Dr. Marcel was testing a potential treatment for Huntington disease on mice. She bred 46 mice that exhibited neurodegeneration (deterioration of the brain), and applied her treatment to 22 of the mice (the remaining 24 received no treatment and were labeled the “control group”). After 6 weeks, she measured the circumference of the brain from all mice. She was interested in testing if the average circumference of the brain differed between the treatment and control groups. Below is a summary of the results.

What is the correct conclusion based on these sample results? (Assume all conditions have been met).

Heparin is a drug frequently used to prevent blood clots from forming in an IV catheter. The typical dose of heparin to prevent clotting in the IV catheter of a newborn infant is 1 ml of 10 units/ml heparin.

A. One unit of heparin is roughly 0.002 mg. How many mg of heparin should be used to prevent clotting in a typical newborn IV catheter? Show your work.

B. Using the value obtained in part A, convert the concentration of 10 units/ml heparin to moles/liter (molar, M). For the type of heparin used to prevent clotting, the formula weight is approximately 5000 g/mol. Show your work.

C. Several years ago, heparin solutions of different concentrations were sold in vials with similar packaging that could be easily confused (see image). This confusion resulted in several widely publicized cases, some fatal, of heparin overdose in newborns. If the person giving the heparin only has access to the 10,000 units/ml concentration heparin solution, how much saline solution would this person need to mix with 0.3 ml of the 10,000 units/ml heparin solution to yield a 10 units/ml solution for use in a newborn? Show your work.

Consider a simple economy that produces two goods: pens and muffins. The following table shows the prices and quantities of the goods over a three-year period.

Use the information from the preceding table to fill in the following table.

From 2016 to 2017, nominal GDP decrease or increase , and real GDP decrease or increase

The inflation rate in 2017 was A- -25% B- 0.3%, C- 25%, D- 80%, E- 125%

Why is real GDP a more accurate measure of an economy's production than nominal GDP?

A) Real GDP includes the value of exports, but nominal GDP does not.

B) Real GDP is not influenced by price changes, but nominal GDP is.

C) Real GDP measures the value of the goods and services an economy produces, but nominal GDP measures the value of the goods and services an economy consumes.

The management of Brinkley Corporation is interested in using simulation to estimate the profit per unit for a new product. The selling price for the product will be $50 per unit. Probability distributions for the purchase cost, the labor cost, and the transportation cost are estimated as follows:

1. Compute profit per unit for the base-case, worst-case, and best-case.
   
   Profit per unit for the base-case: $___  
   
   Profit per unit for the worst-case: $___  
   
   Profit per unit for the best-case: $___  
   
2. Construct a simulation model to estimate the mean profit per unit. If required, round your answer to the nearest cent.
   
   Mean profit per unit = $___  
   
3. Why is the simulation approach to risk analysis preferable to generating a variety of what-if scenarios?
   
   
   
4. Management believes the project may not be sustainable if the profit per unit is less than $9. Use simulation to estimate the probability the profit per unit will be less than $9. If required, round your answer to one decimal place.
   
   ____%

Direct Labor Variances

Ada Clothes Company produced 20,000 units during April. The Cutting Department used 3,800 direct labor hours at an actual rate of $11.50 per hour. The Sewing Department used 6,300 direct labor hours at an actual rate of $11.20 per hour. Assume there were no work in process inventories in either department at the beginning or end of the month. The standard labor rate is $11.40. The standard labor time for the Cutting and Sewing departments is 0.2 hour and 0.3 hour per unit, respectively.

a. Determine the direct labor rate, direct labor time, and total direct labor cost variance for the (1) Cutting Department and (2) Sewing Department. Enter a favorable variance as a negative number using a minus sign and an unfavorable variance as a positive number.

b. The two departments have opposite results. The Cutting Department has a(n) rate variance and a(n) time variance, resulting in a total cost variance. In contrast, the Sewing Department has a(n) rate variance but has a(n) time variance, resulting in a total cost variance.

Suppose the process of producing lightweight parkas by Polly’s Parkas is described by the function q = 10K^0.7(L - 40)^0.3 where q is the number of parkas produced, K the number of computerized stitching-machine hours, and L the number of person-hours of labor. In addition to capital and labor, $15 worth of raw materials is used in the production of each parka.

1. Write total cost function of producing parkas in terms of the quantity produced, and labor and capital used in production.

2. By minimizing cost subject to the production function, derive the cost-minimizing demands for K and L as a function of output (q), wage rates (w), and rental rates on machines (r). Use these results to derive the total cost function: that is, costs as a function of q, r, w, and the constant $10 per unit materials cost.

(Hint: to find the cost function: step 1: set up the minimization problem, with total cost as the objective function, and the constraint production to achieve the quantity q. step 2: Solve the minimization problem using the Lagrange to find the optimal L and K that would achieve the minimum cost. step 3: Substitute the optimal L and K back into the total cost function.)

Direct Labor Variances

The Freedom Clothes Company produced 15,000 units during June of the current year. The Cutting Department used 2,900 direct labor hours at an actual rate of $14.4 per hour. The Sewing Department used 4,800 direct labor hours at an actual rate of $14.1 per hour. Assume there were no work in process inventories in either department at the beginning or end of the month. The standard labor rate is $14.3. The standard labor time for the Cutting and Sewing departments is 0.2 hour and 0.3 hour per unit, respectively.

a. Determine the direct labor rate, direct labor time, and total direct labor cost variance for the Cutting Department and Sewing Department. Enter a favorable variance as a negative number using a minus sign and an unfavorable variance as a positive number.

b. The two departments have opposite results. The Cutting Department has a(n)   rate and a(n)   time variance, resulting in a total cost variance. In contrast, the Sewing Department has a(n)   rate variance, and has a very   time variance, resulting in a total   cost variance.

Ronaldo Company needs a capital of $200,000; it can either use no debt or use a debt for 60% with a 12% interest rate.
It has 9,000 shares outstanding that are expected to stay constant for any financing strategy taken and it has the following information:

Price/ Unit $5
Variable cost/Unit $2
Fixed costs $50,000
Tax rate 40%

The expected units sold based on probability of economic situation:
Economy Probability Units Sold
Good 0.2 140,000
Normal 0.5 80,000
Bad 0.3 10,000

10.87%

$9.9

$10.87

None of the above

10.87%

$13.07

$10.87

$9.903

103.32%

413.33%

0.565

10.4

1.033%

41.33%

0.565

10.4

$9.18

10.654%

7.245%

$20.22

$9.184

10.654%

$7.245

3.434%

A capacitor C1 =1F is connected to a 1V battery using a wire with a total resistance R = 1Ohm

Suppose after the charging is complete the capacitor C1 is connected to another capacitor C2 = 2 F using a wire with a total resistance of R =0.3 Ohm. Now the first capacitor discharges while the second one charges.

2.8 [1pt] How much charge was transferred through the resistor R during the discharge?

ANSWER

2.9 [1pt] How much energy was dissipated in the resistor R during the discharge

ANSWER

Let’s derive the differential equation describing the discharge in this 2-capacitor circuit. Let’s label the charge on the capacitor C1 as q1(t) and the charge on the capacitor C2 as q2(t).

2.10 [1pt] Sketch the circuit diagram, label the charges and their signs at the capacitors plate, and link q1(t) and q2(t).

Hint, what is q1(t=0) and q2(t=0) (t=0 is the instant the connection was made)?

ANSWER

2.11 [1pt] Express the current through the resistor in terms of the charge derivative and write down the voltages across both capacitors and the resistor add up to zero. From the resulting equation, deduce the characteristic charging time without solving it.

ANSWER