Summerville Inc. is considering an investment in one of two common stocks. Given the information in the popup​ window: ​, which investment is​ better, based on the risk​ (as measured by the standard​ deviation) and return of​ each? a. The expected rate of return for Stock A is nothing ​%. ​ (Round to two decimal​ places)

COMMON STOCK A COMMON STOCK B PROBABILITY RETURN PROBABILITY RETURN 0.20 12% 0.20 -6% 0.60 15% 0.30 7% 0.20 18% 0.30 15% 0.20 20%

1. Consider a biased dice, where the probability of rolling a 3 is 4 9 . The dice is rolled 7 times. If X denotes the number of 3’s thrown, then find the binomial distribution for x = 0, 1, . . . 7 and complete the following table (reproducing it in your written solutions). Give your answers to three decimal places.

2. The Maths Students Society (AUMS) decides to conduct small lottery each week to raise money. A participant must pays $2 to enter and chooses three distinct numbers between 1 and 10 (the order does not matter). If their three chosen numbers match the three numbers drawn by AUMS they win a $70 jackpot offered each week, otherwise they recieve nothing. No two entries can use the same numbers.

(a) How many distinct entries can there be?

(b) Write out the probability distribution of returns for one random entry?

(c) A student enters 15 times in one week with different sets of numbers. Determine their probability of winning and the expected return.

(d) A different student enters once each week for 12 weeks. Determine their probability of winning at least once and the expected return.

(e) Suppose 20 entries are made every week for a year. By first calculating the expected amount raised each week, determine how much money AUMS expects to raise in a year?

31. Consider the function f(x) = 3x⁴ − 8x³ + 1.

(a) Find the derivative f 0 (x), and hence the critical points for the function (for this question give both x and y coordinates).

(b) Classify the critical points using the first derivative test to determine if they are local maximum or minimum or neither.

(c) Find any points of inflection for f(x) (give both x and y coordinates).

The language is C++

Below are a list of sequences of numbers. Your job is to program each sequence with any loop of your preference (while, for, do/while). I want the code to output the sequence provided and the next number in the sequence (you can output more but there is 1 sequence that may only have 1 number after).. Please order and notate each sequence in your output –. The output should also be horizontal like that shown below (if you output it vertically it will be -10pts). Each sequence should be programed with only 1 loop and optionally 1 selection statement. Hint: a selection statement may be used for the last 3 problems.

Series 1:

15, 14, 13, 12, 11, ...

Series 2:

1, 2, 5, 14, 41, ...

Series 3:

2, 3, 5, 8, 12, 17, ...

Series 4:

15, 13, 11, 9, 7, ...

Series 5:

71, 142, 283, 564, 1125, 2246, 4487, 8968, ...

Series 6:

10, 5, 1, -2, -4, -5, -5, -4, -2, ...

Series 7:

0, 1, 3, 7, 15, 31, 63, ...

Series 8:

0, 1, 4, 13, 40, 121, ...

Series 9:

15, 29, 56, 108, 208, 400…

series 10: (finite)

0, 1, 3, 6, 10, 10, 11, 13, 16, 16, 17, 19, 19, ...

series 11:

7, 9, 14, 20, 27, 33, 42, 52, 63, 73, 86, ...

Series 12:

13, -21, 34, -55, 89 ...

Series 13:

0, 1, 4, 12, 32, 80, 192, ...

Provide a procedure to separate a mixture composed of 50% Ethyl Aminobenzoate, 40% Benzil, 10% and 1,4-dibromobenzene.

Problem 1: For the following linear programming problem: ???????? ? = 40?1 + 50?2

Subject to constraints:

3?1 − 6?2 ≥ 30

?1 – 15 ≤ 3?2 2

?1 + 3 ?2 = 24

?1, ?2 ≥ 0

1- Find the optimal solution using graphical solution corner points method or iso profit line method. Please, show the values for state variable, decisions variables, and slack and surplus variables

2- Determine the value for basic solution and non-basic solution, binding constraints and nonbinding constrains, and if there are any redundant constraints

3- Identify if there is any special case solution and state it.

solve using linear programming graphical solution

In a team of 50 people, 20 pilots are under 40 years old. 15 pilots are over 40 years old. Five of the non-pilots are under the age of 40, the rest are over the age of 40. Find the probability of being a pilot or over 40 when a random person is selected.

It sampled 40 customers in San Francisco and 50 customers in San Diego to assess potential demand.

On a scale of 1-7 (7 = very likely to buy), San Diego customers had a mean of 3.5 with a standard deviation of 1.1. SF customers had a mean of 4.1 with a standard deviation of 2.3.

Are these markets statistically different?

1.Compute standard error

2.Compute t-calc  

3.Compare |t-calc| to 1.96 (95% confidence in our results) and 2.58 (99% confidence)

4.If |t-calc| > 1.96, reject the null with 95% confidence

●

Standard error for 2 means (sxs_x ̅ ) = ?12?1+?22?2√((s_1^2)/n_1 +(s_2^2)/n_2 )

T-calc for 2 means = ?1−?2??(x ̅_1-x ̅_2)/s_x ̅

1500 pound per hour of a waste mixture of 40% benzene, 50% toluene and 10% of water is burned with 25% excessive air. Determine the total heat released and the percent by volume of each component in the flue gas.
thank you.