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Exercise 8-1 One mole of a real gas initially at a pressure of 1.98 atm and contained in a flask having a volume of 8.27 L is suddenly expanded by opening a valve connecting the flask to a second flask, the latter having a volume of 7.64 L and containing a vacuum. During the process, 0.71 J of heat is absorbed by the gas from the surroundings. The final pressure of the gas is 1.033 atm. (a) What is the ΔU for this process? (b) What is ΔH?

 
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Question is in the picture.

Algebra 2.

MATH 236 in mcgill

Exercise 7. Let V be a finite—dimensional vector space over IF. The vector space V* :£(V, F) is called the dual of V. An element of V* is thus a linear map f : V —> IF, alsoknown as a functional. (i) Let {U1,. .. ,vn} be a basis of V. Show that, for each i E {1, . . . ,n}, there exists aunique ’03“ E V* satisfying1 if 2′ : j vi(vj)6i'{0 ifz’7éj’ Show that {01“, . . . , 11;} is a basis of V*. Deduce that V and V* are isomorphic.(ii) For each 1: E V, let evv : V* —> IF denote the evaluation at 1); that is, evu(f) : f (v)for each f E V*. Check that evv E V**, the dual of V*. Show that the evaluationmap ev : V —> V** is an isomorphism. (A brief comment. The isomorphism of V and V** is canonical, in the sense that it doesnot depend on a basis. The isomorphism of V and V*, on the other hand, is not canonical—it requires the choice of a basis. The notion of duality, and the canonical/non—canonicalisomorphisms exhibited above, appear in relation to several mathematical structures.)

 
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Exercise 7-9

The trial balance before adjustment of Novak Inc. shows the following balances.

Dr.

Cr.

Accounts Receivable$80,000Allowance for Doubtful Accounts2,780Sales Revenue (all on credit)$703,300

Give the entry for estimated bad debts assuming that the allowance is to provide for doubtful accounts on the basis of (a) 4% of gross accounts receivable and (b) 5% of gross accounts receivable and Allowance for Doubtful Accounts has a $1,691 credit balance. (If no entry is required, select “No Entry” for the account titles and enter 0 for the amounts. Credit account titles are automatically indented when the amount is entered. Do not indent manually.)

No.

Account Titles and Explanation

Debit

Credit

(a)

(b)

Exercise 7-9

The trial balance before adjustment of Novak Inc. shows the following balances.

Dr.

Cr.

Accounts Receivable$80,000Allowance for Doubtful Accounts2,780Sales Revenue (all on credit)$703,300

Give the entry for estimated bad debts assuming that the allowance is to provide for doubtful accounts on the basis of (a) 4% of gross accounts receivable and (b) 5% of gross accounts receivable and Allowance for Doubtful Accounts has a $1,691 credit balance. (If no entry is required, select “No Entry” for the account titles and enter 0 for the amounts. Credit account titles are automatically indented when the amount is entered. Do not indent manually.)

No.

Account Titles and Explanation

Debit

Credit

(a)

(b)

 
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21,000

RM purchases…………………………………………………………………………………………..200,000

Direct labor……………………………………………………………………………………………….100,000

Indirect materials………………………………………………………………………………………..5,000

Indirect labor……………………………………………………………………………………………..47,000

Factory utilities………………………………………………………………………………………….18,000

Factory rent………………………………………………………………………………………………36,000

Depreciation – factory equipment………………………………………………………………….24,000

Sales……………………………………………………………………………………………………….960,000

Selling expenses……………………………………………………………………………………….120,000

administrative expenses……………………………………………………………………………..240,000

Income tax rate…………………………………………………………………………………………….30%

Required:

A. Calculate the RM(DM) used.

B. Develop a schedule of cost of goods manufactured.

C. Construct an income statement.

D. Prepare journal entries. Assume that all purchases and sales were made on credit and that all expenses were paid in cash.

Execise 7.6

DEF Manufacturing company used P150,000 of direct materials and incurred P60,000 of direct labor costs during 2018. Indirect

labor amounted to P5,000 while indirect materials used totaled P3,000. Other factory costs included Utilities of P6,000; maintenance of

P8,000; supplies of P4,00; Depreciation of P16,000 and propery taxes of P5,000. Work in process inventory began the year with a

P12,000 balance and ended the year with an P16,000 balance.

Required:

Prepare a schedule of cost of goods manufactured for DEF Manufacturing company for the year ended December 31,2018

 
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Exercise 7-17. Allocating Joint Costs [LO 3]The American Produce Company purchased a truckload of cantaloupes (weighing 4,000 pounds) for $800. American Produce separated the cantaloupes into two grades: superior and economy. The superior-grade cantaloupes had a total weight of 3,200 pounds, and the economy-grade cantaloupes totaled 800 pounds. American Produce sells the superior-grade cantaloupes at $0.35 per pound, and the economy-grade ones at $0.15 per pound.RequiredAllocate the $800 cost of the truckload to the superior-grade and economy-grade cantaloupes using the physical quantity method and the relative sales value method.

============================Exercise 7-17. Allocating Joint Costs [LO 3]The American Produce Company purchased a truckload of cantaloupes (weighing 4,000 pounds) for$800. American Produce…

 
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Let f : R n → R m be continuous, where we equip R n and R m with the Euclidean metric d2. Prove that the following conditions are equivalent: (i) For every bounded set T ⊂ R m, we have that f −1 (T) is bounded. (ii) For every compact set T ⊂ R m, we have that f −1 (T) is compact. [Hint: To show that (ii) implies (i) you may have to prove that cl(f −1 (T)) ⊂ f −1 (cl(T)).]

help please

Exercise 7 (12 points). Let f: R” —> Rm be continuous, where we equip R” and R“ with theEuclidean metric d2.Prove that the following conditions are equivalent: (i) For every bounded set T C R”, we have that f_1(T) is bounded.(ii) For every compact set T C R”, we have that f ’1(T) is compact. [Hint To Show that (ii) implies (i) you may have to prove that cl( f ’1(T)) C f’1(cl(T)).]

 
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At the start of the current year, the company received an order for 2,900 drives from a computer company in China. Management of PowerDrive has mixed feelings about the order. On one hand, they welcome the order because they currently have excess capacity. Also, this is the company’s first international order. On the other hand, the company in China is willing to pay only $116 per unit.

What will be the effect on profit of accepting the order?

Will profit increase or decrease? by how much?

 
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EXERCISE 8.13 The above results assume (lowest-order) single photon exchange is dominant. If two-photon exchange were significant, convince yourself that the e p and e+p cross sections would not be equal.

 
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 convince yourself that (C ([−1, 1]; R), ρp) is a metric space for all p ∈ N, where ρp : C ([−1, 1]; R) × C ([−1, 1]; R) → R is defined as ρp(f, g) = Z 1 −1 |f(x) − g(x)| p dx 1/p for all f, g ∈ C ([−1, 1]; R). We have shown in class that the metric space (C ([−1, 1]; R), ρ∞) is complete, where ρ∞ is the uniform distance. Show that, in contrast, the metric space (C ([−1, 1]; R), ρp) is incomplete for all p ∈ N [Hint: Consider the sequence (fk)k of functions defined for all k ∈ N by fk(x)

Exercise 8 (11 points). Following the steps in Exercise 10.2 of Homework 1, convince yourselfthat (‘6’([—1,1];R),pp) is a metric space for all p E N, where pp: ‘6’([—1, 1];R) x ‘6([—1,1];R)—> Ris defined as 1 Upmtg) = (fl Iva) — germ) for an 129 e ecu—1, 1];R)- We have shown in class that the metric space (‘e’([—1,1];R),pm) is cemplete, where poo is theuniform distance. Show that, in contrast, the metric space (?([71,1];R),pp) is incomplete for all p E N [HintConsider the sequence (fig);c of functions defined for all k E N by fiche) = —1 for all m E [—1, —1/k),fists) = km for all :1: E [—1/k,1/k) and fk($) = 1 for all :5 E [1/k,1].]

 
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Exercise 8-10

Kingbird, Inc. has the following transactions related to notes receivable during the last 2 months of the year. The company does not make entries to accrue interest except at December 31. (Omit cost of goods sold entries.)

Nov. 1 Loaned $64,800 cash to C. Bohr on a 12-month, 7% note.Dec. 11Sold goods to K. R. Pine, Inc., receiving a $1,800, 90-day, 8% note.Dec. 16Received a $19,200, 180-day, 12% note to settle an open account from A. Murdock.Dec. 31Accrued interest revenue on all notes receivable.

Journalize the transactions for Kingbird, Inc. (Credit account titles are automatically indented when amount is entered. Do not indent manually. Record journal entries in the order presented in the problem.)

 
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