1. Given the following weighted intervals in form of (si, fi, vi) where si is the start time, fi is the finish time, and vi is weight, apply the DP algorithm you learn from lecture to compute the set of non-overlapping intervals that have the maximum total weight. (5, 12, 2) (7, 15, 4) (10, 16, 4) (8, 20, 7) (17, 25, 2) (21, 28, 1)

1) Show the dynamic programming table that computes the maximum total weight.

2) With above computed table, show the steps to determine the set of non-overlapping intervals that have the maximum total weight.

QUESTION 1. For each of the following, state whether the occurrence of the variable x occurs bound, or free (i.e. unbound), both, or neither.

1. ∃xCube(x)

2. ∀xCube(a) ∧ Cube(x)

3. ∀x((Cube(a) ∧ Tet(b)) → ¬Dodec(x))

4. ∃yBetween(a,x,y)

5. ¬∀x¬(¬Small(d) ∧ ¬LeftOf(c,x))

QUESTION 2. Correctly label each of the following strings of symbols as a sentence, or well-formed formula (but not a sentence), or neither.

1. Fx ∧ Gy

2. ∃bFb

3. ∃z(Fz → Gb)

4. ∀xFc

5. ∀yFy ∨ ¬Fy

6. ¬∃¬xGx

Help me please with these questions thank you

LABEL EACH OF THE 4 HYPOTHESIS STEPS IN YOUR WORK PLEASE! FOR A 5 STAR RATING

13. A recent study indicates that simply giving college students a pedometer can result increased walking (Jackson & Howton, 2008). Students were given pedometers for a 12- week period and asked to record the average number of steps per day during weeks 1, 6, and 2. The following data are similar to the results obtained in the study.

a) Use a repeated measures ANOVA with = .05 to determine whether the mean number of steps changes significantly from one week to another.

Tai Chi is often recommended as a way to improve balance and flexibility in the elderly. Below are

before-and-after flexibility ratings (on a 1 to 10 scale, 10 being most flexible) for a random sample of 8 men in their 80's who took Tai Chi lessons for six months.

Subject A B C D E F G H

Flexibility rating after Tai Chi 2 4 3 3 3 4 5 10

Flexibility rating before Tai Chi 1 2 1 2 1 4 2 10

(a) Explain why these are paired data.

(b) Calculate and interpret the mean difference.

(c) Researchers would like to know if the true mean difference (after-before) in flexibility rating for men in their 80's who take Tai Chi lessons for 6 months is greater than zero. The P-value of this test is 0.004. Interpret this value.

(d) If the result of this study is statistically significant, can you conclude that the difference in the mean flexibility rating was caused by the Tai Chi lessons? Why or why not?

University Car Wash built a deluxe car wash across the street from campus. The new machines cost $255,000 including installation. The company estimates that the equipment will have a residual value of $22,500. University Car Wash also estimates it will use the machine for six years or about 12,500 total hours. Actual use per year was as follows:

Problem 7-5A Part 1

Required:

1. Prepare a depreciation schedule for six years using the straight-line method. (Do not round your intermediate calculations.)
  

2. Prepare a depreciation schedule for six years using the double-declining-balance method. (Do not round your intermediate calculations.)
  

3. Prepare a depreciation schedule for six years using the activity-based method. (Round your "Depreciation Rate" to 2 decimal places and use this amount in all subsequent calculations.)

Chapter 6 Problem A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility which their consumption will yield is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend. Product X (Price $10) Product Y (Price $2) Product Z (Price $8) Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ 1 42 1 14 1 32 2 82 2 26 2 60 3 118 3 36 3 84 4 148 4 44 4 100 5 170 5 50 5 110 6 182 6 54 6 116 7 182 7 56.4 7 120 (a) Complete the table by computing the marginal utility per dollar for successive units of X, Y, and Z to one or two decimal places. Remember the marginal utility per dollar would be calculated by first getting the marginal utility which is the change in utility as quantity increases and then dividing it by the price. When doing Quantity 1 you are going from 0 units to 1 unit. The utility for 0 units would be $0. (b) How many units of X, Y, and Z will the consumer buy when maximizing utility and spending all income? Show this result using the utility maximization formula. (Meaning they need to spend all of their income of $74) (c) Why would the consumer not be maximizing utility by purchasing 2 units of X, 4 units of Y, and 1 unit of Z?

An experiment was conducted to determine if there was a mean difference in weight for women based on type of aerobics exercise program participated (low impact vs. high impact). Body mass index (BMI) was used as a blocking variable to represent below, at, or above recommended BMI. The data are shown as follows. Conduct a two-factor randomized block ANOVA (alpha = .05) and Bonferroni MCPs using SPSS to determine the results of this study.

The effect of social competence training is tested. 12 Subjects are tested before and after the training for social competence on a seven point scale. Data are ordinal scaled and not normally distributed. The question is, if social competence is enhanced by the training. Use Sign Test. Raw data are listed in the following table: Before 5 3 4 2 1 6 7 3 2 3 5 1 After 6 2 4 4 3 6 7 5 3 5 5 3

(x+0.5)-(n/2)/Squrt N/2

Ti-84

Stat edit enter both lists then stat calc 2 find X

Sub in and you get (3.5+.5)-(12/2)/ Squrt (12/2) =.2721 Got to A2 positive table or Cumulative area from the left for z - score and find z=.6064.

Am I doing this correctly and have I gone far enough please show your work thank you .

It is surprising (but true) that if 23 people are in the same room, there is about a 50% chance that at least two people will have the same birthday. Suppose you want to estimate the probability that if 30 people are in the same room, at least two of them will have the same birthday. You can proceed as follows.

a. Generate random birthdays for 30 different people. Ignoring the possibility of a leap year, each person has a 1/365 chance of having a given birthday (label the days of the year 1 to 365). You can use the RANDBETWEEN function to generate birthdays. What do you expect the average birthday (a number between 1 and 365) among the 30 people be?

b. Once you have generated 30 people's birthdays, how can you tell whether at least two people have the same birthday? One way is to use Excel's RANK function. (You can learn how to use this function in Excel's online help.) This function returns the rank of a number relative to a given group of numbers. In the case of a tie, two numbers are given the same rank. For example, if the set of numbers is 4, 3, 2, 5, the RANK function returns 2, 3, 4, 1. (By default, RANK gives 1 to the largest number.) If the set of numbers is 4, 3, 2, 4, the RANK function returns 1, 3, 4, 1. What do you expect the sum of the birthday ranks for the 30 people be, if there are no two people with the same birthday?

The table below gives the joint distribution between random variables X and Y .

y 0 2 4

x 0 0.03 0.01 0.20

1 0.15 0.10 0.51

(a). [4pts] Find P(X = 0, Y = 2). 1 Problem

2(b). [6pts] Find E[X]. Problem

2(c). [6pts] Find Cov(X, Y ). Problem 2(d). [6pts] Find P(X = 1|Y = 2).