
Concept explainers
A company mixes different amounts of blue paint with yellow paint in a ratio of 2 to 5 to make a green paint. For each of the following fractions, interpret the fraction in two ways in terms of the company’s paint mixtures (but not as ratios). Use double or triple number lines and strip diagrams as supports.

Trending nowThis is a popular solution!
Learn your wayIncludes step-by-step video

Chapter 7 Solutions
Mathematics for Elementary Teachers with Activities (5th Edition)
Additional Math Textbook Solutions
Calculus: Early Transcendentals (2nd Edition)
College Algebra (7th Edition)
Elementary Statistics (13th Edition)
Pre-Algebra Student Edition
Thinking Mathematically (6th Edition)
- Suppose we have a linear program in standard equation form maximize c'x subject to Ax=b, x≥ 0. and suppose u, v, and w are all optimal solutions to this linear program. (a) Prove that zu+v+w is an optimal solution. (b) If you try to adapt your proof from part (a) to prove that that u+v+w is an optimal solution, say exactly which part(s) of the proof go wrong. (c) If you try to adapt your proof from part (a) to prove that u+v-w is an optimal solution, say exactly which part(s) of the proof go wrong.arrow_forward(a) For the following linear programme, sketch the feasible region and the direction of the objective function. Use you sketch to find an optimal solution to the program. State the optimal solution and give the objective value for this solution. maximize +22 subject to 1 + 2x2 ≤ 4, 1 +3x2 ≤ 12, x1, x2 ≥0 (b) For the following linear programme, sketch the feasible region and the direction of the objective function. Explain, making reference to your sketch, why this linear programme is unbounded. maximize ₁+%2 subject to -2x1 + x2 ≤ 4, x1 - 2x2 ≤4, x1 + x2 ≥ 7, x1,x20 Give any feasible solution to the linear programme for which the objective value is 40 (you do not need to justify your answer).arrow_forwardfind the domain of the function f(x)arrow_forward
- For each of the following functions, find the Taylor Series about the indicated center and also determine the interval of convergence for the series. 1. f(x) = ex-2, c = 2 Π == 2. f(x) = sin(x), c = 2arrow_forwardQUESTION 5. Show that if 0 ≤r≤n, then r+2 r r (c) + (+³) + (+³) +- + (*) -(+) n n+ = r (1)...using induction on n. (2) ...using a combinatorial proof.arrow_forwardUse a power series to approximate each of the following to within 3 decimal places: 1. arctan 2. In (1.01)arrow_forward
- For each of the following power series, find the interval of convergence and the radius of convergence: n² 1.0 (x + 1)" n=1 շո 3n 2. Σ n=1 (x-3)n n3arrow_forwardUse a known series to find a power series in x that has the given function as its sum: 1. xcos(x³) 2. In (1+x) xarrow_forwardif n is odd integer then 4 does not divide narrow_forward
- or W Annuities L Question 2, 5.3.7 > Find the future value for the ordinary annuity with the given payment and interest rate. PMT = $2,000; 1.65% compounded quarterly for 11 years. The future value of the ordinary annuity is $ (Do not round until the final answer. Then round to the nearest cent as needed.) example Get more help Q Search 30 Larrow_forwardFind the cdf of a random variable Y whose pdf is given by; 2, 0≤x≤1 1/3, 0≤x≤1 a) f(x)=3, 2≤x≤4 0, elsewhere 2, 1≤x≤2 b) f(x)= (3-x)2, 2≤x≤3 0, elsewherearrow_forwardFor all integers a and b, a + b is not ≡ 0(mod n) if and only if a is not ≡ 0(mod n)a or is not b ≡ 0(mod n). Is conjecture true or false?why?arrow_forward
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
- Intermediate AlgebraAlgebraISBN:9781285195728Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,





