Given the price elasticities and price changes for the following products A–E in the table below, show how much the quantity will change (indicating an increase or decrease) and what effect this will have on total revenue (indicating an increase or decrease). Round your answers to 1 decimal place.

Enter the exponential decay function described in the situation and answer the question asked. You may find using a graphing calculator helpful in solving this problem.

Carbon-14 is a radioactive isotope of carbon that is used to date fossils. There are about 1.5 atoms of carbon-14 for every trillion atoms of carbon in the atmosphere, which known as 1.5 ppt (parts per trillion). Carbon in a living organism has the same concentration as carbon-14. When an organism dies, the carbon-14 content decays at a rate of 11.4% per millennium (1,000 years). Write the equation for carbon-14 concentration (in ppt) as a function of time (in millennia) and determine how old a fossil must be that has a measured concentration of 0.3 ppt. Round your answer to two decimal places.

The exponential decay function is c (t) = _________ .

The fossil is about ________ millennia old.

Please show the steps

1) Radio waves travel at the speed of light, 300,000 km/s. The wavelength of a radio wave received at 100 megahertz is            1) _______

A) 3.0 m.

B) 300 m.

C) 0.3 m.

D) 30 m.

E) none of these

22) Two charged particles repel each other with a force F. If the charge of one of the particles is doubled and the distance between them is also doubled, then the force will be    22) ______

A) F/4.

B) 2 F.

C) F/2.

D) F.

E) none of these

23) Two charged particles attract each other with a force F. If the charges of both particles are doubled, and the distance between them also doubled, then the force of attraction will be            23) ______

A) 2 F.

B) F/4.

C) F.

D) F/2.

E) none of these

1. An investment website can tell what devices are used to access the site. The site managers wonder whether they should enhance the facilities for trading via smartphones so they want to estimate the proportion of users who access the site using smartphones. They draw a random sample of 200 investors from their customers. Suppose that the true proportion of smartphone users is 36%.
   1. What would you expect the shape of the sampling distribution for the sample proportion to be?
      
   2. What should the mean of this sampling distribution be?
      
   3. If the sample size was increased to 500, would either of your answers to parts (a) or (b) change? Explain.
      
   4. What would the standard deviation of the sampling distribution of the proportion of smartphone users be?
      
   5. What is the probability that the sample proportion of smartphone users is above 0.36?
      
   6. What is the probability that the sample proportion of smartphone users is between 0.3 and 0.4?
      
   7. What is the probability that the sample proportion of smartphone users is below 0.28?

A city has just added 110 new female recruits to its police force. The city will provide a pension to each new hire who remains with the force until retirement. In addition, if the new hire is married at the time of her retirement, a second pension will be provided for her husband. A consulting actuary makes the following assumptions: (i) Each new recruit has a 0.3 probability of remaining with the police force until retirement. (ii) Given that a new recruit reaches retirement with the police force, the probability that she is not married at the time of retirement is 0.35. (iii) The number of pensions that the city will provide on behalf of each new hire is independent of the number of pensions it will provide on behalf of any other new hire. Determine the probability that the city will provide at most 62 pensions to the 110 new hires and their husbands. Enter your answer as a number accurate to 4 decimal places.

Consider a single firm producing an allergy medication under patent. (You can think of the quantity of allergy medication in terms of bottles of medication). The demand for allergy medication is given by ?? = 100 ? 0.1????. The marginal cost of producing allergy medication is given by ???? = 5 + 0.3???? .

a. Graphically illustrate the profit maximizing quantity of allergy medication and the price the firm charges. Though you do not have an equation, draw in an average cost curve for the monopolist in your graph.

b. Label profit in your graph. In the graph you’ve drawn, is the monopolist earning positive economic profit? Does this tell you whether the monopoly is operating in the long run or the short run?

c. Calculate and label the allocative efficient quantity of allergy medication in your graph.

d. Does the monopolist charge a markup above marginal cost? If so, calculate the size of the markup.

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.78.

(a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 19 specimens from the seam was 4.85. (Round your answers to two decimal places.)

  ,

(b) Compute a 98% CI for true average porosity of another seam based on 13 specimens with a sample average porosity of 4.56. (Round your answers to two decimal places.)

  ,

(c) How large a sample size is necessary if the width of the 95% interval is to be 0.3? (Round your answer up to the nearest whole number.)
specimens

(d) What sample size is necessary to estimate true average porosity to within 0.25 with 99% confidence? (Round your answer up to the nearest whole number.)
specimens

STAT 14_3:

Ronit has a box with beads. The beads are opaque or transparent and available in several colors.
The probability of a random bead being red is 0.3. The probability of a bead being transparent is 0.6.
Of the red beads - the probability of a random bead being transparent is 0.5.

a. Remove 8 beads from the box at random and upon return. What is the probability that exactly two of them will be red?

b. Take beads out of the box accidentally and on return until you first remove a transparent bead
i. What is the probability of getting more than 4 beads?
ii. The first two beads taken out were not transparent. What is the probability of getting 7 beads out of the box?

c. Remove 10 beads from the box at random and upon return. What is the probability that exactly three of them will be red and transparent, two opaque and red and 5 transparent and red?

Robert Company makes bottles. The followings are the extracted information:

The Company gets a special order of 8,000 units. If the Company accepts the order, it has to incur an additional package cost $0.3 per unit.

a)  Calculate the profit /(loss) impact if the Company accepts the special order, (assume no other fixed costs are affected.) if the special order unit price is $20.

b) Advise if the Company should accept the special order quantitatively.  

Problem 13.35. A biotech manufacturing company can make test kits at a cost of $ 20.00. Each “kit” for which there is a glove demand the week it is manufactured can be sold for $ 100.00. However, due to the short life of its components, each “kit” that cannot be sold during that week has to be discarded at a cost of $ 5.00

The weekly demand for that product is a random variable with the following pmf:

1) Calculate the expected value of the demand for “kits” during one week (5 pts)

2) Calculate the variance of demand for a week (5 pts)

3) The company could manufacture 50 “kits” per shift. If they decide to go into business, how many shifts must they work (1, 2, or 3) to maximize the expected profit?