Derive the mirror equation. ( 1/p + 1/q = 2/R )

pshyics : optics

Good 1 and Good 2 are perfect substitutes. Suppose that good 1 is an ordinary good.

a. Should both good 1 and good 2 be normal goods?

b. Should good 2 be an ordinary good?

Explain using income effects and/or substitution effects.

PLEASE ANSWER #1 AND #2

(1) A 90 kg man lying on a surface of negligible friction shoves a 75 g stone away from himself, giving it a speed of 4.0 m/s. What speed does the man acquire as a result?

(2) A 5.0 kg block with a speed of 3.0 m/s collides with a 10 kg block that has a speed of 2.2 m/s in the same direction. After the collision, the 10 kg block is observed to be traveling in the original direction with a speed of 2.7 m/s.

(a) What is the velocity of the 5.0 kg block immediately after the collision?

(b) By how much does the total kinetic energy of the system of two blocks change because of the collision?

(c) Suppose, instead, that the 10 kg block ends up with a speed of 3.8 m/s. What then is the change in the total kinetic energy?

(d) Account for the result you obtained in (c).

Consider the following reaction at 215 K: 2 A (aq) + 1 B (aq) → 1 C (aq) + 1 D (aq)

An experiment was performed with the following intitial concentrations: [A]i = 1.37 M, [B]i = 2.03 M, [C]i = 0.65 M, [D]i = 0.11 M.

The reaction was allowed to proceed until equilibrium was reached at which time it was determined that [A] = 0.61 M. What was the maximum amount of work that could have been performed as the reaction began? Maximum amount of work performed as the reaction began (in kJ)=

1) Describe in 1-2 short paragraphs, a) the purpose of the following types of financial statements and b) why as a leader/manager you must be familiar with them:

   - Balance sheet

   - Income statement

   - Capital statement

2) If, as a manager, you could only pick one financial ratio to look at on a weekly/monthly basis, which would it be?

   a) Write/type out the equation

   b) Discuss (1-2 short paragraphs) why you picked that equation, what information that would give you on your business’ or department’s performance, and how you would use that to better your business/department.

Question 1

a) For the data in Homework 2, Question 1, calculate the ANOVA table. Use the ANOVA Table to conduct an F-Test to see if the model is significant (use α = 0.05).

Data:

b) Give a 95% confidence interval for the mean sale price for 2000 sq. ft. houses.

c)   Give a 95% prediction interval for the sale price of an individual 2000 sq. ft. house.

d)   For the data in Homework 2, Question 2, calculate the ANOVA table for the data. Use the ANOVA Table to conduct an F-Test to see if the model is significant (use α = 0.05).

Data:

Question 2

A research firm collected data on a sample of n = 30 drivers to investigate the relationship between the age of a driver and the distance the driver can see. The data is given below:

Use SAS to fit a simple linear regression and answer the following questions:

a) Find the least squares estimate for the regression line Y_i = b₀ + b₁X_i + e_i.

b) Estimate the standard deviation of the error term e_i

c)   Test the null hypothesis that b₁ = 0, using α = 0.05. Is the model useful?

d)   Calculate R²? Explain what this means, and comment on whether or not it suggests the model is good.

e)   Calculate the correlation coefficient? Explain what this means, and comment on whether or not it suggests the model is good.

f)    What would you expect the distance that a 50 year old driver can see to be?

g)   Give a 95% prediction interval for the distance that an individual 50 year old can see.

h) Give a 95% confidence interval for the mean distance that 50 year olds can see.

Euclidean metric) The metric

d

((

x

1

,x

2

)

,

(

y

1

,y

2

)) =

√

(

x

1

−

x

2

)

2

+ (

y

1

−

y

2

)

2

on

R

2

generates the standard (product) topology on

R

2

.

1.) You plan to deposit $1,000 in Year 1, $1,200 in Year 2 and $2,000 in year 4 in your savings account. You think that you can earn 6% per year. How much will you have in your account in Year 6?

2.) Bank X promises to pay you $5,200 per year for 8 years, whereas Bank Y offers to pay you $7,300 per year for 5 years.

a) Which of these cash flow streams has the higher present value (PV) if the discount rate is 5 percent? (Hint: compare the PVs of annuity X ($5,200 per year for 8 years) with annuity B ($7,300 per year for 5 years)

b) Which one should you choose between Bank X and Bank Y?

3.) Today, Dinero Bank offers you a $60,000, five-year term loan at 7.5 percent annual interest (APR). What will your annual loan payment be? (Hint: Find PMT)

4.) You buy an annuity that will pay you $24,000 a year for 25 years. The payments are paid on the first day of each year. What is the value of this annuity today if the discount rate is 8.5 percent? (Hint: annuity due)

SHOW HOW YOU GOT ANSWERS PLEASE!!

In 1-2 sentences each, answer the following questions:

1. In healthcare, what is the principle of justice concerned with?

2. When applied in a healthcare context, who does justice tell us to prioritize?

3. In terms of healthcare policy, what would beneficence & non-maleficence favor? ➢ (Note: Be more specific than simply “Doing good and avoiding harm”)