Consider the data set. 2, 4, 6, 8, 9

(a) Find the range. (Enter an exact number.) Correct: Your answer is correct. (

b) Use the defining formula to compute the sample standard deviation s. (Enter a number. Round your answer to two decimal places.)

(c) Use the defining formula to compute the population standard deviation σ. (Enter a number. Round your answer to two decimal places.)

Q1. A hydroelectric power plant uses the reaction of ethylene (?2?4) with oxygen to generate vapour. The products of this reaction are carbon dioxide and water. Additionally, the reaction produces −1323.16?? per mol of ethylene consumed. a) How much ethylene is required by the power plant if 8500 kg of steam at 120 °C is produced in an hour? (assume 100% yield) (12.5 marks) b) Recalculate your answer for a 75 % yield. (12.5 marks) Assumptions. The heat capacities of water are C?? = 4.19 kJ⁄kg°C, ??? = 1.996 ??⁄??°C, the heat of ?? vaporization for water is ∆h? = 2256.9 ⁄??, and the power plant takes water from a source at 15 °C.

A jar contains 4 Orange, 3 Blue, and 2 Green marbles.

(a) Two marbles are selected one at a time at random without replacement, so order is observed in the sample. Define the events:A=“the first marble is Orange”, B= “the second marble is Orange”. Find(i)P(A), (ii)P(B), (iii)P(A∪B) =P(at least one Orange marble is obtained in the 2 draws).

Show your work.

(b) Suppose instead three marbles are chosen at random from the jar by choosing 3 in one hand; no or-der is observed. What is the probability that the sample of 3 marbles contains 1 marble of each color?

$4,000 is invested at 4%p.a compounding semi-annually for the first 2 years and at 12% p.a compounding quarterly for the following 3 years. What is the future value at the end of 5 years?

Parramore Corp has $14 million of sales, $2 million of inventories, $4 million of receivables, and $2 million of payables. Its cost of goods sold is 75% of sales, and it finances working capital with bank loans at an 7% rate. Assume 365 days in year for your calculations. Do not round intermediate steps.

1. What is Parramore's cash conversion cycle (CCC)? Do not round intermediate calculations. Round your answer to two decimal places.
     days
2. 
   
3. If Parramore could lower its inventories and receivables by 7% each and increase its payables by 7%, all without affecting sales or cost of goods sold, what would be the new CCC? Do not round intermediate calculations. Round your answer to two decimal places.
     days
4. 
   
5. How much cash would be freed up, if Parramore could lower its inventories and receivables by 7% each and increase its payables by 7%, all without affecting sales or cost of goods sold? Do not round intermediate calculations. Round your answer to the nearest cent. Write out your answer completely. For Example, 13.2 million should be entered as 13,200,000.
   $
6. 
   
7. By how much would pretax profits change, if Parramore could lower its inventories and receivables by 7% each and increase its payables by 7%, all without affecting sales or cost of goods sold? Do not round intermediate calculations. Round your answer to the nearest cent. Write out your answer completely. For Example, 13.2 million should be entered as 13,200,000.
   $

(a) Find the Riemann sum for

f(x) = 4 sin(x), 0 ≤ x ≤ 3π/2,

with six terms, taking the sample points to be right endpoints. (Round your answers to six decimal places.)
R₆ =

(b) Repeat part (a) with midpoints as the sample points.
M₆ =

If m ≤ f(x) ≤ M for a ≤ x ≤ b, where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then

m(b − a) ≤

≤ M(b − a).

Use this property to estimate the value of the integral.

Preform the following calculations on the sample below:

{ 6, 2, 0, 4, 7, 8, 5, -1, 7, -2, 0 }

1. What is the sample size of the dataset
2. Calculate the mean
3. Find the median
4. Find the mode
5. Calculate the sample variance and sample standard deviation )
6. Find the 10^th and 75^th percentile of the data ().

A body weighing 2 pounds forces hangs from a spring with constant 4 lb / ft. The medium in which the body moves offers a resistance force to movement that is numerically equal to its instantaneous speed. If the weight is released 1/3 feet above its balance position with a downward speed of 9 feet per second, determine the speed at which time it passes through the balance position. Consider negative downward and positive upward magnitudes.