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Competency 018—The teacher understands mathematical reasoning and problem solving. Working together at their constant rates, hoses A and B can fill an empty pool in 10 hours. Which of the following statements about the mean and standard deviation of battery life for the two distributions is true? Option A is incorrect because if a is negative, then the value of a times 10 to the power of b will also be negative and thus cannot represent a distance. Options C and D are incorrect because the function must have degree at least 6. Students predict how the graph of y equals ax squared plus bx plus c will be affected by changing the value of a, and check their predictions using a graphing calculator. Option A is correct because multiplying the left side of the given matrix equation gives. Option B is incorrect because the inverse does not lie on the ray OP. The graph is a plot on an x, y plane. Option B is correct because 0 decimal 00001 equals 10 to the power of negative 5 equals 10 times 10 to the power of negative 6, k can be of the form a times 10 to the power of b for 1 is less than or equal to a is less than 10 and b is less than negative 1.
A certain roof consists of 2 rectangular sides, each having dimensions 15 feet by 60 feet. Option A is correct because one formula for the area of a triangle is A = 1 half ab sine C. (Note that b and a sine C are the lengths of the base and corresponding altitude. ) The number of cogs that will fit around the wheel with spaces in between is 9 times pi over pi over 4 = 36 cogs. A researcher measured the length of an object to be k centimeters, where k is less than 0 decimal 0 0 0 0 1. Option D is correct because the terms of the sequence described are the consecutive integers starting at negative 13, the first 27 terms of the sequence, from negative 13 to 13, have a sum of 0. Options A and B are incorrect because the only vertical asymptote of the graph occurs at x = 2. Angle ACB must be complementary to both angle D C E and angle B A C, so angle B A C is congruent to angle D C E, and triangle A B C is similar to triangle C D E by the AA similarity criterion. The battery life, in years, for each of two brands of car batteries, X and Y, is approximately normally distributed, as shown above. A line from point P to point P prime is dimensioned as perpendicular to the y axis. If a student mistakenly states that negative 1 half left paren negative 2 thirds x plus 1 half right paren equals 1 third x plus 1 half, it is most likely that the mistake results from a misunderstanding of which of the following? Option C is incorrect because the placebo effect should show an improvement in the group receiving the placebo. The length of line B D. - The area of triangle BCE.
Option A is incorrect because, by the Pythagorean theorem, the length of line BD is the square root of 2 squared plus 1 squared = the square root of 5, which is not an integer. Each cog is pi over 8 centimeters wide, and there is a space of pi over 8 centimeters between consecutive cogs. 99 and a 14 inch diameter pizza with one topping costs$12. Option D is incorrect because if m is less than 0 and b is less than 0, the line would have a negative y-intercept. Options B, C and D are incorrect because they do not describe an activity in which students explore an idea or question on their own. Let f be the function defined by f of x = negative x + 1 over x for all x ≠ 0. A student is trying to prove that the statement above is true for all integers x by proving its contrapositive. Open Science Practices. What is the level of the solution in the vat after the wheel has been immersed? Option B is correct because the fact that the graph intersects the x-axis in four places indicates that the function has 4 real zeros, and the fact that the graph has 5 local extrema indicates that the function has degree at least 6. Which of the following shows a point P and its image P prime under this transformation? Competency 005—The teacher understands attributes of functions, relations and their graphs.
8 and curves smoothly down through 5, 1, starting at about a 45° angle and ending almost horizontally. Option C is incorrect because the work does not show an error in the application of the associative property of multiplication. Assume that x is not even, and then deduce that x squared is not even. While studying, you may wish to read the competency before and after you consider each sample question. If her average speed for the entire trip was 36 miles per hour (mph), what was her average speed for the final 20 minutes of the trip? Point P lies on the semicircle at coordinates 0.
The y axis is labeled l n y and has values marked from 0 to 2 in increments of 1. Triangles ABC and CDE are right triangles, and ⊥ line A C is perpendicular to line C E. If the length of line BD is 30, what is the length of line D E? C. - d. - Option B is correct because at x = b the limit of the function exists but does not equal the value of the function. The graph of the function given is a parabola with vertex at (a, b), where 0 is less than a is less than b. The line containing the three points shown has a negative slope and a positive y-intercept, so m is less than 0 and b is greater than 0. Domain VI—Mathematical Learning, Instruction and Assessment. A rate of 5 miles in 20 minutes is equivalent to a rate of 15 miles in an hour. If the diameter of the wheel is 9 centimeters, how many cogs are on the wheel? Option D is correct because the placebo effect refers to a perceived or actual improvement by the group receiving the placebo compared to the group receiving no treatment. This gives a total distance of 36 times 5 over 6 = 30 miles. Gauth Tutor Solution. Feedback from students. The fractions of the pool that hoses A and B can each fill in 1 hour are 1 over x and 1 over 2x respectively. For these points, there is exactly one x-value for each y-value, so the function is one-to-one on this interval.
Option B is incorrect because the area of triangle BCE is 1 half bh = 1 half(3)(1) = 1 decimal 5, which is not an integer. This number is represented by the point with coordinates ( negative 1 decimal 6, negative 1 decimal 2), which can only be point C. Options A and D are incorrect because the multiplicative inverse cannot be obtained by reflecting P across the y-axis and the origin, respectively. Competency 021—The teacher understands assessment and uses a variety of formal and informal assessment techniques to monitor and guide mathematics instruction and to evaluate student progress. Option D is incorrect because the graph corresponds to the transformation of a point (x, y) to the point ( negativex, y). One point is to the left of the y axis and well above the x axis. F has 4 real zeros and degree at most 4.
Option D is correct because the contrapositive of the given statement is "If x is not even, then x squared is not even. " The bulb life, in hours, for 27 lightbulbs of the same brand is recorded below. Option C is incorrect because 24 is the length of segment line CD, not the length of segment line D E. Option D is incorrect because 32 equals A B + C D, which is much greater than the length of segment line D E. Competency 014—The teacher understands coordinate, transformational and vector geometry and their connections. Option C is incorrect because it does not describe the contrapositive. For a function to be one-to-one on an interval there must be exactly one x-value for each y-value. Competency 013—The teacher understands the results, uses and applications of Euclidian geometry. One point is below the x axis and well to the right of the y axis. Options A, B, and C are incorrect because the portion of the parabola on each of these intervals includes points on both sides of the axis of symmetry. Section 4: Sample Selected-Response Questions Mathematics 7–12 (235). Distributive property of multiplication over addition. These two functions are equivalent. The figure shows a circle that represents a wheel inscribed inside a rectangle that represents a vat of fluid. In the resulting matrix, row 1 is x prime, and row 2 is y prime. People taking the placebo report fewer headaches than people taking nothing.
The angle at the top is dimensioned as y°. If left brace a sub n right brace sup infinity sub n equals 1 is a sequence such that a sub 1 equals 1, a sub 2 equals 3, and a sub n plus 3 equals fraction a sub n plus 1 all over a sub n plus 2 for all integers n is greater than or equal to 0, what is the value of a sub 4? The function f is strictly increasing for all x is less than a and is strictly decreasing for all x is greater than b.