Calculate the pH of a solution made by combining 45 mL of 0.3 F acetic acid with 28 mL of 0.4 F sodium acetate. Assume that pKa for acetic acid is 5.00. ?

A beam with a cross-section of 0.3 m x 0.7 m has an effective depth of 0.638 m and a span of 4.30 m. Use the following data below to determine (a) the steel requirement due to flexure, (b) ultimate threshold torsion, and (c) spacing of stirrup due to combined shear and torsion:

M_u = 322 KN-m

V_u = 317 KN

T_u = 42 KN-m

f'c =28 MPa

f_yt = 414 MPa

12 mm stirrup diameter

cover of 0.04 m

An autosomal gene is segregating two alleles, R and r, with respective frequencies 0.3 and 0.7. If mating is random, what are the expected frequencies of the genotypes? Now suppose that every individual in the population mates with a sibling. What will the genotype frequencies be among the offspring? Suppose instead that every individual mates with a first cousin. What will the genotype frequencies be among their offspring? Finally, suppose that after many generations of random mating, every individual in the population reproduces by self- fertilization. What will the genotype frequencies be among the offspring of this kind of inbreeding?

Consider a vertical plate of dimension 0.25 m × 0.3 m that is at Ts= 90°C in a quiescent environment at ?T?= 20°C. In the interest of minimizing heat transfer from the plate, which orientation, (A) or (B), is preferred? What is the convection heat transfer from the front surface of the plate when it is in the preferred orientation? Evaluate the properties of air at the film temperature.

Determine the convection heat transfer from the front surface of the plate when it is in the preferred orientation, in W.

1. You are given Pr(A) = 0.3, Pr(B) = 0.5 and Pr(A ∪ B) = 0.6. (a) WhatisPr(A∩B)?

(b) What is Pr(notA)?

2. A bag contains 30 balls of the same size. Each ball is either red or green.

The probability of choosing a green ball is 0.7. How many of the balls are red?

3. Given nPr =42 and nCr =7 find the value of r?

4. We have Pr(A|B) = 0.3 and Pr(B) = 0.45. What is Pr(A ∩ B)?

5. How many 3 digit numbers can be created from the set {1, 2, 3, 4, 5, 6} if the digits cannot be repeated?

6. What is the probability of choosing 10 cards at random from a standard deck of 52 cards and getting exactly 2 queens?

7. What is the variance of the numbers 3, 7, and 8?

8. We have a discrete probability distribution where P r(X = 1) = 0.2,

Pr(X = 2) = 0.3 and Pr(X = 3) = 0.5. Determine μ.

9. We have a discrete probability distribution where P r(X = 1) = 0.6,

Pr(X=3)=0.1,Pr(X=5)=0.3andμ=2.4. Determineσ2.

10. We have a binomial distribution where the probability of success is 0.4 and the number of trials is 3,000. What is the variance of the distribution?

HELP 1-10!!!!!!!!

Consider a 0.3 L aqueous solution that contains 2.6 g of caffeine. The solubility of caffeine in water is 2.2 g/100 mL and the solubility in methylene chloride is 10.2 g/100 mL.

a) How much caffeine can be extracted with 70 mL of methylene chloride?

b) How much caffeine will be extracted if the aqueous solution is extracted twice with 30 mL of methylene chloride?

c) Which is more effective a or b?

A cylinder of mass 0.3 kg and radius 8 cm (and I = 1/2 mR2 ) is placed at the top of a long, straight ramp of length 2 meters. The cylinder is released from rest and allowed to roll without slipping to the bottom. When it reaches the bottom, it is rotating at a rate of 6.5 rev/s. Answers included. Need the process.

a) What is the linear speed at the bottom of the ramp? 3.3m/s

b) What is the total KE of the cylinder at the bottom of the ramp? 2.4J

c) Use conservation of mechanical energy for the Earth-cylinder system to find the height of the ramp. .8m

d) What were the linear and angular accelerations of the cylinder down the incline (hint: use kinematics)? 2.7m/s^2

6. Given the Earth's albedo of A = 0.3, what surface temperature do you predict at equilibrium? Is this consistent with the Earth's actual average temperature of 14C? How do you explain the discrepancy?

4. Suppose that an economy's production function is Cobb-Douglas with parameter a=0.3.

a. What fractions of income do capital and labor receive?

b. Suppose that immigration increases the labor force by 10 percent. What happens to the total output (in percent)? The rental price of capital? The real wage?

c. Suppose that a gift of capital from abroad raises the capital of stock by 10 percent. What happens to the total output (in percent)? The rental price of capital? The real wage?

d. Suppose that a technological advance raises the value of the parameter A by 10 percent. What happens to the total output (in percent)? The rental price of capital? The real wage?