The resting surface charge density of a membrane is 0.5 uC/cm^2. The resting membrane potential is 0.5 V. It drops to 0 V in 5 ms. If there are 25 Na channels per um^2 that open up during depolarization, what is the average current that flows through a sodium channel during this time (5 ms)? How many sodium ions move through the channel in 5 ms?

8.   a) Name 2 types of censoring that can occur during follow-up in a cohort study or clinical trial.

R problem

1. Student records. Create an S3 class studentRecord for objects that are a list with the named elements ‘name’, ‘subjects completed’, ‘grades’, and ‘credit’. Write a studentRecord method for the generic function mean, which returns a weighted GPA, with subjects weighted by credit. Also write a studentRecord method for print, which employs some nice formatting, perhaps arranging subjects by year code.

Finally create a further class for a cohort of students, and write methods for mean and print which, when applied to a cohort, apply mean or print to each student in the cohort.

A man named Bob Smith believes that he is Santa Claus (who delivers presents to all the children around the world on Christmas Eve). In fact, he is not Santa, but he has believed this for many years. He signs his name "Santa." He signs many contracts as "Santa," and he refers to his wife as "Mrs. Claus" even though her name is actually Betty Smith. She puts up with it, because he really does believe he is Santa, and because she loves him and because his wages from his job at Hasbro toys pays the bills.

One day he enters a contract with your company to hire you to build him a gigantic workshop in his backyard so he can build his toys and stable his "eight tiny reindeer." In return he will pay you $120,000 for the construction. When his wife learns of this deal, she tries to reject it because it is voidable due to his lack of contractual capacity.

Was this contract voidable, or valid and enforceable? Fully explain your answer.

9. The table below represents the college degrees awarded in a recent academic year by gender. Choose a degree at random.

Find the probability that it is a) A bachelor’s degree b) A doctorate or a degree awarded to a woman c) A doctorate awarded to a woman d) Not a master’s degree e) doctorate awarded to a man. Answer in a,b,c,d,e format. (IE A=, B=, etc).

             Bachelor’s Master’s Doctorate

Men 542,731 201,322 27,390

Women 785,334 311,267 21,680

Melanoma treatment. An experiment evaluated the use of genetically engineered white blood cells in the treatment of patients with melanoma.^y Patients were divided into three cohorts. Patient cohort 1 received genetically engineered lymphocytes that were cultured ex vivo for 19 days. Cohort 2 received cells that were cultured for between 6 and 9 days. Cohort 3 received cells that were generated by a second rapid expansion performing after 8 to 9 days. Cell doubling times were as follows.

Cohort 1               8.7          11.9        10.0

Cohort 2               11.4        1.0          1.3          1.0          2.0          0.6          0.8          0.7          0.9          1.9

Cohort 3               0.9          3.3          1.2          1.1

Either create a file with these data or download the file MORGAN2006.* from the companion website. Most statistical programs require you to enter that data into two columns: one column for the explanatory variable (COHORT) and the other for the response variable (DOUBLING). Your final data table should have 2 columns and 18 rows.

If you do not have access to a statistical program, consider using BrightStat. com.^z Use of BrightStat.com is free. However, you must register as a user in order to access its ANOVA features.

(a)   Calculate the means, standard deviations, and sample sizes of each group. Use the “double the standard deviation” benchmark to assess whether group variances are significantly different. Is there evidence of heteroscedasticity?

(b)   Conduct Levene’s test for unequal variance. Show all hypothesis testing steps. What do you conclude?

Cruz Inc. manufactures a popular premium toy. During its first year, the company incurred these costs:

$427000 Cost to manufacture 7000 toys
$110000 Research and development costs
$35000 Cost to ship completed products to retailers

Cruz sells 80% of its products for $183 each.

1. What will Cruz report as sales revenue for Year1?  

2. What will Cruz report as the cost of goods sold for Year1?  

3. What will Cruz report as net income for Year1?  

4. What will Cruz report as inventory on the balance sheet as of the end of Year1?  

Note: We suggest you use ray diagrams to qualitatively understand these questions. A candle 6.10 cm high is placed in front of a thin converging lens of focal length 33.0 cm. What is the image distance i when the object is placed 93.0 cm in front of the same lens?

What is the size of the image? (Note: an inverted image will have a `negative' size.)

Is the image real(R) or virtual(V); upright(U) or inverted(I); larger(L) or smaller(S) or unchanged(UC); in front of the lens(F) or behind the lens(B)? Answer these questions in the order that they are posed. (for example, if the image is real, inverted, larger and behind the lens then enter `RILB'.)

The object is now moved to 41.0 cm in front of the lens, what is the new image distance i?

What is the new size of the image?

Is the new image real(R) or virtual(V); upright(U) or inverted(I); larger(L) or smaller(S) or unchanged(UC); in front of the lens(F) or behind the lens(B)? Answer these questions in the order that they are posed. (for example, if the image is real, inverted, larger and behind the lens then enter `RILB'.)

The object is now moved to 21.0 cm in front of the lens, what is the new image distance i?

What is the new size of the image?

Is the new image real(R) or virtual(V); upright(U) or inverted(I); larger(L) or smaller(S) or unchanged(UC); in front of the lens(F) or behind the lens(B)? Answer these questions in the order that they are posed. (for example, if the image is real, inverted, larger and behind the lens then enter 'RILB'.)

The object is now moved to 6.5 cm in front of the lens, what is the new image distance i?

What is the new size of the image?

Is the new image real(R) or virtual(V); upright(U) or inverted(I); larger(L) or smaller(S) or unchanged(UC); In front of the lens(F) or behind the lens(B)? Answer these questions in the order that they are posed. (for example, if the image is real, inverted, larger and behind the lens then enter 'RILB'.)