Mathematics with Applications and Mylab Math with Pearson EText -- Title-Specific Access Card Package
12th Edition
ISBN: 9780134862668
Author: Lial, Margaret L.
Publisher: Pearson Education Canada
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Chapter 8.4, Problem 31E
To determine
To calculate: The odds of the event that bachelor’s degree recipient is in Business discipline.
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- - Prove that if (n − 1)! + 1 is divisible by n (> 1), then n must be prime.arrow_forwardChrom ESS $425 5. Ar Dive for x 21) Name 1. Classify the triangles based on their side lengths and angle measures. 89° 30° Acute Scalene Right Scalene 130° Date A +100 Obtuse Equiangular Isosceles Equilateral What additional information would you need to prove these triangles congruent by ASA? If marrow_forwardFrom the differential equation y′ = x + sin(y):a) A solution curve passes through the point (1, π/2). What is its slope at that point?b) Justify why for x > 1 the solutions are increasing.c) Show that the concavity of each solution has the function 1 + x cos(y) + 1/2 sin(2y).Justify each of the steps.d) A solution curve passes through the point (0, 0). Show that the curve has a minimumrelative at (0, 0).arrow_forwardQ/Discuss the stability critical point of the ODES X00+6x-x2 + 4X = 0 and draw the phase portrait-arrow_forward9. Needing a break from studying, you take a walk to the Pogonip koi pond, whereupon a wild-eyed stranger pops out from behind a redwood tree and directs the following polemic in your general direction: "The lies those so-called teachers at that university promulgate, let me tell you. I know the truth that they don't want you to know. As plain as day, " = 0 for all n ≥0. It's an easy induction proof, see?" He hands you a leaflet, where you see the proof that they don't want you to see: We proceed by strong induction on n. Base case: n = 0. We have 10: Induction step: Assume that d1 = = = 0. dx dxk dx = 0 for all kn. Then, by the product rule, nd dx da 1x+1 = 1/1(x²x²) = x²±²x² + x 11 x² d = x.0+x¹.0 0. dx This completes the induction. That derivative rule doesn't seem like the one you learned, but there's nothing obviously wrong with the proof. Is he right, are the math professors propping up the interests of Big Calculus? Or should he have paid better attention in CSE 16? What's going…arrow_forwardApply Euler's method on the next differential equation with the initial initial value and in the given interval. You must include: a) table and b) graph.\\\[\frac{d y}{d x}=y^{2}-4 x, \quad y(0)=0.5 ; \quad 0 \leq x \leq 2, \quad \Delta x=0.25\]arrow_forward7. Define the sequence {b} by bo = 0 Ել ։ = 2 8. bn=4bn-1-4bn-2 for n ≥ 2 (a) Give the first five terms of this sequence. (b) Prove: For all n = N, bn = 2nn. Let a Rsuch that a 1, and let nЄ N. We're going to derive a formula for Σoa without needing to prove it by induction. Tip: it can be helpful to use C1+C2+...+Cn notation instead of summation notation when working this out on scratch paper. (a) Take a a² and manipulate it until it is in the form Σ.a. i=0 (b) Using this, calculate the difference between a Σ0 a² and Σ0 a², simplifying away the summation notation. i=0 (c) Now that you know what (a – 1) Σ0 a² equals, divide both sides by a − 1 to derive the formula for a². (d) (Optional, just for induction practice) Prove this formula using induction.arrow_forward3. Let A, B, and C be sets and let f: A B and g BC be functions. For each of the following, draw arrow diagrams that illustrate the situation, and then prove the proposition. (a) If ƒ and g are injective, then go f is injective. (b) If ƒ and g are surjective, then go f is surjective. (c) If gof is injective then f is injective. Make sure your arrow diagram shows that 9 does not need to be injective! (d) If gof is surjective then g is surjective. Make sure your arrow diagram shows that f does not need to be surjective!arrow_forward4. 5. 6. Let X be a set and let f: XX be a function. We say that f is an involution if fof idx and that f is idempotent if f f = f. (a) If f is an involution, must it be invertible? Why or why not?2 (b) If f is idempotent, must it be invertible? Why or why not? (c) If f is idempotent and x E range(f), prove that f(x) = x. Prove that [log3 536] 5. You proof must be verifiable by someone who does not have access to a scientific calculator or a logarithm table (you cannot use log3 536≈ 5.7). Define the sequence {a} by a = 2-i for i≥ 1. (a) Give the first five terms of the sequence. (b) Prove that the sequence is increasing.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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