Calculate the cell potential, at 25^oC, for the reaction

3 Zn(s) + 2 Cr⁺³(aq)[0.010 M] --> 3 Zn⁺²(aq)[0.020 M] + 2 Cr(s)

given,

Cr⁺³(aq) + 3e^- --> Cr(s) . . . . . . . E^o= -0.74 V

Zn⁺²(aq) + 2e^- --> Zn(s) . . . . . . E^o = -0.76 V

Question options:

Santa Fe Retailing purchased merchandise “as is” (with no returns) from Mesa Wholesalers with credit terms of 3/10, n/60 and an invoice price of $17,500. The merchandise had cost Mesa $11,935. Assume that both buyer and seller use a perpetual inventory system and the gross method.

1. Prepare entries that the buyer records for the (a) purchase, (b) cash payment within the discount period, and (c) cash payment after the discount period.
2. Prepare entries that the seller records for the (a) sale, (b) cash collection within the discount period, and (c) cash collection after the discount period.

Santa Fe Retailing purchased merchandise “as is” (with no returns) from Mesa Wholesalers with credit terms of 2/10, n/60 and an invoice price of $23,600. The merchandise had cost Mesa $16,095. Assume that both buyer and seller use a periodic inventory system and the gross method. 1. Prepare entries that the buyer should record for (a) the purchase, (b) cash payment within the discount period, and (c) cash payment after the discount period. 2. Prepare entries that the seller should record for (a) the sale, (b) cash collection within the discount period, and (c) cash collection after the discount period.

(10 pts) Suppose that when I drive to school, I encounter one traffic light on Lewis Road and one traffic light on Santa Rosa Rd. Let the random variable X = number of red lights that I encounter on Lewis and Y = number of red lights that I encounter on Santa Rosa. Suppose that the marginal distributions of X and Y are as shown in the following probability table:

X=-1 X=1 Total
Y=-1 0.5
Y=1 0.5
Total 0.5 0.5 1.0
Notice that E(X) = E(Y) = .5, and Var(X) = Var(Y) = .25.

a) Fill in the table in such a way that Corr(X,Y) = 1. Verify that indeed it checks out.
X=-1 X=1 Total
Y=-1 0.5
Y=1 0.5
Total 0.5 0.5 1.0


b) Fill in the table in such a way that Corr(X,Y) = -1. Verify that indeed it checks out.
X=-1 X=1 Total
Y=-1 0.5
Y=1 0.5
Total 0.5 0.5 1.0


c) Fill in the table in such a way that Corr(X,Y) = 0. Verify that indeed it checks out.
X=-1 X=1 Total
Y=-1 0.5
Y=1 0.5
Total 0.5 0.5 1.0

Consider the variable W=X+Y, representing the total number of red lights I encounter on my drive to school.
d) Calculate E(W)





e) For each of the cases in parts a), b) and c), calculate SD(W)

1. (10pt) Let V and W be a vector space over R. Show that V × W together with (v0,w0)+(v1,w1)=(v0 +v1,w0 +w1) for v0,v1 ∈V, w0,w1 ∈W

   and

   λ·(v,w)=(λ·v,λ·w) for λ∈R, v∈V, w∈W is a vector space over R.

2. (5pt)LetV beavectorspaceoverR,λ,μ∈R,andu,v∈V. Provethat (λ+μ)(u+v) = ((λu+λv)+μu)+μv.

   (In your proof, carefully refer which axioms of a vector space you use for every equality. Use brackets and refer to Axiom 2 if and when you change them.)

1. Determine if the following statements are true or false. If a statement is true, prove it in general, If a statement is false, provide a specific counterexample.

Let V and W be finite-dimensional vector spaces over field F, and let φ: V → W be a linear transformation.

A) If φ is injective, then dim(V) ≤ dim(W).

B) If dim(V) ≤ dim(W), then φ is injective.

C) If φ is surjective, then dim(V) ≥ dim(W).

D) If dim(V) ≥ dim(W), then φ is surjective.

E) If V = {0} , then φ is injective.

F) If dim(V) NOT= dim(W), then φ is not bijective.

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A professor thinks that the mean number of hours that students study the night before a test is 1.75. He selected a random sample of 12 students and found that the mean number of study hours was 2.44 and the standard deviation is 1.26 hours. Test the professor’s claim at α = 0.01.

a 1-6) Give the hypotheses for H₀ (a1, a2 and a3) and H1 (a4, a5 and a6)

H₀
a1) µ or p

a2) =, ≥, ≤

a3) number

H₁
a4) µ or p

  
a5) ≠, >, <

  
a6) number

b) Calculate the test statistic. t = _______ (Round your answer to 3 decimals.)

c 1-3) Formulate the decision rule for the p value approach.

Reject H₀ if (c1,c2,c3)
c1) t or p

c2) > or <

  
c3) number

d 1-2) Give the p value (d1 − round to 2 decimals) < p < (d2 - round to 2 decimals) and make a decision (d3).
d1)

  
d2)

  
d3) reject Ho or do not reject Ho

Reject HoDo not reject HoClick for List  

e1-2) Give your conclusion. At α = .___, there (is/is not) enough evidence to conclude that the mean number of hours that students study the night before a test is not 1.75.

e1)

  
e2) is or is not

When only two treatments are involved, ANOVA and the Student’s t test (Chapter 11) result in the same conclusions. Also, for computed test statistics, t^₂ = F. To demonstrate this relationship, use the following example. Fourteen randomly selected students enrolled in a history course were divided into two groups, one consisting of 6 students who took the course in the normal lecture format. The other group of 8 students took the course as a distance course format. At the end of the course, each group was examined with a 50-item test. The following is a list of the number correct for each of the two groups.

1. a-1. Complete the ANOVA table. (Round your SS, MS, and F values to 2 decimal places and p value to 4 decimal places.)

1. a-2. Use a α = 0.01 level of significance. (Round your answer to 2 decimal places.)

2. Using the t test from Chapter 11, compute t. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

3. There is any difference in the mean test scores.