Math

A. The inequality will be less than or equal to, since he may spend $100 or less on his purchase.

Tom needs to buy ink cartridges and printer paper. Each ink cartridge costs $30. Each ream of paper costs $5. He has $100 to spend. Which of the following inequalities may be used to find the combinations of ink cartridges and printer paper that he may purchase?

B. dependent variable.

A student makes the graph shown above of the amount of money the student has in savings versus time. In this scenario, the amount of money in the student's savings account is the: A. independent variable. B. dependent variable. C. slope. D. x-intercept.

B. Notice that choice C cannot be correct since x does not equal one. (x = 1 results in a zero on the denominator.) x-2 = x-1 + 2 x-1 x+1 x-1 x-4 = x-1 x-1 x+1 (x+1)(x-4) = (x-1)(x-1) x^2 - 3x - 4 = x^2 - 2x + 1 -5 = x

A. x = 2 B. x = -5 C. x = 1 D. No solution

The slope may be written as m = 4-0 / -3-(-4), which simplifies to m=4.

What is the slope of the leg marked x in the triangle graphed below? A. 2 B. 3.5 C. 4 D. 4.5

B. The associative property of multiplication states that when three or more numbers are multiplied, the product is the same regardless of the way in which the numbers are grouped. Choice C shows that the product of 2,3 , and 4 is the same with two different groupings of the factors. Choice A demonstrates the distributive property. Choice B shows grouping, but the factors are different. Choice D demonstrates the commutative property of multiplication. Therefore, the correct choice is C.

Which of the following problems demonstrates the associative property of multiplication? A. 2(3+4) = 2(3)+2(4) B. (3x6) x 2 = (4x3) x 3 C. (2x3) x 4 = 2 x (3x4) D. 6x4 = 4x6

C. The volume of a cylinder may be calculated using the formula V = πr^2h, where r represents the radius and h represents the height. Substituting 1.5 for r and 3 for h gives V = π(1.5)^2(3), which simplifies to V = 21.2.

A can has a radius of 1.5 inches and a height of 3 inches. Which of the following best represents the volume of the can? A. 17.2 in^3 B. 19.4 in^3 C. 21.2 in^3 D. 23.4 in^3

C. One strategy is to draw polygons with fewer sides and look for a pattern in the number of polygons' diagonals. A quadrilateral has two more diagonals than a triangle, a pentagon has three more diagonals than a quadrilateral, and a hexagon has four more diagonals than a pentagon. Continue this pattern to find that a dodecagon has 54 diagonals.

Determine the number of diagonals of a dodecagon. A. 12 B. 24 C. 54 D. 108

C. The mean is the average of the data and can be found by dividing the sum of the data by the number of data: 16+18+20+21+34+45+49 / 7 = 29. The median is the middle data point when the data are ranked numerically. The median is 21. Therefore, the correct choice is C.

Given this stem and leaf plot, what are the mean and median? A. Mean = 28 and median = 20 B. Mean = 29 and median = 20 C. Mean = 29 and median = 21 D. Mean = 28 and median = 21

D. using number cubes to show how to make ten in more than one way TO develop understanding of operations, kindergarten students should represent addition and subtraction with objects, fingers, drawing, and other representations. Number cubes provide students with hands-on experience in decomposing 10 into number pairs (eg. 8+2, 6+4, etc.) and can help build students' fluency with number operations.

A kindergarten teacher wants students to be able to decompose the number ten into number pairs. Which of the following student activities is likely to be most effective in meeting this objective? A. comparing two sets with quantities less than or equal to ten B. describing the role of ten in the place value system C. solving a series of addition problems with sums that equal ten D. using number cubes to show how to make ten in more than one way

C. Triangles can be classified as scalene, isosceles, or equilateral. Scalene triangles have no equal side measurements and no equal angle measurements. Isosceles triangles have two sides of equal measurement and two angles of equal measurement. Equilateral triangles have three sides of equal measurement and three angles of equal measurement. A right triangle is isosceles only if its two acute angles are congruent. Therefore, the correct choice is C.

Which of the following best describes an isosceles triangle? A. A triangle with no sides of equal measurement and one obtuse angle B. A triangle with three sides of equal measurement C. A triangle with two sides of equal measurement and two acute angles D. A triangle with one right angle and two non-congruent acute angles.

B. The equation y + 3 = 7 is solved by subtracting 3 from both sides to yield y = 4. Substituting y = 4 into x-1 = y yields x-1 = 4. Adding 1 to both sides of this equation yields x = 5. Therefore, the correct choice is B.

Which of the following is the correct solution for x in the system of equations x - 1 = y and y + 3 = 7? A. x = 6 B. x = 5 C. x = 4 D. x = 8

C. 11 1/2 inches Since the inner cross-sectional area of the pipe must be at least 25pi square inches and the area of a circle is found by pi r ^2 when r is the radius, it follows that in this situation 25pi = pi r ^2. By taking the square root of both sides of the equation, radius r=5 inches. Thus, the diameter of the inner region must be 2r = 2x5 = 10 inches. The outer diameter includes a 5/8 inch wall of pipe on both sides, so the entire diameter must be at least 10 + 5/8 + 5/8 = 11 1/2 inches. Of the pipes described in the response options, the smallest pipe that would accommodate the flow is the one with the outer dimension of 11 1/2 inches, since it is the smallest pipe with an outer diameter equal to or greater than 11 1/4 inches.

A pipe must have an inner cross-sectional area, shaded in the diagram above, of at least 25pi square inches to accommodate a flow of water. The walls of the pipe have a thickness of 5/8 inch. Which of the following pipes, measured by its outer diameter (d), is the smallest that could be used to accommodate the flow? A. 6 1/4 inches B. 10 1/4 inches C. 11 1/2 inches D. 16 3/8 inches

B. Variability refers to the spread of a data set, often measured by standard deviation or interquartile range. Data sets in which the data points occur most frequently near the data's central value have lower variability, whereas data sets in which the data points occur frequently at large distances from its central value have higher variability. The graph shown that has the greatest variability is the one in which the values in the data set are the most distantly spaced from the data's central value.

A random sample of 20 students from two different schools were selected to determine how far, in miles, the students live from their school. The data are shown in the graphs below. Which data set has the greatest variability?

C. 450 cubic centimeters The volume of the block is found by multiplying the length times the width times the height of the block. To complete the computation, the dimensions must all be in the same unit and that unit should be centimeters, since the response must be given in cubic centimeters. Thus 0.5 meter x 100 centimeters/1 meter = 50 centimeters and 9 millimeters x 100 centimeters/1000 millimeters = 0.9 centimeters. The volume of the block is therefore 10 cm x 50 cm x 0.9 cm = 450 cubic centimeters.

A rectangular block has a width of 10 centimeters, a length of 0.5 meter, and a thickness of 9 millimeters. What is the volume of the block in cubic centimeters? A. 4.5 cubic centimeters B. 45 cubic centimeters C. 450 cubic centimeters D. 4500 cubic centimeters

D. $10.20 The fare is $2.50 plus $0.40 for each 1/5 mile traveled. Since there are five 1/5 mile segments in 1 mile, there are 5 x 3 = 15 one-fifth mile segments in a 3 mile trip. The fare for the trip is therefore $0.40 x 15 + $2.50 = $8.50. To calculate a 20% tip on this fare, multiply the fare by 0.2. Thus the total payment by the passenger will be $8.50 x 0.2 + $8.50 = $8.50 x 1.2 = $10.20.

A taxi fare consists of a fixed cost of $2.50 plus $0.40 for each 1/5 of a mile traveled. If a passenger rides the taxi for 3 miles and includes a 20% tip, how much does the passenger pay in full? A. $5.16 B. $7.03 C. $9.70 D. $10.20

B. 2.5 If students are arranged in ascending order by number of siblings, the median of 26 students occurs between the 13th and 14th student. The bars on the graph for 0, 1, and 2 siblings represent the first 13 students. Therefore, the 13th student has 2 siblings, and the 14th student is included in the next bar, with 3 siblings. The median is the average of these two numbers, or (2+3)/2 = 2.5 siblings.

The bar graph above shows the number of siblings for each of 26 students in a class. What is the median number of siblings per student for this class? A. 2 B. 2.5 C. 3 D. 3.5

B. 48.3 cm Since line AD and line BC both have a length of 7.7 centimeters and both are perpendicular to line AB, the points A, B, C, and D create a rectangle. The perimeter of the shaded region is composed of three sides of rectangle ABCD and the circumference of semicircle DJC. Using the ruler shown in the diagram, the length of line AB measures approximately 12.8 centimeters. Therefore, the length of line DC, the diameter of semicircle DJC, which is equal to the length of line AB, is also 12.8 centimeters. The circumference of a circle is pi times the diameter of the circle. For semicircle DJC, the perimeter is half the perimeter of the circle, or 1/2 (pi x 12.8) = 20.1 centimeters. The perimeter of the shaded region is therefore approximately 7.7 + 12.8 + 7.7 +20.1 = 48.3 centimeters.

The length of line AD is measured as 7.7 centimeters and is equal to the length of line BC. It is given that line DC is the diameter of semicircle DJC. What is the approximate perimeter of the shaded portion of the figure in the diagram above? (Use 3.14 for pi) A. 40.6 cm B. 48.3 cm C. 54.1 cm D. 68.4 cm

C. providing systematic and explicit instruction with guided practice and corrective feedback The Institute of Education Sciences identifies strong evidence that instruction in Tiers 2 and 3 should be explicit and systematic. In particular, instruction should include numerous clear models of easy and difficult problems, with accompanying teacher think-alouds.

Which of the following instructional approaches is recommended for students who need Tier 2 assistance according to assessment results determined by Response to Intervention (RtI) procedures? A. focusing on strategies for breaking difficult problems into manageable parts B. focusing on one-on-one instruction and considering special education services C. providing systematic and explicit instruction with guided practice and corrective feedback D. providing students with multiple opportunities to solve open-ended and nonstandard problems

C. The original price may be modeled by the equation: (x-0.45x) + 0.0875(x-0.45x) = 39.95 which simplifies to 0598125x = 39.95. Dividing each side of the equation by the coefficient of x gives x = 66.79.

A dress is marked down 45%. The cost, after taxes, is $39.95. If the tax rate is 8.75%, what was the original price of the dress? A. $45.74 B. $58.61 C. $66.79 D. $72.31

A. A ⌒ B means "A intersect B," or the elements that are common to both sets. "A intersect B" represents "A and B," that is, an element is in the intersection of A and B if it is in A and it is in B. The elements 2, 5, and 8 are common to both sets.

See image for question and options.

B. The perimeter is equal to the sum of the lengths of the two bases, 2 and 6 units, and the diagonal distances of the other two sides. Using the distance formula, each side length may be represented as d = √20 = 2√5. Thus, the sum of the two sides is equal to 2√20, or 4√5. The whole perimeter is equal to 8 + 4√5.

What is the perimeter of the trapezoid graphed below? A. 4 + √10 B. 8 + 4√5 C. 4 + 2√5 D. 8 + 2√22

C. 2.383 Since 19/8 = 2.375 and 12/5 = 2.4 and the value of the decimal 2.383 is greater than 2.375 but less than 2.4, it follows that 2.383 is between the two given values

Which of the following decimals is between 19/8 and 12/5? A. 2.177 B. 2.295 C. 2.383 D. 2.469

C. There are 36 months in a year. The following proportion may be written: 450 / 3 = x / 36. The equation 3x = 16,200, may be solved for x. Dividing both sides of the equation by 3 gives x = 5,400.

Amy saves $450 every 3 months. How much does she save after 3 years? A. $4,800 B. $5,200 C. $5,400 D. $5,800

C. 10 centimeters An isosceles triange with a base of 12 centimeters can be decomposed into two right triangles each with a base of 6 centimeters and the same height, h, as the isosceles triangle. Thus, the area of the isosceles triangle is equal to the area of the two right triangles. It follows that 48 = 2 (1/2 x 6 x h) and 8 = h and b = 6 for lengths of the legs of one of the right triangles and the Pythagorean theorem, c^2 = a^2 + b^2, to find the length of the hypotenuse (c) of the right triangle, which is also one of the legs of the isosceles triangle: c = Square root of (8^2 + 6^2) = square root of 100 = 10 centimeters.

An isosceles triangle has a base length of 12 centimeters and an area of 48 square centimeters. Which of the following lengths is a side of the isosceles triangle? A. 4 centimeters B. 2 x square root of 13 centimeters C. 10 centimeters D. 4 x square root of 13 centimeters

C. 18.75 acres Since the pounds of seeds needed and acres planted are expressed as a ratio, then the number of acres that can be planted with any number of pounds of seeds can be found using proportional reasoning. For a = the number of acres that can be planted, then 0.64 pounds of seed / 1 acre = 12 pounds of seed / a acres and a = (12x1)/0.64 = 18.75 acres.

For a certain crop, the ratio of pounds of seeds to acres planted is 0.64 : 1. How many acres can be planted with 12 pounds of seeds? A. 5.33 acres B. 7.68 acres C. 18.75 acres D. 20.40 acres

B. 5,000 In the number 452.08, the 4 is in the hundreds place, with a value of 4(100) = 400, and 8 is in the hundredths place, with a value of 8(0.01) = 0.08. To find how many times greater 400 is than 0.08, divide 400 by 0.08: 400 / 0.08 = 5,000. Therefore, the value of the 4 is 5,000 times greater than the value of the 8.

In the number 452.08, the value of the digit 4 is how many times greater than the value of the digit 8? A. 2,000 B. 5,000 C. 20,000 D. 50,000

B. The histogram only shows that there are eight trees between 70 and 75 feet tall. It does not show the individual heights of the trees. That information cannot be obtained from this graph. Therefore, the correct choice is B.

The 5th grade teachers at Washington Elementary School are doing a collaborative unit on cherry trees. Miss Wilson's math classes are making histograms summarizing the heights of black cherry trees located at a local fruit orchard. How many of these trees at this local orchard are 73 feet tall? A. 8 B. That information cannot be obtained from this graph. C. 9 D. 17

C. Aaron ran four miles from home and then back again, so he ran a total of eight miles. Therefore, statement III is false. Statements I and II, however, are both true. Since Aaron ran eight miles in eighty minutes, he ran an average of one mile every ten minutes, or six miles per hour; he ran two miles from point A to B in 20 minutes and four miles from D to E in 40 minutes, so his running speed between both sets of points was the same.

The graph shows Aaron's distance from home at times throughout his morning run. Which of the following statements is (are) true? I. Aaron's average running speed was 6 mph II. Aaron's running speed from point A to point B was the same as from point D to E. III. Aaron ran a total distance of four miles. A. I only B. II only C. I and II D. I, II, and III

D. The total rainfall is 25.38 inches. Thus, the ratio 4.5 / 25.38' represents the percentage of rainfall received during October. 4.5 / 25.38 = 0.177 or 17.7%.

The table below shows the average amount of rainfall Houston receives during the summer and autumn months. What percentage of rainfall received during this timeframe, is received during the month of October? A. 13.5% B. 15.1% C. 16.9% D. 17.7%

A. 6 The ratio of the length of the base of triangle ABC to the length of the base of triangle QRS is 3/12 = 1/4. By similarity, the height (h) of triangle ABC will be 1/4 the height (h) of triangle QRS. Thus 1/4 H = 4h. Since the area of triangle QRS is 1/2 b H = 1/2 b x 4h, then h=4 and so the area of triangle ABC is 1/2 x 3 x 4 = 6.

Triangle ABC is similar to triangle QRS. If the area of triangle QRS = 96, what is the area of triangle ABC? A. 6 B. 8 C. 24 D. 32

C. heart Continuing the pattern, the triangle appears as the 1st, 5th, 9th shape and so on; thus, it will be the shape that occurs in the position that is any multiple of 4, plus 1. Since 96 is a multiple of 4, the triangle will be the 97th shape. The 98th shape will be the square, and the 99th shape will be the heart.

Use the pattern below to answer the question that follows (words represent the image of the shapes, I cannot include the images). Triangle, square, heart, star In the pattern above, the triangle is the first shape, the square is the second shape, and so on. If the pattern repeats, what shape will be the 99th shape to appear? A. triangle B. square C. heart D. star

B. encouraging student interaction and cooperative learning Conjectures are statements that are based on inductive reasoning that appear to be true. A conjecture needs to be proven either true or false, and this can be done by constructing viable arguments and critiquing the reasoning of others. This involves building a logical progression of statements, developing counterexamples, communicating ideas, and responding to the arguments made by other students. These mathematical practices are best conducted in a classroom where students are interacting and engaged in cooperative learning.

A teacher would like to provide opportunities for elementary students to make conjectures and construct arguments related to mathematics. Which of the following approaches is likely to be most effective in meeting this goal? A. engaging students in computer-assisted instruction and visual media B. encouraging student interaction and cooperative learning C. incorporating the use of progressive and innovatice textbooks D. ensuring that all students work at the same pace and level of complexity

B. 2 hours This question requires finding the least amount of time that the two objects will sound together. The two objects will sound together at any time that is a common multiple of 6 minutes and 40 minutes. To find the least amount of time when the two objects sound together requires finding the least common multiple of 6 and 40. The LCM (6, 40) = 2^3 x 3 x 5 = 120. Thus the next time the alarm and bell will ring together is in 120 minutes and since there are 60 minutes in 1 hour, 120 minutes x 1 hour/60 minutes = 2 hours.

An alarm rings every 6 minutes and a bell rings every 40 minutes. If the alarm and bell have both just sounded together, what is the least amount of time that will pass before the alarm and bell both sound together again? A. 1 hour and 20 minutes B. 2 hours C. 3 hours and 20 minutes D. 4 hours

D. An object has rotational symmetry if it can be rotated more than 0 degrees but less than 360 degrees and still look the same as it did in its original orientation. The figure shown that is made up of three identical spiral arms extending from a center point can be rotated 120 degrees (one-third of a full rotation) and will look identical to its original orientation.

Which of the following figures has rotational symmetry?

C. 25 If n = the number of oranges, then $3.50/5 oranges = $20.00 / n and n = (5x20) / 3.90 = 25.6. Thus, the most oranges that could be purchased for $20 is 25.

A store sells 5 oranges for $3.90. At this rate, what is the maximum number of oranges that could be purchased with $20.00? A. 15 B. 16 C. 25 D. 26

C. comparing two decimals using the meanings of the digits in each place By exploring the relationship between base-ten numerals and the expanded form of a decimal number, as shown in the example, students gain a better understanding of the meaning of the digits in each place and make connections between decimals and fractions (with denominators that are powers of ten). This understanding of the place value system will prepare students to develop the skill of comparing two decimals.

Fifth-grade students are learning to write numbers in expanded form, an example of which is shown above. Which of the following would be the most appropriate follow-up activity? A. representing a variety of rational numbers B. identifying fractions that can be written as terminating decimals C. comparing two decimals using the meanings of the digits in each place D. finding common denominators that are multiples of ten

D. Since a and b are even integers, each can be expressed as the product of 2 and an integer. So if we write a = 2x and b = 2y, 3(2x)^2 + 9(2y)^3 = c. 3(4x^2) + 9(8y^3) = c 12x^2 + 72y^3 = c 12(x^2 + 6y^3) = c Since c is the product of 12 and some other integer, 12 must be a factor of c. Incidentally, the numbers 2, 3, and 6 must also be factors of c since each is also a factor of 12.

If a, b, and c are even integers and 3a^2 + 9b^3 = c, which of these is the largest number which must be a factor of c? A. 2 B. 3 C. 6 D. 12

A. pi/4 Let r represent dthe radius of the circle. The length of each side of the square, then, is 2r. The area of the circle is pi r^2 and the area of the square is 2rx2r = 4r^2. The probability of a point randomly chosen inside the sqare also being inside the circle is represented by the ratio of the area of circle to the area of the square, pi r^2 / 4r^2 = pi/4

The figure above shows a circle inscribed in a square. What is the probability that a point chosen at random inside the square will also be inside of the circle? A. pi/4 B. 1/pi C. pi/6 D. 2/pi

D. 7 1/3 The graph increases linearly such that for the point (4,3), the value of y/x = 3/4. When y = 5 1/2, then (5 1/2)/x = 3/4 and x = (4x5 1/2)/3 = (4 x 11/2)/3 = 22/3 = 7 1/3.

The graph above represents a proportional relationship between two variables. What is the value of x when y = 5 1/2? A. 3 3/4 B. 4 1/2 C. 6 2/5 D. 7 1/3

B. 2 gallons If g = the number of gallons of water, then 3 1/3 gallons of water divided by 50 pounds of concrete = g divided by 30 pounds of concrete and g = (3 1/3 x 30)/50 = (10/3 x 30)/50 = 100/50 = 2 gallons of water.

The instructions to make a mixture of concrete specify to mix 50 pounds of cement with 3 1/3 gallons of water. If only 30 pounds of cement are used, how much water should be used in the mixture? A. 1 4/5 gallons B. 2 gallons C. 2 1/5 gallons D. 5 1/9 gallons

A. Explain why the sequence will continue to alternate between even and odd numbers. A fourth-grade student who has a strong understanding of generating and analyzing patterns will not only be able to find subsequent terms in the sequence, but will also be able to identify features of the pattern that are not explicit in the rule itself. For example, with the sequence provided, the student should not only recognize the rule is to add 5, but should also be able to explain features such as why the numbers will continue to alternate between even and odd.

Use the sequence below to answer the question that follows. 1, 6, 11, 16, 21, . . . A fourth-grade student is presented with the pattern shown in the sequence of numbers above. Which of the following tasks would be the most appropriate and informative for assessing the student's ability to generate and analyze patterns? A. Explain why the sequence will continue to alternate between even and odd numbers. B. Write an explicit equation to describe the sequence. Identify the common factors shared by the terms in the sequence. D. Find the next four terms in the sequence.

C. using the points (-3, 1) and (1, -11), the slope may be written as m = -11-1 / 1 - (-3) or m = -3. Substituting the slop of -3 and the x- and y-values from the point (-3, 1), into the slope-intercept form of an equation gives 1 = -3(-3) + b, which simplifies to 1 = 9+b. Subtracting 9 from both sides of the equation gives b = -8. Thus, the linear equation that includes the data in the table is y = -3x - 8.

What linear equation includes the data in the table below? X: -3, 1, 3, 5, 9 Y: 1, -11, -17, -23, -35 A. y = -3x - 11 B. y = -6x - 8 C. y = -3x -8 D. y = -12x - 11

A. {-2, -1, 0, 1, 2} The additive inverse of any number (n) is the number that, when added to n, yields zero. the set {-2, -1, 0, 1, 2} is the only set in which all values have an additive inverse: -2+2 = 0, -1+1 = 0, and 0+0 = 0.

Which of the following sets contains an additive inverse for every element that is in the set? A. {-2, -1, 0, 1, 2} B. {1/5, 1/3, 0, 1, 3, 5} C. {1/4, 1/2, 0, 1, 2, 4} D. {-5, -3, 0, 1, 3, 5}

The original triangle was reflected across the x-axis. When reflecting across the x-axis, the x-values of each point remain the same, but the y-values of the points will be opposites. (1,4) to (1,-4) and (5,4) to (5,-4) and (3,8) to (3,-8).

Which of the following transformations has been applied to triangle abc? A. translation B. rotation of 90 degrees C. reflection D. dilation

D. There are 70 students to be seated at tables with 6 chairs each. What is the fewest number of students that will be left standing? To find the number of tables of 6 that would be filled by 70 students, divide 70 by 6. In this problem, the quotient is 11, which means that 11 tables can be filled completely with 6 students each, and the remainder is 4, which means that 4 students will be left standing. This is the best example provided for modeling division with a remainder.

Which of the following word problems is most appropriate for modeling the operation of division with a remainder? A. A waiter collects all of the tips for the day and gives 40% to the cook, keeping the remaining $54. What was the total amount of money in tips collected by the waiter that day? B. How many 3/8 inch segments can be cut from a string that is 7 1/2 inches long? C. A gardener cultivates 3/5 of an acre of land. If the gardener plants chili peppers on 1/3 of the cultivated land, on how many acres does the gardener grow chili peppers? D. There are 70 students to be seated at tables with 6 chairs each. What is the fewest number of students that will be left standing?

D. The point (5, -5) lies on the line which has a slope of -2 and which passes through (3, -1). If (5, -5) is one of the endpoints of the line, the other would be (1, 3).

If the midpoint of a line segment graphed on the xy-coordinate plane is (3,-1) and the slope of the line segment is -2, which of these is a possible endpoint of the line segment? A. (-1,1) B. (0,-5) C. (7,1) D. (5,-5)

C. The slope of a line can be found from any two points by the formula slops = y2 - y1 / x2 - x1. A sketch of the point in choice C reveals a line with a negative slope. Substituting the last two points into the formula yields slope = -3 - 1 / 0 - (-6) which reduces to -4/6 or -2/3. The points in choice A form a line with a positive slope. The points in choice B form a line with a negative slope of -3/2. The points in choice D form a horizontal line. Therefore, the correct choice is C.

Mr. Amad draws a line with a slope of -2/3 on the white board through three points. Which of the sets could possibly be these three points? A. (-6,-2) (-7,-4) (-8,-6) B. (-4,7) (-8,13) (-6,10) C. (-3,-1) (-6,1) (0,-3) D. (-2,-3) (-1,-3) (0,-3)

D. 9pi - 18 square inches Since angle LMN is a right angle and its measure is 90 degrees, the circle sector intercepted by angle LMN is 90 degrees / 360 degrees = 1/4 of the circle. Therefore, the area of the shaded region is composed of the area of the entire circle, given by pi r^2, minus 3/4 the area of the circle, minus the area of right triangle LMN. Thus, for radius r equals 6, the area of the shaded region equals pi 6^2 - 3/4 pi 6^2 - 1/2 (6)(6) = 36 pi - 27 pi - 18 = 9pi - 18 square inches.

The center of the circle is point M and its radius is 6 inches. If angle LMN is a right angle, which of the following expressions represents the area of the shaded region? A. 36-6pi square inches B. 36pi - 18 square inches C. 12 - pi square inches D. 9pi - 18 square inches

D. The area of the square is equal to (30)^2, or 900 square centimeters. The area of the circle is equal to π(15)^2, or approximately 707 square centimeters. The area of the shaded region is equal to the difference of the area of the square and the area of the circle, or 900 cm^2 - 707 cm^2, which equals 193 cm^2. So, the area of the shaded region is about 193 cm^2.

What is the area of the shaded region in the figure shown below? A. 177 cm^2 B. 181 cm^2 C. 187 cm^2 D. 193 cm^2

D. encouraging students to decompose one of the numbers so that it can make a ten with the other number Standard 1.CA.1 of the Indiana Academic Standards for Mathematics specifies that grade 1 students "demonstrate fluency with addition facts and corresponding subtraction facts within 20" and be able to use various strategies to solve addition and subtraction problems within 20. For example, 8+6 can be decomposed into 8+2+4 so that a ten can be made; the problem is then solved as 10+4 = 14.

Which of the following strategies would be most appropriate for helping first-grade students develop skill in adding two numbers within 20? A. showing students how to regroup using the standard addition algorithm B. leading students to discover the relationship between addition and multiplication C. helping students recognize that a digit in the tens place is ten times a digit in the ones place D. encouraging students to decompose one of the numbers so that it can make a ten with the other number

B. A cube has six square faces. The arrangement of these faces in a two-dimensional figure is a net of a cube if the figure can be folded to form a cube. Figures A, C, and D represent three of the eleven possible nets of a cube. If choice B is folded, however, the bottom square in the second column will overlap the fourth square in the top row, so the figure does not represent a net of a cube.

Which of these is NOT a net of a cube?

D. Number lines can help students understand the concepts of positive and negative numbers. Fraction strips are most commonly used with fractions. Venn diagrams are commonly used when comparing groups. Shaded regions are commonly used with fractions or percentages. Therefore, the correct choice is D.

A 6th grade math teacher is introducing the concept of positive and negative numbers to a group of students. Which of the following models would be the most effective when introducing this concept? A. Fraction strips B. Venn diagrams C. Shaded regions D. Number lines

A. 1/3 There are 10 marbles initially, 4 blue and 6 red. The probability of the first draw producing a red marble is therefore 6/10. If a red marble is drawn, there will be 4 blue and 5 red marbles remaining, for a total of 9 marbles remaining. The probability of the second draw producing a red marble is 5/9. Thus the probability of both dependent events occurring is 6/10 x 5/9 = 30/90 = 1/3.

A bag contains 4 blue marbles and 6 red marbles. If two marbles are drawn from the bag without replacement, what is the probability that both of the marbles drawn will be red? A. 1/3 B. 2/5 C. 1/2 D. 3/5

D. 2 (v-5) If the bicyclist's original speed, v, were decreased by 5 miles per hour. the resulting speed could be written as the expression (v-5). If this speed is half the speed of the car, and the speed of the car is represented by c, then (v-5) = 1/2c and c = 2 (v-5).

A bicyclist is traveling at a speed of v miles per hour. If she decreases her speed by 5 miles per hour, she will be traveling at half the speed of a driver of a car. Which of the following expressions represents the driver's speed in miles per hour? A. 1/2 v + 5 B. 1/2 (v+5) C. 2v - 5 D. 2 (v-5)

C. 16 gallons According to the scale provided on the map, two grid units = 1/2 inch = 50 miles. The route shown on the map is approximately 9 segments of 1/2 inch each, so the trip distance can be estimated as 9 segments x 50 miles per segment = 450 miles. Since the fuel consumption is defined as 29 miles per gallon, the fuel consumption for the trip would be 450 miles / 29 miles per gallon = 15.5, or about 16 gallons.

A car travels from city A to city B along the route shown. If the car's average fuel usage is 29 miles per gallon, which of the following is the best estimate of the fuel usage for the entire trip? A. 5 gallons B. 9 gallons C. 16 gallons D. 21 gallons

D. When the dress is marked down by 20%, the cost of the dress is 80% of its original price; thus, the reduced price of the dress van be written as 80/100 (x) or 4/5 (x), where x is the original price. When discounted an extra 25%, the dress costs 75% of the reduced price or 75/100(4/5x), or 3/4(4/5x), which simplifies to 3/5x. So the final price of the dress is three-fifths of the original price.

A dress is marked down by 20% and placed on a clearance rack, on which is a posted sign reading, "Take an extra 25% off already reduced merchandise." What fraction of the original price is the final sales price of the dress? A. 9/20 B. 11/20 C. 2/5 D. 3/5

A. Students write an equation to describe a situation and reflect on the results in the context of the situation. Standard 5.AT.1 specifies that students "solve real-world problems involving multiplication and division of whole numbers (eg. by using equations to represent the problem)."

A fifth-grade teacher wants students to model with mathematics, as defined by the Indiana Academic Standards for Mathematics. Which of the following activities best illustrates modeling with mathematics? A. Students write an equation to describe a situation and reflect on the results in the context of the situation. B. Students strategically select and use tools to measure or draw an object or figure. C. Students use mathematical language, diagrams, and other visuals to explain or represent an algorithm. D. Students identify rotational and line-symmetric figures and draw lines of symmetry.

B. The manufacturer wishes to minimize the surface area A of the can while keepings its volume V fixed at 0.5 L = 500 mL = 500 cm^3. The formula for the surface area of a cylinder is A = 2πrh + 2πr^2, and the formula for volume is V = πr^2h and substitute the resulting expression into the surface area formula for r and h. The volume of the cylinder is 500 cm^3, so 500 = πr^2h and h = 500/πr^2. Therefore, A = 2πrh + 2πr(500/πr^2) + 2πr^2 = 1000/r + 2πr^2. Find the critical point(s) by setting the first derivative equal to zero and solving for r. Note that r represents the radius of the can and must therefore be a positive number. A = 1000r^-1 + 2πr^2 A' = -1000r^-2 + 4πr 0 = -1000/r^2 + 4πr 1000/r^2 = 4πr 1000 = 4πr^3 3^√1000/4π = r = 4.3 cm So when r = 4.3 cm, the minimum surface area is obtained. When the radius of the can is 4.3 cm, its height is h = 500/π(4.3)^2 = 8.6 cm, and surface area is approximately 1000/4.3 + 2π(4.3)^2 = 348.73 cm^2. Confirm that the surgace area is greater when the radius is slightly smaller or larger than 4.3 cm. For instance, when r = 4 cm, the surface area is approximately 350.5 cm^2, and when r = 4.5 cm, the surface area is approximately 349.5 cm^2.

A manufacturer wishes to produce a cylindrical can which can hold up to 0.5 L of liquid. To the nearest tenth, what is the radius of the can which requires the least amount of material to make? A. 2.8 cm B. 4.3 cm C. 5.0 cm D. 9.2 cm

A. 540 miles per hour Convert the flight time of 1 hour and 18 minutes into hours. Since there are 60 minutes in an hour, 18 minutes is 18/60 = 3/10 = 0.3 hours. The total flight time, then, is 1 + 0.3 = 1.3 hours. Average speed is distance divided by time (s = d/t), so the average speed of the plane is 702 miles / 1.3 hours = 540 miles per hour.

A plane travels between two cities in 1 hour and 18 minutes. If the distance of the flight is 702 miles, what is the average speed of the plane in miles per hour? A. 540 miles per hour B. 581 miles per hour C. 595 miles per hour D. 603 miles per hour

B. distributive property The distributive property is defined as a(b+c) = ab + ac. Starting with 25-(3+11), rewrite the expression as 25-1(3+11). By calculating 25-1(3+11) = 25+(-1x3)+(-1x11) = 25-3-11, the student has correctly applied the distributive property.

A student rewrites the expression 25 - (3 + 11) as 25 - 3 - 11. Which of the following number properties did the student use? A. associative property B. distributive property C. multiplicative inverse D. additive inverse

B. The student finds the area of a rectangle using unit squares and explains why it is the same as the product of the side lengths. Students should understand area as the sum of unit squares, and also as the product of side lengths. By showing that these methods give the same area, students connect area found by addition to area found by multiplication.

A third-grade teacher would like to design an assessment to measure student understanding of the following learning standard: Understand concepts of area and relate area to multiplication and to addition. Which of the following activities is most appropriate for assessing a third-grade student's mastery of the standard above? A. The student explains why the area of a square is the same as its side length squared and how this relates to the diagonal of the square. B. The student finds the area of a rectangle using unit squares and explains why it is the same as the product of the side lengths. C. The student verifies the formula for the area of a right triangle by showing that it has half the area of a rectangle. D. The student represents lengths on a number line and explains how multiplication is related to making copies of the lengths.

D. 36 The perimeter of a triangle is the sum of the lengths of the sides. In the triangle described, one leg is parallel to the x-axis and one leg is parallel to the y-axis. The lengths of these two legs of the triangle can be found by using the coordinates of the vertices: 5-(-7) = 12 and 8-(-1) = 9. Since the vertices given create a right triangle, the length of the hypotenuse can be found using the Pythagorean theorem c^2 = 12^2 + 9^2 = 144 + 81 = 225 and c = Square Root of 225 = 15. The perimeter is the sum of the side lengths, 12+9+15 = 36.

A triangle has vertices located at (5,8), (-7, 8), and (5, -1) on a coordinate plane. What is the perimeter of the triangle? A. 16 B. 18 C. 28 D. 36

A. 2 1/3 hours Average speed is distance divided by time ( s = d/t), so the average speed of the truck is 140 miles / 7/2 hours = 40 miles per hour. The car is traveling at an average speed of 20 miles per hour faster than the truck or at (40 + 20) miles per hour = 60 miles per hour. The time it will take the car to travel 140 miles is found by dividing the distance traveled by the average speed: t = d/s = 140 miles / 60 miles per hour= 7/3 hours = 2 1/3 hours.

A truck was driven 140 miles in 3 1/2 hours. if a car is driven at the same distance at an average speed of 20 miles per hour faster than the truck's average speed, how long will it take the car? A. 2 1/3 hours B. 2 3/8 hours C. 2 2/3 hours D. 2 7/8 hours

D. developing an understanding of fraction equivalents These standards identify the following strands on which instructional time in grade 4 should focus: 1) number sense, 2) computation, 3) algebraic thinking, 4) geometry, 5) measurement, and 6) data analysis. Response D is an important skill included in the number sense strand.

According to the Indiana Academic Standards for Mathematics, instructional time in a fourth-grade class should focus on which of the following critical skills? A. drawing three-dimensional figures B. using comparative language and order relationships C. applying proportional reasoning D. developing an understanding of fraction equivalence

A. To convert a percent to a fraction, remove the percent sign and place the number over 100. That means 15% can be written as 15/100, which reduces to 3/20. To convert a percent to a decimal, remove the percent sign and move the decimal two places to the left. To convert a percent to a ratio, first write the ratio as a fraction, and the rewrite the fraction as a ratio. Therefore, the correct choice is A.

Elementary teachers in one school surveyed their students and discovered that 15% of their students have iPhones. Which of the following correctly states 15% in fraction, decimal, and ratio equivalents? A. 3/20, 0.15, 3:20 B. 3/25, 0.15, 3:25 C. 15/10, 1.5%, 15:10 D. 2/1, 1.5%, 2:1

C. The surface area of a sphere may be calculated using the formula SA = 4πr^2. Substituting 9 for r gives SA = 4π(9)^2, which simplifies to SA = 1017.36. So the surface area of the ball is approximately 1017.36 square inches. There are twelve inches in a foot so there are 12^2 = 144 square inches in a square foot. In order to convert this measurement to square feet, then, the following proportion may be written and solved for x: 1/144 = x/1017.36. So x = 7.07. He needs approximately 7.07 square feet of wrapping paper.

Eric has a beach ball with a radius of 9 inches. He is planning to wrap the ball with wrapping paper. Which of the following is the best estimate for the number of square feet of wrapping paper he will need? A. 4.08 B 5.12 C. 7.07 D. 8.14

C. To find the probability of an event, divide the number of favorable outcomes by the total number of outcomes. When there are two events in which the first depends on the second, multiply the first ratio by the second ratio. IN the first part of the problem, the probability of choosing a licorice jelly bean is two out of twenty possible outcomes, or 2/20. Then, because one jelly bean has already been chosen, there are four cinnamon beans out of a total of 19, or 4/19. By multiplying the two ratios and dividing by a common denominator, one arrives at the final probability of 2/95.

In a pack of 20 jelly beans, there are two licorice- and four cinnamon-flavored jelly beans. What is the probability of choosing a licorice jelly bean followed by a cinnamon jelly bean? A. 2/5 B. 8/20 C. 2/95 D. 1/50

D. foster the development of reasoning, argumentation, and representation. The Indiana Process Standards for Mathematics and the NCTM process standards emphasize the importance of developing mathematical reasoning, argumentation, and representation in students.

In alignment with the Process Standards for Mathematics of the Indiana Academic Standards and the NCTM Standards for Mathematics, elementary mathematics activities should: A. encourage the use of shortcuts and mnemonic devices to improve fluency. B. contribute to a portfolio that students assemble to demonstrate their progress. C. incorporate a wide variety of technology to meet the needs of diverse learners. D. foster the development of reasoning, argumentation, and representation.

B. The probability may be written as P(E and H) = P(E) x P(H). Substituting the probability of each even gives (E and H) = 1/2 x 1/2, which simplifies to 1/4.

Kayla rolls a die and tosses a coin. What is the probability she gets an even number and heads? A. 1/6 B. 1/4 C. 1/3 D. 1

A. 40 degrees When transversal lines (lines AB and AC in the diagram) cross a pair of parallel lines (here lines m and n), congruent corresponding angles are formed. Thus, alternate interior angles ABC and BAD are congruent, and since angle BAD is a vertical angle to angle 1, angle ABC is also congruent to angle 1. Since the measure of angle ABC is given as 40 degrees, the measure of angle 1 is 40 degrees.

Line m is parallel to line n. If m angle ABC = 40 degrees, what is m angle 1? A. 40 degrees B. 45 degrees C. 50 degrees D. 60 degrees

B. This is a formative assessment because she is assessing students while she is still teaching the unit. Summative assessments are given at the end of the unit. Formal assessments are usually a quiz or test. Informal assessments include asking individual students questions. Therefore, the correct choice is B.

Mrs. Miller is teaching a unit on number and operations with her 5th grade class. At the beginning of class, she asks the students to work in groups to sketch a Venn diagram to classify whole numbers, integers, and rational numbers on a white board. Which of the following types of assessments has the teacher used? A. Summative assessment B. Formative assessment C. Formal assessment D. Informal Assessment

C. The number 589 can be estimated to be 600. The number 9 can be estimated to be 10. The number of chicken nuggets is approximately 600x10, which is 6,000 nuggets. Therefore, the correct choice is C.

Mrs. Vories, a 5th grade teacher, asks her class to use compatible numbers to help her determine approximately how many chicken nuggets she needs to buy for a school-wide party. The school has 589 students and each student will be served nine nuggets. Which student correctly applied the concept of compatible numbers? A. Madison estimates: 500 x 10 = 5,000 nuggets B. Audrey estimates: 600 x 5 = 3,000 nuggets C. Ian estimates: 600 x 10 = 6,000 nuggets D. Andrew estimates: 500 x 5 = 2,500 nuggets

B. Sophia needs to find multiples of 3 (3, 6, 9, 12, 15 . . .) and multiples of 4 (4, 8, 12, 16 . . .) and find the least common multiple between them, which is 12. The greatest common divisor of 3 and 4 is 1. The least common divisor between two numbers is always 1. The greatest common multiple can never be determined. Therefore, the correct choice is B.

Sophia is at the market buying fruit for her family of four. Kiwi fruit is only sold in packages of three. If Sophia would like each family member to have the same number of kiwi fruits, which of the following approaches can Sophia use to determine the fewest number of kiwi fruits she should buy? A. Sophia needs to determine the greatest common multiple of 3 and 4. B. Sophia needs to determine the least common multiple of 3 and 4. C. Sophia needs to determine the least common divisor of 3 and 4. D. Sophia needs to determine the greatest common divisor of 3 and 4.

A. using a visual fraction model to arrive at and justify conclusions Standard 3.NS.7 of the Indiana Academic Standards for Mathematics states that students should be able to "explain why fractions are equivalent (eg. by using a visual fraction model)." Using visual models to compare fractions that have the same numerator but different denominators (eg 2/5 and 2/3) helps students develop a deep understanding of the structure of fractions and how changing the denominator of a fraction affects the value of the fraction.

Students in a third-grade class are comparing pairs of fractions that have the same numerators but different denominators. Which of the following activities is most likely to promote understanding of this concept? A. using a visual fraction model to arrive at and justify conclusions B. finding the decimal equivalent of each fraction for comparison C. converting between proper and improper fractions D. finding a common denominator for the fraction pairs

B. 11 5/12 years The sector representing 10-year-olds is 120/360 = 1/3 of the circle. The sector representing 11-year-olds is 60/360 = 1/6 of the circle. The remaining 180 degrees is divided evenly between 12-year-olds and 13-year-olds, 90 degrees each, meaning those sectors are each 90/360 = 1/4 of the circle. The mean age can be 1/3(10) + 1/6(11) + 1/4(12) + 1/4(13) = 10/3 + 11/6 + 12/4 + 13/4 = (40+22+36+39)/12 = 11 5/12.

The circle graph shows the ages of players on a soccer team. The central angle of the sector representing 10-year-olds is 120 degrees and the central angle of the sector representing 11-year-olds is 60 degrees. If there are an equal number of 12-year-olds and 13-year-olds on the team, what is the mean age of the players on the soccer team? A. 11 1/3 years B. 11 5/12 years C. 11 1/2 years D. 12 1/4 years

C. (76-64.60) / 76 x 100 Using the percent proportion relationship, A/B = P/100, for A = part and B = whole and P = percent, then A = the discount amount of $76 - $64.60 and B = the original price of $76 and P = the percent discount. Therefore, (76-64.60) / 76 = P/100 and P = (76 - 64.60) / 76 x 100.

The original price of a jacket is $76. The jacket is put on sale for $64.60. Which of the following expressions could be used to determine the percent discount applied to the original price? A. 64.60/76 x 100 B. (76-64.60) / 76 x 100 C. 76/64.60 x 100 D. (76-64.60) / 64.60 x 100

C. 3% A percent is a fraction with a denominator of 100 (per one hundred). The fraction of Earth's distance from the sun to Neptune's distance from the sun is represented by: Earth's distance from sun / Neptune's distance from sun = 1.5 x 10^8 / 4.5 x 10^9 = 1.5/4.5 x 10^8/10^9. Simplifying both of the fractions yields 1.5/4.5 = 1/3 and 10^8/10^9 = 1/10. Thus, 1.5 x 10^8 / 4.5 x 10^9 = 1/3 x 1/10 = 1/30 = 0.03, which is approximately 3%.

Use the attached image to answer the question. The distance of Earth from the sun is approximately what percentage of the distance of Neptune from the sun? A. 0.03% B. 0.3% C. 3% D. 30%

D. 9.5 - 1.5n Each successibe output of this linear function can be found by subtracting 1.5 from the previous value. It can be said that the output of the function is decreasing at a constant linear rate, or slope, of -1.5. Recall that when the input is 1, the output is 8, or 9.5 - 1.5 x 1. When the input is 2, the output is 6.5, or 9.5 - 1.5 x 2. If follows that when the input of the function is n, the output must be 9.5 - 1.5n.

Use the table below to answer the question that follows (I could not include a table, but listed the information relative to its' place in the table). Input, Output 1, 8 2, 6.5 3, 5 4, 3.5 ..., ... n, The table gives several values of a linear function. Which of the following expressions represents the output of the function if the input is n? A. 1.5n + 8 B. 9.5n - 1.5 C. 1.5(n+8) D. 9.5 - 1.5n

C. The student makes a drawing to show that equal shares of identical wholes do not always have the same shape. Reasoning involves analyzing a situation and deducing properties and characteristics. A student who shows that identical wholes can be cut in more than one way to produce the same fraction of the whole is using mathematical reasoning.

Which of the following activities performed by a second-grade student best demonstrates that the student is using mathematical reasoning? A. The student measures the length of an object by selecting and using an appropriate measurement tool. B. The student uses a vertical subtraction method that requires borrowing. C. The student makes a drawing to show that equal shares of identical wholes do not always have the same shape. D. The student reads the time on an analog clock and writes it in the digital form.

B. Students model add-to, take-from, and take-apart situations using cubes connected to form lengths. The National Research Council identifies one strand of proficiency in mathematics as strategic competence, which refers to the ability to formulate mathematical problems, represent them, and solve them. Students who are modeling add-to, take-from, and other situations using connected cubes are developing their ability to generate mathematical representations, an important facet of strategic competence.

Which of the following activities would be best to foster strategic competence in the first-grade students? A. Students practice addition and subtraction facts within 20 to improve fluency. B. Students model add-to, take-from, and take-apart situations using cubes connected to form lengths. C. Students skip-count up or down by tens from any number less than 120. D. Students measure the lengths of various objects using rulers and observe the relationship between inches and feet.

C. explaining why a procedure for multiplication works using place value and properties of operations Mathematical communication requires the use of precise language to explain and justify mathematical ideas. By reflecting on and precisely communicating a justification for a procedure, a student who builds a viable argument based on previously established results (ie. the concept of place value) can gain deeper understanding of mathematical concepts and skills.

Which of the following activities would be most appropriate to foster a fourth-grade student's skills in using mathematical language to communicate relationships and concepts? A. making a word problem for a classmate to solve that involves an application of the order of operations B. using flash cards to learn mathematical vocabulary and practice for a quiz C. explaining why a procedure for multiplication works using place value and properties of operations D. reading and writing whole numbers up to one million in words and in number form

A. Students justify the formula for the area of a parallelogram by decomposing quadrilaterals and rearranging the resulting shapes. A mathematical proof involves using reasoning to build a viable argument. The area formula for a parallelogram is the same as the formula for a rectangle. This can be justified by decomposing a parallelogram into composite shapes and rearranging the shapes into a rectangle, which shows why the two formulas are equivalent.

Which of the following descriptions best demonstrates sixth-grade students engaging in the process of mathematical proof? A. Students justify the formula for the area of a parallelogram by decomposing quadrilaterals and rearranging the resulting shapes. B. Students compare two different multiplication algorithms and discuss which one is faster and more easy to use. C. Students substitute values into a function and graph the resulting ordered pair of numbers in the coordinate plant. D. Students classify two-dimensional figures into subsets involving regular, concave, and convex polygons.

A. Choice A is correct because standards for fourth grade state that students will be able to use a protractor to determine the approximate measures of angles in degrees to the nearest whole number. Choices B, C, and D are stated in the standards for fifth grade. Therefore, the correct choice is A.

Which of the following learning goals is most appropriate for a fourth grade unit on geometry and measurement? A. The students will be able to use a protractor to determine the approximate measures of angles in degrees to the nearest whole number. B. The students will be able to describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane. C. The students will be able to determine the volume of a rectangular prism with whole number side lengths in problems related to the number of layers times the number of unit cubes in the area of the base. D. The students will be able to classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties.

C. An inverse proportional relationship is written in the form y = k/x, thus the equation y = 3/x shows that y is inversely proportional to x.

Which of the following represents an inverse proportional relationship? A. y = 3x B. y = 1/3(x) C. y = 3/x D. y = 3x^2

A. If a number is divisible by 2 and 3, it is also divisible by the lowest common multiple of these two factors. The lowest common multiple of 2 and 3 is their product, 6.

Which of the following statements is true? A. A number is divisible by 6 if the number is divisible by both 2 and 3. B. A number is divisible by 4 if the sum of all digits is divisible by 8. C. A number is divisible by 3 if the last digit is divisible by 3. D. A number is divisible by 7 if the sum of the last two digits is divisible by 7.

C. When rolling two dice, there is only one way to roll a sum of two (rolling a 1 on each die) and twelve (rolling 6 on each die). In contrast, there are two ways to obtain a sum of three (rolling a 2 and 1 or a 1 and 2) and eleven (rolling a 5 and 6 or a 6 and 5), three ways to obtain a sum or four (1 and 3; 2 and 2; 3 and 1) or ten (4 and 6; 5 and 5; 6 and 4), and so on. Since the probability of obtaining each sum is inconsistent, choice C is not an appropriate simulation. Choice A is acceptable since the provability of picking A, 1, 2, 3, 4, 5, 6, 7, 8, 9, or J from the modified deck of cards is equally likely, each with a probability of 4/52-8 = 4/44 = 1/11. Choice B is also acceptable since the computer randomly generates one number from eleven possible numbers, so the probability of generating any of the numbers is 1/11.

Which of these does NOT simulate randomly selecting a student from a group of 11 students? A. Assigning each student a unique card value of A, 2, 3, 4, 5, 6, 7, 8, 9, or J, removing queens and kings from a standard deck of 52 cards, shuffling the remaining cards, and drawing a single card from the deck B. Assigning each student a unique number 0-10 and using a computer to randomly generate a number within that range C. Assigning each student a unique number from 2 to 12; rolling two dice and finding the sum of the numbers on the dice D. All of these can be used as a simulation of the event.