Solve the following DEs

1.) dy/dx + y =e^3x

2.) x^2y' +xy = 1

3,) x(dy/dx)-y = x^2 sin(x)

4.) y' - 2y = e^2x, y(0) = 2

5.) cos(x)(dy/dx) + ysin(x) = 1, y(pi/4) = 0

2. Two expert French chefs judged chocolate mousse made by students in a Paris cooking school. Each chef ranked the best

   chocolate mousse as 1.

   Student	1	2	3	4	5
   Rank by Chef Pierre	4	2	3	1	5
   Rank by Chef Andre	4	1	2	3	5

   Use a 5% level of significance to test whether there is a positive association between ranks given by Chef Pierre and by Chef Andre.

   1. 2.1 State the null hypothesis in words.

   2. 2.2 Compute the value of the test statistic

Which of the following doesn’t belong?

(Group of answer choices)

1. Type 1 alveolar cells.

2. zymogenic cells.

3. enteroendocrine cells

4. oxyntic cells.

5. goblet cells.

Enamel:

1. is made of the same material as bone.

2. is the hardest substance in the human body.

3. none of the above.

4. all of the above.

5. forms the surface of the crowns of teeth.

Pharyngeal constrictor muscles:

1. assist with gustation.

2. are used mainly used in relaxed expiration.

3. assist with mastication.

4. none of the above

5. are used for deglutition.

Question 1

The single sample t-test compares the ________ of a single sample (group) to a known population mean.

1) mean

2) standard deviation

3) scores

4) variance

Question 2

The distributions from which the scores are taken should be normally distributed. Hint: Refer to your book and look at Assumptions.

1) True

2) False

Question 3

To run the single sample t-test in SPSS you need to click on the following:

Analyze

Compare Means

One-Sample t Test

1) True

2) False

Question 4

In SPSS, the number entered into the TEST VALUE section is the ___________ mean.

1) average

2) sample

3) population

4) none of these answers are correct

Question 5

The output for the single sample t-test has _____ sections.

1) 3

2) 5

3) 8

4) 2

Question 6

Given an alpha level of .05, the values in the one-sample, t test output below indicate a statistically significant result.

1) True

2) False

Question 7

Given an alpha level of .05, the correct statistical decision for the results output below is to reject the null hypothesis.

1) True

2) False

The superintendent of a large school district speculated that high school students involved in extracurricular activities had a lower mean number of absences per year than high school students not in extracurricular activities. She generated a random sample of students from each group and recorded the number of absences each student had in the most recent school year. The data are listed below. Test the superintendent’s claim at the α=.01 significance level. [To receive full credit, your response should be sure to state your hypotheses, check the relevant requirement(s), find a test value, find a critical value or p-value (either is OK), make your decision, and state your conclusion.]

Students in EC Activities: 4 1 2 0 5 6 2 1 0 3 0 1 1 4 8 6 9 2 0 4 2 10 5 6 1

Students not in EC Activities: 5 7 0 9 4 3 12 8 4 2 0 5 5 4 9 14 6 10 9 6 3

1)Lets do a simple bayesian calculation.

60% of frogs are female, the rest male.

All male frogs sing, but only 10% of female frogs sing.

You hear a frog singing.

What is the posterior probability that this singing frog is male?

(hint! The probability of any frog singing is the probability  of a singing female (.6 x .1) plus that of a singing male (.4 x 1))

1)23%

2)35%

3)75%

4)87%

2)Which is the most complicated model for molecular sequence evolution?  

1)Jukes Cantor

2)F81

3)HKY

4)GTR

3)You run modeltest on your data and determine that you do not have equal frequencies of bases, but you don't see any evidence that transversions are any more or less common than translations. Which model should you use?

1)JC

2)F81

3)HKY

4)GTR

4)The support values on trees generated via bayesian methods convey:

1)How likely that clade is

2)What proportion of trees that are likely to come from the provided data contain the clade in question

3)How many substitions are found in the sequences between two taxa

4)The quality of the analysis

1. You found two things at Mapua! The first item weighs weight1 and is worth value1, and the second item weighs weight2 and is worth value2. What is the total maximum value of the items you can take with you, assuming that your max weight capacity is maxW and you can't come back for the items later?

Please make a matlab program

Consider a monopoly facing inverse demand function ?(?) = 12 − ?, where ? = ?1 + ?2 denotes the monopolist’s production across two plants, 1 and 2. Assume that total cost in plant 1 is given by ??1 (?1 ) = (5 + 4?1)?1, while that of plant 2 is ??2 (?2 ) = [5 + (4 + ?)?2]?2, where parameter ? ≥ 0 represents plant 2’s inefficiency to plant 1. When ? = 0, the total (and marginal) cost of both plants coincide; but when ? > 0, plant 2 has a higher total and marginal cost than plant 1. a) Write down the monopolist’s joint profit maximization problem ? = ?1 + ?2. b) Find the optimal production in each plant. c) How does total optimal production change in the inefficiency of plant 2, ?? Answer this question by finding ?? ??. What is the optimal production in each plant if ? = 0?

Need explanation how these values are found using algebra, answers needing to be a percentage; "r" is the forward rate:  

1 year coupon: $97=100/(1+r₁)¹

2 year coupon: $94= 100/(1+r₂)²

3 year coupon: $93= 100/(1+r₃)³

4 year coupon: $90= 100/(1+r₄)⁴

Which of the following statements are correct for 2 moles of an ideal gas?

1)   A plot of P versus T at constant V will give a straight line.

2)   A plot of V versus T at constant P will give a straight line having a slope = R / P.

3)   A plot of PV /T versus P will give a straight line having a zero slope.

4)   A plot of PV versus T will give a straight line having a zero slope.

5)   A plot of PV /RT versus P will give a straight line having a slope = 2.

• A.

  2, 3 & 4

• B.

  1 & 3

• C.

  2, 4 & 5

• D. 1, 3 & 5

• E.

  1 & 2