex, zeros, and maximum or minimum points. The document also covers how changing variables in the standard parabola equation affects the shape, direction, and location of the graphed parabola. Some examples of word problems involving parabolas are presented as well.
Perm And Comb Review Answers
This document contains a permutation and combination review test with multiple choice, short answer, and long answer questions. The test covers topics like permutations of letters, binomial expansions, and arrangements of identical objects on a shelf. It provides questions without answers to assess understanding of fundamental permutation and combination concepts.
Imaginary Mar 16 09
A rectangular piece of cardboard had its length and width determined by cutting out 3 cm by 3 cm squares from each corner and folding up the sides to form an open box with a volume of 450 cm3. An equation was needed to calculate the original length and width of the cardboard based on this information.
Quadratic Lesson 5feb12
The document provides instructions to multiply out several quadratic expressions, including (x+1)2, (x+2)2, (x+3)2, (x-1)2, (x-2)2, (x-3)2. It then gives examples of converting quadratic equations into the standard form of y = ax2 + bx + c, including converting y = x2 + 4x - 5, y = 3x2 - 12x + 16, and y = -2x2 - 5x + 3. It concludes by stating it is now time for Exercise 5.
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Lesson 4 Apr 8 2010
Dave needs a new computer for university costing $3,294 before taxes. Financing is available at 18.99% compounded monthly over 48, 36, or 24 months. The monthly payments and total paid are calculated for each term. Daniel can also lease the same computer for $106.92/month over 48 months, $132.32/month over 36 months, or $182.88/month over 24 months. The document then provides information about leasing, including what costs make up monthly lease payments and details that would be in a lease agreement.
Lesson 2 Apr 6 2010
The document discusses various interest rates and compounding periods for investments, savings accounts, and credit cards, and uses calculations to determine future values, effective interest rates, and the best investment options based on interest rates and compounding frequencies. Formulas like the Rule of 72 are presented for estimating doubling times given interest rates.
Lesson 3 Apr 7 2010
The monthly payments and total amount paid will increase as the loan term decreases from 48 months to 36 months to 24 months due to the interest being applied over a shorter period of time.
Lesson 1 Apr5 2010
The document defines key terms and concepts related to circles and their equations. It explains that a circle consists of points equidistant from a fixed center point, and defines the radius as the distance from the center to any point on the circle. It provides the standard equation for a circle with center at the origin, and notes that the standard form includes variables h and k to indicate the center coordinates and r for the radius. It also describes a second form for the circle equation that can be converted to standard form by completing the square.
Lesson 1 Apr 5 2010
This document discusses personal finance concepts like the time value of money and compound interest. It provides the basic formulas for calculating future value (FV), present value (PV), interest rate (I%), number of periods (N), principal (P), payments (PMT), periodic interest rate (r), number of compounding periods per year (n), and time (t). The document works through examples of using these formulas to calculate things like how much money you will have after investing a principal amount over a period of time at a given interest rate.
Pretest
The document contains 6 math problems: 1) Find the value of k that gives equal roots of the quadratic equation f(x)=x^2 + 4x + k. 2) Determine the nature of the roots of the quadratic equation 13x^2 - 15x = 4. 3) Solve the equation x - 3 = 2 for x. 4) Find the quadratic equation with integer coefficients given the roots 3 + 9i and 10. 5) Solve the equation x + 8 = 10x - 81 for x. 6) Solve the equation x/3 = 6 - 2x for x.
Lesson 03 Appsof Integrals Mar23
This document discusses using the shell method to calculate volumes of solids generated by revolving regions between functions around axes. It provides examples of revolving the function f(x)=x^2 around the x-axis and y-axis, and revolving the region between f(x)=0.5x^2-2x+4 and g(x)=4+4x-x^2 around both the x-axis and y-axis. Instructions are given to use the shell method to find each volume.
Lesson 08 Mar 23
Absolute value refers to the distance from zero on the number line. There are two values, -2 and 2, that have an absolute value of 2. Absolute value can never be negative because distance cannot be negative. The document provides examples of using absolute value to solve equations.
Lesson 07 Mar 20
This document discusses solving rational equations by finding the least common denominator, combining like terms, and then solving the resulting equation for the variable. It contains an exercise with questions 1, 6, and 7 about solving rational equations.
Vectors 03 Mar 20
This document provides instructions and problems for solving vector problems by drawing scale diagrams, adding vectors using the triangle method, and calculating distances and directions from starting points. Specifically, it asks the reader to: 1) draw scale diagrams of vectors for a person walking 13 blocks E15°S and a boat headed 300° at 45 km/h; 2) add the vectors using the triangle method; and 3) solve problems involving distances and directions for a man walking in different directions and a jogger moving north and east over time.
Lesson 06 Mar 19
An equation containing a radical is called a radical equation. This document refers to exercises 18 questions 1 through 5 and also questions 8 and 9 which involve solving or working with radical equations. The goal is to extract the key essential information about radical equations from the given document in 3 sentences or less.
Vectors 02 Mar 19
The document provides information about vector addition and trigonometric equations. It discusses drawing scale diagrams to represent vectors and their directions and magnitudes. Methods for adding vectors are described, including the triangle method used when vectors are tip-to-tail and the parallelogram method used when vectors are tail-to-tail. An example of each method is worked out to find the resultant vector.
Lesson 02 Appsof Integrals Mar19
The document contains instructions to find the volumes of solids generated by revolving regions bounded by graphs about axes. It gives the volume as 183.981 when revolving the region between the graphs y = 2x + 4 and y = ex about the x-axis. It also gives the volumes as 7/15 when revolving the region between y = x^2 + 1 and y = x + 1 about the x-axis and 4/5 when revolving the same region about the line y = -1.
Vectors 02 Mar 19
The document provides information about vector addition and trigonometric equations. It discusses drawing scale diagrams to represent vectors and their directions and magnitudes. Specific examples are given of adding vectors using the triangle method when vectors are tip-to-tail and the parallelogram method when they are tail-to-tail. Measurements from the scale diagrams along with a protractor can be used to find the resultant vector.
Vectors 01 Mar 18
The document discusses vectors and provides examples of identifying quantities as scalar or vector. It also discusses four notations for writing vectors using arrows, bearings, angle-direction-direction, and angle-direction of direction. Examples are given to demonstrate each notation. The document also discusses stating the direction of vectors in five ways and using diagrams of parallelograms to name vectors that are equal, opposite, collinear, or parallel but not equal to other vectors in the diagram.
Lesson 05 Mar 18
The document describes a problem where a rectangular piece of cardboard has a length longer than its width. Square pieces are cut from the corners and the sides are folded up to form a box with a volume of 450 cm3. The original length of the cardboard was 16 cm and the width was 11 cm.
Lesson 04 Mar 17
This document discusses methods for finding the roots of quadratic equations. It introduces the discriminant formula to determine the type of roots, and explains how to use the quadratic formula to find the exact values of the roots. It also shows how to write a quadratic equation given the sum and product of its roots, or given two integer roots.
Lesson 01 Appsof Integrals Mar17
The document discusses calculating the volume of solids of revolution using integrals. It provides the formula for finding the volume of a solid rotated about the x-axis between x=a and x=b using a cross-sectional area function A(x). It then works through an example of finding the volume of a right circular cone of height 4 and base radius 1, and confirms the result matches the standard volume formula for a cone.
Lesson 03 mar 16
This document provides instructions to solve equations by graphing them. The reader is directed to graph two or more equations simultaneously and find the point(s) of intersection, which will represent the solution(s) to the system of equations. The document references exercise problems 15 questions 1 through 3, which likely involve graphing and solving systems of equations.
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