Capital Budgeting

A ski resort plans to eventually add five new chairlifts. One lift costs $2 million, preparing slope costs another $1.3 million. The lift allows 300 additional skiers ,but there are only 40 days a year when the extra capacity will be needed. (The resort sell alls 300 lift tickets on those 40 days.) Running the new lift will cost ...continues

Using probability with standard deviation

A particular type of electronic component for use in PCs is mass produced and subject to quality control checks since it is known that 2% of all components produced in this way are defective. The quality of a day's output is monitored as follows. A sample of 10 components is drawn from the day's output (which may be assumed to ...continues

Taylor series, the convergence of sequence, and series of functions

Questions are in attached files. Thank you.

Advanced Calculus: power series, the pointwise and uniform convergence of sequences of functions, and the uniform limit of continuous continuous function

The question is in attached file. Suppose a sequence of continuous functions, { ƒn }, has the property that ƒn  ƒ and  > 0,   > 0 such that if | x – y | <  then n, | ƒn (x) – ƒn (y)| <  Prove that ƒ is continuous.

Expanded Notation

Write each of the following sums in decimal form. a. 5(1/10)2+ 7(10)+ 3(1/10)5 (supposed to be exponent 2 and 5) b. 8(1/10)+ 3(10)3+ 9(1/10)2 (should be exp 3 and 2) c. 5(1/10)3+ 2(1/10)2+ (1/10)6 (should be exp 3,2,6)

Equations

Show that there are exactly four distinct sets of integers which satisfy the attached equations:

Cryptology

Decipher the following CFQGE KAZEMF ZMAGVMC NMO VYSV which was obtained by a formula of the type y=kx (mod 26)

Decoding a message encoded in a columnar transposition cipher.

Use columnar transposition cipher with keyword: Greek (keep e's in order), to decode the following message: VOESA IVENE MRTNL EANGE WTNIM HTMEE ADLTR NISHO DWOEH

Factoring

Factor the following: a. 81a4- 16b4 (should be exponent 4) b. 12x2+ x- 35 (should be exponent 2)

Simpify the expression.

Simplify the following expressions: a. 3x-2/2x2+x-3 Divide by 9x-6/2x-2 b.(108)1/2- (48)1/2+ (192)1/2 (should be exponent 1/2) c. (20x3+3x2-4x+5)/(4x2+3x-7) (should be exponent 3 and 2,2).