Straighterline MAT201 PRECALCULUS GRADED EXAM 4 (New Version August 2024)

Question 1 Correct 6.25 points out of 6.25 Solve the problem. A vendor at a carnival sells cotton candy and caramel apples for each. The vendor is charged to set up his booth. Furthermore, the vendor’s average cost for each product he produces is approximately . a. Write a linear cost function representing the cost (in ) to produce products. b. Write a linear revenue function representing the revenue (in ) for selling products. c. Determine the number of products to be produced and sold for the vendor to break even. Select one: a. b. c. d. $2.00 $60 $0.80 C(x) $ x R(x) $ x a. C(x) = 60 b. R(x) = 1.2x c. Products = 50 a. C(x) = 0.8x + 60 b. R(x) = 2x c. Products = 75 a. C(x) = 0.8x + 60 b. R(x) = 2x c. Products = 50 a. C(x) = 60 b. R(x) = 1.2x c. Products = 75 Straighterline PRECALCULUS GRADED EXAM 4 (New Version August 2024) We are a team of experts offering course/class attendance (including final proctored exams!!) for all Straighterline, Online ATI, HESI, NCLEX, Portage Learning, Sophia, Nursing, Business etc courses. We also write essays, discussion posts, research papers and school assignments. Should you need any of these services, Contact us via email: or : +1 (540) 753-5914. Guaranteed Passing!Question 2 Correct 6.25 points out of 6.25 Graph the solution set. Select one: a. b. c. y ≤ −2x + 5 y ≥ 3 x − 2 2 8/21/24, 6:12 PM Graded Exam #4: Attempt review Correct 6.25 points out of 6.25 Question 4 Correct 6.25 points out of 6.25 d. Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. Select one: a. The equations are dependent. b. The system is inconsistent. c. d. Solve the system by the substitution method. Select one: a. b. c. d. 5x + y = −5 − 15x − 3y = 9 {(x, y) ∣ 5x + y = −5}; {}; {(1, −10)} {(0, −5)} y = x2 + 1 −4x − y = 2 {(1, 2), (−1, 2)} {(−1, 2), (−3, 10)} { } {(0, 1), (0, −2)} 8/21/24, 6:12 PM Graded Exam #4: Attempt review Incorrect 0.00 points out of 6.25 Question 6 Correct 6.25 points out of 6.25 Solve the system of equations by using the addition method. Select one: a. b. c. d. Determine the values of and that produce the maximum value of the objective function on the feasible region. Determine the maximum value of the objective function on the feasible region. Maximize: Select one: a. ; Maximum value: b. ; Maximum value: c. ; Maximum value: d. ; Maximum value: x2 − xy = −3 2x2 + 3xy = 14 { } {(−1, −4), (1, 4)} {(1, 4), (1, −4), (−1, 4), (−1, −4)} {(1, 4), (1, −4)} x y x ≥ 0, y ≥ 0 110x + 70y ≤ 8600 x + y ≤ 100 z = 35x + 30y x = 55, y = 45 3275 x = 40, y = 60 3200 x = 60, y = 40 3300 x = 45, y = 55 3225 8/21/24, 6:12 PM Graded Exam #4: Attempt review Incorrect 0.00 points out of 6.25 Question 8 Correct 6.25 points out of 6.25 Solve the system using Gaussian elimination or Gauss-Jordan elimination. Select one: a. b. c. d. Write the system of equations as a matrix equation of the form , where is the coefficient matrix, is the column matrix of variables, and is the column matrix of constants. Select one: a. b. c. d. −4x − 6y + 5z 8x + 4y − 7z 4x − 2y − 2z = 13 = −7 = −15 {(8, 5, 4)} {(5, 8, 4)} { } {(8, 4, 5)} AX = B A X B −5x − 2y 3x + 3y = −7 = 6 [ −5 3 −2 3 ] [ xy ] = [ −7 6 ] [ 5 ] [ ] = [ ] −3 2 −3 x y −7 6 [ −5 3 2 ] [ ] = [ ] −3 x y −7 6 [ −5 3 −2 3 ] [ xy ] = [ 7 ] −6 8/21/24, 6:12 PM Graded Exam #4: Attempt review Correct 6.25 points out of 6.25 Question 10 Correct 6.25 points out of 6.25 Solve the problem. A math course has exams weighted , , , and , respectively, toward the final grade. Suppose that a student earns grades of , , , and , respectively, on the four exams. The weights are given in matrix and the test grades are given in matrix . Compute and interpret the result. Select one: a. ; The value is the student's overall course grade. b. ; The value is the student's overall course grade. c. ; The value is the student's overall course grade. d. ; The value is the student's overall course grade. Using the determinant , determine if the points are collinear. , , Select one: a. Yes b. No 4 15% 10% 20% 55% W G WG Test 1 Test 2 Test 3 Test 4 W = [ 0.15 0.10 0.20 0.55] G = ⎡⎢⎢⎢⎣ 75 84 92 86 ⎤⎥⎥⎥⎦ Test 1 Test 2 Test 3 Test 4 [80.15] 80.15 [85.35] 85.35 [50.55] 50.55 [84.25] 84.25 ∣∣∣∣ x1 x2 x3 y1 y2 y3 1 1 1 ∣∣∣∣ (8, 9) (2, 2) (−4, −5) 8/21/24, 6:12 PM Graded Exam #4: Attempt review Correct 6.25 points out of 6.25 Question 12 Correct 6.25 points out of 6.25 Perform the elementary row operation on the given matrix. Select one: a. b. c. d. Determine the standard form of an equation of the parabola subject to the given conditions. Vertex: ; Directrix: Select one: a. b. c. d. R2 ⇔ R3 ⎡⎢⎢⎣ −8 −3 5 2 7 0 −9 −6 3 −4 6 6 ⎤⎥⎥⎦ ⎡⎢⎢⎣ −8 2 5 2 7 0 −9 −3 3 −4 9 6 ⎤⎥⎥⎦ ⎡⎢⎢⎣ −8 5 −3 2 0 7 −9 3 −6 −4 6 6 ⎤⎥⎥⎦ ⎡⎢⎢⎣ −3 −8 5 7 2 0 −6 −9 3 6 −4 6 ⎤⎥⎥⎦ ⎡⎢⎢⎣ −8 −3 2 2 7 7 −9 −6 −3 −4 6 9 ⎤⎥⎥⎦ (0, 0) y = −8 y2 = 32x x2 = 32y x2 = −8y y2 = −8x 8/21/24, 6:12 PM Graded Exam #4: Attempt review Correct 6.25 points out of 6.25 Question 14 Correct 6.25 points out of 6.25 Determine the standard form of an equation of the parabola subject to the given conditions. Vertex: ; Directrix: Select one: a. b. c. d. Provide the missing information. Given where , the ordered pairs representing the endpoints of the vertices are and _________. The ordered pairs representing the endpoints of the minor axis are and . Select one: a. b. c. d. (−1, −3) x = −5 (x + 1)2 = 16 (y + 3) (y + 3)2 = −5 (x + 1) (y + 3)2 = 16 (x + 1) (x + 1)2 = −5 (y + 3) + = 1 (x − h)2 a2 (y − k)2 b2 a b 0 (h + a, k) (h, k + b) (h, k − b) (h − a, k) (h − k, a) (h + a, k) (k − a, h) 8/21/24, 6:12 PM Graded Exam #4: Attempt review Correct 6.25 points out of 6.25 Question 16 Correct 6.25 points out of 6.25 Solve the problem. A homeowner wants to make an elliptical rug from a -foot by -foot rectangular piece of carpeting. a. What lengths of the major and minor axes would maximize the area of the new rug? b. Write an equation of the ellipse with maximum area. Use a coordinate system with the origin at the center of the rug and horizontal major axis. Select one: a. a. Major axis: feet. Minor axis: feet b. b. a. Major axis: feet. Minor axis: feet b. c. a. Major axis: feet. Minor axis: feet b. d. a. Major axis: feet. Minor axis: feet b. Provide the missing information. Suppose that an infinite series approaches a value as . Then the series converges. Otherwise, the series ___________. Select one: a. diverges b. stops c. breaks 30 10 30 10 x2 + = 1 900 y2 100 32 16 x2 + = 1 256 y2 64 30 10 x2 + = 1 225 y2 25 15 5 x2 + = 1 225 y2 25 a1 + a2 + a3+. . . +an L n → ∞ 8/21/24, 6:12 PM Graded Exam #4: Attempt review Correct 6.25 points out of 6.25 Question 18 Incorrect 0.00 points out of 6.25 Solve the problem. Suppose you wish to prove the statement that follows using mathematical induction. , for all positive integers . Let be the statement . Show that is true. Select one: a. Since , is true. b. Since , , is true. c. Since , is true. d. Since , is true. Find and for a geometric sequence from the given information. and Select one: a. and b. and c. and d. and 4 + 9 + 14+. . . +(5n − 1) = n (5n + 3) 2 n Sn 4 + 9 + 14+. . . +(5n − 1) = n (5n + 3) 2 S1 (5(1) − 1) = 4 S1 4 + (5(1) − 1) = 2 (4 + 5(1) − 1) 2 S1 4 + 9 = 13 = 2 (5(2) + 3) 2 S1 1 (5(1) + 3) = (8) = 4 2 1 2 S1 a1 r {an} a2 = −6 a6 = − 243 128 a1 = 8 r = − 3 4 a1 = − 32 3 r = − 3 4 a1 = 8 r = − 4 3 a1 = 8 r = 3 4 8/21/24, 6:12 PM Graded Exam #4: Attempt review Correct 6.25 points out of 6.25 Question 20 Correct 6.25 points out of 6.25 Provide the missing information. If items are arranged in order, then each arrangement is called a __________ of items. Select one: a. permutation b. copy c. polymorphism Provide the missing information. If two events and are mutually exclusive, then = _____. As a result, can be computed from the formula Select one: a. b. c. d. Quiz navigation Show one page at a time Finish review n n A B P(A ∩ B) P(A ∪ B) P(A ∪ B) = P(A) + P(B) 0 3 1 1 4 8/21/24, 6:12 PM Graded Exam #4: Attempt review 8/21/24, 6:12 PM Graded Exam #4: Attempt review