a. Consider a population in which the frequency of allele B is p=0.7, and the frequency of the allele b is q=0.3. If W BB= 1, W Bb= 0.9, and W bb= 0.8, what will be the frequency of B after one generation?

b. If the allele frequency for a dominant allele is 0.84, what is the allele frequency for the recessive allele?

The weights of ice cream cartons are normally distributed with a mean weight of 8 ounces and a standard deviation of 0.3 ounce.

​(a) What is the probability that a randomly selected carton has a weight greater than 8.09 ​ounces?

​(b) A sample of 16 cartons is randomly selected. What is the probability that their mean weight is greater than 8.09

ounces?

Is there any relationship between returns to scale and economies of scale? Assume a production function q = 100(K^0.7*L^0.3), where K is capital and L is labor. Derive the marginal product of labor and the marginal product of capital. Show that the marginal product of labor is decreasing (hint: beginning with K = 2, and L = 50)

Weights of 10-ounce bag corn chips follow a normal distribution with µ=10 and σ=0.3 ounces. Find the probability that

–(i) the sample mean weight of 49 randomly selected bags exceeds 10.25 ounces.

–(ii) the sample mean weight of 49 randomly selected bags is less than 10.20 ounces.

Suppose the alphabet is S = {A B C D} and the known probability distribution is P_A = 0.3, P_B = 0.1, P_C = 0.5, and P_D = 0.1. Decode the Huffman coding result {11000010101110100} to the original string based on the probability distribution mentioned above. The codeword for symbol “D” is {111}. Please writing down all the details of calculation.

A car is to be hoisted by elevator to the fourth floor of a parking garage, which is 48 ft above the ground. Part A If the elevator can accelerate at 0.8 ft/s2, decelerate at 0.3 ft/s2, and reach a maximum speed of 8 ft/s, determine the shortest time to make the lift, starting from rest and ending at rest.

A 2.0-g particle moving at 8.6 m/s makes a perfectly elastic head-on collision with a resting 1.0-g object. (a) Find the speed of each particle after the collision.

(b) Find the speed of each particle after the collision if the stationary particle has a mass of 10 g.

(c) Find the final kinetic energy of the incident 2.0-g particle in the situations described in parts (a) and (b).

In which case does the incident particle lose more kinetic energy? case (a) case (b)  

1.)

a. Create a graph of the data below, then calculate the slope to find the spring constant 'k'.

b. Describe the functional relationship between all of this data (in other words, how does all of this connect?)

c. Calculate the gravitational potential energy and the spring potential energy of the 0.2, 0.4, 0.6, 0.8, and 1.0 kg masses.

d. Are there any patterns between these two types of potential energy? Why or why not?

A point charge of 6.0 x10^-8 C sits on the floor in the middle of a room that is 10 m long. You hold a small cardboard square measuring 1.0 cm x 1.0 cm face down, and carry it across the room at a height of 2.0 m, passing over the position of the point charge. Plot the flux through the square as a function of position, but before doing so, make sure to include the following:

-An explanation of your calculation. Also, show quantitatively that the field at the center of the square is approximately the field at one of the edges.

-A table showing your calculation with the distances, E field, flux values, and other calculations you made.

-Finally, make a plot of the flux as a function of position. Axes must be properly labeled with units.

100 moles/hour of pure ethane at 25 degrees Celsius and 1.0 atm are burned with 50.0% excess air producing a desired product of carbon dioxide and an undesired product of carbon monoxide. The fractional conversion of the ethane is 80.0% (on a molar basis). 95% of ethane that reacts goes to carbon dioxide. Determine the molar flow rate and molar composition of the gaseous product stream, which is at 400 degrees Celsius and 1.0 atm.

Completely label your diagram, list the temperature, pressure, flow rate, and composition (mole fractions with indexes) for eac stream, supply values and units for knowns and question marks for unknowns.

Chemical Reactions:
I: __C2H6 + __O2 ---> __CO2 + __ H2O
II: __C2H6 + __O2 ---> ___CO + ___H2O