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Janice owns a hair salon and needs $20,000 to renovate her salon. She borrows the money on a 30-month personal bank note. The simple interest rate charged is 5.75%. a) How much interest does Janice... To help pay for new costumes for a play, the Manlius Theater invests $1500 in a 30-month CD paying 2.8% interest compounded monthly. Determine the amount the theater will receive when it cashes in... A partial payment is made on the date(s) indicated. Use the United States rule to determine the balance due on the note at the date of maturity. The Effective Date is the date the note was written.... The given curve is rotated about the x-axis. Set up, but do not evaluate, an integral for the area of the resulting surface by integrating (a) With respect to x (b) With respect to y. x 2 = e y , 1 ... If 5 cards are dealt from a standard 52-card deck, how many different ways can 3 kings and 2 queens be dealt? Use the following results of a coffee taste test given at a local grocery store. If one of these individuals is randomly selected, determine the probability the individual selected a) Is a man. b) Is... Use the following results of a coffee taste test given at a local grocery store. If one of these individuals is randomly selected, determine the probability the individual selected a) Prefers Johns... Determine the mean, median, mode, and midrange of the set of data. Where appropriate, round your answer to the nearest tenth. 2, 2, 2, 2, 5, 5, 5, 5, 8, 10, 15, 17, 21, 25 Sketch the region enclosed by the given curves and find its area. y = x 3 , y = x Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y = 1/x, y = 0, x = 1, x... Find the average value of the function on the given interval. h(u) = In n u [1,5] Find the area of the region enclosed by the loop of the curve x = 1 t 2 , y = t t 3 yA 1 Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function. Table 1 f(x) = arctan(x 2 ) 1 2x" = 1 + x + x? + x + ... R = 1 n=0 00 x" e* = E- n=0 n! 1 + 1! R = 0 2! + 3!... Use a double integral to find the area of the region D. r=1- cos e r=1+ cos 0 Show that the equation represents a circle and find the center and radius. x 2 + y 2 + x = 0 Use the Chain Rule to find z/s and z/t. z = (sin )/r, r = st, = s 2 + t 2 Find the first partial derivatives of the function. g(x, t) = e xt Determine whether the sequence converges or diverges. If it converges, find the limit. a n = ln(n + 1) ln n Determine whether the sequence converges or diverges. If it converges, find the limit. tan-'n an n The National Association for Law Placement estimated that 86.7% of law school graduates in 2015 found employment. An economist thinks the current employment rate for law school graduates is different... The mean mass of 13 textbooks is 875 grams, and n novels have a total mass of 13 706 grams. Find the mean mass of a novel, given that the textbooks and novels together have a mean mass of 716.6 grams. The frequency densities of the four classes in a histogram are in the ratio 4 : 3 : 2 :1. The frequencies of these classes are in the ratio 10 :15 : 24 : 8. Find the total width of the histogram,... Eighty people downloaded a particular application and recorded the time taken for the download to complete. The times are given in the following table. a. Find the number of downloads that completed... One of the units used to measure pressure is pounds per square inch (psi). The mean pressure in the four tyres of a particular vehicle is denoted by xpsi. Given that 1 pound is approximately equal to... A number between 10 and 100 inclusive is selected at random. Find the probability that the number is a multiple of 5, given that none of its digits is a 5. The word MARMALADE contains four vowels and five consonants. Find the number of possible arrangements of its nine letters if: a. There are no restrictions on the order b. The arrangement must begin... A Mathematics teacher has 10 different posters to pin up in their classroom but there is enough space for only five of them. They have three posters on algebra, two on calculus and five on... A bank provides each account holder with a nine-digit card number that is arranged in three blocks, as shown in the example opposite. Find, in index form, the number of card numbers available if: a.... Ten cars are to be parked in a car park that has 20 parking spaces set out in two rows of 10. Find how many different patterns of unoccupied parking spaces are possible if: a. The cars can be parked... Recently, Ashland MultiComm Services has been criticized for its inadequate customer service in responding to questions and problems about its telephone, cable television, and Internet services.... The population of some countries has a relative growth rate of 3% (or more) per year. At this rate, how many years (to the nearest tenth of a year) will it take a population to double? In 44 of the 68 years from 1950 through 2018 (in 2011 there was virtually no change), the S&P 500 finished higher after the first five days of trading. In 36 out of 44 years, the S&P 500 finished... The market research team at AdRight is assigned the task of identifying the profile of the typical customer for each treadmill product offered by CardioGood Fitness. The market research team decides... For the following exercises, prove the identity given. cot x tan x = 2 cot(2x) If a box contains 10 left-handed and 20 right-handed screws, what is the probability of obtaining at least one right-handed screw in drawing 2 screws with replacement? Determine whether the series is absolutely convergent, conditionally convergent, or divergent. n=1 (-1)^ n 4 Refer to Data Set 8 in Appendix B and use the word counts measured for men and women from the couples listed in the first two columns of Data Set 8. Find the best predicted word count of a woman... List the first five terms of the sequence. 2 n + 1 DG n=3 Find dx/dt, dy/dt, and dy/dx. x t 2 ln t, y t 2 2 t22 Gina has 250/500/50 liability insurance and $50,000 PIP insurance. One afternoon, she changed lanes too quickly, hit the metal guard rail, and then hit a tour bus. Four people are seriously hurt and... The Jordans are considering buying a house with a market value of $250,000. The assessed value of the house is a dollars. The annual property tax is $2.45 per $100 of assessed value. What is the... Determine and b so that the given function is harmonic and find a harmonic conjugate. u = e x cos v Are the following functions analytic? Use (1) or (7). f(z) = i/z 8 Integrate counterclockwise around the unit circle. Let m : Z Z m be the natural homomorphism given by m (a) = (the remainder of a when divided by m) for a Z. a. Show that m : Z[x] Z m [x] given by m (a 0 + a 1 x + + a n x n ) = m (a 0 ) + ... Determine whether the polynomial in Z[x] satisfies an Eisenstein criterion for irreducibility over Q. 4x 10 - 9x 3 + 24x - 18 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 An airline overbooks 15% of the time. 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...
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