A spring with a mass of 2 kg has a damping constant 14 kg/s. A force of 3.6 N is required to keep the spring stretched 0.3 m beyond its natural length. The spring is stretched 0.7 m beyond its natural length and then released. Find the position of the mass at any time t. (Assume that movement to the right is the positive x-direction and the spring is attached to a wall at the left end.) What is x(t)?

A statistician claims that the proportion of students who will vote for Mr. K to be the next president is 0.54 with the standard deviation of 0.3.

1. Identify the hypothesis test
2. If 1000 students are randomly selected and 455 of them will not vote for Mr. K, what is the P-value? What can you conclude based on 5% significant level?
3. Construct a 95% Confidence Interval
4. If Mr. K is ended up losing the election, does this make sense? Why or why not?

4. Calculate the percent recovery for each component if 0.047 g of fast component and 0.038g of slow component, when you started with 0.103 g of mixture.

5. What is the Rf value for slow component using 30% ethyl acetate/hexane? Distance of first spot 0.3 cm, distance of the second spot 4.7 cm and the solvent traveled 6.1 cm.

These questions relate to a TLC and colum chromatography organic chemistry lab

A 10 m³ mixture solution contains molecules A, B and C in water at ambient temperature.

Calculate:

(a) Each species mass concentration.

(b) Their molar concentration.

(c) Total mass concentration and molar concentration.

(d) Mass and mole fraction.

given:

V_mix= 10 m³

m_A= 0.3 kg , m_B= 0.5 kg , m_C= 0.4 kg , m_H2O= 9.8 kg

MW_A= 50 , MW_B= 250 , MW_C= 10 , MW_H2O= 18

Calculating the variance and standard deviation: Barbara is considering investing in a stock and is aware that the return on that investment is particularly sensitive to how the economy is performing. Her analysis suggests that four states of the economy can affect the return on the investment. Using the table of returns and probabilities below, find the expected return and the standard deviation of the return on Barbara’s investment.

Q.2.Two sinusoidal waves combining in a medium are described by the wave functions y1 = (0.3m ) cos (2πx +40πt) y2=( 0.3 m) sin (2πx +40πt ) (i). What will be the resultant displacement wave function expression and what type of the resultant wave will be generated by it. [3] (ii). What will be the amplitude, frequency and the speed of the resultant wave? [3] (iii).Find the transverse velocity and transverse acceleration at x= 0.25m, and t= 2sec?

The probability that a student correctly answers on the first try (the event A) is P(A) = 0.3. If the student answers incorrectly on the first try, the student is allowed a second try to correctly answer the question (the event B). The probability that the student answers correctly on the second try given that he answered incorrectly on the first try is 0.4. Find the probability that the student answers the question on the first or second try.

a) 0.88

b) 0.12

c) 0.70

d) 0.42

e) 0.58

Suppose that the USDA expects that 53.3 billion bushels of soybeans will be produced this year at a price of $8.50/bushel. Assume that the elasticity of supply is 0.3 and that the elasticity of demand is -0.2 (both very inelastic).

1. Derive the linear supply and demand curves for this equilibrium.

2. What quota is required to increase the soybean price to $9.25/bushel? And what is the economic cost of this solution (i.e., what is the change in producer surplus and change in consumer surplus, and what is the sum of these changes)?

1. An investor holds a portfolio which is expected to yield a rate of return of 18% with a standard deviation of 2.5%. The investor is considering buying a new share (investment being 5% of the total investment in the new portfolio). The share has the following distribution of return:

The correction coefficient between the new portfolio and the new security is 0.3; calculate the portfolio return and standard deviation of the portfolio.                                       [10 marks]

How to create a compacted data set by combining the columns Old, Older, Young, Younger and place them in into one single new column called age using python pandas.