True or False

1. Prevalence refers to the proportion of participants with a risk factor or disease at a particular point in time

2. Censoring occurs when the event of interest (disease) is observed on every individual, usually due to time constraints.

3. Relative risk is an ideal form of measurement for a retrospective cohort study design because it allows researchers to recruit both individuals with the outcome of interest and individuals without the outcome of interest, then match individuals from each of the respective groups to individuals of the other group to determine if a specific exposure caused the outcome of interest.

4. The incidence rate is computed by taking the ratio of the number of new cases of disease to the total number of person-time units available

5. The prevalence of a disease depends on the incidence of the disease as well as the duration of the disease.

Public Health Problem II: Examine the association between health provider burnout and hospital re-admissions. Hypothesis: Health care provider burnout increases the likelihood of hospital re-admissions for patients

This will be a retrospective cohort study to determine if there’s a correlation between provider burnout and an increase likelihood of hospital re-admissions for patients
we will measure instances of patient readmissions with a group of hospital providers that are staffed appropriately and with an abundance of resources vs a group of providers who are overwhelmed, understaffed and under resourced

Describe potential threats to validity. Describe what techniques you will use to minimize each threat. Be sure to delineate the potential impact of each threat on your observed results
- Nondifferential misclassification of the exposure
- Nondifferential misclassification of the disease
- Confounding
- Selection bias
- Information bias
- Generalizability

1. The primary of a step-up transformer connected to a 120 V source has 200 turns. If the output is 480 V, how many turns does the secondary have?

2. The primary of a step-down transformer connected to a 240 V source has 1500 turns. The secondary has 200 turns.   What is the output voltage of this transformer?

3. A laptop computer requires 24 volts to operate properly. A transformer with 600 turns in the primary needs to have how many turns in the secondary to operate the computer from a 120 V source?

4. If the output current for the transformer in the previous problem is 4.5 A, calculate the input current.

5. A transformer has an input of 24 V and an output of 36 V. If the input is changed to 12 V what will the output be?

6. A model electric train requires 12 V to operate. When connected to a household voltage of 120 V, a transformer is needed. If the primary coil has 250 turns, how many turns must the secondary coil have?

7. A transformer has 25 turns in the primary coil and 200 turns in the secondary coil. If 24 V is connected to the primary coil and a 20-Ω device is connected to the secondary coil, calculate the current in Amperes passing through the device.

8. Neon signs need 12,000 V to operate. If a transformer operates off a 240 V source and has 1000 turns in its primary coil, how may turns must the secondary coil have?

9. A power of 200 kW is delivered by power lines with 48,000 V difference between them. Calculate the current, in amps, in these lines.

10. If the lines in problem #9 above, have a resistance of 100-Ω, calculate the change of voltage along each line.

A sinusoidal voltage is given by v(t)=7 cos(172t+28^o) V. What is the first time in ms for t>0 for which v(t) has a zero crossing?

Let V and W be finite dimensional vector spaces over a field F with dimF(V ) = dimF(W ) and let T : V → W be a linear map. Prove there exists an ordered basis A for V and an ordered basis B for W such that [T ]AB is a diagonal matrix where every entry along the diagonal is either a 0 or a 1.

Prove

1. For each u ∈ R n there is a v ∈ R n such that u + v= 0

2. For all u, v ∈ R n and a ∈ R, a(u + v) = au + av

3. For all u ∈ R n and a, b ∈ R, (a + b)u = au + bu

4.  For all u ∈ R n , 1u=u

Assume that random variable x^2 has a chi-squared distribution with v degree of freedom. Find the value of “A” for the following cases

1) P(X^2 <=A) =.95 when v = 6

2) P(X^2>=A) =.01 when v = 21

3) P(A <= X^2 <= 23.21)= .015 when v = 10.

As shown in the figure below, a bullet is fired at and passes through a piece of target paper suspended by a massless string. The bullet has a mass m, a speed v before the collision with the target, and a speed (0.496)v after passing through the target. The collision is inelastic and during the collision, the amount of kinetic energy lost by the bullet and paper is equal to [(0.263)Kb BC] , that is, 0.263 of the kinetic energy of the bullet before the collision. Determine the mass M of the target and the speed V of the target the instant after the collision in terms of the mass m of the bullet and speed v of the bullet before the collision. (Express your answers to at least 3 decimals.)

V =  ? v

M =  ? m

1)

A) Write v as a linear combination of u₁, u₂, and u₃, if possible. (Enter your answer in terms of u₁, u₂, and u₃. If not possible, enter IMPOSSIBLE.)

v = (−1, 7, 2), u₁ = (2, 1, 5), u₂ = (2, −3, 1), u₃ = (−2, 3, −1)

B) Write v as a linear combination of u and w, if possible, where u = (1, 3) and w = (2, −1). (Enter your answer in terms of u and w. If not possible, enter IMPOSSIBLE.)

v = (−3, −9)

C) Find w such that 2u + v − 3w = 0.

u = (0, 0, −6, 2),

v = (0, −3, 5, 1)

In a certain city, 30% of the families have a MasterCard, 20% have an American Express card, and 25% have a Visa card. Eight percent of the families have both a MasterCard and an American Express card. Twelve percent have both a Visa card and a MasterCard. Six percent have both an American Express card and a Visa card.

31. Is possession of a Visa card independent of possession of a MasterCard? Why or why not?

32. If a family has a Visa card, what is the probability that it has a MasterCard?

33.Is possession of an American Express card mutually exclusive of possession of a Visa card? Why or why not?

34.What is the probability of selecting a family that has either a Visa card or an American Express card?

35.If a family has a MasterCard, what is the probability that it has a Visa card?

36.What is the probability of selecting a family that has either a Visa card or a MasterCard?