Same topic:

1. Consider all passwords of length 10 made up of numbers, lower-case letters, and upper-case letters (from the English alphabet).

a) If you pick such a password at random, what is the likelihood that it contains exactly 5 lower-case letters?

b) If you pick such a password at random, what is the likelihood that it contains at most 9 lower-case letters?

2. Suppose you’re an ornithologist who specializes in American crows (Corvus brachyrhynchos), and you’ve collected data on 100 such birds. Each bird was classified by sex (male or female), and by size (large or small).

The counts follow:

• Male, Large: 38,

• Male, Small: 13,

• Female, Large: 23,

• Female, Small: 26.

Based on these numbers, what is the probability that a randomly chosed crow from this group is large?

What is the probability that a crow is large if it is already known to be male? Is the event of being large independent of the event of being male?

1. Schell Publishing received a $70,000 promissory note at 12% ordinary interest for 60 days from one of its customers. After 20 days, Schell discounted the note at the bank at a discount rate of 14.5%. The note was made on March 21.

a. (What is the maturity date on the note?

b. What is the maturity value of the note?

c. What is the discount date of the note?

d. How many days is the discount period for?

e. What is the bank discount that the bank will receive?

f. What proceeds will Schell receive after discounting the note?

Problem 4-01 (Algorithmic)

The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year’s program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown:

To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized.

1. If the promotional budget is limited to $16,400, how many commercial messages should be run on each medium to maximize total audience contact? What is the allocation of the budget among the three media? If required, round your answers to the nearest dollar.
   

   Let	T = number of television spot advertisements
   	R = number of radio advertisements
   	O = number of online advertisements

   	Budget ($)
   T =
   R =
   O =
   	Total Budget = $

   
   What is the maximum total audience that would be reached? Round your answer to the nearest whole number.
   
   
   
2. By how much would audience contact increase if an extra $100 were allocated to the promotional budget? Round your answer to the nearest whole number.
   

Are the vectors v1 = (1 , 2, 3), v2 = (2, 4, 6), and v3 = (1, 1, 3) linearly independent or dependent? Since v2 is a scalar multiple of v1, both v1 and v2 are linearly dependent, but what does that say about the linear dependence of the three vectors as a whole?

how is geometry used in Architecture and/or Engineering? Think about terms you have learned so far, including parts of a circle and be sure to include these and examples in your discussion. Write your response in 1-2 paragraphs.

A large tank with total capacity of 400 gallons is filled with 300 gallons of fluid in which 50 lbs. of salt is dissolved. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 3 gal/min. The well mixed solution is pumped out at a slower rate of 2 gal/min.

a. Find the number A(t) of pounds of salt in the tank at time t.

b. When will the tank overflow?

9. Let G be a bipartite graph and r ∈ Z>0. Prove that if G is r-regular, then G has a perfect matching.1

10. Let G be a simple graph. Prove that the connection relation in G is an equivalence relation on V (G)

Dr. Bellus wants to study how people's perception of attractiveness is affected by the gender of the subjects, and the facial expression of the object. Each participant views six headshots (in random order) of the same person, who demonstrates different facial expressions (joy, surprise, fear, anger, sadness, and disgust) in each picture. The participants are then asked to rate the attractiveness level of each picture. The rating is the dependent variable. Below is the selected output of a two-factor split plot ANOVA.

(a) Identify the between-subjects factor and within-subjects factor.

(b) Are the effects significant (α = .05)? What do these results tell us about people's perception of attractiveness?

(c) Is MCP necessary? If so, which effect(s) should we conduct MCP on?

Show that the numbers 1, 3, 3^2 , . . . , 3^15 and 0 for a complete system of residues (mod 17). Do the numbers 1, 2, 2^2 , . . . , 2^15 and 0 constitute a complete system of residues (mod 17)?

if you have a numerically integrate an arithmetic function. What technique is considered to be the most efficient in terms of accuracy versus effort? Is this always so? explain.

Suppose you and two other mathematicians are milling around the food table before aseminar, eyeing the last four slices of cheese. How can you divide the four slices equallyamong the three of you?(a) Based on common sense, how much cheese should each of you get?5

(b) One of your mathematician friends suggests the following solution: “Let’s eachtake one of the slices of cheese, which leaves one slice for us to share. Instead ofcutting the remaining piece in thirds, let’s cut it into quarters, and each take aquarter of the leftover slice. We’re going to keep doing this, always cutting theremaining slice into quarters, taking a slice until there are only crumbs too smallto be of interest to anyone. Sound good?”i. How much cheese will you have accrued after the third iteration? Fourth?Write the amount of cheese you will get via this process as an infinite sumusing sigma notation.ii. Based on your answer in part (a) what can you say about the value of thesum in part i?

Michael is considering two job offers. • The manager position pays a salary of $59,000.00 per year and includes two weeks of paid vacation, five sick days per year, paid health insurance and a fully paid retirement plan. • The technician position pays an hourly wage of $30.00 per hour and includes five vacation days per year, five sick days per year, health insurance costs $35.00 per month, and a retirement plan that costs 1% of after tax income. The government takes out 6.2% for Social Security, 1.45% for Medicare, and 15% for income tax. Assume that Michael will take 10 vacation days and five sick days per year. 5-Calculate the after tax monthly income for the technician position. 6-The manager position includes two weeks (10 days) of vacation. Calculate the monthly cost for vacation for the manager position. Explain how you calculated your answer. 7-Calculate the monthly cost of a retirement plan for the technician position. 8-Calculate the NET monthly income for the manager position. Recall that "net" means after all deductions are taken, including taxes, health insurance, vacation, sick leave and retirement. 9-Calculate the NET monthly income for the technician position. Recall that "net" means after all deductions are taken, including taxes, health insurance, vacation, sick leave and retirement.

Write a program to compute 2 point Gauss quadrature on a single interval. Your input should be a function with f,a,and b. Verify it by checking that the error in using the rule for f(x)=x^3 - 3x^2 +x - 7 is zero. In matlab please.