Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 6, Problem 11A
Four studs of the following lengths in inches are to be machined from bar stock:
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4. Let A {w, e, s, t, f, i, e, l, d, s, t, a, t, e}.
(a) How many different words (they do not have to make sense) can you spell with the letters in A?
(b) Is your answer from above the same as the cardinality of the powerset of A, i.e. of P(A)?
(c) What is |A|?
5. How many numbers can you make out of the digits 1, 2, 3, 4, 6 if the rule is that every digit has to be
larger than the digit preceding it? For example 124 is ok, 122 is not ok. Every digit can be used only
once, but you do not have to use every digit. A tree might help.
Can you help me with f and g?What they are asking is, what do you shade in? Not the power set. At least for F
Chapter 6 Solutions
Mathematics for Machine Technology
Ch. 6 - Express 316,74,12, and 58 as equivalent fractions...Ch. 6 - Subtract 751611332 .Ch. 6 - Multiply 218312 .Ch. 6 - Divide 764916 .Ch. 6 - Determine the length A in Figure 6-3. All...Ch. 6 - Determine the length B in Figure 6-3. All...Ch. 6 - Prob. 7ACh. 6 - Prob. 8ACh. 6 - Refer to the shaft shown in Figure 6-4. Determine...Ch. 6 - The outside diameter of an aluminum tube is...
Ch. 6 - Four studs of the following lengths in inches are...Ch. 6 - Find dimensions A, B, C, and D Of the idler...Ch. 6 - How long does it take to cut a distance of 114feet...Ch. 6 - An angle iron 4712inches long has two drilled...Ch. 6 - A tube has an inside diameter of 34inch and a wall...Ch. 6 - Two views of a mounting block are shown in Figure...Ch. 6 - The composition of an aluminum alloy by weight is...Ch. 6 - Pieces of the following lengths are cut from a...
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- 4. Assume that a risk-free money market account is added to the market described in Q3. The continuously compounded rate of return on the money market account is log (1.1). (i) For each given μ, use Lagrange multipliers to determine the proportions (as a function of μ) of wealth invested in the three assets available for the minimum variance portfolio with expected return μ. (ii) Determine the market portfolio in this market and calculate its Sharp ratio.arrow_forward3. A market consists of two risky assets with rates of return R₁ and R2 and no risk-free asset. From market data the following have been estimated: ER₁ = 0.25, ER2 = 0.05, Var R₁ = 0.01, Var R2 = 0.04 and the correlation between R1 and R2 is p = -0.75. (i) Given that an investor is targeting a total expected return of μ = 0.2. What portfolio weights should they choose to meet this goal with minimum portfolio variance? Correct all your calculations up to 4 decimal points. (ii) Determine the global minimum-variance portfolio and the expected return and variance of return of this portfolio (4 d.p.). (iii) Sketch the minimum-variance frontier in the μ-σ² plane and indicate the efficient frontier. (iv) Without further calculation, explain how the minimum variance of the investor's portfolio return will change if the two risky assets were independent.arrow_forward2. A landlord is about to write a rental contract for a tenant which lasts T months. The landlord first decides the length T > 0 (need not be an integer) of the contract, the tenant then signs it and pays an initial handling fee of £100 before moving in. The landlord collects the total amount of rent erT at the end of the contract at a continuously compounded rate r> 0, but the contract stipulates that the tenant may leave before T, in which case the landlord only collects the total rent up until the tenant's departure time 7. Assume that 7 is exponentially distributed with rate > 0, λ‡r. (i) Calculate the expected total payment EW the landlord will receive in terms of T. (ii) Assume that the landlord has logarithmic utility U(w) = log(w - 100) and decides that the rental rate r should depend on the contract length T by r(T) = λ √T 1 For each given λ, what T (as a function of X) should the landlord choose so as to maximise their expected utility? Justify your answer. Hint. It might be…arrow_forward
- Please ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.arrow_forwardConsider the proof below: Proposition: If m is an even integer, then 5m +4 is an even integer. Proof: We see that |5m+4=10n+4 = 2(5n+2). Therefore, 5m+4 is an even integer. **Note: you may assume the proof is valid, just poorly written. Based upon the Section 1.3 screencast and the reading assignment, select all writing guidelines that are missing in the proof. Proof begins by stating assumptions ✓ Proof has an invitational tone/uses collective pronouns Proof is written in complete sentences Each step is justified ☐ Proof has a clear conclusionarrow_forwardThe general solution X'=Ax is given. Discuss the nature of the solutions in a neighborhood of (0,0) -2-2 (²) |a) A = (23) X(A) = (₁ (fi)e* + (2 (2) eht -2-5arrow_forward
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