SAT Practice Test 2 Math Test: Calculator, for Assistive Technology

Download SAT Practice Test 2 Math Test: Calculator, for Assistive Technology

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WF-5LSA07-CMMath TestCalculator38 QuestionsTurn to Section 4 of your answer sheet to answer the questions in this section.DirectionsFor questions 1 through 30, solve each problem, choose the best answer from the choices provided, and fill in the corresponding circle on your answer sheet. For questions31 through 38, solve the problem and enter your answer in the grid on the answer sheet. Please refer to the directions before question 31 on how to enter your answers in the grid. You may use scratch paper for scratch work.Notes1.The use of a calculator is permitted.2.All variables and expressions used represent real numbers unless otherwise indicated.3.Figures provided in this test are drawn to scale unless otherwise indicated.4.All figures lie in a plane unless otherwise indicated.5.Unless otherwise indicated, the domain of a given function f is the set of all real numbers x for which f of x is a real number.ReferenceBegin skippable figure descriptions.The figure presents information for your reference in solving some of theproblems.Reference figure1 is a circle with radiusr. Two equations are presented below reference figure1.A equals pi times the square of r.C equals 2 pi r.Reference figure2 is a rectangle with length and widthw. An equation is presented below reference figure2.A equals w.Reference figure3 is a triangle with baseb and heighth. An equation is presented below reference figure3.A equals onehalfbh.Reference figure4 is a right triangle. The two sides that form the right angle are labeled a and b, and the side opposite the right angle is labeledc. An equation is presented below reference figure4.c squared equals a squared plus b squared.Special Right TrianglesReference figure5 is a right triangle with a 30degree angle and a 60degree angle. The side opposite the 30degree angle is labeledx. The side opposite the 60degree angle is labeledx times the squareroot of3. The side opposite the right angle is labeled2x.Reference figure6 is a right triangle with two 45degree angles. Two sides are each labeleds. The side opposite the rightangle is labeled stimes the squareroot of2.Reference figure7 is a rectangular solid whose base has length and widthw and whose height ish. An equation is presented below reference figure7.V equalswh.Reference figure8 is a rightcircularcylinder whose base has radiusr and whose height ish. An equation is presented below reference figure8.V equals pitimes the square of rtimesh.Reference figure9 is a sphere with radiusr. An equation is presented below reference figure9.V equalsfourthirds pi times the cube ofr.Reference figure10 is a cone whose base has radiusr and whose height ish. Anequation is presented below reference figure10.V equals onethird times pi times the square of rtimesh.Reference figure11 is an asymmetrical pyramid whose base has length and widthw and whose height ish. An equation is presented below reference figure11.V equalsonethirdwh.End skippable figure descriptions.Additional Reference InformationThe number of degrees of arc in a circle is360.The number of radians of arc in a circle is 2pi.The sum of the measures in degrees of the angles of a triangle is180.The S A TPage 1Copyright 2015 by the College BoardW F-5LSA07Question 1.A musician has a new song available for downloading or streaming. The musician earns $0.09 each time the song is downloaded and $0.002 each time the song is streamed. Which of the following expressions represents the amount, in dollars, that the musician earns if the song is downloaded dtimes and streamed stimes?A. 0.002d, plus 0.09sB. 0.002d, minus 0.09sC. 0.09d, plus 0.002sD. 0.09d, minus 0.002sExplanation for question 1.Question 2.A quality control manager at a factory selects 7lightbulbs at random for inspection out of every 400lightbulbs produced. At this rate, how many lightbulbs will be inspected if the factory produces 20,000lightbulbs?A.300B.350C.400D.450Explanation for question 2.Question 3 refers to the following equation. l equals 24 plus 3.5mQuestion 3.One end of a spring is attached to a ceiling. When an object of mass mkilograms is attached to the other end of the spring, the spring stretches to a length of lcentimeters as shown in the preceding equation. What is m when l is 73?A.14B.27.7C.73D.279.5Explanation for question 3.Questions 4 and 5 refer to the following information.The amount of money a performer earns is directly proportional to the number of people attending the performance. The performer earns$120 at a performance where 8people attend.Question 4.How much money will the performer earn when 20people attend a performance?A.$960B.$480C.$300D.$240Explanation for question 4.Question 5.The performer uses 43% of the money earned to pay the costs involved in putting on each performance. The rest of the money earned is the performers profit. What is the profit the performer makes at a performance where 8people attend?A.$51.60B.$57.00C.$68.40D.$77.00Explanation for question 5.Question 6.When 4times the numberx is added to 12, the result is8. What number results when 2timesx is added to7?A.negative 1B.5C.8D.9Explanation for question 6.Question 7 is based on the following equation. y equals xsquared, minus 6x plus 8Question 7.The preceding equation represents a parabola in the xyplane. Which of the following equivalent forms of the equation displays the xintercepts of the parabola as constants or coefficients?A. y minus 8, equals, x squared, minus 6xB. y plus 1, equals, parenthesis, x minus 3, close parenthesis, squaredC. y equals, x, parenthesis, x minus 6, close parenthesis, plus 8D. y equals, parenthesis, x minus 2, close parenthesis, times, parenthesis, x minus 4, close parenthesisExplanation for question 7.Question 8.In a video game, each player starts the game with kpoints and loses 2points each time a task is not completed. If a player who gains no additional points and fails to complete 100tasks has a score of 200points, what is the value of k?A.0B.150C.250D.400Explanation for question 8.Question 9.A worker uses a forklift to move boxes that weigh either 40pounds or 65pounds each. Let x be the number of 40pound boxes and y be the number of 65pound boxes. The forklift can carry up to either 45boxes or a weight of 2,400pounds. Which of the following systems of inequalities represents this relationship?A. open bracket, 40x plus 65y is less than or equal to 2,400; and, x plus y is less than or equal to 45.B. open bracket, the fraction x over 40, plus, the fraction y over 65, is less than or equal to 2,400; and, x plus y is less than or equal to 45.C. open bracket 40x plus 65y is less than or equal to 45; and, x plus y is less than or equal to 2,400.D. open bracket, x plus y is less than or equal to 2,400; and 40x plus 65y is less than or equal to 2,400.Explanation for question 9.Question 10.A function f satisfies f of 2 equals 3 and f of 3 equals 5. A function g satisfies g of 3 equals 2 and g of 5 equals 6. What is the value of f of, g of 3?A.2B.3C.5D.6Explanation for question10.Question 11 refers to the following table.Number of hours Tony plans to read the novel per day3Number of parts in the novel8Number of chapters in the novel239Number of words Tony reads per minute250Number of pages in the novel1,078Number of words in the novel349,168Question 11.Tony is planning to read a novel. The preceding table shows information about the novel, Tonys reading speed, and the amount of time he plans to spend reading the novel each day. If Tony reads at the rates given in the table, which of the following is closest to the number of days it would take Tony to read the entire novel?A.6B.8C.23D.324Explanation for question11.Question 12.On January1, 2000, there were 175,000tons of trash in a landfill that had a capacity of 325,000tons. Each year since then, the amount of trash in the landfill increased by 7,500tons. If y represents the time, in years, after January1,2000, which of the following inequalities describes the set of years where the landfill is at or above capacity?A. 325,000 minus 7,500, is less than or equal to yB. 325,000 is less than or equal to 7,500yC. 150,000 is greater than or equal to 7,500yD. 175,000 plus 7,500y, is greater than or equal to325,000Explanation for question12.Question 13.A researcher conducted a survey to determine whether people in a certain large town prefer watching sports on television to attending the sporting event. The researcher asked 117people who visited a local restaurant on a Saturday, and 7people refused to respond. Which of the following factors makes it least likely that a reliable conclusion can be drawn about the sportswatching preferences of all people in the town?A.Sample sizeB.Population sizeC.The number of people who refused to respondD.Where the survey was givenExplanation for question13.Question 14 refers to the following figure.Begin skippable figure description.The figure, titled Miles Traveled by Air Passengers in CountryX, 1960 to 2005, shows a graph of a scatterplot with the line of best fit. The horizontal axis is labeled Year and the years appearing on it from left to right are from 1960through 2010, in increments of 10years. There are vertical gridlines at every 5years. The vertical axis is labeled Number of miles traveled, in billions, and the numbers appearing on it from bottom to top are from 0 to 600, in increments of 100billion miles. There are horizontal gridlines at every 50billion miles. The scatterplot shows a cluster of data points that begins in the year 1960 at 30billion miles, extends upward and to the right, showing a pattern of line, and ends in 2005 at 590billion miles. The line of best fit extends in the pattern that the cluster shows. It starts from about 1961 at 0 miles and slants upward to the right, ending in 2010 at about 620billion miles.End skippable figure description.Question 14.According to the line of best fit in the preceding scatterplot, which of the following best approximates the year in which the number of miles traveled by air passengers in CountryX was estimated to be 550billion?A.1997B.2000C.2003D.2008Explanation for question14.Question 15.The distance traveled by Earth in one orbit around the Sun is about 580,000,000miles. Earth makes onecomplete orbit around the Sun in one year. Of the following, which is closest to the average speed of Earth, in miles per hour, as it orbits the Sun?A.66,000B.93,000C.210,000D.420,000Explanation for question15.Question 16 refers to the following table.Results on the Bar Exam of Law School GraduatesPassed bar examDid not pass bar examTook review course1882Did not take review course793Question 16.The preceding table summarizes the results of 200law school graduates who took the bar exam. If one of the surveyed graduates who passed the bar exam is chosen at random for an interview, what is the probability that the person chosen did NOT take the review course?A. 18 over 25B. 7 over 25C. 25 over 200D. 7 over 200Explanation for question 16.Question 17.The atomic weight of an unknown element, in atomic mass units (amu), is approximately 20%less than that of calcium. The atomic weight of calcium is 40amu. Which of the following best approximates the atomic weight, in amu, of the unknown element?A.8B.20C.32D.48Explanation for question 17.Question 18.A survey was taken of the value of homes in a county, and it was found that the mean home value was $165,000 and the median home value was $125,000. Which of the following situations could explain the difference between the mean and median home values in the county?A.The homes have values that are close to each other.B.There are a few homes that are valued much less than the rest.C.There are a few homes that are valued much more than the rest.D.Many of the homes have values between $125,000 and $165,000.Explanation for question 18.Questions 19 and 20 refer to the following information.A sociologist chose 300students at random from each of two schools and asked each student how many siblings he or she has. The results are shown in the following table.Students Sibling SurveyNumber of siblingsLincoln SchoolWashington School0120140180110260303301041010There are a total of 2,400students at LincolnSchool and 3,300students at WashingtonSchool.Question 19.What is the median number of siblings for all the students surveyed?A.0B.1C.2D.3Explanation for question 19.Question 20.Based on the survey data, which of the following most accurately compares the expected total number of students with 4siblings at the two schools?A.The total number of students with 4siblings is expected to be equal at the twoschools.B.The total number of students with 4siblings at LincolnSchool is expected to be 30 more than at WashingtonSchool.C.The total number of students with 4siblings at WashingtonSchool is expected to be 30 more than at LincolnSchool.D.The total number of students with 4siblings at WashingtonSchool is expected to be 900 more than at LincolnSchool.Explanation for question 20.Question 21.A project manager estimates that a project will take xhours to complete, where x is greater than 100. The goal is for the estimate to be within 10hours of the time it will actually take to complete the project. If the manager meets the goal and it takes yhours to complete the project, which of the following inequalities represents the relationship between the estimated time and the actual completiontime?A. x plus y is less than 10B. y is greater than x plus 10C. y is less than x minus 10D. negative 10 is less than y minus x, which is less than 10Explanation for question 21.Questions 22 and 23 refer to the following information. I, equals the fraction P over, 4pirsquared, end fractionAt a large distancer from a radio antenna, the intensity of the radio signalI is related to the power of the signalP by the preceding formula.Question 22.Which of the following expresses the square of the distance from the radio antenna in terms of the intensity of the radio signal and the power of the signal?A. r squared, equals, the fraction IP over 4piB. r squared, equals, the fraction P over 4pi,IC. r squared, equals, the fraction 4pi,I, over PD. r squared, equals, the fraction I over 4pi,PExplanation for question 22.Question 23.For the same signal emitted by a radio antenna, ObserverA measures its intensity to be 16times the intensity measured by ObserverB. The distance of ObserverA from the radio antenna is what fraction of the distance of ObserverB from the radio antenna?A. 1 over 4B. 1 over 16C. 1 over 64D. 1 over 256Explanation for question 23.Question 24 is based on the following equation. x squared plus y squared, plus 4x minus 2y, equals negative1Question 24.The preceding is the equation of a circle in the xyplane. What is the radius of the circle?A.2B.3C.4D.9Explanation for question 24.Question 25.The graph of the linear functionf has intercepts at the points with coordinates a, comma 0, and 0 comma b, in the xyplane. If a, plus b equals 0 and a, does not equal b, which of the following is true about the slope of the graph off?A.It is positive.B.It is negative.C.It equals zero.D.It is undefined.Explanation for question25.Question 26 refers to the following figure.Begin skippable figure description.The figure presents the graph of the functionf in the xyplane. The graph is labeledy equals f of x. The horizontal axis is labeledx, the vertical axis is labeledy, and the origin is labeledO. There are evenly spaced horizontal and vertical gridlines, in increments of 1unit, along each axis. The graph consists of 4connected line segments. The first line segment slants upward and to the right. It starts at the point that is 4units to the left of the yaxis and 1unit above the xaxis, and it ends on the yaxis, 3units above the xaxis. The second line segment slants downward and to the right. It starts where the first line segment ends, and ends at the point that is 1unit to the right of the yaxis and 1unit above the xaxis. The third line segment moves horizontally. It starts where the second line segment ends, and ends at the point that is 3units to the right of the yaxis and 1unit above the xaxis. The fourth line segment slants downward and to the right. It starts where the third line segment ends, and ends at the point that is 4units to the right of the yaxis and 1unit below the xaxis.End skippable figure description.Question 26.The complete graph of the functionf is shown in the preceding xy-plane. Which of the following are equalto1?I. f of negative 4II. f of three halvesIII. f of 3A.III onlyB.I and III onlyC.II and III onlyD.I, II, and IIIExplanation for question26.Question 27 refers to the following figure.Begin skippable figure description.The figure presents a graph. The horizontal axis is labeled Time, in minutes. The vertical axis is labeled Temperature, in degrees Celsius. Numbers from 0 to 70, in increments of 10, appear along both axes with gridlines extending from each number. Sixteen points are plotted on the graph with eight circles and eight squares. A key indicates that a square means insulated and a circle means noninsulated. Each 10minute interval has a pair of points plotted for insulated and noninsulated as follows.0 minutes: insulated, 60degrees; noninsulated, 60degrees.10 minutes: insulated, 52degrees; noninsulated 42degrees.20 minutes: insulated, 47degrees; noninsulated 34degrees.30 minutes: insulated, 41degrees; noninsulated 30degrees.40 minutes: insulated, 38degrees; noninsulated 29degrees.50 minutes: insulated, 36degrees; noninsulated 28degrees.60 minutes: insulated, 33degrees; noninsulated 28degrees.70 minutes: insulated, 31degrees; noninsulated 28degrees.End skippable figure description.Question 27.Two samples of water of equal mass are heated to 60degrees Celsius parenthesis, degreesC, close parenthesis. One sample is poured into an insulated container, and the other sample is poured into a non-insulated container. The samples are then left for 70minutes to cool in a room having a temperature of 25degreesCelsius. The preceding graph shows the temperature of each sample at 10minute intervals. Which of the following statements correctly compares the average rates at which the temperatures of the two samples change?A.In every 10minute interval, the magnitude of the rate of change of temperature of the insulated sample is greater than that of the noninsulated sample.B.In every 10minute interval, the magnitude of the rate of change of temperature of the noninsulated sample is greater than that of the insulated sample.C.In the intervals from 0 to 10minutes and from 10 to 20minutes, the rates of change of temperature of the insulated sample are of greater magnitude, whereas in the intervals from 40 to 50minutes and from 50 to 60minutes, the rates of change of temperature of the noninsulated sample are of greatermagnitude.D.In the intervals from 0 to 10minutes and from 10 to 20minutes, the rates of change of temperature of the noninsulated sample are of greater magnitude, whereas in the intervals from 40 to 50minutes and from 50 to 60minutes, the rates of change of temperature of the insulated sample are of greater magnitude.Explanation for question27.Question 28 refers to the following figure.Begin skippable figure description.The figure presents a tilted square ABCD in the xyplane. The horizontal axis is labeledx, and the vertical axis is labeledy. There are evenly spaced horizontal gridlines and evenly spaced vertical gridlines labeled negative 6 through 6, in increments of 2units, along both axes. VertexA is 5units to the left of the yaxis and 2units below the xaxis, vertexB is 1unit to the left of the yaxis and 6units above the xaxis, vertexC is 7units to the right of the yaxis and 2units above the xaxis, and vertexD is 3units to the right of the yaxis and 6units below the xaxis. PointE is on diagonalAC, lies on the xaxis, and is 1unit to the right of the yaxis.End skippable figure description.Question 28.In the preceding xyplane, ABCD is a square and pointE is the center of the square. The coordinates of pointsC and E are 7 comma 2, and 1comma 0, respectively. Which of the following is an equation of the line that passes through pointsB andD?A. y equals negative 3x minus 1B. y equals negative 3, parenthesis, x minus 1, close parenthesisC. y equals negative onethirdx plus 4D. y equals negative onethirdx minus 1Explanation for question28.Question 29 is based on the following system of equations. y equals 3 y equals a, xsquared, plus bQuestion 29.In the preceding system of equations, aandb are constants. For which of the following values of aandb does the system of equations have exactly two realsolutions?A. a, equals negative 2, b equals 2B. a, equals negative 2, b equals 4C. a, equals 2, b equals 4D. a, equals 4, b equals 3Explanation for question29.Question 30 refers to the following figure.Begin skippable figure description.The figure presents a polygon with six sides of equal length and six interior angles of equal measure, and a square. The polygon and the square have one side in common.End skippable figure description.Question 30.The preceding figure shows a regular hexagon with sides of lengtha and a square with sides of lengtha.If the area of the hexagon is 384 times the square root of3 square inches, what is the area, in square inches, of the square?A.256B.192C. 64 times the square root of 3D. 16 times the square root of 3Explanation for question30.DirectionsFor questions 31 through 38, solve the problem and enter your answer in the grid, as described below, on the answer sheet.1.Although not required, it is suggested that you write your answer in the boxes at the top of the columns to help you fill in the circles accurately. You will receive credit only if the circles are filled in correctly.2.Mark no more than one circle in any column.3.No question has a negative answer.4.Some problems may have more than one correct answer. In such cases, grid only one answer.5.Mixed numbers such as three and one half must be gridded as 3.5 or sevenslashtwo. (If three,one,slash,two, is entered into the grid, it will be interpreted as thirty one halves, not three and one half.)6.Decimal answers: If you obtain a decimal answer with more digits than the grid can accommodate, it may be either rounded or truncated, but it must fill the entire grid.The following are four examples of how to record your answer in the spaces provided. Keep in mind that there are four spaces provided to record each answer.Examples 1 and 2Begin skippable figure description.Example 1: If your answer is a fraction such as seventwelfths, it should be recorded as follows. Enter 7 in the first space, the fractionbar (aslash) in the second space, 1 in the third space, and 2 in the fourth space. All four spaces would be used in this example.Example 2: If your answer is a decimal value such as 2.5, it could be recorded as follows. Enter 2 in the secondspace, the decimal point in the third space, and 5 in the fourth space. Only three spaces would be used in thisexample.End skippable figure description.Example 3Begin skippable figure description.Example 3: Acceptable ways to record twothirds are: 2 slash 3, .666, and .667. End skippable figure description.Example 4Note: You may start your answers in any column, spacepermitting. Columns you dont need to use should be left blank.Begin skippable figure description.Example 4: It is not necessary to begin recording answers in the first space unless all four spaces are needed. For example, if your answer is 201, you may record 2 in the second space, 0 in the third space, and 1 in the fourth space. Alternatively, you may record 2 in the first space, 0 in the second space, and 1 in the third space. Spaces not needed should be left blank.End skippable figure description.Question 31.A coastal geologist estimates that a certain countrys beaches are eroding at a rate of 1.5feet per year. According to the geologists estimate, how long will it take, in years, for the countrys beaches to erode by 21feet?Explanation for question31.Question 32.If hhours and 30minutes is equal to 450minutes, what is the value ofh?Explanation for question32.Question 33.In the xyplane, the point with coordinates 3 comma 6 lies on the graph of the function f of x equals, 3x squared, minus bx, plus 12. What is the value ofb?Explanation for question33.Question 34.In one semester, Doug and Laura spent a combined 250hours in the tutoring lab. If Doug spent 40more hours in the lab than Laura did, how many hours did Laura spend in the lab?Explanation for question34.Question 35 is based on the following equation. a, equals 18t plus 15Question 35.Jane made an initial deposit to a savings account. Each week thereafter she deposited a fixed amount tothe account. The preceding equation models the amounta, in dollars, that Jane has deposited after tweekly deposits. According to the model, how many dollars was Janes initial deposit? (Disregard the $ sign when gridding your answer.)Explanation for question35.Question 36 refers to the following figure.Begin skippable figure description.The figure presents a circle with centerO touched by two lines, where one line touches the circle at the single point, labeledL, on the upper right part of the circle, another line touches the circle at the single point, labeledN, on the lower right part of the circle, and the two lines intersect at pointM outside and to the right of the circle. Radii OL and ON are drawn, and the angle formed by line segments LM and NM is labeled 60degrees.End skippable figure description.Question 36.In the preceding figure, pointO is the center of the circle, line segmentsLM and MN are tangent to the circle at pointsL andN, respectively, and the segments intersect at pointM as shown. If the circumference of the circle is 96, what is the length of minor arc LN?Explanation for question36.Questions 37 and 38 refer to the following information.A botanist is cultivating a rare species of plant in a controlled environment and currently has 3000 of these plants. The population of this species that the botanist expects to grow next year, , N sub next year, can be estimated from the number of plants this year, , N sub this year, by the following equation. N sub next year, equals, N sub this year, plus 0.2, parenthesis, N sub this year, close parenthesis, times, brace, 1 minus the fraction, N sub this year over K, close brace.The constant K in this formula is the number of plants the environment is able tosupport.Question 37.According to the formula, what will be the number of plants two years from now if K equals 4000? (Round your answer to the nearest whole number.)Explanation for question37.Question 38.The botanist would like to increase the number of plants that the environment can support so that the population of the species will increase more rapidly. If the botanists goal is that the number of plants will increase from 3000 this year to 3360 next year, how many plants must the modified environment support?Explanation for question38.Stop.If you finish before time is called, you may check your work on this section only. Do not turn to any other section.Answers and explanations for questions1 through38 are provided in the next section of this document.Answers and Explanations for Questions1 through38Explanation for question 1.Choice C is correct. Since the musician earns $0.09 for each download, the musician earns 0.09ddollars when the song is downloaded dtimes. Similarly, since the musician earns $0.002 each time the song is streamed, the musician earns 0.002sdollars when the song is streamed stimes. Therefore, the musician earns a total of 0.09dplus 0.002sdollars when the song is downloaded dtimes and streamed stimes.Choice A is incorrect because the earnings for each download and the earnings for time streamed are interchanged in the expression.Choices B and D are incorrect because in both answer choices, the musician will lose money when a song is either downloaded or streamed. However, the musician only earns money, not loses money, when the song is downloaded or streamed.Explanation for question 2.Choice B is correct. The quality control manager selects 7lightbulbs at random for inspection out of every 400lightbulbs produced. A quantity of 20,000lightbulbs is equal to the fraction 20,000 over 400, which is equal to 50 batches of 400lightbulbs. Therefore, at the rate of 7lightbulbs per 400lightbulbs produced, the quality control manager will inspect a total of 50 times 7, equals 350lightbulbs.Choices A, C, and D are incorrect and may result from calculation errors or misunderstanding of the proportional relationship.Explanation for question 3.Choice A is correct. The value of m when l is 73 can be found by substituting the 73 for l in l equals 24 plus 3.5m and then solving for m. The resulting equation is 73 equals 24 plus 3.5m; subtracting 24 from each side gives 49 equals 3.5m. Then dividing each side of 49 equals 3.5m by 3.5 gives 14 equals m. Therefore, when l is 73, m is 14.Choice B is incorrect and may result from adding 24 to 73, instead of subtracting 24 from 73, when solving 73 equals 24 plus 3.5m.Choice C is incorrect because 73 is the given value for l, not for m.Choice D is incorrect and may result from substituting 73 for m, instead of for l, in the equation l equals 24 plus 3.5m.Explanation for question 4.Choice C is correct. The amount of money the performer earns is directly proportional to the number of people who attend the performance. Thus, by the definition of direct proportionality, M equals kP, where M is the amount of money the performer earns, in dollars, P is the number of people who attend the performance, and k is a constant. Since the performer earns $120 when 8people attend the performance, one can substitute 120 for M and 8 for P, giving 120 equals 8k. Hence, k equals 15, and the relationship between the number of people who attend the performance and the amount of money, in dollars, the performer earns is M equals 15P. Therefore, when 20people attend the performance, the performer earns 15, parenthesis, 20, close parenthesis, equals 300dollars.Choices A, B, and D are incorrect and may result from either misconceptions about proportional relationships or computational errors.Explanation for question 5.Choice C is correct. If 43% of the money earned is used to pay for costs, then the rest, 57%, is profit. A performance where 8people attend earns the performer $120, and 57% of $120 is 120dollars times 0.57, equals 68dollars 40cents.Choice A is incorrect. The amount $51.60 is 43% of the money earned from a performance where 8people attend, which is the cost of putting on the performance, not the profit from the performance.Choice B is incorrect. It is given that 57% of the money earned is profit, but 57% of $120 is not equal to $57.00.Choice D is incorrect. The profit can be found by subtracting 43% of $120 from $120, but 43% of $120 is $51.60, not $43.00. Thus, the profit is 120dollars minus 51dollars 60cents, equals 68dollars 40cents, not 120dollars minus 43dollars, equals 77dollars.Explanation for question 6.Choice B is correct. When 4 times the number x is added to 12, the result is 12 plus 4x. Since this result is equal to 8, the equation 12 plus 4x, equals 8 must be true. Subtracting 12 from each side of 12 plus 4x, equals 8 gives 4x equals negative4, and then dividing both sides of 4x equals negative4 by 4 gives x equals negative1. Therefore, 2timesx added to7, or 7 plus 2x, is equal to 7 plus 2, parenthesis, negative1, close parenthesis, equals 5.Choice A is incorrect because negative1 is the value of x, not the value of 7 plus 2x.Choices C and D are incorrect and may result from calculation errors.Explanation for question 7.Choice D is correct. The xintercepts of the parabola represented by y equals xsquared, minus 6x, plus8 in the xyplane are the values of x for which y is equal to 0. The factored form of the equation, y equals, parenthesis, x minus 2, close parenthesis, times, parenthesis, x minus 4, close parenthesis, shows that y equals 0 if and only if x equals 2 or x equals 4. Thus, the factored form, y equals parenthesis, x minus 2, close parenthesis, times, parenthesis, x minus 4, close parenthesis, displays the xintercepts of the parabola as the constants 2 and4.Choices A, B, and C are incorrect because none of these forms shows the xintercepts 2 and 4 as constants or coefficients.Explanation for question 8.Choice D is correct. Since a player starts with k points and loses 2points each time a task is not completed, the players score will be k minus 2n after ntasks are not completed (and no additional points are gained). Since a player who fails to complete 100tasks has a score of 200points, the equation 200equals k, minus 100, parenthesis, 2, close parenthesis, must be true. This equation can be solved by adding 200 to each side, giving kequals400.Choices A, B, and C are incorrect and may result from errors in setting up or solving the equation relating the players score to the number of tasks the player fails to complete. For example, choice A may result from subtracting 200 from the lefthand side of 200equals k, minus 100, parenthesis, 2, close parenthesis, and adding 200 to the righthand side.Explanation for question 9.Choice A is correct. Since x is the number of 40pound boxes, 40x is total weight, in pounds, of the 40pound boxes; and since y is the number of 65pound boxes, 65y is total weight, in pounds, of the 65pound boxes. The combined weight of the boxes is therefore 40x plus 65y, and the total number of boxes is xplusy. Since the forklift can carry up to 45boxes or up to 2,400pounds, the inequalities that represent these relationships are 40x plus 65y, is less than or equal to 2,400 and x plus y is less than or equal to 45.Choice B is incorrect. The second inequality correctly represents the maximum number of boxes on the forklift, but the first inequality divides, rather than multiplies, the number of boxes by their respective weights.Choice C is incorrect. The combined weight of the boxes, 40x plus 65y, must be less than or equal to 2,400pounds, not 45; the total number of boxes, xplusy, must be less than or equal to 45, not 2,400.Choice D is incorrect. The second inequality correctly represents the maximum weight, in pounds, of the boxes on the forklift, but the total number of boxes, xplusy, must be less than or equal to 45, not 2,400.Explanation for question 10.Choice B is correct. It is given that gof3, equals 2. Therefore, to find the value of f of g of 3, substitute 2 for g of 3: f of g of 3, equals, f of 2, which equals 3.Choices A, C, and D are incorrect and may result from misunderstandings about function notation.Explanation for question 11.Choice B is correct. Tony reads 250words per minute, and he plans to read for 3hours, which is 180minutes, each day. Thus, Tony is planning to read 250 times 180, equals 45,000words of the novel per day. Since the novel has 349,168words, it will take Tony the fraction 349,168 over 45,000, is approximately equal to 7.76days of reading to finish the novel. That is, it will take Tony 7 full days of reading and most of an 8thday of reading to finish the novel. Therefore, it will take Tony 8days to finish the novel.Choice A is incorrect and may result from an incorrect calculation or incorrectly using the numbers provided in the table.Choice C is incorrect and may result from taking the total number of words in the novel divided by the rate Tony reads per hour.Choice D is incorrect and may result from taking the total number of words in the novel divided by the number of pages in the novel.Explanation for question 12.Choice D is correct. Since there were 175,000tons of trash in the landfill on January1,2000, and the amount of trash in the landfill increased by 7,500tons each year after that date, the amount of trash, in tons, in the landfill y years after January1,2000, can be expressed as 175,000 plus 7,500y. The landfill has a capacity of 325,000tons. Therefore, the set of years where the amount of trash in the landfill is at (equal to) or above (greater than) capacity is described by the inequality 175,000 plus 7,500y, is greater than or equal to 325,000.Choice A is incorrect. This inequality does not account for the 175,000tons of trash in the landfill on January1,2000, nor does it accurately account for the 7,500tons of trash that are added to the landfill each year after January1,2000.Choice B is incorrect. This inequality does not account for the 175,000tons of trash in the landfill on January1,2000.Choice C is incorrect. This inequality represents the set of years where the amount of trash in the landfill is at or below capacity.Explanation for question 13.Choice D is correct. Survey research is an efficient way to estimate the preferences of a large population. In order to reliably generalize the results of survey research to a larger population, the participants should be randomly selected from all people in that population. Since this survey was conducted with a population that was not randomly selected, the results are not reliably representative of all people in the town. Therefore, of the given factors, where the survey was given makes it least likely that a reliable conclusion can be drawn about the sportswatching preferences of all people in the town.Choice A is incorrect. In general, larger sample sizes are preferred over smaller sample sizes. However, a sample size of 117people would have allowed a reliable conclusion about the population if the participants had been selected at random.Choice B is incorrect. Whether the population is large or small, a large enough sample taken from the population is reliably generalizable if the participants are selected at random from that population. Thus, a reliable conclusion could have been drawn about the population if the 117 survey participants had been selected at random.Choice C is incorrect. When giving a survey, participants are not forced to respond. Even though some people refused to respond, a reliable conclusion could have been drawn about the population if the participants had been selected at random.Explanation for question 14.Choice C is correct. According to the graph, the horizontal line that represents 550billion miles traveled intersects the line of best fit at a point whose horizontal coordinate is between 2000 and 2005, and slightly closer to 2005 than to 2000. Therefore, of the choices given, 2003 best approximates the year in which the number of miles traveled by air passengers in CountryX was estimated to be 550billion.Choice A is incorrect. According to the line of best fit, in 1997 the estimated number of miles traveled by air passengers in CountryX was about 450billion, not 550billion.Choice B is incorrect. According to the line of best fit, in 2000 the estimated number of miles traveled by air passengers in CountryX was about 500billion, not 550billion.Choice D is incorrect. According to the line of best fit, in 2008 the estimated number of miles traveled by air passengers in CountryX was about 600billion, not 550billion.Explanation for question 15.Choice A is correct. The number of miles Earth travels in its one-year orbit of the Sun is 580,000,000. Because there are about 365days per year, the number of miles Earth travels per day is the fraction 580,000,000 over 365, is approximately equal to 1,589,041. There are 24hours in one day, so Earth travels at the fraction 1,589,041 over 24, is approximately equal to 66,210miles per hour. Therefore, of the choices given, 66,000miles per hour is closest to the average speed of Earth as it orbits theSun.Choices B, C, and D are incorrect and may result from calculation errors.Explanation for question 16.Choice B is correct. According to the table, there are 18 plus 7, equals 25graduates who passed the bar exam, and 7 of them did not take the review course. Therefore, if one of the surveyed graduates who passed the bar exam is chosen at random, the probability that the person chosen did not take the review course is 7 over 25.Choices A, C, and D are incorrect. Each of these choices represents a different probability from the conditional probability that the question asks for.Choice A represents the following probability. If one of the surveyed graduates who passed the bar exam is chosen at random, the probability that the person chosen did take the review course is 18 over 25.Choice C represents the following probability. If one of the surveyed graduates is chosen at random, the probability that the person chosen passed the bar exam is the fraction 25 over 200.Choice D represents the following probability. If one of the surveyed graduates is chosen at random, the probability that the person chosen passed the exam and took the review course is the fraction 7 over 200.Explanation for question 17.Choice C is correct. To find the atomic weight of an unknown element that is 20%less than the atomic weight of calcium, multiply the atomic weight, in amu, of calcium by parenthesis, 1 minus 0.20, close parenthesis: parenthesis, 40, close parenthesis, times, parenthesis, 1 minus 0.20, close parenthesis, equals, parenthesis, 40, close parenthesis, times, parenthesis, 0.8, close parenthesis, which equals 32.Choice A is incorrect. This value is 20% of the atomic weight of calcium, not an atomic weight 20% less than the atomic weight of calcium.Choice B is incorrect. This value is 20 amu less, not 20% less, than the atomic weight of calcium.Choice C is incorrect. This value is 20% more, not 20% less, than the atomic weight of calcium.Explanation for question 18.Choice C is correct. The mean and median values of a data set are equal when there is a symmetrical distribution. For example, a normal distribution is symmetrical. If the mean and the median values are not equal, then the distribution is not symmetrical. Outliers are a small group of values that are significantly smaller or larger than the other values in the data. When there are outliers in the data, the mean will be pulled in their direction (either smaller or larger) while the median remains the same. The example in the question has a mean that is larger than the median, and so an appropriate conjecture is that large outliers are present in the data; that is, that there are a few homes that are valued much more than the rest.Choice A is incorrect because a set of home values that are close to each other will have median and mean values that are also close to each other.Choice B is incorrect because outliers with small values will tend to make the mean lower than the median.Choice D is incorrect because a set of data where many homes are valued between $125,000 and $165,000 will likely have both a mean and a median between $125,000 and $165,000.Explanation for question 19.Choice B is correct. The median of a data set is the middle value when the data points are sorted in either ascending or descending order. There are a total of 600data points provided, so the median will be the average of the 300th and 301stdata points. When the data points are sorted in order:1.Values 1 through 260 will be 0.2.Values 261 through 450 will be 1.3.Values 451 through 540 will be 2.4.Values 541 through 580 will be 3.5.Values 581 through 600 will be 4.Therefore, both the 300th and 301st values are 1, and hence the median is1.Choices A, C, and D are incorrect and may result from either a calculation error or a conceptual error.Explanation for question 20.Choice C is correct. When survey participants are selected at random from a larger population, the sample statistics calculated from the survey can be generalized to the larger population. Since 10 of 300 students surveyed at LincolnSchool have 4siblings, one can estimate that this same ratio holds for all 2,400students at LincolnSchool. Also, since 10 of 300 students surveyed at WashingtonSchool have 4siblings, one can estimate that this same ratio holds for all 3,300students at WashingtonSchool. Therefore, approximately 3 the fraction 10 over 30, times 2,400, equals 803students at LincolnSchool and the fraction 10 over 30, times 3,300, equals 110students at WashingtonSchool are expected to have 4siblings. Thus, the total number of students with 4siblings at WashingtonSchool is expected to be 110 minus 80, equals 30 more than the total number of students with 4siblings at LincolnSchool.Choices A, B, and D are incorrect and may result from either conceptual or calculation errors. For example, choiceA is incorrect; even though there is the same ratio of survey participants from LincolnSchool and WashingtonSchool with 4siblings, the two schools have a different total number of students, and thus, a different expected total number of students with 4siblings.Explanation for question 21.Choice D is correct. The difference between the number of hours the project takes, y, and the number of hours the project was estimated to take, x, is the absolute value of y minus x, end absolute value. If the goal is met, the difference is less than 10, which can be represented as the absolute value of y minus x, end absolute value, is less than 10 or negative10, is less than y minus x, which is less than 10.Choice A is incorrect. This inequality states that the estimated number of hours plus the actual number of hours is less than 10, which cannot be true because the estimate is greater than 100.Choice B is incorrect. This inequality states that the actual number of hours is greater than the estimated number of hours plus 10, which could be true only if the goal of being within 10hours of the estimate were not met.Choice C is incorrect. This inequality states that the actual number of hours is less than the estimated number of hours minus 10, which could be true only if the goal of being within 10hours of the estimate were not met.Explanation for question 22.Choice B is correct. To rearrange the formula I, equals, the fraction P over 4, pi r squared, end fraction in terms of rsquared, first multiply each side of the equation by r squared. This yields r squared, I, equals, the fraction P over 4pi. Then dividing each side of r squared, I, equals, the fraction P over 4pi by I gives r squared, equals the fraction P over 4pi,I.Choices A, C, and D are incorrect and may result from algebraic errors during rearrangement of the formula.Explanation for question 23.Choice A is correct. If IsubA is the intensity measured by ObserverA from a distance of rsubA, and IsubB is the intensity measured by ObserverB from a distance of rsubB, then IsubA, equals, 16IsubB. Using the formula I equals, the fraction P, over 4pirsquared, end fraction, the intensity measured by ObserverA is IsubA, equals, the fraction P, over 4pir, subA, squared, end fraction, which can also be written in terms of IsubB as IsubA, equals, 16IsubB, which equals 16, times, parenthesis, the fraction P, over 4pir, subB, squared, end fraction, close parenthesis. Setting the right-hand sides of these two equations equal to each other gives the fraction P, over 4pir, subA, squared, end fraction, equals 16 times, parenthesis, the fraction P, over 4pir, subB, squared, end fraction, close parenthesis, which relates the distance of ObserverA from the radio antenna to the distance of ObserverB from the radio antenna. Canceling the common factor the fraction P over 4pi and rearranging the equation gives r, sub B, squared, equals 16r, subA, squared. Taking the square root of each side of r, subB, squared, equals 16r, subA, squared gives r, subB, equals 4r, subA, and then dividing each side by 4 yields r, subA, equals, onefourthr, subB. Therefore, the distance of ObserverA from the radio antenna is onefourth the distance of ObserverB from the radio antenna.Choices B, C, and D are incorrect and may result from errors in deriving or using the formula the fraction P, over 4pir, subA, squared, end fraction, equals, parenthesis, 16, close parenthesis, times, parenthesis, the fraction Pover 4pir, sub B, squared, end fraction, close parenthesis.Explanation for question 24.Choice A is correct. The equation of a circle with center with coordinates hcommak, and radius r is parenthesis, x minus h, close parenthesis, squared, plus, parenthesis, y minus k, close parenthesis, squared, equals rsquared. To put the equation xsquared plus ysquared, plus 4x, minus 2y, equals negative1 in this form, complete the square as follows: xsquared plus ysquared, plus 4x minus 2y, equals negative1, which is parenthesis, xsquared plus 4x, close parenthesis, plus, parenthesis, ysquared minus 2y, close parenthesis, equals, negative1, and then parenthesis, xsquared plus 4x plus4, close parenthesis, minus4, plus, parenthesis, ysquared minus 2y plus1, close parenthesis, minus1, equals, negative1, which is equivalent to parenthesis, x plus 2, close parenthesis, squared, plus, parenthesis, y minus 1, close parenthesis, squared, minus 4, minus 1, equals negative1, and finally parenthesis, x plus 2, close parenthesis, squared, plus parenthesis, y minus1, close parenthesis, squared, equals 4, which equals 2squared.Therefore, the radius of the circle is 2.Choice C is incorrect because it is the square of the radius, not the radius.Choices B and D are incorrect and may result from errors in rewriting the given equation in standard form.Explanation for question 25.Choice A is correct. In the xyplane, the slope m of the line that passes through the points with coordinates xsub1 comma ysub1, and with coordinates xsub2 comma ysub2, is given by the formula mequals, the fraction whose numerator is ysub2, minus ysub1, and whose denominator is xsub2, minus xsub1. Thus, if the graph of the linear functionf has intercepts at the point with coordinates a, comma 0, and the point with coordinates zero comma b, then the slope of the line that is the graph of yequals fofx is m equals the fraction whose numerator is 0 minusb, and whose denominator is a, minus 0, which equals the negative fraction b over a. It is given that a, plus b equals 0, and so a,equals negativeb. Finally, substituting negativeb for a in mequals the negative fraction bovera gives m equals the negative fraction b over negativeb, which equals1, which is positive.Choices B, C, and D are incorrect and may result from a conceptual misunderstanding or a calculation error.Explanation for question 26.Choice D is correct. The definition of the graph of a function f in the xyplane is the set of all points with coordinates x comma, fofx. Thus, for negative4 is less than or equal to a, which is less than or equal to4, the value of f of a, is 1 if and only if the unique point on the graph of f with xcoordinate a has ycoordinate equal to 1. The points on the graph of f with xcoordinates negative4, comma, three halves, and 3 are, respectively, the point with coordinates negative4 comma1, the point with coordinates three halves comma1, and the point with coordinates 3comma1. Therefore, all of the values of f given in I, II, and III are equal to1.Choices A, B, and C are incorrect because they each omit at least one value ofx for which f of x equals1.Explanation for question 27.Choice D is correct. According to the graph, in the interval from 0 to 10minutes, the noninsulated sample decreased in temperature by about 18degrees Celsius, while the insulated sample decreased by about 8degrees Celsius; in the interval from 10 to 20minutes, the noninsulated sample decreased in temperature by about 9degrees Celsius, while the insulated sample decreased by about 5degrees Celsius; in the interval from 40 to 50minutes, the noninsulated sample decreased in temperature by about 1degree Celsius, while the insulated sample decreased by about 3degrees Celsius; and in the interval from 50 to 60minutes, the noninsulated sample decreased in temperature by about 1degree Celsius, while the insulated sample decreased by about 2degrees Celsius. The description in choiceD accurately summarizes these rates of temperature change over the given intervals. (Note that since the two samples of water have equal mass and so must lose the same amount of heat to cool from 60degrees Celsius to 25degrees Celsius, the faster cooling of the noninsulated sample at the start of the cooling process must be balanced out by faster cooling of the insulated sample at the end of the cooling process.)Choices A, B, and C are incorrect. None of these descriptions accurately compares the rates of temperature change shown in the graph for the 10minute intervals.Explanation for question 28.Choice B is correct. In the xyplane, the slope m of the line that passes through the points with coordinates xsub1, comma, ysub1, and the point with coordinates xsub2, comma, ysub2, is m equals, the fraction whose numerator is ysub2 minus ysub1, and whose denominator is xsub2 minus xsub1. Thus, the slope of the line through the pointsC with coordinates 7 comma2 and E with coordinates 1 comma0 is the fraction with numerator 2 minus 0, and denominator 7 minus 1, end fraction, which simplifies to twosixths equals onethird. Therefore, diagonalAC has a slope of onethird. The other diagonal of the square is a segment of the line that passes through pointsB and D. The diagonals of a square are perpendicular, and so the product of the slopes of the diagonals is equal to negative1. Thus, the slope of the line that passes throughB andD is negative 3, because onethird, parenthesis, negative3, close parenthesis, equals negative1. Hence an equation of the line that passes throughB andD can be written as y equals, negative3x plusb, where b is the yintercept of the line. Since diagonal BD will pass through the center of the square, E with coordinates 1 comma0, the equation 0 equals negative3, parenthesis, 1, close parenthesis, plus b holds. Solving this equation for b gives bequals3. Therefore, an equation of the line that passes through pointsB andD is y equals, negative3x plus3, which can be rewritten as y equals negative3, parenthesis, xminus1, close parenthesis.Choices A, C, and D are incorrect and may result from a conceptual error or a calculation error.Explanation for question 29.Choice B is correct. Substituting 3 for y in y equals a, xsquared plusb gives 3 equalsa, xsquared plusb, which can be rewritten as 3 minusb equals a, xsquared. Since yequals3 is one of the equations in the given system, any solution x of 3minusb equals a,xsquared corresponds to the solution xcomma3 of the given system. Since the square of a real number is always nonnegative, and a positive number has two square roots, the equation 3minusb equals a,xsquared will have two solutions for x if and only if (1) a is greater than 0 and b is less than3, or (2) a is less than 0 and b is greater than3. Of the values for aandb given in the choices, only a, equals negative2, bequals4 satisfy one of these pairs of conditions.Alternatively, if a, equals negative2 and b equals 4, then the second equation would be y equals negative2x squared, plus4. The graph of this quadratic equation in the xyplane is a parabola with yintercept with coordinates 0 comma4, that opens downward. The graph of the first equation, y equals 3, is the horizontal line that contains the point with coordinates 0 comma 3. As shown below, these two graphs have two points of intersection, and therefore, this system of equations has exactly two real solutions. (Graphing shows that none of the other three choices produces a system with exactly two real solutions.)Begin skippable figure description.The figure presents the graph of a line and a parabola in the xyplane. The horizontal axis is labeledx, the vertical axis is labeledy, and the origin is labeledO. Numbers negative2 through 2, in increments of 1, appear along the xaxis, and there are vertical gridlines at those numbers. Numbers 1 through 4, in increments of 1, appear along the yaxis, and there are horizontal gridlines at those numbers. The line is a horizontal line with y equals 3. The parabola is a curve that is symmetric with respect to the yaxis and opens downward with its highest point on the yaxis at 4. The curve increases as it moves from left to right, crossing the line with y equals 3, until it reaches the yaxis at 4. Then it starts decreasing, crossing the line with y equals 3, and continues to decrease as it moves to the right. The line and the parabola intersect at two points, one to the left of the yaxis and one to the right of the yaxis.End skippable figure description.Choices A, C, and D are incorrect and may result from calculation or conceptual errors.Explanation for question 30.Choice A is correct. The regular hexagon can be divided into 6 equilateral triangles of side lengtha by drawing the six segments from the center of the regular hexagon to each of its 6vertices. Since the area of the hexagon is 384times the square root of3 squareinches, the area of each equilateral triangle will be the fraction with numerator 384 times the square root of 3, and denominator6, equals, 64 times the square root of3 squareinches.Drawing any altitude of an equilateral triangle divides it into two 30degree-60degree-90degree triangles. If the side length of the equilateral triangle is a, then the hypotenuse of each 30degree-60degree-90degree triangle is a, and the altitude of the equilateral triangle will be the side opposite the 60degreeangle in each of the 30degree-60degree-90degree triangles. Thus, the altitude of the equilateral triangle is the fraction the square root of 3 over 2, end fraction, times, a, and the area of the equilateral triangle is one half, parenthesis, a, close parenthesis, times, parenthesis, the fraction the square root of 3 over 2, end fraction, times, a, close parenthesis, equals, the fraction the square root of 3, over 4, end fraction, times, a, squared. Since the area of each equilateral triangle is 64 times the square root of3 square inches, it follows that a, squared equals, the fraction 4 over the square root of 3, times, parenthesis, 64 times the square root of 3, close parenthesis, equals 256squareinches. And since the area of the square with side length a is a,squared, it follows that the square has area 256squareinches.Choices B, C, and D are incorrect and may result from calculation or conceptual errors.Explanation for question 31.The correct answer is 14. Since the coastal geologist estimates that the countrys beaches are eroding at a rate of 1.5feet every year, they will erode by 1.5xfeet in xyears. Thus, if the beaches erode by 21feet in xyears, the equation 1.5x equals 21 must hold. The value of x is then the fraction 21 over 1.5, which equals14. Therefore, according to the geologists estimate, it will take 14years for the countrys beaches to erode by 21feet.Explanation for question 32.The correct answer is 7. There are 60minutes in each hour, and so there are 60hminutes in hhours. Since hhours and 30minutes is equal to 450minutes, it follows that 60h plus 30, equals450. This equation can be simplified to 60h equals420, and so the value of h is thefraction 420 over 60, equals7.Explanation for question 33.The correct answer is 11. It is given that the function f of x passes through the point with coordinates 3 comma 6. Thus, if x equals 3, the value of f of x is 6 (since the graph of f in the xyplane is the set of all points with coordinates x, comma, f of x. Substituting 3 for x and 6 for fofx in fofx equals, 3x squared, minus bx, plus 12, gives 6 equals, 3, parenthesis, 3, close parenthesis, squared, minusb, parenthesis, 3, close parenthesis, plus 12. Performing the operations on the righthand side of this equation gives 6equals, 3, parenthesis, 9, close parenthesis, minus 3b plus 12, equals, 27 minus 3b plus 12, which equals, 39 minus 3b. Subtracting 39 from each side of 6equals 39 minus 3b, gives negative33 equals negative3b, and then dividing each side of negative 3b equals negative33 by negative3 gives that the value ofb is11.Explanation for question 34.The correct answer is 105. Let D be the number of hours Doug spent in the tutoring lab, and let L be the number of hours Laura spent in the tutoring lab. Since Doug and Laura spent a combined total of 250hours in the tutoring lab, the equation D plus L equals250 holds. The number of hours Doug spent in the lab is 40 more than the number of hours Laura spent in the lab, and so the equation D equals L plus 40 holds. Substituting Lplus40 forD in D plus L equals 250 gives parenthesis, L plus 40, close parenthesis, plus L, equals 250, or 40 plus 2L equals 250. Solving this equation gives L equals 150. Therefore, Laura spent 105hours in the tutoring lab.Explanation for question 35.The correct answer is 15. The amount, a, that Jane has deposited after t fixed weekly deposits is equal to the initial deposit plus the total amount of money Jane has deposited in the t fixed weekly deposits. This amount a is given to be a, equals 18t plus 15. The amount she deposited in the t fixed weekly deposits is the amount of the weekly deposit times t; hence, this amount must be given by the term 18t in a, equals 18t plus 15 (and so Jane must have deposited 18dollars each week after the initial deposit). Therefore, the amount of Janes original deposit, in dollars, is a, minus 18t equals 15.Explanation for question 36.The correct answer is 32. Since segmentsLM and MN are tangent to the circle at pointsL andN, respectively, anglesOLM and ONM are rightangles. Thus, in quadrilateral OLMN, the measure of angleO is 360degrees minus, parenthesis, 90degrees plus 60degrees plus 90degrees, close parenthesis, equals, 120degrees. Thus, in the circle, central angleO cuts off the fraction 120 over 360, equals one third of the circumference; that is, minor arc LN is onethird of the circumference. Since the circumference is 96, the length of minor arc LN is one third times 96, equals32.Explanation for question 37.The correct answer is 3284. According to the formula, the number of plants oneyear from now will be 3,000 plus 0.2, parenthesis, 3,000, close parenthesis, times, parenthesis, 1 minus the fraction 3,000 over 4,000, close parenthesis, which is equal to 3150. Then, using the formula again, the number of plants twoyears from now will be 3,150 plus 0.2, parenthesis, 3,150, close parenthesis, times, parenthesis, 1 minus the fraction, 3,150 over 4,000, close parenthesis, which is 3283.875. Rounding this value to the nearest whole number gives3284.Explanation for question 38.The correct answer is 7500. If the number of plants is to be increased from 3000 this year to 3360 next year, then the number of plants that the environment can support, K, must satisfy the equation 3,360 equals 3,000 plus 0.2, parenthesis, 3,000, close parenthesis, times, parenthesis, 1 minus the fraction, 3,000 over K, close parenthesis. Dividing both sides of this equation by 3000 gives 1.12 equals, 1 plus 0.2, times, parenthesis, 1 minus the fraction 3,000 over K, close parenthesis, and therefore, it must be true that 0.2, times, parenthesis, 1 minus the fraction 3,000 over K, close parenthesis, equals 0.12, or equivalently, 1minus the fraction 3,000 over K, equals 0.6. It follows that the fraction 3,000 over K, equals 0.4, and so Kequals the fraction, 3,000 over 0.4, equals 7,500.Stop. This is the end of the answers and explanations for questions1 through38.