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Chapter 1 Solutions
Student Solutions Manual For Ewen's Elementary Technical Mathematics, 12th
- 1 (VaR and ES) Suppose X ~ f(x) with 1+x, if 0> x > −1 f(x) = 1−x if 1 x > 0 Find VaRo.05 (X) and ES0.05 (X).arrow_forward(^) k Recall that for numbers 0 ≤ k ≤ n the binomial coefficient (^) is defined as n! k! (n−k)! Question 1. (1) Prove the following identity: (22) + (1121) = (n+1). (2) Use the identity above to prove the binomial theorem by induction. That is, prove that for any a, b = R, n (a + b)" = Σ (^) an- n-kyk. k=0 n Recall that Σ0 x is short hand notation for the expression x0+x1+ +xn- (3) Fix x = R, x > 0. Prove Bernoulli's inequality: (1+x)" ≥1+nx, by using the binomial theorem. - Question 2. Prove that ||x| - |y|| ≤ |x − y| for any real numbers x, y. Question 3. Assume (In) nEN is a sequence which is unbounded above. That is, the set {xn|nЄN} is unbounded above. Prove that there are natural numbers N] k for all k Є N. be natural numbers (nk Є N). Prove thatarrow_forwardQuestion content area top Part 1 Find the measure of ABC for the congruent triangles ABC and Upper A prime Upper B prime Upper C primeA′B′C′. 79 degrees79° 1533 2930 Part 1 m ABCequals=enter your response heredegreesarrow_forward
- Joy is making Christmas gifts. She has 6 1/12 feet of yarn and will need 4 1/4 to complete our project. How much yarn will she have left over compute this solution in two different ways arrow_forwardSolve for X. Explain each step. 2^2x • 2^-4=8arrow_forwardFind the range and all the answers. Remark that the range isn’t between -(pi/2) and (pi/2)arrow_forward
- One hundred people were surveyed, and one question pertained to their educational background. The results of this question and their genders are given in the following table. Female (F) Male (F′) Total College degree (D) 30 20 50 No college degree (D′) 30 20 50 Total 60 40 100 If a person is selected at random from those surveyed, find the probability of each of the following events.1. The person is female or has a college degree. Answer: equation editor Equation Editor 2. The person is male or does not have a college degree. Answer: equation editor Equation Editor 3. The person is female or does not have a college degree.arrow_forwardPlease draw a detailed grapharrow_forwardFor allarrow_forward
- not use ai pleasearrow_forward3) Let G be the group generated by elements a and b satisfying the relations a² = 63, 66 = 1, and a ¹ba = b¹. Which of the following is equivalent to the element z = a a-2ba3b3? A) b-2a-1 B) ab² C) ab D) ba E) b²aarrow_forward1) Find all complex solutions to cos(z) =arrow_forward
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
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