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Algebra 2 Semester 2 Final Practice ProblemsMultiple ChoiceIdentify the choice that best completes the statement or answers the question.____1.Which statement is logically equivalent to ?a.c.b.d.____2.Determine if the statements are logically equivalent.p ? ??q and ??(p ? q)a.yesb.no____3.Simplify using significant digits.a.5.4 m3c.5.39 m3b.5 m3d.5.391 m3____4.Given ; , ; , find .a.47c.43b.53d.1____5.Find where ; , ; a.30c.–90b.–12d.8____6.What is the z-intercept for the equation ?a.c.b.d.____7.Solve the system.a.c.b.d.No solution____8.What is the range of the discrete function ?a.–8, –5, 7d.b.e.None correctc.____9. equalsa.d.b.e.c.____10.Solve the system.a.c.b.d.____11.What is the solution of the system of equations? a.(, )d.(,?)b.(,?)e.None correctc.(,?)____12.At which of the given values is the graph discontinuous?a.x = c.x = b.x = 0d.x = ____13.Determine if the graph is continuous, discontinuous, and/or discrete. Determine if it is a function or a relation. Determine the domain and range.a.Continuous relation.D: all real numbers; R: all real numbersb.Continuous function.D: all real numbers; R: all real numbersc.Continuous function.D: all real numbers; R: 0 ? y ? 7d.Continuous relation.D: all real numbers; R: 0 ? y ? 7____14.Determine if the graph is continuous, discontinuous, and/or discrete. Determine if it is a function or a relation. Determine the domain and range.a.Continuous relation.D: all real numbers; R: y ??–3b.Discrete relation.D: all real numbers; R: all real numbersc.Continuous function.D: all real numbers; R: y ??–3d.Discontinuous function.D:?x = –3; R: all real numbers____15.Determine if the graph is continuous, discontinuous, and/or discrete. Determine if it is a function or a relation. Determine the domain and range.a.Discontinuous function.D: , R: all real numbers except y = 4b.Discontinuous relation.D: all real numbers except x = 1, R: c.Discontinuous function.D: all real numbers except x = 1, R: d.Discontinuous relation.D: , R: ____16.Solve .a.x = –12 or x = –9c.x = 0, x = 4, or x = 3b.x = 0, x = –4, or x = –3d.x = –4 or x = –3____17.The sum of the digits of a two-digit number is 8. If the number is multiplied by 4, the result is 104. Write and solve a system of equations. Find the number.a.The number is 35.c.The number is 18.b.The number is 17.d.The number is 26.____18.The data {1, 5, 8, 5, 1} represent a random sample of the number of days absent from school for five students at Riverview High School. Find the mean and the standard deviation of the data.a.The mean is 4, and the standard deviation is about 2.68.b.The mean is 4.4, and the standard deviation is about 2.76.c.The mean is 20, and the standard deviation is about 7.6.d.The mean is 4, and the standard deviation is about 7.2.____19.Which equation is represented in the graph?a.c.b.d.____20.What is the equation of a line that passes through and is perpendicular to the line ?a. c.b. d.____21.Add the rational expressions.a.c.b.d.____22. equalsa.d.b.e.c.____23.Simplify .a.c.b.d.____24.Multiply . Assume that all expressions are defined.a.c.b.d.____25.Write an equation in slope-intercept form for the line perpendicular to y = x – 2 that passes through the point (3, –2).a.y = x – c.y = x + b.y = x – 2d.y = x – ____26.The equations of four lines are given. Identify the perpendicular lines.Line 1: Line 2: Line 3: Line 4: a.Lines 2 and 4 are perpendicular.b.Lines 1 and 3 are perpendicular.c.None of the lines are perpendicular.d.Lines 1 and 3 are perpendicular; Lines 2 and 4 are perpendicular.____27.Simplify the expression . Assume any variables are positive.a.c.b.d.____28.Simplify the expression a.c.b.d.____29.Find the distance between S(4, –2) and U(–1, 7). Give the answer to the nearest tenth.a.7.2 unitsc.10.3 unitsb.4 unitsd.2 units____30.Find CD and EF. Give the answers in simplest radical form.a., c., b., d., ____31.There are 8 singers competing at a talent show. In how many different ways can the singers appear?a.5,040c.40,320b.56d.64____32.Describe the correlation illustrated by the scatter plot.a.no correlationc.cannot determineb.negative correlationd.positive correlation____33.Find the value of the sine, cosine, and tangent functions for ? where , , and .a. ; ; c. ; ; b. ; ; d. ; ; ____34.Find the values of the six trigonometric functions for ??a.sin ? = ; cos ? = ;tan ? = ; csc ? = ;sec ? = ; cot ? = c.sin ? = ; cos ? = ;tan ? = ; csc ? = ;sec ? = ; cot ? = b.sin ? = ; cos ? = ;tan ? = ; csc ? = ;sec ? = ; cot ? = d.sin ? = ; cos ? = ;tan ? = ; csc ? = ;sec ? = ; cot ? = ____35.A camera is mounted at a point 4,400 ft from the base of a rocket launching pad. Assuming the rocket goes straight up, what is the height of the rocket from its launching pad when the camera angle is 30°? Round your answer to the nearest foot.a.3,811 ftc.2,200 ftb.7,621 ftd.2,540 ft____36.Graph y = 2().a.c.b.d.____37.Simplify . Assume that no variable can equal zero.a.c.b.d.____38.Simplify . Assume that no variable can equal zero.a.c.b.d.____39.Find an equation for the inverse of – 5.a. 3(x + 5)c. –5x b. + 5d. 3x + 5____40.Which ordered pair is a solution to the system of linear inequalities?a.c.b.d.____41.Which ordered pair is a solution to the system of inequalities? a.d.b.e.c.____42.Which is the best estimate of the correlation coefficient of the data in the graph?a.–0.1c.–0.9b.0.9d.0.1____43.Simplify .a.c.b.d.____44.Which equation is the inverse of ?a.c.b.d.____45.What equation is the inverse of ?a.d.b.e.c.____46.What is the remainder if is divided by ?a.–9c.–29b.15d.–17____47.What is the length of side s?a.c.16b.4d.____48.Let , , and . Find the composite function a.c.b.d.____49.If and , then equalsa.282d.570b.144e.None correctc.48____50.Given the objective function and the graph and vertices shown, find the maximum value for C.a.310d.480b.300e.None correctc.140____51.What is the measure of the reference angle for ?a.c.b.d.____52.An account earns interest at an annual rate of 5% compounded quarterly. If the account begins with a principal amount of $3000, what will its approximate value be after 5?years?a.$3846.11c.$3384.58b.$3499.96d.$4038.42____53.Solve .a.c.b.d.____54.Simplify .a.c.b.d.____55.Divide .a.c.b.d.____56.Divide .a.c.b.d.____57.Find the lengths x and y. Express your answers in simplest radical form.a., c., b., d., ____58.Given and , write the composite function and state its domain. a. , c. , b. , d. , , ____59.Given and , find (x).a.c.b.d.____60.Given and , find .a.c.b.d.____61.A shop makes tables and chairs. Each table takes 8 hours to assemble and 2 hours to finish. Each chair takes 3 hours to assemble and 1 hour to finish. The assemblers can work for at most 200 hours each week, and the finishers can work for at most 60 hours each week. The shop wants to make as many tables and chairs as possible. Write the constraints for the problem, and graph the feasible region. Let t be the number of tables and c be the number of chairs.a.c.b.d.____62.A small publishing company is planning to publish 2 books this month: book A and book B. The publishing cost is $6 each for book A and $8 each for book B. The total cost can be no more than $7,200. The company cannot publish more than 560 copies of book A and 720 copies of book B. The profit per book A is $10, and the profit per book B is $15. Find the number of books of each type that the company should publish to maximize its profits.a.The objective function is maximized at (240, 720), so the company should publish 240 copies of book A and 720 copies of book B.b.The objective function is maximized at (560, 720), so the company should publish 560 copies of book A and 720 copies of book B.c.The objective function is maximized at (560, 480), so the company should publish 560 copies of book A and 480 copies of book B.d.The objective function is maximized at (1200, 0), so the company should publish 1200 copies of book A and 0 copies of book B.____63.Maximize the objective function under the constraints .a.No maximum exists.c.(10,0)b.d.(8, 0)____64.The probability of drawing a green marble from a marble bag is 40%. What are the odds in favor of drawing a green marble?a.5:2c.2:3b.3:2d.2:5____65.Find the measure of the reference angle for .a.213°c.–33°b.123°d.33°____66.Find sin 300°.a.c.b.d.____67.Write an exponential function to model the situation. Then predict the value of the function after 5 years (to the nearest whole number).A population of 460 animals that increases at an annual rate of 16%.a.c.b.d.____68.The function , where x is the time in years, models a declining feral cat population. Predict the number of feral cats there will be in 6 years.a.About 1,085 feral catsc.About 201 feral catsb.About 1,205 feral catsd.About 109 feral cats____69.Solve by completing the square: a.c.b.d.____plete the square: ____ a.c.b.d.____71.Solve by completing the square: a.x = 3 or x = –2c.x = 3 or x = 0b.x = 6 or x = –2d.x = 6 or x = 3____72.Simplify. Assume that all variables are positive. a.c.b.d.____73.Simplify .a.c.–b.–d.____74.Solve . Write the solutions in terms of i, if necessary.a.c.b.d.____75.Solve . Write the solutions in terms of i.a.x = –3 + 3i or –3 – 3ic.x = 3i or –3ib.x = –6 + 3i or –6 – 3id.x = –3 + 3i____76.Use the unit circle to find the exact value of the trigonometric ratio cos 135°.a.c.b.d.____77.Write the exponential equation in logarithmic form.a.c.b.d.____78.Write the logarithmic equation in exponential from.a.c.b.d.____79.Find the roots of . State the multiplicity of each root.a. is a factor once, and is a factor twice.The root has a multiplicity of 1, and the root 6 has a multiplicity of 2.b. is a factor once, and is a factor twice.The root 5 has a multiplicity of 1, and the root has a multiplicity of 2.c. is a factor once, and is a factor twice.The root has a multiplicity of 1, and the root –6 has a multiplicity of 2.d. is a factor once, and is a factor twice.The root 5 has a multiplicity of 1, and the root has a multiplicity of 2.____80.Multiply . Write the answer in the form .a.c.b.d.____81.Solve .a.c.b.d.____82.What are the solutions of ?a.x?=??±?id.x?=??±?ib.x?=??±?ie.None correctc.x?=??±?i____83.What is in logarithmic form?a.c.b.d.____84.What are the roots of ?a.d.b.e.c.____85.Multiply .a.c.b.d.____86.Solve .a.z = 26c.z = 6b.z = 676d.z = ____87.Solve .a. 4096c. 81b. d. 9____88.Solve .a.c.b.d.____89.Solve a.c.b.d.____90.Solve .a.z = –5c.z = –1b.z = –3d.No solution.____91.If , then x equalsa.d.b.e.None correctc.____92.How long is side a to the nearest tenth of an inch?a.12.4 in.c.13.1 in.b.11.5 in.d.14.6 in.____93.What is length of side q to the nearest tenth of a meter?a.d.4.9 mb.9.8 me.c.3.4 m____94.A researcher visits a wildlife refuge and captures and tags 31?rabbits. The next day, the researcher captures 35?rabbits, and 9 of them are tagged from the previous day. What is the best estimate for the number of rabbits in the refuge?a.121c.131b.98d.127____95.Which describes the roots of ?a.2 real rootsc.2 complex rootsb.1 real rootd.None correct____96.Which choice is NOT a real zero of ?a.c.–7b.7d.–2____97.A set of test scores is normally distributed with a mean of 53 and a standard deviation of 6. Between what two scores do 68% of the data fall?a.47 and 59d.50 and 56b.41 and 65e.None correctc.48 and 58____98.Given a triangle with find c. Round to the nearest tenth.a.c.b.d.____99.Find the number of solutions of the equation by using the discriminant.a.Cannot determine the number of solutions. The discriminant can only be used for a quadratic equation, and is not a quadratic equation.b.The equation has two real roots.c.The equation has two complex roots.d.The equation has one real root.____100.Use the discriminant to describe the roots of .a.The equation has one real root.b.Cannot determine without graphing.c.The equation has two complex roots.d.The equation has two real roots.____101.Find the zeros of the polynomial function .a.x = 8, x = –2c.x = 0; x = 8, x = –2b.x = –8, x = 2d.x = 0; x = –8, x = 2____102.Graph the piecewise function .a.c.b.d.____103.Evaluate for and .a.; c.; b.; d.; ____104.Sydney participated in a cross-country skiing race of 250 kilometers. He covered 100 kilometers in the first 5 days. Due to a storm, he only covered 70 kilometers in the next week. A burst of good weather allowed him to finish the race in just 2 more days. Sketch a graph of distance versus time for Sydney’s race. Then, write a piecewise function for the graph.a.c.b.d.____105.The heights of 1250 students at a local school were recorded and found to be approximated by the normal curve below. Identify the mean and standard deviation of the data.a.69, 6c.69, 3b.60, 3d.72, 4____106.In a certain normal distribution of scores, the mean is 30 and the standard deviation is 4. Find the z-score corresponding to a score of 26. If necessary, round your answer to the nearest hundredth.a.1.00c.7.50b.6.5d.–1.00Numeric Response107.Find the determinant of .108.Find where ; , and ; .109.Find (hg)(–18) where ; D?=?{Reals}, and ; D?=?{Negative integers}.110.Find the standard deviation for the following data: 18, 11, 10, 13, 15. Round your answer to the nearest tenth if necessary.111.There are 10 places to sit at a table. How many ways can 10 people be seated at the table?112.There are five tiles in a bag, labeled with the letters A, B, C, D, and E. The tiles are chosen at random from the bag, without replacing them, until all five have been removed. In how many different orders can the tiles be removed?113.Simplify .114.Simplify .115.What is the distance between and ? Round to the nearest tenth.116.A cartographer constructs a map of Georgia over a grid system such that Macon is at (115,?15) and Atlanta is at (175,?95). Find the distance between the cities to the nearest kilometer if each unit represents one kilometer.117.Find the number of permutations of the letters in GRAPHED.118.Find the number of possible permutations of 4?objects.119.What is the cosecant of ?120.Simplify .121.A 20-centimeter straw is placed so that it fits exactly at a 60° angle in a glass, as shown. How tall is the glass, to the nearest centimeter?122.Let and . Evaluate 123.The odds in favor of an event are . What is the probability of the event?124.Find the measure of the reference angle for the given angle. Express your answer in degrees.125.A savings account earns interest at an annual rate of 4%, compounded semi-annually. If the account begins with a principal amount of $1000, what will its value be after 8?years?126.A jar contains 10 marbles: 4 red, 2 blue, 4 green. The red marbles are numbered 1-4, the blue marbles are numbered 5-6, and the green marbles are numbered 7-10. Find the probability that a marble drawn from the jar is odd or green.127.A savings account earns interest at an annual rate of 3.5%, compounded continuously. If the account begins with a value of $2500, what will its value be after 3?years?128.What is the multiplicity of the root of 0 for the equation ?129.Solve .130.Solve the equation.131.Find a. Round to the nearest tenth.132.Find b. Round to the nearest tenth.133.The weights of candles produced in a factory have a mean of 9.5?ounces and a standard deviation of 0.4?ounces. A randomly selected candle weighs 9.94?ounces. How many standard deviations is this above the mean?134.Evaluate for .plete the truth table for .pq??qp ? ??qTTTFFTFF136.Simplify using correct significant digits. 10.63?km?+?2.427?km +?0.3?kmSimplify. Identify any excluded values.137..138.Find if ; D =?{Integers} ; and ; D =?{Positive whole numbers} .139.Given ; D = {Reals}, ; D = {Integers}. Find the algebraic difference .140.Find (fg)(–4) where ; D?=?{Reals}, and ; D?=?{Positive integers}.141.Solve the system of equations by substitution..142.Solve the system of equations by substitution.143.Determine whether the function in the graph is continuous, discontinuous, and/or discrete. Then find its domain and range.144.Determine whether the graph is continuous, discontinuous, and/or discrete. Determine whether it is a function or a relation. Determine the domain and range of the function.145.Determine whether the graph is continuous, discontinuous, and/or discrete. If the function is discontinuous, name the x-value(s) where the discontinuity occurs.146.Determine whether the graph is continuous, discontinuous, and/or discrete. Determine whether it is a function or a relation. Determine the domain and range.147.Factor .148.Solve and classify the system.149.Solve .150.Find the range and standard deviation for the following set of data. Round your answer to the nearest tenth.14, 15, 10, 11, 13151.Find the range and standard deviation for the following set of data.13, 19, 12, 17, 5152.Solve by elimination.153.Find the z-intercept of the graph of . Express coordinates as decimals.154.Graph .155.Write the equation of the line that is parallel to the graph of and crosses the point .156.Find the equation of the line that passes through the point and is perpendicular to the line .157.Find the equation of the line parallel to that crosses .158.Subtract the rational expression.159.Add the two rational expressions.160.Simplify the expression.161.Find the inverse of Determine whether the inverse is a function.162.Determine whether (14, 25), (19, 32), and (17, 35) are solutions of the system of linear inequalities.163.Tickets to a concert cost $25 for lower-level seats and $10 for upper-level seats. A company plans to buy up to 50 tickets for employees and spend up to $800. Write and graph a system of linear inequalities to represent all the possible combinations of lower-level and upper-level tickets the company can buy.Simplify.164.165.166.167.Simplify .168.Find the exact value of the cosecant, secant, and cotangent of .169.Explain how the graph of is related to the graph of .170.Graph . Identify the domain, the asymptote, and the range.171.Find an equation for the inverse of .172.Find an equation for the inverse of .173.Find an equation for the inverse of . Identify the domain and range of each relation.174.Use synthetic division to divide by .175.Use a trigonometric ratio to find the length of s.176.Let and . Find the composite function .177.Let and . Find the composition functions and .178.A furniture manufacturer builds cabinets and tables. The profits are $100 per cabinet and $80 per table. The cabinets use 4?square?feet of oak and take 3?hours to build. The tables use 5?square?feet of oak and take 5?hours to build. There are only 60?square?feet of oak available for manufacturing. No more than 50?hours may be spent building the furniture.a.Write the function equation for the profit made by the manufacturer. Let x?=?the number of cabinets. Let y?=?the number of tables.b.Write all the constraints to which the profit function is subjected.c.Graph the constraints and shade the feasible region.d.List all the vertices of the feasible region.e.Evaluate the profit function for each vertex. How many cabinets and tables should be manufactured to maximize the profit? Why?179.A baker is making pastries to sell at a fair. A small pastry costs $1.30 to prepare. A large pastry costs $2.30 to prepare. The baker will make 180 pastries. Usually, about four times as many people buy small pastries as large pastries. How can the baker keep costs to a minimum while still making sure people have the pastries they want?180.A cook is preparing food to sell at a high school football game. At most 120 people are expected to buy a hamburger or hot dog. The cost of preparing a hot dog is $0.35. The cost of preparing a hamburger is $0.45. Usually, two times as many people buy hot dogs as hamburgers. How can the cook keep costs to a minimum while still making sure that most people get their food choice?181.Solve by completing the square. 182.Solve .183.Solve by completing the square.184.Simplify. Assume that all variables are positive.185.Write the rational exponent as a radical expression.186.A jar contains 5?blue tiles numbered 1–5 and 5?green tiles labeled 6–10. A tile is drawn from the jar at random. Are the events that the tile is green and the tile is an odd number inclusive or mutually exclusive? Explain.187.Solve . Write the solutions in terms of i.188.Simplify .189.Solve the equation. Write the solutions in the form .190.Use the unit circle to find the exact value of 120°.191.Write the exponential equation in logarithmic form.192.Write the logarithmic equation in exponential form.193.Write the logarithmic equation in exponential form.194.Solve the equation.195.A researcher visits a park and captures and marks 26 squirrels. On a return visit the next week, the researcher captures 49 squirrels, and 16 of them are marked from the previous week. Estimate the squirrel population in the park.196.Use the discriminant to describe the roots of the equation.197.A frame maker has 24?inches of framing material with which to make a picture frame. He wants to frame a picture that has an area of 56?square?inches. The equation gives the width of the frame that meets these requirements. Use the discriminant to explain why these requirements can not be met.198.Find the roots of the polynomial function.199.Solve .200.Write a piecewise function rule for the graph.201.Evaluate the piecewise function for x?=?0 and x?=?4.202.Write a piecewise function rule for the graph.203.Students took a test consisting of a math portion and a science portion. The scores for the math portion are normally distributed with a mean of 41 and a standard deviation of 6. The scores for the science portion are normally distributed with a mean of 66 and a standard deviation of 8.a.Nathalie received a score of 47 on the math portion. How many standard deviations away from the mean is Nathalie’s score?b.What percent of the math scores are between Natalie’s score and the mean portion score? Explain.c.What percent of the math scores are less than Natalie’s score? Explain.d.Micah received a score of 43 on the math portion and a score of 80 on the science portion. Find the z-score for each of Micah’s scores.e.On which portion did Micah score better compared to the rest of his class?204.A set of test scores is normally distributed with a mean of 85 and a standard deviation of 2. What percent of the scores are between 83 and 85?205.The life expectancy (in hours) of a fluorescent tube is normally distributed with a mean 6000 and a standard deviation 500. Find the probability that a tube lasts for more than 7500 hours. Express your answer as a decimal.Algebra 2 Semester 2 Final Practice ProblemsAnswer SectionMULTIPLE CHOICE1.ANS:AREF:Investigation 1: Logic and Truth Tables2.ANS:AREF:Investigation 1: Logic and Truth Tables3.ANS:AREF:Lesson 18: Calculating with Units of Measure4.ANS:AREF:Lesson 20: Performing Operations with Functions5.ANS:AREF:Lesson 20: Performing Operations with Functions6.ANS:AREF:Investigation 3: Graphing Linear Equations in Three Variables7.ANS:AREF:Lesson 21: Solving Systems of Equations Using the Substitution Method8.ANS:AREF:Lesson 22: Analyzing Discrete and Continuous Functions9.ANS:AREF:Lesson 23: Factoring Polynomials10.ANS:AREF:Lesson 24: Solving Systems of Equations Using the Elimination Method11.ANS:AREF:Lesson 24: Solving Systems of Equations Using the Elimination Method12.ANS:CREF:Lesson 22: Analyzing Discrete and Continuous Functions13.ANS:BREF:Lesson 22: Analyzing Discrete and Continuous Functions14.ANS:CREF:Lesson 22: Analyzing Discrete and Continuous Functions15.ANS:CREF:Lesson 22: Analyzing Discrete and Continuous Functions16.ANS:BREF:Lesson 23: Factoring Polynomials17.ANS:DREF:Lesson 24: Solving Systems of Equations Using the Elimination Method18.ANS:AREF:Lesson 25: Finding Measures of Central Tendency and Dispersion19.ANS:AREF:Lesson 34: Graphing Linear Equations II20.ANS:AREF:Lesson 36: Using Parallel and Perpendicular Lines21.ANS:AREF:Lesson 37: Adding and Subtracting Rational Expressions22.ANS:AREF:Lesson 37: Adding and Subtracting Rational Expressions23.ANS:AREF:Lesson 40: Simplifying Radical Expressions24.ANS:AREF:Lesson 31: Multiplying and Dividing Rational Expressions25.ANS:AREF:Lesson 36: Using Parallel and Perpendicular Lines26.ANS:DREF:Lesson 36: Using Parallel and Perpendicular Lines27.ANS:CREF:Lesson 40: Simplifying Radical Expressions28.ANS:CREF:Lesson 40: Simplifying Radical Expressions29.ANS:CREF:Lesson 41: Using the Pythagorean Theorem and the Distance Formula30.ANS:AREF:Lesson 41: Using the Pythagorean Theorem and the Distance Formula31.ANS:CREF:Lesson 42: Finding Permutations and Combinations32.ANS:BREF:Lesson 45: Finding the Line of Best Fit33.ANS:CREF:Lesson 46: Finding Trigonometric Functions and their Reciprocals34.ANS:BREF:Lesson 46: Finding Trigonometric Functions and their Reciprocals35.ANS:DREF:Lesson 46: Finding Trigonometric Functions and their Reciprocals36.ANS:AREF:Lesson 47: Graphing Exponential Functions37.ANS:DREF:Lesson 48: Understanding Complex Fractions38.ANS:BREF:Lesson 48: Understanding Complex Fractions39.ANS:AREF:Lesson 50: Finding Inverses of Relations and Functions40.ANS:AREF:Lesson 43: Solving Systems of Linear Inequalities41.ANS:AREF:Lesson 43: Solving Systems of Linear Inequalities42.ANS:AREF:Lesson 45: Finding the Line of Best Fit43.ANS:AREF:Lesson 48: Understanding Complex Fractions44.ANS:AREF:Lesson 50: Finding Inverses of Relations and Functions45.ANS:AREF:Lesson 50: Finding Inverses of Relations and Functions46.ANS:AREF:Lesson 51: Using Synthetic Division47.ANS:AREF:Lesson 52: Using Two Special Right Triangles48.ANS:AREF:Lesson 53: Performing Composition of Functions49.ANS:AREF:Lesson 53: Performing Composition of Functions50.ANS:AREF:Lesson 54: Using Linear Programming51.ANS:AREF:Lesson 56: Finding Angles of Rotation52.ANS:AREF:Lesson 57: Finding Exponential Growth and Decay53.ANS:AREF:Lesson 58: Completing the Square54.ANS:AREF:Lesson 59: Using Fractional Exponents55.ANS:BREF:Lesson 51: Using Synthetic Division56.ANS:AREF:Lesson 51: Using Synthetic Division57.ANS:AREF:Lesson 52: Using Two Special Right Triangles58.ANS:DREF:Lesson 53: Performing Composition of Functions59.ANS:BREF:Lesson 53: Performing Composition of Functions60.ANS:DREF:Lesson 53: Performing Composition of Functions61.ANS:AREF:Lesson 54: Using Linear Programming62.ANS:AREF:Lesson 54: Using Linear Programming63.ANS:BREF:Lesson 54: Using Linear Programming64.ANS:CREF:Lesson 55: Finding Probability65.ANS:DREF:Lesson 56: Finding Angles of Rotation66.ANS:CREF:Lesson 56: Finding Angles of Rotation67.ANS:CREF:Lesson 57: Finding Exponential Growth and Decay68.ANS:DREF:Lesson 57: Finding Exponential Growth and Decay69.ANS:CREF:Lesson 58: Completing the Square70.ANS:BREF:Lesson 58: Completing the Square71.ANS:BREF:Lesson 58: Completing the Square72.ANS:BREF:Lesson 59: Using Fractional Exponents73.ANS:AREF:Lesson 62: Using Complex Numbers74.ANS:AREF:Lesson 62: Using Complex Numbers75.ANS:AREF:Lesson 62: Using Complex Numbers76.ANS:DREF:Lesson 63: Understanding the Unit Circle and Radian Measures77.ANS:BREF:Lesson 64: Using Logarithms78.ANS:BREF:Lesson 64: Using Logarithms79.ANS:BREF:Lesson 66: Solving Polynomial Equations80.ANS:BREF:Lesson 69: Simplifying Complex Expressions81.ANS:AREF:Lesson 62: Using Complex Numbers82.ANS:AREF:Lesson 62: Using Complex Numbers83.ANS:AREF:Lesson 64: Using Logarithms84.ANS:AREF:Lesson 66: Solving Polynomial Equations85.ANS:AREF:Lesson 69: Simplifying Complex Expressions86.ANS:BREF:Lesson 70: Solving Radical Equations87.ANS:CREF:Lesson 70: Solving Radical Equations88.ANS:CREF:Lesson 70: Solving Radical Equations89.ANS:CREF:Lesson 70: Solving Radical Equations90.ANS:BREF:Lesson 70: Solving Radical Equations91.ANS:AREF:Lesson 70: Solving Radical Equations92.ANS:AREF:Lesson 71: Using the Law of Sines93.ANS:AREF:Lesson 71: Using the Law of Sines94.ANS:AREF:Lesson 73: Using Sampling95.ANS:AREF:Lesson 74: Finding the Discriminant96.ANS:AREF:Lesson 76: Finding Polynomial Roots I97.ANS:AREF:Lesson 80: Finding the Normal Distribution98.ANS:BREF:Lesson 71: Using the Law of Sines99.ANS:CREF:Lesson 74: Finding the Discriminant100.ANS:AREF:Lesson 74: Finding the Discriminant101.ANS:CREF:Lesson 76: Finding Polynomial Roots I102.ANS:AREF:Lesson 79: Understanding Piecewise Functions103.ANS:AREF:Lesson 79: Understanding Piecewise Functions104.ANS:AREF:Lesson 79: Understanding Piecewise Functions105.ANS:CREF:Lesson 80: Finding the Normal Distribution106.ANS:DREF:Lesson 80: Finding the Normal DistributionNUMERIC RESPONSE107.ANS:100REF:Lesson 14: Finding Determinants108.ANS:–36REF:Lesson 20: Performing Operations with Functions109.ANS:200REF:Lesson 20: Performing Operations with Functions110.ANS:2.9REF:Lesson 25: Finding Measures of Central Tendency and Dispersion111.ANS:3628800REF:Lesson 33: Applying Counting Principles112.ANS:120REF:Lesson 33: Applying Counting Principles113.ANS:9REF:Lesson 40: Simplifying Radical Expressions114.ANS:–2REF:Lesson 40: Simplifying Radical Expressions115.ANS:16.4REF:Lesson 41: Using the Pythagorean Theorem and the Distance Formula116.ANS:100REF:Lesson 41: Using the Pythagorean Theorem and the Distance Formula117.ANS:5040REF:Lesson 42: Finding Permutations and Combinations118.ANS:24REF:Lesson 42: Finding Permutations and Combinations119.ANS:5/4REF:Lesson 46: Finding Trigonometric Functions and their Reciprocals120.ANS:49/128REF:Lesson 48: Understanding Complex Fractions121.ANS:17REF:Lesson 52: Using Two Special Right Triangles122.ANS:625REF:Lesson 53: Performing Composition of Functions123.ANS:12/19REF:Lesson 55: Finding Probability124.ANS:45REF:Lesson 56: Finding Angles of Rotation125.ANS:$1372.79REF:Lesson 57: Finding Exponential Growth and Decay126.ANS:0.7REF:Lesson 60: Distinguishing Between Mutually Exclusive and Independent Events127.ANS:$2776.78REF:Lesson 57: Finding Exponential Growth and Decay128.ANS:8REF:Lesson 66: Solving Polynomial Equations129.ANS:2.5REF:Lesson 70: Solving Radical Equations130.ANS:505REF:Lesson 70: Solving Radical Equations131.ANS:4.6REF:Lesson 71: Using the Law of Sines132.ANS:20.4REF:Lesson 71: Using the Law of Sines133.ANS:1.1REF:Lesson 80: Finding the Normal Distribution134.ANS:70REF:Lesson 79: Understanding Piecewise FunctionsPROBLEM135.ANS:pq??qp ? ??qTTFTTFTTFTFFFFTTREF:Investigation 1: Logic and Truth Tables136.ANS:13.4 kmREF:Lesson 18: Calculating with Units of Measure137.ANS:1.5 cubic feetREF:Lesson 18: Calculating with Units of Measure138.ANS:x = REF:Lesson 20: Performing Operations with Functions139.ANS:REF:Lesson 20: Performing Operations with Functions140.ANS:The common domain is positive integers only, therefore .REF:Lesson 20: Performing Operations with Functions141.ANS:REF:Lesson 21: Solving Systems of Equations Using the Substitution Method142.ANS:REF:Lesson 21: Solving Systems of Equations Using the Substitution Method143.ANS:Discontinuous; Domain: , Range: REF:Lesson 22: Analyzing Discrete and Continuous Functions144.ANS:discontinuous; discrete function; domain:x = –8, –6, 3, 4; range: y = 2REF:Lesson 22: Analyzing Discrete and Continuous Functions145.ANS:discontinuous function; point of discontinuity at REF:Lesson 22: Analyzing Discrete and Continuous Functions146.ANS:Discontinuous relation;Domain = all real numbers;Range = all real numbersREF:Lesson 22: Analyzing Discrete and Continuous Functions147.ANS:REF:Lesson 23: Factoring Polynomials148.ANS:; consistent, independentREF:Lesson 24: Solving Systems of Equations Using the Elimination Method149.ANS:(–6,?–2)REF:Lesson 24: Solving Systems of Equations Using the Elimination Method150.ANS:range = 5; standard deviation = 1.9REF:Lesson 25: Finding Measures of Central Tendency and Dispersion151.ANS:Range: 14; Standard deviation: 4.8REF:Lesson 25: Finding Measures of Central Tendency and Dispersion152.ANS:REF:Lesson 24: Solving Systems of Equations Using the Elimination Method153.ANS:(0, 0, 0.6)REF:Investigation 3: Graphing Linear Equations in Three Variables154.ANS:REF:Lesson 34: Graphing Linear Equations II155.ANS:REF:Lesson 36: Using Parallel and Perpendicular Lines156.ANS:REF:Lesson 36: Using Parallel and Perpendicular Lines157.ANS:REF:Lesson 36: Using Parallel and Perpendicular Lines158.ANS:REF:Lesson 37: Adding and Subtracting Rational Expressions159.ANS:REF:Lesson 37: Adding and Subtracting Rational Expressions160.ANS:REF:Lesson 37: Adding and Subtracting Rational Expressions161.ANS:REF:Lesson 50: Finding Inverses of Relations and Functions162.ANS:(14, 25) yes; (19, 32) no; (17, 35) noREF:Lesson 43: Solving Systems of Linear Inequalities163.ANS: REF:Lesson 43: Solving Systems of Linear Inequalities164.ANS:REF:Lesson 44: Rationalizing Denominators165.ANS:REF:Lesson 48: Understanding Complex Fractions166.ANS:2187REF:Lesson 59: Using Fractional Exponents167.ANS:REF:Lesson 44: Rationalizing Denominators168.ANS:csc B = , sec B = , cot B = REF:Lesson 46: Finding Trigonometric Functions and their Reciprocals169.ANS:Since the bases are reciprocals, the graphs are reflection images of each other over the y-axis.REF:Lesson 47: Graphing Exponential Functions170.ANS:The domain is the set of all real numbers. The asymptote is the line (the x-axis). The range is the set of all positive real numbers.REF:Lesson 47: Graphing Exponential Functions171.ANS:?REF:Lesson 50: Finding Inverses of Relations and Functions172.ANS:y?=?x?–?REF:Lesson 50: Finding Inverses of Relations and Functions173.ANS:The inverse is .RelationDomainRangex is any real numbery is any real numberREF:Lesson 50: Finding Inverses of Relations and Functions174.ANS:REF:Lesson 51: Using Synthetic Division175.ANS:REF:Lesson 52: Using Two Special Right Triangles176.ANS:REF:Lesson 53: Performing Composition of Functions177.ANS:;REF:Lesson 53: Performing Composition of Functions178.ANS:a.Profit = 100x + 80yb., , , c.d., , , e.15 cabinets and 0 tables; Sample: The vertex produced a higher profit than the other vertices when entered in the objective function.REF:Lesson 54: Using Linear Programming179.ANS:Make no more than 144 small pastries and no more than 36 large pastries.REF:Lesson 54: Using Linear Programming180.ANS:Prepare no more than 80 hot dogs and no more than 40 hamburgers.REF:Lesson 54: Using Linear Programming181.ANS:REF:Lesson 58: Completing the Square182.ANS: REF:Lesson 58: Completing the Square183.ANS:REF:Lesson 58: Completing the Square184.ANS:REF:Lesson 59: Using Fractional Exponents185.ANS:REF:Lesson 59: Using Fractional Exponents186.ANS:Inclusive; Sample Drawing the tile numbered 7 or 9 satisfies both events, so they are not mutually exclusive.REF:Lesson 60: Distinguishing Between Mutually Exclusive and Independent Events187.ANS:REF:Lesson 62: Using Complex Numbers188.ANS:–54iREF:Lesson 62: Using Complex Numbers189.ANS:REF:Lesson 62: Using Complex Numbers190.ANS:REF:Lesson 63: Understanding the Unit Circle and Radian Measures191.ANS:REF:Lesson 64: Using Logarithms192.ANS:REF:Lesson 64: Using Logarithms193.ANS:REF:Lesson 64: Using Logarithms194.ANS: ? ± REF:Lesson 65: Using the Quadratic Formula195.ANS:about 80 squirrelsREF:Lesson 73: Using Sampling196.ANS:No real rootsREF:Lesson 74: Finding the Discriminant197.ANS:The discriminant is –80. Since it is negative, the equation has no real solutions, so there is no width that can be used with only 24?inches of framing material.REF:Lesson 74: Finding the Discriminant198.ANS:REF:Lesson 76: Finding Polynomial Roots I199.ANS: and REF:Lesson 78: Solving Quadratic Equations II200.ANS:REF:Lesson 79: Understanding Piecewise Functions201.ANS:REF:Lesson 79: Understanding Piecewise Functions202.ANS:REF:Lesson 79: Understanding Piecewise Functions203.ANS:a.1b.34%; Sample: 95% of the scores lie between 29 and 53 since 29 and 53 are 2 standard deviations away from the mean. 68% of the scores lie between 35 and 47 since 35 and 47 are 1 standard deviation away from the mean score. Since the data are distributed symmetrically about the mean, half of the scores, or 34% are between the mean and 47.c.84%; Sample: 50% of the scores are below the mean, and 34% are between the mean and Natalie’s score of 47. Therefore, 84% of the scores are less than 47.d.Math: z-score = 0.33; Science: z-score = 1.75e.ScienceREF:Lesson 80: Finding the Normal Distribution204.ANS:34%REF:Lesson 80: Finding the Normal Distribution205.ANS:0.0015REF:Lesson 80: Finding the Normal Distribution ................
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