Classify the given a C as algebraic or transcendental over the given field F. If is algebraic over F, find deg(, F).

Find irr(, Q) and deg(, Q) for the given algebraic number a C Be prepared to prove that your polynomials are irreducible over Q if challenged to do so. ( 3 ) +7

Prove that if p is an irreducible in a UFD, then p is a prime.

Let D be a Euclidean domain and let v be a Euclidean norm on D. Show that if a and b are associates in D, then v(a) = v(b).

A compound shape is given opposite. a. Show that the total perimeter of the shape is given by the expression 6x + 12. b. Show that the total area of the shape is given by the expression 10x 6. c. A...

a. Draw the next two diagrams in the sequence. b. Copy and complete this table. c. Describe the pattern linking the number of white tiles and the number of blue tiles. d. Use your rule in part (c) to...

These diagrams show the first three patterns in a sequence of growing tile patterns. a. Draw the next two diagrams in the sequence. b. Copy and complete this table. c. Describe the pattern linking...

Figure 5.10 shows the velocity of an object for 0 t 8. Calculate the following estimates of the distance the object travels between t = 0 and t = 8, and indicate whether each is an upper or lower...

If the quantity of a substance decreases by 4% in 10 hours, find its half-life.

A companys cost of producing q liters of a chemical is C(q) dollars; this quantity can be sold for R(q) dollars. Suppose C(2000) = 5930 and R(2000) = 7780. (a) What is the profit at a production...

Supply and demand data are in Tables 6.3 and 6.4. (a) Which table shows supply and which shows demand? (b) Estimate the equilibrium price and quantity. (c) Estimate the consumer and producer surplus....

For Problems indicate all critical points on the given graphs. Determine which correspond to local minima, local maxima, global minima, global maxima, or none of these. 4 2 y - X 24 4 6 6 8 10

For the functions f and g in problem find (a) f(g(1)) (b) g(f(1)) (c) f(g(x)) (d) g(f(x)) (e) f(t)g(t) f(x) = 1x, g(x) = 3x + 4

For the functions f and g in problem find (a) f(g(1)) (b) g(f(1)) (c) f(g(x)) (d) g(f(x)) (e) f(t)g(t) f(x) = x 2 , g(x) = x + 1

Use the information given in the diagram to write a plan for proving that 1 2. A B 1 E 2 C D

Find the value of the variable. 3 4.5 Z 1.5

Find the length of the hypotenuse of the right triangle. 42 X 40

Imagine that I have a jar that contains 50 blue marbles and 20 red marbles. a. What is the probability of selecting a red marble from the jar? b. What is the probability of selecting a blue marble...

How many main effects and interaction effects are possible in a 2 6 factorial design?

How does a multiple-baseline design differ from a reversal design?

What is the PV+ of the test? A drug company is developing a new pregnancy-test kit for use on an outpatient basis. The company uses the pregnancy test on 100 women who are known to be pregnant, for...

What is the mean and standard deviation of time_100? Suppose we construct a new variable called time_100 = 100 time (e.g., for week 1, time_100 = 1280).

Derive the probability-mass function for X. Let X be the random variable representing the number of hypertensive adults in Example 3.12.

What is the expected number of students in the class who will develop influenza? Suppose we want to check the accuracy of self-reported diagnoses of angina by getting further medical records on a...

What is the probability that all three of these individuals have Alzheimers disease? Mental Health Estimates of the prevalence of Alzheimers disease have recently been provided by Pfeffer et al. [8]....

If a sample size of 5 is selected from this population, what is the probability that 1 or more women are positive for bacteriuria? Renal Disease The presence of bacteria in a urine sample...

What is the probability that 3 or more rats will die in the first 4 hours? Cancer, Epidemiology An experiment is designed to test the potency of a drug on 20 rats. Previous animal studies have shown...

Suppose 2 rats die in the first 4 hours. What is the probability that 2 or fewer rats will die in the next 4 hours? Cancer, Epidemiology An experiment is designed to test the potency of a drug on 20...

What is the probability that 1 rat will die in the 8-hour period? Cancer, Epidemiology An experiment is designed to test the potency of a drug on 20 rats. Previous animal studies have shown that a...

What is the probability that 2 rats will die in the 8-hour period? Cancer, Epidemiology An experiment is designed to test the potency of a drug on 20 rats. Previous animal studies have shown that a...

What is the sensitivity of the test for heavy-smoking students (students who smoke ¥ 45 cigarettes per week)? Suppose the self-reports are completely accurate and are representative of the number...

Fill in the blank 1. A(n) ___________ is a person or object that is a member of the population being studied? 2. _______ statistics consists of organizing and summarizing information collected, while...

Rats with cancer are divided into two groups. One group receives 5 milligrams (mg) of a medication that is thought to fight cancer, and the other receives 10 mg. After 2 years, the spread of the...

If the population tested is representative of the general population, then what are the PV+ and PV using this test? Hypertension Laboratory measures of cardiovascular reactivity are receiving...

Does there seem to be any difference in the effect of the antibiotics on clearance of otitis media? Express your results in terms of relative risk (RR). Consider separate analyses for unilateral and...

Answer Problem 5.7 for boys in this age range and economic environment? Suppose boys in this age range who live below the poverty level have a mean carbohydrate intake of 121 g/1000 cal with a...

Is the proportion 100 out of 1000 a prevalence rate, an incidence rate, or neither? Cardiovascular Disease A fascinating subject of recent interest is the Hispanic paradox: Census data show that...

What is the expected proportion of Hispanic men who will be identified by health surveys as having a previous heart attack in the past 5 years (who are by definition survivors) if we assume that the...

In the general population, what is the probability that an individual will have the birth defect, assuming that maternal and paternal genes are inherited independently? Genetics Suppose a birth...

What is the specificity of this test? Cancer Breast cancer is considered largely a hormonal disease. An important hormone in breast-cancer research is estradiol. The data in Table 3.18 on serum...

What is the probability of breast cancer among 50- to 59-year-old women in the general population who have a serum-estradiol level of ¥ 20 pg/mL? What is another name for this quantity? Cancer...

If 50% of the Olmstead County population is male and 50% is female, what was the overall CHD mortality rate in Olmstead County in 1998? Cardiovascular Disease Mayo Clinic investigators have tracked...

If an abnormal ECG as determined by S-T segment depression is regarded as the gold standard for the presence of heart disease and an AAI of < 1.0 is regarded as a possible test criterion for heart...

Suppose the reproducibility of the AAI test were improved using better technology. Would the sensitivity of the test increase, decrease, or remain the same? why? Cardiovascular Disease The ankle-arm...

Carry out the test in Problem 7.38 using the critical value method with an level of .05, and summarize your findings? The standard deviation of daily iron intake in the larger population of 9- to...

Compute a 95% CI for the underlying variance of daily iron intake in the low-income group. What can you infer from this CI? The standard deviation of daily iron intake in the larger population of 9-...

Suppose an otitis-prone family is defined as one in which at least three siblings of five develop otitis media in the first 6 months of life. What proportion of five-sibling families is otitis prone...

The hospital also finds that on high-pollution days the number of admissions is Poisson-distributed with mean = 4.0 admissions per day. Answer Problem 4.67 for high pollution days? Environmental...

What percentage of boys in this age range have carbohydrate intake above 140 g/1000 cal? Nutrition Suppose that total carbohydrate intake in 12- to 14-year old boys is normally distributed, with mean...

If we assume that the distribution of is normally distributed, then what % of (observer, trainer) pairs have a mean difference of 2 mm Hg in absolute value (i.e., either 2 mm Hg or 2 mm Hg)?...

If an FEV of less than 2.5 L is regarded as showing some functional impairment (occasional breathlessness, inability to climb stairs, etc.), then what is the probability that a currently smoking man...

Answer the question in Problem 13.29 to assess whether there are differences in efficacy between each pair of antibiotics?

An excess of eosinophils is sometimes consistent with a violent allergic reaction. What is the exact probability that a normal adult will have 5 or more eosinophils? Infectious Disease The...

a. What is the probability that a customer does not use a credit card? b. What is the probability that a customer pays in cash or with a credit card?

What is the standard error of the mean for each group? Pulmonary Disease The data in Table 6.10 concern the mean triceps skin-fold thickness in a group of normal men and a group of men with chronic...

Compute a 95% CI for the mean age? Refer to the data in Table 2.13. Regard this hospital as typical of Pennsylvania hospitals. Table 2.13: Hospital-stay data

Is there a difference between men and women in their preference for working for some government agency? Conduct a test to determine whether there is enough evidence to infer that women (SEX: 1 =...

An article in the Journal of American College Health reports that, in a survey of 1845 college students from a large, southeastern public university, 27% were at risk for at least one sleep disorder,...

Restaurants sometimes provide customer reaction cards so that customers can evaluate their dining experience at the establishment. What kinds of decisions might be made on the basis of this...

What is the coefficient of determination and what does it tell us about the relationship between two variables?

Compute the standard deviation based on the sample of six means. What is another name for this quantity? Table 6.2: Sample of birth-weights (oz) obtained from 1000 consecutive deliveries at Boston...

Select the third point from each of the six samples, and compute the sample sd from the collection of six third points? Table 6.2: Sample of birth-weights (oz) obtained from 1000 consecutive...

How do the actual sample results in Problems 6.48 and 6.49 compare? Obstetrics Figure 6.4b (p. 172) plotted the sampling distribution of the mean from 200 samples of size 5 from the population of...

If the central-limit theorem holds, what proportion of the sample means should fall within 0.5 lb of the population mean (112.0 oz)? Obstetrics Figure 6.4b (p. 172) plotted the sampling distribution...

Do you feel the central-limit theorem is applicable for samples of size 5 from this population? Explain. Obstetrics Figure 6.4b (p. 172) plotted the sampling distribution of the mean from 200 samples...

Compare your results in Problems 6.52 and 6.53 with the actual proportion of sample means that fall in these ranges? Obstetrics Figure 6.4b (p. 172) plotted the sampling distribution of the mean from...

Suppose (x - 0 ) / (s/n) = -1.52 and a one- sample t test is performed based on seven subjects. What is thaw two-tailed p-values? Renal Disease The mean serum-creatinine level measured in 12...

What is the p-value for the test conducted in Problem 7.36? Nutrition Iron-deficiency anemia is an important nutritional health problem in the United States. A dietary assessment was performed on 51...

Refer to Exercise 22.4. Set up the opportunity loss table. In exercise 22.4 Given the following payoff table, draw the decision tree: -1 4 10 S1 S2 S3 20 -10

If the expected difference is 0.10 ln units, then what is the power of such a study if a two-sided test is to be used with = .05? Diabetes Plasma-glucose levels are used to determine the presence of...

An order for an automobile can specify either an automatic or a standard transmission, either with or without air conditioning, and with any one of the four colors red, blue, black, or white....

What test can be used to assess if there is a change in mean LVM over 4 years? Cardiovascular Disease, Pediatrics Left ventricular mass (LVM) is an important risk factor for subsequent cardiovascular...

Carry out the test procedure mentioned in Problem 8.28, and report a p-value? Ophthalmology A camera has been developed to detect the presence of cataract more accurately. Using this camera, the gray...

What are the appropriate null and alternative hypotheses to compare the means of the two groups? Pulmonary Disease A possible important environmental determinant of lung function in children is the...

Provide a 95% CI for the true mean difference in FEV between 5- to 9-year-old children whose parents smoke and comparable children whose parents do not smoke? Pulmonary Disease A possible important...

Suppose another investigator wants to reproduce the results of the Amish study. She can recruit 100 subjects with the II genotype and 100 subjects with the ID genotype. How much power will the study...

Perform the test in Problem 8.112, and report a p-value (two-tailed)? Microbiology A study sought to demonstrate that soy beans inoculated with nitrogen-fixing bacteria yield more and grow adequately...

Suppose there is some overlap between the 95% CIs in Problem 8.110. Does this necessarily imply there is no significant difference between the mean pod weights for the two groups? Why or why not?...

Provide a 95% CI for the mean pod weight in each group? Microbiology A study sought to demonstrate that soy beans inoculated with nitrogen-fixing bacteria yield more and grow adequately without the...

Implement the test in Problem 9.47, and report a twotailed p-value? Table 9.15: (Weight change, control period) (weight change, lack-of-consistency period) among 23 adolescent diabetic boys 4, A....

What significance test can be used to assess whether there is a relationship between receiving an antibiotic and receiving a bacterial culture while in the hospital? Refer to Table 2.13 (p. 36)....

Suppose that we conduct a test of significance using 5% as our level of significance. a. What is the probability of making a Type I error (if the null hypothesis is true)? b. Suppose we conduct 10...

Are the present diagnosis and prior episodes of urethritis associated? Sexually Transmitted Disease Suppose researchers do an epidemiologic investigation of people entering a sexually transmitted...

Provide a point estimate and a 95% confidence interval for the prevalence of otorrhea at 2 weeks in the observation group? Otolaryngology Many children have tympanostomy tubes surgically inserted in...

Perform the test in Problem 10.21 and report a p-value (two-tailed). Interpret your results in words? Otolaryngology Many children have tympanostomy tubes surgically inserted in their ears to reduce...

Based on all matched pairs, how much power did the study just mentioned have vs. the alternative hypothesis that a widower is twice as likely to die before a married person of the same age and...

Provide a stem-and-leaf plot of the age at first sperm-positive urine specimen? Pediatrics, Endocrinology A study was performed among 40 boys in a school in Edinburgh to look at the presence of...

Suppose we are uncertain whether a normal distribution provides a good fit to the distribution of age at spermatogenesis. Answer this question using the results from Problems 10.4710.49. (Assume that...

Suppose mean age at spermatogenesis = 13.67 years, with standard deviation = 0.89 years and we assume that the age at spermatogenesis follows a normal distribution. The pediatrician would like to...

If we assume that all boys have no sperm cells at age 11 (11.0 years) and all have sperm cells at age 18, then estimate the probability of first developing sperm cells at ages 12 (i.e., between 12.0...

One assumption of the test in Problem 10.68 is that the distribution of serum retinol is approximately normal. To verify this assumption, the investigators obtained a frequency distribution of serum...

Implement the test in Problem 10.74, and report a p-value? Zoology A study was performed to look at the preference of different species of birds for different types of sunflower seeds. Two bird...

Which of the following is the primary purpose of randomly assigning subjects to treatments in an experiment? A. To produce similar (experimental) groups so any differences in the response variable...

What test can be performed to study the association between case/control status and risk score? Specifically, we are interested in testing whether cases tend to have consistently higher risk scores...

Is this an observational study or an experiment? How are you deciding? The researcher is now interested in seeing whether a higher proportion of men in the group that crossed the Capilano Canyon...

Fit a regression line relating 5-year lung-cancer mortality to annual cigarette consumption when each is expressed in the log 10 scale? Cancer The following statistics are taken from an article by...

To test the significance of this regression line, is it necessary to perform any additional tests other than those in Problem 11.20? If so, perform them. Cancer The following statistics are taken...

Fill in the cells in the following table so there is no association between the explanatory and response variables. Female Total Male Played sports in high school Yes 200 160 No Total 150 210 360

Fill in the cells in the following table so there is no association between the explanatory and response variables. Member of Fraternity or Sorority Yes No Total Yes 152 Has one or more alcoholic...

Approximately what does the box portion of a boxplot display? A. The middle quarter of the data B. The middle half of the data C. The lower quarter of the data D. The upper quarter of the data