Suppose you have a pair of tetrahedra. One is red on one face, yellow on two faces, and green on one face. The other is white and has faces marked 1, 2, 3 ,4

a. Complete the table

b. If both tetrahedra are tossed, what is the probability of a red (facing down) and a 3 (facing down)? Of a yellow (facing down) and a number >1 on the other (facing down?) Of a green (facing down) and a number >4 (facing down) on the other? Of a yellow (facing down) on the colored one and a sum of >2 of faces showing on the other?

1.) Two 100 g pieces of metal, one copper and one aluminum, that start at the same temperature are put in an oven for 2 minutes. When they are taken out of the oven, the copper feels warmer than the aluminum. This can be explained by the relative values of specific heat for the two metals. Copper must have a [ Select ] ["higher", "lower"] specific heat capacity than the aluminum, because [select one: higher heat capacity men a high melting point. OR the molar mass of copper is greater than aluminium, OR the higher heat capacity means a larger temperature change, OR the same quantity of heat resulted in a higher (DELTA) T compared to aluminum. 2.) The molar enthalpy of combustion of methane, CH4 (molar mass of 16.0 g/mol), is 840 kJ/mol.

The molar enthalpy of combustion of ethanol, C2H5OH (molar mass of 46.1 g/mol), is 1360 kJ/mol.

The molar enthalpy of combustion of butane, C4H10 (molar mass of 58.1 g/mol), is 2970 kJ/mol.

What is the correct match for ranking the energy density of these three compounds

Highest energy density

      [ Choose ]            C2H5OH            C4H10            CH4      

Middle energy density

      [ Choose ]            C2H5OH            C4H10            CH4      

Lowest energy density

3.)

A gas has a volume of 115 mL at an initial, unknown pressure. The same sample of gas has a volume of 320 mL at a pressure of 715 torr. What can be said about the initial pressure?

4.)

Isoamyl acetate is the key molecule responsible for the smell of bananas and it has the chemical formula, C7H14O2.

Allyl valerate is a key molecule responsible for the smell of pineapples and it has the chemical formula C8H14O2.

Suppose you are in a very still room (no fans or ventilation system in use to move air around) and a coworker opens vials containing 200 mL samples of gases of each (a) isoamyl acetate and (b) allyl valerate at the same time. If you are standing on the opposite side of the room, which will you smell first and why?

                           [ Select ]                       ["pineapple", "banana"]         because the molecule with the                           [ Select ]                       ["smaller", "larger"]         molar mass diffuses through the air in the room faster.

5.)

Nitroglycerin is a well known explosive. It has a chemical formula of C3H5N3O9 (molar mass is 227.1 g/mol) and when it detonates the balanced equation for the reaction is:

4C3H5N3O9 ----> 6N2 + 12CO2 + 10H2O + O2

If one gram of nitroglycerin gives off 6.260 kJ of energy upon detonation, what is the enthalpy change in the thermochemical equation for this reaction?

4C3H5N3O9 ----> 6N2 + 12CO2 + 10H2O + O2   (DELTA) H = ??

Two ice pucks (one orange and one blue) of equal mass are involved in a perfectly elastic glancing collision. The orange puck is initially moving to the right at voi = 6.55 m/s, strikes the initially stationary blue puck, and moves off in a direction that makes an angle of ? = 40.0° with the horizontal axis while the blue puck makes an angle of ? = 50.0° with this axis. Note that for an elastic collision of two equal masses, the separation angle ? + ? = 90.0°. Determine the speed of each puck after the collision in meters per second. v0f = ? vbf = ?

There are 5 boxes. One box is empty; two boxes each contains one marble; and the remaining two boxes each contains two marbles. Suppose that the colors of the marbles are not known, but it is known that each marble can only be either red or green, with equal probability. Suppose that ONE box is randomly chosen from the 5 boxes, and let R denote the number of the red marble(s) the box has, and G be the number of the green marble(s) the box has. (Of course either R or G, or both, can be 0.)

(a) Write out the joint probability distribution of R and G.

(b) P(R > 0 ) = ?

(c) Write out the marginal distribution of G.

(d) P(G=1 | R=1) = ?

(e) E[R | G=1] = ?

(f) Are R and G independent? (Yes or no, you must justify your answer mathematically; otherwise, no credits can be given.)

(g) Calculate the correlation between R and G.

In one or two sentences describe the corrosion failure mode. What is one visual cue to indicate corrosion? Does corrosion always necessitate part replacement?

1. Maritza has one share of stock and one bond. The total value of the two securities is 1,090 dollars. The bond has a YTM of 12.18 percent, a coupon rate of 11.16 percent, and a face value of 1,000 dollars; pays semi-annual coupons with the next one expected in 6 months; and matures in 17 years. The stock pays annual dividends and the next dividend is expected to be 6.53 dollars and paid in one year. The expected return for the stock is 17.05 percent. What is the price of the stock expected to be in 1 year?

1. Use two diagrams (one for Alberta, one for the world) to explain why the following might be
true: A drought around the world raises the total revenue that farmers received from the sale of
grain, but a drought only in Alberta reduces the total revenue that Alberta farmers receive.
2. You have the following information about good X and good Y:
• Income elasticity of demand for good X: -3• Cross-price elasticity of demand for good X with respect to the price of good Y: 2
Would an increase in income and a decrease in the price of good Y unambiguously decrease the
demand for good X? Why or why not?
3. A price change causes the quantity demanded of a good to decrease by 30 percent, while the
total revenue of that good increases by 15 percent. Is the demand curve elastic or inelastic?
Explain.

Two fair dice, one blue and one red, are tossed, and the up face on each die is recorded. Define the following events:

E:E: {{ The sum of the numbers is even }}

F:F: {{ The difference of the numbers is 3 or more }}

Find the following probabilities:


P(E)=

P(F)=

P(EandF)=

P(E|F)=

P(F|E)=

Draw two arrows. One to represent healthy posture of the spine and one arrow that represents abnormal posture of the spine. Draw an outline of a person if this helps to support your response.