VII. Deduce the line or lines necessary to show the validity of the following arguments. Be sure to cite the lines from which each conclusion follows and give its justification . Please copy these arguments into your exam booklet.

1.

1. (~F v X) ↄ (P v T)

2. F ↄ P

3. ~P

––––––––––––––––

T

2.

1. (H v ~B) ↄ R

2. (H v ~M) ↄ P

3. H

–––––––––––––––

R ∙ P

VII. Deduce the line or lines necessary to show the validity of the following arguments. Be sure to cite the lines from which each conclusion follows and give its justification . Please copy these arguments into your exam booklet.

1.

1. (~F v X) ↄ (P v T)

2. F ↄ P

3. ~P

––––––––––––––––

T

2.

1. (H v ~B) ↄ R

2. (H v ~M) ↄ P

3. H

–––––––––––––––

R ∙ P

The velocity of sound, v (m/s), increases as the square rootof the absolute temperature, T (K):

   v = v_o ?(T/T_o)

where v_o is the velocity of sound at temperatureT_o.

a) Make a rough sketch of how the graph of v versus T wouldlook.

b) If one measures v for several temperatures, T, how couldyou plot the data so as to get a straight line?

c) What would be the slope of this straight line, in terms ofv_o and T_o?

d) What would be the SI units of this slope?

The surface area of a right-circular cone of radius r and height h is S=πrr2+h2−−−−−−√, and its volume is V=1/3πr2h.

(a) Determine h and r for the cone with given surface area S=4 and maximal volume V.
h=  , r=

(b) What is the ratio h/r for a cone with given volume V=4 and minimal surface area S?
hr=

(c) Does a cone with given volume V and maximal surface area exist?
A. yes
B. no

Be sure to answer all parts.

Calculate E o , E, and ΔG for the following cell reactions:

(a) Mg(s) + Sn2+(aq) ⇌ Mg2+(aq) + Sn(s) where [Mg2+] = 0.045 M and [Sn2+] = 0.065 M

E ^o = _________ V

E = ____________ V

ΔG = __________kJ

(b) 3Zn(s) + 2Cr3+(aq) ⇌ 3Zn2+(aq)+ 2Cr(s) where [Cr3+] = 0.080 M and [Zn2+] = 0.0055 M

E ^o = __________ V

E = ____________ V

ΔG = ___________kJ

For any n ≥ 1 let Kn,n be the complete bipartite graph (V, E) where V = {xi : 1 ≤ i ≤ n} ∪ {yi : 1 ≤ i ≤ n} E = {{xi , yj} : 1 ≤ i ≤ n, 1 ≤ j ≤ n} (a) Prove that Kn,n is connected for all n ≤ 1. (b) For any n ≥ 3 find two subsets of edges E 0 ⊆ E and E 00 ⊆ E such that (V, E0 ) and (V, E00) are spanning trees which are not isomorphic.

Assume you are carrying out the titration of 50 mL of a 0.025 M solution of acetic acid with 0.1023 MNaOH. Acetic acid has aKaof 1.8×10−5.

(a) Calculate the pH of the solution at V= 0, V= 0.3Veq, V=Veq, and V= 1.2Veq. (Veq is the equivalence point volume)

(b) If a phenolphthalein indicator was used in this titration, where would the apparent endpoint occur? Assume the apparent endpoint would occur at the end of the color range of the indicator (pH’s of 8.0-9.6).

if the mean=m,variance= v, observed value=o

we have four groups, g1 age 18-28,the observed resposibility of accident=127,m=0.809,v=0.848

for the same group the observed (not responsible) of accidents=192,m=1.22,v=1.849

group2 age 29-39 years ,o=155(responsible),m=0.5961,v=0.838

same group o=397 (not responsible),m=1.5269,v1.8336

group 3 age 40-50 o=127(responsible),m=0.635,v=0.841

same group o=277(not responsible),m=1.385,v=1.835

group 4 age >=51 ,o=54(responsible),m=0.446,v=0.849

same group o=54(not responsible),m=1.628,v=1.856

1-for the data shown which type of test we must use and why

2- using the test find the expected value for all responsible and not responsible accidents participations

3-if the test used is kai square find using (ovserved-expected)^2/expexted for all the data groups( resposible and not)

4- give an explanation or interpret the statistical test results for the significant values after finding p-value for the test

1. A priority queue is a special queue that adjusts the location of items based on some priority value. When inserted, a new value is placed in the queue ahead of every other item that has a lower priority than it. This gives us a queue that removes items from the front removing highest priority first, and from items with similar priority the ones that were inserted first. For example, if we inserted the following items with the priority {A, 1}, {B,2}, {C,2}, {D,3}, {E,1} where the lower number is a lower priority, our queue will have the items from front to back: D,B,C,A,E. Using the partial code below, you are to implement the Enqueue method so that the new node is inserted into the appropriate place in the queue based on the priority. (Assume that a higher number is higher priority, for example 0 is lowest and 10 is highest)

class Node<V,P>

{

      public V value;

      public P priority;

      public Node<V,P> next;

      Node(V value, P priority)

      {

           this.value = value;

           this.priority = priority;

      }

}

class PriorityQueue<V,P>

{

      private Node<V,P> head;

      private Node<V,P> tail;

      ...

      public void Enqueue(V value, P priority)

      {

Yeast make alcohol in the absence of oxygen by a process called fermentation (i.e., anaerobic respiration). Complete fermentation of one of the sugar glucose (C₆ H₁₂ O₆) will generate two moles of ethanol (C₂ H₆ O), two moles of carbon dioxide (CO₂) gas, and tow moles of the important molecule ATP (C₁₀ H₁₆ N₅ O₁₃ P₃), using in cellular transfers. You perform an experiment to make alcohol, so you set up an anaerobic fermentation system using yeast. You add 135 grams of glucose to your system and allow the sugar to be fermented to completion, trapping all fermentation products. (a) How many molecules of ATP were produced in your experiment? What is the total mass of the ATP. (b) The volume of the fermenation tank was 15 Liters, and the temperature was kept constant during the experiment at 25 ⁰C. Is it possible to determine the final tank pressure of the CO₂ gas produced by this experiment? Will the Ideal Gas Law work here? (c) What was the total volume of ethanol produced in this experiment? The density of ethanol is 0.789g/mL.