Physics Modern Physics Level: High School
Compare the energy released per kilogram of deuterium for D-T fusion to the energy released per kilogram of 235U for 235U fission.Note: A gram of deuterium contains 3.01 x 1023 atoms.
Statistics Statistics Level: University
Rubax, a US manufacturer of athletic shoes, estimates the following linear trend model for shoe sales:Qt = a + bt + c1D1 +c2D2 +c3D3
WhereQt = sales of athletic shoes in the tth quarter
T + 1, 2,….., 28[j2001(I), 2001(II)….,2007{IV}
D1 = 1 if t is quarter I (winter); 0 otherwise
D2 = 1 if t is quarter II (spring); 0 otherwise
D3 = 1 if t is quarter III (summer); 0 otherwise
The regression analysis produces the following results:
| Dependent Variable: | QT | R-Square | F-Ratio | P-Value on F | ||||
| Observations: | 28 | 0.9651 | 159.01 | 0.0001 | ||||
| Variable | Parameter Estimate | Standard Error | T-Ratio | P-Value | ||||
| Intercept | 184500 | 10310 | 17.90 | 0.0001 | ||||
| T | 2100 | 340 | 6.18 | 0.0001 | ||||
| D1 | 3280 | 1510 | 2.17 | 0.0404 | ||||
| D2 | 6250 | 2220 | 2.82 | 0.0098 | ||||
| D3 | 7010 | 1580 | 4.44 | 0.0002 |
a. Is there sufficient statistical evidence of an upward trend in shoe sales?
b. Do these data indicate a statistically significant seasonal pattern of sales for Rubax shoes? If so, what is the seasonal pattern exhibited by the data?
c. Using the estimated forecast equation, forecast slates of Rubax shoes for 2008(III) and 2009 (II).
d. How might you improve this forecast equation?
Statistics Statistics Level: University
The British Columbia Tourist Association distributes pamphlets, maps, and other tourist-related information to people who call a toll-free number and request information. The marketing manager decided to develop a multiple regression model to predict the number of calls that will be received in the coming week. A random sample of 20 weeks is selected. The collected data are summarized below.| Calls Received | Ads Place Previous Week | Calls Received the Previous Week | Airline Bookings |
| 345 | 12 | 297 | 3,456 |
| 456 | 14 | 502 | 3,456 |
| 356 | 13 | 340 | 3,600 |
| 605 | 16 | 450 | 5,500 |
| 209 | 14 | 350 | 2,400 |
| 306 | 10 | 340 | 2,890 |
| 457 | 15 | 401 | 3,757 |
| 259 | 12 | 340 | 2,590 |
| 540 | 13 | 480 | 4,840 |
| 460 | 16 | 440 | 3,560 |
| 378 | 14 | 348 | 3,460 |
| 456 | 16 | 518 | 3,679 |
| 209 | 14 | 350 | 2,400 |
| 306 | 10 | 340 | 2,890 |
| 457 | 15 | 401 | 3,757 |
| 259 | 12 | 340 | 2,590 |
| 540 | 13 | 480 | 4,840 |
| 460 | 16 | 440 | 3,560 |
| 356 | 13 | 340 | 3,600 |
| 605 | 16 | 450 | 5,500 |
a. Specify a suitable multiple regression equation to estimate with the data.
b. What percentage of the total variation in the number of calls is explained by the regression model?
c. Is the overall multiple regression equation statistically significant? Explain.
d. Which, if any, of the independent variables is statistically significant? Test using a significance level of 0.05.
Statistics Statistics Level: University
The following log-linear demand curve for a price-setting firm is estimated using the ordinary least squares method: where Q and P are the quantity and price respectively for good X, M is consumer income, and is the price of good R.a.Express the estimated demand equation in logarithms.
b.Is X a normal or an inferior good? And how are goods X and R related? Explain.
c.Estimate the own-price elasticity for good X, the cross-price elasticity for goods X and R, and the income elasticity for good X.
d.Holding all other things constant, if household income were to fall by 22%, what would we expect to happen to quantity demanded? Explain.
e.Holding all other things constant, if own price were to increase by 22%, what would we expect to happen to quantity demanded? Explain.
f.Holding all other things constant, if the price of R were to fall by 8%, what would we expect to happen to quantity demanded? Explain.
The estimation results are presented below:
| DEPENDENT VARIABLE: | LNQ | R-SQUARE | F-RATIO | P-VALUE ON F |
| OBSERVATIONS: | 64 | 0.8464 | 110.25 | 0.0001 |
| PARAMETER | STANDARD | - | - | - |
| VARIABLE | ESTIMATE | ERROR | T-RATIO | P-VALUE |
| INTERCEPT | 5.65 | 3.20 | 1.77 | 0.0825 |
| LNP | -1.02 | 0.59 | -1.73 | 0.0890 |
| LNM | 0.45 | 0.22 | 2.05 | 0.0452 |
| LNPR | -2.0 | 0.75 | -2.67 | 0.0098 |
Statistics Statistics Level: University
The 1998 GSS states, "There are always some people whose ideas are considered bad or dangerous by other people. For instance, somebody who is against all churches and religion...If such a person wanted to make a speech in myour (city/town/community) against churches and religion, should he/she be allowed to speak or not?" Among the male GSS respondents, 631 said they would allow the speech and 154 would not allow it. Among the female respondents, 762 would allow and 303 would not allow the speech. What are the conditional odds in favor of allowing an atheist to speak?
Statistics Statistics Level: University
In several presedential elections, researchers have observed a "gender gap" in which men and women vote for candidates in different proportions. Test this hypothesis by calculating X2 and Yule's Q for these frequencies from the 1998 General Social Survey:Did you vote for Clinton or Dole?
| Gender | |||
| Men | Women | ||
| Clinton | 351 | 572 | |
| Dole | 283 | 306 |
Physics Modern Physics Level: High School
Atoms
The angular momentum quantum number l=1. What is the degeneracy of the component of the angular momentum about the z-axis?
Physics Modern Physics Level: High School
Atoms
Draw an energy level diagram for a vibrating particle as a function of the zero point energy. Do the same for rotational motion. Be sure to specify the spacing in each of the diagrams.
Physics Modern Physics Level: High School
Atoms
Calculate the energies of the first four rotational levels of HI, R = 160pm, allowing it to rotate in three dimensions about its center of mass. Express the answer in J and KJ per mole.
Physics Heat & Thermodynamics Level: Middle School
One and one half moles of an ideal monatomic gas expand adiabatically, performing 7500 J of work in the process. What is the change in temperature of the gas during this expansion?
Physics Heat & Thermodynamics Level: High School
A water heater can generate 32,000 kJ/h. How much water can it heat from 15 degrees Celsius to 50 degrees Celsius per hour?
Physics Heat & Thermodynamics Level: High School
The density of water at 4 degrees Celsius is 1.00 x 10^3 kg/m^3. what is water's density at 94 degrees Celsius?
Physics Kinematics Level: High School
Mechanics
A flat uniform circular disk (radius=2.00 m; mass=100 kg) is initially stationary. The disk is free to rotate in the horizontal plane about a frictionless axis perpendicular to the center of the disk. A 40 kg person, standing 1.25 m from the axis, begins to run on the disk in a circular path and has a tangential speed of 2.00 m/s relative to the ground. Find the resulting angular speed of the disk (in rad/s)a. 0.500 rad/s
b. 2.00 rad/s
c. 1.25 rad/s
d. 0.250 rad/s
e. 1.00 rad/s
Physics Kinematics Level: High School
Mechanics
A thin uniform rod is initially positioned in the vertical direction, with its lower end attached to a frictionless axis that is mounted on the floor. The rod has a length of 2.00 m and is allowed to fall, starting from rest. Find the tangential speed of the free end of the rod, just before the rod hits the floor after rotating through 90 degree.a. 3.59 m/s
b. 4.26 m/s
c. 5.89 m/s
d. 7.67 m/s
e. 6.83 m/s
Physics Kinematics Level: High School
Mechanics
A meter stick is placed flat on a table, and one end of the meter stick is attached to the table. The other end of the meter stick can thus rotate freely around this attached end (the axis) over the surface of the table. Two forces, both parallel to the tabletop, are applied to the stick in such a way that the net torque is zero. One force has a magnitude of 4.00 N and is applied perpendicular to the stick at the free end. The other force is applied on the opposite side of the above perpendicular force, but it has a magnitude of 6.00 N and acts at a 60.0 degree angle with respect to the stick. Where along the stick is the 6.00 N force applied? Express this distance with respect to the axis of rotation.a. 0.667 m
b. 0.770 m
c. 0.834 m
d. 0.725 m
e. 0.783 m
