Contemporary Mathematics for Business & Consumers
8th Edition
ISBN: 9781305886803
Author: Brechner
Publisher: Cengage
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Chapter 1.I, Problem 1RE
Read and write the following whole numbers in numerical and word form.
| Number | Numerical Form | Word Form | ||||
| 1. | 22938 | 22.938 | Twenty-two thousand, nine hundred thirty-eight | |||
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By considering appropriate series expansions,
ex · ex²/2 . ¸²³/³ . . ..
=
= 1 + x + x² +……
when |x| < 1.
By expanding each individual exponential term on the left-hand side
and multiplying out, show that the coefficient of x 19 has the form
1/19!+1/19+r/s,
where 19 does not divide s.
Let
1
1
r
1+
+ +
2 3
+
=
823
823s
Without calculating the left-hand side, prove that r = s (mod 823³).
For each real-valued nonprincipal character X mod 16, verify that
L(1,x) 0.
Chapter 1 Solutions
Contemporary Mathematics for Business & Consumers
Ch. 1.I - Read and write the following whole numbers in...Ch. 1.I - Round the following numbers to the indicated...Ch. 1.I - Read and write the following whole numbers in...Ch. 1.I - Read and write the following whole numbers in...Ch. 1.I - Read and write the following whole numbers in...Ch. 1.I - Read and write the following whole numbers in...Ch. 1.I - Read and write the following whole numbers in...Ch. 1.I - Read and write the following whole numbers in...Ch. 1.I - Write the following whole numbers in numerical...Ch. 1.I - Write the following whole numbers in numerical...
Ch. 1.I - Write the following whole numbers in numerical...Ch. 1.I - Match the following numbers in word form with the...Ch. 1.I - Match the following numbers in word form with the...Ch. 1.I - Match the following numbers in word form with the...Ch. 1.I - Match the following numbers in word form with the...Ch. 1.I - Match the following numbers in word form with the...Ch. 1.I - Round the following numbers to the indicated...Ch. 1.I - Round the following numbers to the indicated...Ch. 1.I - Round the following numbers to the indicated...Ch. 1.I - Round the following numbers to the indicated...Ch. 1.I - Round the following numbers to the indicated...Ch. 1.I - Prob. 20RECh. 1.I - Round the following numbers to the indicated...Ch. 1.I - Round the following numbers to the indicated...Ch. 1.I - 23. According to the American Wind Energy...Ch. 1.I - According to the Financial Times, in a recent...Ch. 1.II - Add the following sets of whole numbers and verify...Ch. 1.II - Prob. 4TIECh. 1.II - Prob. 1RECh. 1.II - Prob. 2RECh. 1.II - Prob. 3RECh. 1.II - Prob. 4RECh. 1.II - Prob. 5RECh. 1.II - 2,339+118+3,650+8,770+81+6=Ch. 1.II - Prob. 7RECh. 1.II - Prob. 8RECh. 1.II - Prob. 9RECh. 1.II - Estimate the following by rounding each number all...Ch. 1.II - Prob. 11RECh. 1.II - Prob. 12RECh. 1.II - Prob. 13RECh. 1.II - At Cherry Valley Farms, a farmer plants 350 acres...Ch. 1.II - Prob. 15RECh. 1.II - Prob. 16RECh. 1.II - Prob. 17RECh. 1.II - Prob. 18RECh. 1.II - Prob. 19RECh. 1.II - Prob. 20RECh. 1.II - Prob. 21RECh. 1.II - Prob. 22RECh. 1.II - Prob. 23RECh. 1.II - Subtract the following numbers.
24. Subtract 5,868...Ch. 1.II - Subtract the following numbers.
25. Subtract...Ch. 1.II - The beginning inventory of the Designer Shoe Salon...Ch. 1.II - Prob. 27RECh. 1.II - 28. Use the U.S Postal Service Mail Volume graph...Ch. 1.II - Prob. 29RECh. 1.II - An Allied Vans Lines moving truck picks up loads...Ch. 1.II - A personal balance sheet is the financial picture...Ch. 1.III - Multiply the following numbers and verify your...Ch. 1.III - Divide the following numbers and verify your...Ch. 1.III - Prob. 1RECh. 1.III - Multiply the following numbers and verify your...Ch. 1.III - Prob. 3RECh. 1.III - Prob. 4RECh. 1.III - Prob. 5RECh. 1.III - Prob. 6RECh. 1.III - Prob. 7RECh. 1.III - Prob. 8RECh. 1.III - Prob. 9RECh. 1.III - Prob. 10RECh. 1.III - Prob. 11RECh. 1.III - Dazzling Designs made custom drapery for a client...Ch. 1.III - Prob. 13RECh. 1.III - There are 34 stairs from bottom to top in each of...Ch. 1.III - Prob. 15RECh. 1.III - 16. Bob Powers, a consulting electrical engineer,...Ch. 1.III - Prob. 17RECh. 1.III - Prob. 18RECh. 1.III - Prob. 19RECh. 1.III - Prob. 20RECh. 1.III - Prob. 21RECh. 1.III - Prob. 22RECh. 1.III - Prob. 23RECh. 1.III - Tip-Top Roofing has 50,640 square feet of roofing...Ch. 1.III - 25. A calculator uses eight circuit boards, each...Ch. 1.III - 26. Eric Shotwell borrows $24,600 from the...Ch. 1.III - A 16-person college basketball team is going to a...Ch. 1.III - You have just purchased a 65-acre ranch for a...Ch. 1.III - As the IT manager for FastNet Enterprises, you...Ch. 1.III - 30. You are the owner of Decorama Flooring. Todd...Ch. 1 - 1. The number system most widely used in the world...Ch. 1 - Prob. 2CRCh. 1 - Prob. 3CRCh. 1 - Prob. 4CRCh. 1 - Prob. 5CRCh. 1 - Rounding all the way is a process of rounding...Ch. 1 - Prob. 7CRCh. 1 - 8. When performing addition, we write the addends...Ch. 1 - 9. The mathematical process of taking away, or...Ch. 1 - Prob. 10CRCh. 1 - Prob. 11CRCh. 1 - Prob. 12CRCh. 1 - Prob. 13CRCh. 1 - 14. Show four ways to express 15 divided by 5....Ch. 1 - Read and write the following whole numbers in...Ch. 1 - Read and write the following whole numbers in...Ch. 1 - Prob. 3ATCh. 1 - Prob. 4ATCh. 1 - Round the following numbers to the indicated...Ch. 1 - Round the following numbers to the indicated...Ch. 1 - Prob. 7ATCh. 1 - Prob. 8ATCh. 1 - Prob. 9ATCh. 1 - Prob. 10ATCh. 1 - Prob. 11ATCh. 1 - Prob. 12ATCh. 1 - Prob. 13ATCh. 1 - Prob. 14ATCh. 1 - Prob. 15ATCh. 1 - The following chart shows the number of meals...Ch. 1 - Prob. 17ATCh. 1 - 18. The stadium parking lot at Fairview College...Ch. 1 - Prob. 19ATCh. 1 - Facebook reported that for one three-month period,...Ch. 1 - You are in charge of organizing the annual...Ch. 1 - Prob. 22ATCh. 1 - Prob. 23ATCh. 1 - A banana nut bread recipe calls for 2 cups of...Ch. 1 - Brian Hickman bought 2,000 shares of stock at $62...Ch. 1 - 26. The Canmore Mining Company produces 40 tons of...Ch. 1 - Prob. 27ATCh. 1 - The Iberia Corporation purchased a new warehouse...Ch. 1 - A flatbed railroad car weighs 150 tons empty and...Ch. 1 - The Spring Creek Police Department has been asked...Ch. 1 - Prob. 31ATCh. 1 - John Rock has narrowed down his selection of a new...Ch. 1 - Prob. 33AT
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- *Construct a table of values for all the nonprincipal Dirichlet characters mod 16. Verify from your table that Σ x(3)=0 and Χ mod 16 Σ χ(11) = 0. x mod 16arrow_forwardFor each real-valued nonprincipal character x mod 16, verify that A(225) > 1. (Recall that A(n) = Σx(d).) d\narrow_forward24. Prove the following multiplicative property of the gcd: a k b h (ah, bk) = (a, b)(h, k)| \(a, b)' (h, k) \(a, b)' (h, k) In particular this shows that (ah, bk) = (a, k)(b, h) whenever (a, b) = (h, k) = 1.arrow_forward
- 20. Let d = (826, 1890). Use the Euclidean algorithm to compute d, then express d as a linear combination of 826 and 1890.arrow_forwardLet 1 1+ + + + 2 3 1 r 823 823s Without calculating the left-hand side, Find one solution of the polynomial congruence 3x²+2x+100 = 0 (mod 343). Ts (mod 8233).arrow_forwardBy considering appropriate series expansions, prove that ez · e²²/2 . e²³/3 . ... = 1 + x + x² + · ·. when <1.arrow_forward
- Prove that Σ prime p≤x p=3 (mod 10) 1 Р = for some constant A. log log x + A+O 1 log x ,arrow_forwardLet Σ 1 and g(x) = Σ logp. f(x) = prime p≤x p=3 (mod 10) prime p≤x p=3 (mod 10) g(x) = f(x) logx - Ր _☑ t¯¹ƒ(t) dt. Assuming that f(x) ~ 1½π(x), prove that g(x) ~ 1x. 米 (You may assume the Prime Number Theorem: 7(x) ~ x/log x.) *arrow_forwardLet Σ logp. f(x) = Σ 1 and g(x) = Σ prime p≤x p=3 (mod 10) (i) Find ƒ(40) and g(40). prime p≤x p=3 (mod 10) (ii) Prove that g(x) = f(x) logx – [*t^¹ƒ(t) dt. 2arrow_forward
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