persons withdrawing from addiction is given by summarizing over individuals with different ages and numbers of years of addiction remaining:


 Thomasina Cameron
 1 years ago
 Views:
Transcription
1 COST BENEFIT ANALYSIS OF NARCOTIC ADDICTION TREATMENT PROGRAMS with Specil Reference to Age Irving Leveson,l New York City Plnning Commission Introduction Efforts to del with consequences of poverty, rce, nd other socil problems hve resulted in prolifertion of tretment nd rehbilittion progrms for criminls, ddicts, nd the mentlly ill. These hve included skills trining, professionl nd nonprofessionl psychotherpy, drug therpy, nd incrcertion nd surveillnce. Mny such efforts re experimentl or pilot projects. To dte there hs been little in the wy of systemtic efforts to evlute, either publicly or privtely, the success of these progrms. The mount of informtion in the public domin is growing, nd public gencies providing funds re beginning to insist tht evlutions tke plce. To ttin comprbility mong such evlutions requires greement on methodologies of generl pplicbility. A "simplified" methodology which permits comprisons mong divergent ddiction rehbilittion nd tretment methods is developed nd illustrted here. It is believed tht the techniques hve pplicbility to mny other progrms. A criticl feture of rehbilittion efforts is tht they tend to del with very different groups. We would like to hve cost benefit informtion for ech tretment pplied to ech popultion type. In lieu of this, we find it necessry to ssume ech tretment to be most pproprite to prticulr popultion type. We exmine costs nd benefits for ech group nd then djust for differences between groups in ese of tretment nd in the vlue of benefits from successful tretment. In relted pproch, the efficient choice of client group for given progrm is considered. There hs been gret concern over the growth in the drug problem mong youth nd its fr reching implictions for institutions such s schools nd the militry. There hs been gret concern over the lck of consensus on ny tretment method to effectively del with the young. At the sme time, there hs been prolifertion of tretment progrms ttempting to del with the young which require ssessment. These efforts re criticlly bound up with discovery of the bsic cuses of ddiction. Rther thn develop more generl methodology for compring progrms deling with divergent popultion groups, we focus here on the role of ge in the success in tretment progrms. ssistnce. Becuse of finite life expectncy nd the possibility tht mny persons "mture out" of ddiction s they grow older, the number of yers of ddiction remining is greter for younger ddicts. The number of remining yers of ddiction is represented by R. The benefits of reduction of mn yer of ddiction (bi) re represented s function of ge (i) s3well s the number of yers (j) of ddiction remining.3 Future benefits re discounted by n pproprite rte (r). The full expression for the benefits of N = E Ni persons withdrwing from ddiction is given by summrizing over individuls with different ges nd numbers of yers of ddiction remining: B = E E N11 (1) i=1 j=1 (l+r)i Eqution 1 cn be gretly simplified. First, we ssume tht the number of yers of ddiction remining is solely function of ge. Therefore we cn write Nj B = E (2) j=1 (l+r)j Now we exmine the ssumptions implicitly required to use simpler mesures of success thn the full expression in Eqution 2. Most studies ignore differences mong ge groups in benefits per ddict successfully treted. The effectiveness mesure becomes E = E N. (l+r)j where B = be. The most commonly used mesure of success is the proportion () of persons dmitted to tretment (A) who successfully withdrw. The reduction in the number of ddicts is N = A. If we compred different progrms treting the sme types of people, bl would equl b2 nd would equl t,, so tht the probbility of successful withdf'wl would be sufficient to guge success. Otherwise, use of this mesure is equivlent to ssumming tht (3) The Underlying Cost  Benefit Model The benefit to society of hving one less ddict depends on the number of yers tht n ddict would hve remined ddicted without E = 1 j=1 (l+& (4) 327
2 s well s ignoring ge differences in benefits per mn yer verted. It guges success by the number of ddicts successfully withdrwing without regrd to l'ngth of time they would hve been ddicted. In doing so, it overemphsizes very immedite gins. Reducing the verge number of ddicts over number of yers requires mesuring success by the number of mn yers of ddiction verted, or Assume tht progrms with lrger hve lower. If cross progrms is proportionl to, the rtio of the cost effectiveness rtios is the sme s the rtio of the costs per person treted. If vries more thn, the costs per person treted would hve to be lower in the progrms with the higher k for them to compre fvorbly with the others. If cu is smll reltive to or is lrge M = N. This cn be derived from Eqution 3 s ct A M cs (9) M = N. R. j=1 where r = o nd B = b M. This mesure is prticulrly simple to use. However, it overemphsizes benefits which re deferred in time. If we wish to tke into ccount tht we vlue benefits tody more thn those which will not be received for mny yers, it is necessry to discount future benefits by n pproprite discount rte (r). The mesure which does this is the discounted number of mn yers of ddiction verted, designted s E s defined in Eqution 3. (5) Next we consider cost effectiveness. Where is used, discounted could esily be substituted. Let individuls going through progrm either be treted successfully t cost or unsuccessfully t cost cu. The verge cost (ct) of treting n ddict in progrm hving proportion successfully treted of is ct = cs + (1) cu The cost of treting A ddicts is A ct, so tht the cost per successfully treted is A A et (6). Designting the cost per suc  cessfully treted ddict s c, c = + cu (7) As the proportion successfully treted increses, cost per success flls becuse the costs of reltively fewer unsuccessful cses re included. The rtio of costs of ddicts dmitted to tretment to mn yers of ddiction verted (cost effectiveness rtio) is ct A cs + (1 ) cu. M (8) Empiricl Evidence on Age Differences We hve exmined the evidence on differences mong ge groups in the benefits of successful tretment nd the chnces for successful tretment. The nlysis indictes () tht differences in the prevlence of opite use mong ge groups reflects some sort of mturtion (nd/or mortlity) since without mturtion they imply implusible ptterns in the number of users over time, (b) derives the verge number of yers of ddiction remining by ethnic group bsed on ge ptterns under lterntive ssumptions bout pst rtes of growth of ddiction, nd (c) compres the higher retention rtes of the New York City Methdone Progrm for the youngest ddicts with the lower derived mturtion rtes nd suggests tht the young my do the sme or worse if "nturl" mturtion ccounts for prt of the dropping out of older persons. (This mteril is vilble upon request.) A Cursory Look t Mjor Progrms Virtully ny progrm will py in terms of benefits to the nonddict popultion. Even if we incrcerte persons t cost of over $8,000 per yer for severl yers, if crime of $10,000 to $20,000 per person per yer is verted,6 the progrm cn be justified. However, this clcultion does not consider tht, even with high pyoff, funds for ddiction services my be limited, nd it does not tke into ccount the undesirbility of involuntry incrcertion. While it my be cler tht the pyoff to ddiction progrms in generl is very high, there is still mjor issue s to wht proportion of the ddict popultion cn be delt with by ech pproch. As of the end of 1969, there were bout 11,000 New York City ddicts in tretment progrms. In ddition, there were bout 5,000 in pretril detention7 nd others serving prison terms or on prole. Nerly ll tretment funding comes from the New York Stte Nrcotic Addiction Control Commission which hs current operting budget of $38 million per yer nd $200 million cpitl construction progrm. The three 328
3 lrgest progrms for the tretment of drug ddicts in New York City re the progrm of the New York Stte Nrcotic Addiction Control Commission, the Methdone Mintennce Progrm, nd the Phoenix House Progrm of New York City's Addiction Services Agency. The Stte progrm combines voluntry or involuntry incrcertion with therpeutic nd rehbilittion services for up to five yers, followed by n ftercre phse involving surveillnce. The progrm, depending strongly on court nd prentl coercion, hs suffered bscondnce rtes of over one third per yer nd high rtes of recidivism. However, it hs been successful in moving persons from n institutionl setting into ftercre. Furthermore, it is the only one of the three lrgest progrms to hve given primry ttention to younger ddicts. One third of the persons in the progrm re under ge 20 nd two thirds re under ge 25. The vilbility of rehbilittion services under the progrm ppers to be incresing. At the end of 1969 there were 5,000 ddicts in the progrm, with lrge expnsion plnned s new fcilities being constructed become vilble. The Methdone Progrm uses the drug Methdone, itself ddicting but providing no "high," to block the effects of opites. After few weeks of withdrwl, the drug is dministered orlly on n outptient bsis for n indefinite period of time. There re bout 2,000 ddicts currently under tretment, nd doubling of efforts is under wy. This progrm tends to concentrte on older ddicts s indicted by comprisons with the Nrcotics Register for September 1969: Methdone Progrm Nrcotics Register Less thn 25 10% 33% nd over The Methdone Progrm is the only one of the three to mke public regulr evlution reports. The evidence of high retention rtes, improvement in employment experiences, nd reduced criminlity hve led to belief tht this is the most effective method currently vilble. The Phoenix House progrm relies on encounter techniques involving confronttion of ddicts with ech other nd with ex ddicts. After two yers of institutionliztion, process of grdul re entry into the community begins. Phoenix House hs generlly served bout thousnd persons, but only smll frction hve re entered the community through the progrm. Scnt informtion is vilble with which to compre the effectiveness of mjor progrm lterntives, even using simplified frmework devised to minimize dt requirements. success rte for persons on drug mintennce for 36 months. Lck of success in tht progrm reflects both voluntry nd involuntry termintion stemming from fctors such s criminl behvior nd lcoholism. The Stte progrm reported tht fter its first 21 months of opertion, 44 percent of the 1,893 persons returned to the community hd not resumed drug use. Thirty percent were returned to rehbilittion center fter it ws discovered tht they were reusing nrcotics, nd 26 percent could no longer be locted (wrrnts were issued ginst them).8 In view of the fct tht the progrm hd only 188 persons on ftercre fter its first yer nd 836 fter 21 months, the verge length of time in the community would hve to hve been substntilly less thn one yer. In view of the short time, the progrm's experience is discourging. A study of roughly similr progrm, tht of the Cliforni Rehbilittion Center t Coron, found tht 35 percent were in good stnding (or hd been removed from the progrm while in good stnding) one yer fter relese. After three yers the figure hd fllen 19 percent.9 There is nothing in the experience of the New York Stte progrm to dte to indicte it is doing ny better thn this. If we tke seriously the public mndte to prepre ddicts for entry into the community, the fct tht only hndful of Phoenix House residents hve ctully done so fter their period of institutionliztion must be treted s if the proportion delt with successfully is negligible. This progrm could only be considered successful if society were willing to plce high vlue on withdrwl in setting of permnent institutionliztion. We re now in position to compre progrms on the ssumption tht they continue to tret the sme types of people s they now tret with the sme degree of success. If we compre the benefits of the Methdone progrm designted by subscript 1 reltive to the Stte progrm designted by subscript 2, we hve B1 b1 B2 b2 02 t2 (10) The number of persons dmitted to ech progrm is ssumed to be the sme. Assuming the Cliforni experience to be pplicble to New York Stte, equls bout.7/.2 or 3 1/2. The men ges nd corresponding yers of ddiction remining for the three mjor progrms re s follows: The Methdone progrm reported bout.7 329
4 Approximte Yers Age Remining Nrcotic Addiction Commission Addiction Services Agency Methdone Mintennce 32 8 The ge distribution of the Methdone progrm implies tht the cost of the progrm must be bout 2/3 of the others to compenste for the difference in yers of ddiction remining, if ll hd eqully high success rtes. If the yers of ddiction remining were discounted, this difference would be modified somewht. The vlue to society of treting the kinds of persons treted by the Stte progrm my be higher thn those treted with Methdone. There is some evidence tht older ddicts commit fewer crimes. Younger ddicts cn be expected to remin on drugs longer, with greter dverse effects on helth.. Furthermore, tretment of younger ddicts my hve greter benefits of preventing other persons from being induced to use drugs. However, there would hve to be rtio of bl to b2 s low s bout 3/7 in order for the Stte progrm to hve eqully lrge benefits. When one considers costs, the problem of progrm choice becomes more difficult. In the pst, the Stte progrm required over $8,000 in operting costs lone per mn yer of incrcertion, nd currently employs nerly one person for every ddict in residentil or ftercre ctivities. Completion of the progrm probbly requires n verge of bout $15,000 per person. For comprble cost, the Methdone progrm could provide detoxifiction nd drug mintennce for more thn decde. After tht time, it my be possible for mturtion effects to be substituted for drug mintennce. While there my not be lrge difference between the Stte nd the Methdone progrms in the cost per completed progrm, those progrms within the lowest proportion of persons treted successfully will tend to hve the lowest cost per person dmitted to tretment. This occurs becuse the cost per person treted (ct) is n verge of the cost per person treted successfully (cs) nd the cost of persons who do not successfully complete the progrm, some of whom hve prtil tretment (cu). (See Eqution 6.) Higher costs per person dmitted to tretment in more successful progrm will tend to offset prt of the gins from more successful tretment. The lter stges in tretment t which persons drop out the lrger will cu be reltive to cs, nd the less the cost per person dmitted to tretment will vry with the probbility of success. When the cost per dmission is considered, the weight of evidence is probbly still hevily in fvor of Methdone, since in the Stte progrm there is probbly only modest difference in cost between those who successfully withdrw nd those who do not. However, this bers closer scrutiny, since success my depend on the mount of rehbilittion provided nd the Stte hs been expnding the mount of rel rehbilittion service provided. Furthermore, some deduction of welfre of the ddict must be mde for the involuntry nture of the Stte progrm nd the dependence on Methdone. On the surfce, the Addiction Services Agency progrm is by fr the chepest, estimted by the gency to cost $7,500 for the entire 2 1/4 yer process. While in theory it could hve n dded benefit beyond the time of mturtion out of drug use becuse it is directed to improvement in mny spects of socil djustment, this does not occur without re entry.10 Choice of Age Group within Progrm Selecting ge groups for tretment so s to mximize the number of mn yers of ddiction verted is equivlent to minimizing the number of ddicts. If the success of tretment were the sme t ech ge, we would concentrte on the youngest ddicts who hve the gretest number of yers of ddiction remining. On the other hnd, if the number of yers of ddiction remining were the sme t ech ge nd success of tretment were greter for older persons, we would concentrte on the oldest ddicts. (We re defining success net of ny norml mturtion tendencies.) Here we consider the optiml ge when vritions in both yers of ddiction remining nd success of tretment re tken into ccount. The number of mn yers of ddiction verted for progrm is given by M=Ak. (11) For simplicity, we ssume tht the verge number of yers of ddiction remining in progrm cn be represented s proportion (p) of the difference between some fixed ge ( *) nd the verge ge () of persons being treted = p (* ). (12) Thus if * is ge 40 nd p =.6, ddicts ge 20 would be expected to remin ddicted for nother 12 yers on the verge. Those who were still ddicted t ge 30 would be expected to remin ddicted for nother 6 yers. We further ssume tht the rte of success in withdrwl from ddiction cn be represented by liner function of ge where t > O. = s + t, (13) Combining these equtions we hve M = A s p ( * ) + A t p ( * ). (14) 330
5 Multiplying through nd differentiting with respect to ge ddiction will be prevented for lrger number of yers when the young withdrw, rther thn relying on the more visible success rte lone. d = At *p Asp 2Atp. (15) Finl Comments The second derivtive is d2m d 2 =  2 A t p (16) which, since A, t nd p re positive, is negtive indicting mximum. Setting the first derivtive equl to zero nd solving, we derive the optiml level of = * s 2 2t (17) One inference tht cn be drwn from this result is tht the effect of ge differences in the success rte on the optiml ge is importnt. If, for exmple, s were .3 nd t were.03, indicting success rte of.4 t ge 20, nd.7 t ge 30, the term would dd five yers to the optiml ge. If s is positive, however, the optiml ge is reduced. For exmple, if s =.2 nd t =.02, indicting success of.6 t ge 20 nd.8 t ge 30, the optiml ge would be reduced by five yers. With the functionl form we hve chosen for, p does not enter into the result since it does not chnge the terms of trde between ge groups. Unfortuntely, we hve little informtion with which to determine *. Our curves of yers of ddiction remining suggest tht over the rnge of ges the curves could be pproximted by n * t bout 40, with different p's for ech ethnic group.11 In tht ge rnge, figure of ge 20 for á* would be vlid. 2 is very pproximte of course. If * This were s high s 25 nd function such 2 s = were pproximtely correct, we would come out with n optiml ge very close to the verge ge now being treted in the Methdone progrm. If, insted, s the progrm clims, success vries little with ge so tht function such s = t is pproprite, then to corroborte the ges now treted we would need n * of round 70 which is completely impossible. Even if * is s high s 50, s.2 nd t.02, then the Methdone progrm should be concentrting on persons s much s 10 yers younger thn they re now, even though the proportion successfully withdrwing would be lower if it did. This would tke into ccount the likelihood tht The results of this nlysis re illustrtive nd suggestive rther thn definitive. They tend to support the efficcy of the Methdone progrm reltive to the Stte progrm, if the gol is to minimize the number of ddicts. However, they rise serious questions bout the merits of the Methdone progrm's prctice of treting disproportionte number of older ddicts. Combining informtion on the number of yers of ddiction remining from successful withdrwl t ech ge with ssumptions bout success in chieving withdrwl t ech ge, suggests tht it my be possible for the Methdone progrm to increse its impct on the number of ddicts by the order of mgnitude of t lest one fourth, with no dditionl expenditures, by shifting emphsis in tretment to younger groups. Footnotes 1. Director of Reserch nd Director of Helth Plnning, Office of Comprehensive Plnning. The views expressed re those of the uthor nd need not represent those of the City Plnning Commission, the Community Renewl Progrm, or ny of their ffilites or consultnts. Beginnings on this study were mde while t the Rnd Corportion. The comments of Zili Amsel, Sidney Leveson nd Clrence Teng were most helpful. 2. The term ddict is used to imply users of hrd drugs whether or not physiologiclly or psychologiclly ddicted. 3. One study of ddicts with men ge 30.7 showed men ge of most rrests of See Bernrd Greenfield, "The Riverside Study  Ten Yers Lter." Pper prepred for the New York City Deprtment of Helth, Helth Reserch Trining Progrm, Summer If we mke the ssumption tht the rtio of the benefits per mn yer of ddiction verted to the discount function is n inverse function of ge then or bj (l+r) k B = E Nj j=i B = M. The benefits of reducing ddiction re proportionl to the number of mn yers of ddiction 331
6 verted nd inversely relted to the ge of those ssisted. 5. The model could esily be extended to llow for some positive benefit for nonsuccesses due to period of withdrwl prior to recidivism. 6. See Irving Leveson, "Drug Addiction: Some Evidence on Prevention nd Deterrence," pper presented t the meetings of the Econometric Society, Detroit, Michign, December 1970 nd John Holhn, The Economics of Drug Addiction in Wshington, D.C.: A Model for Estimtion of Costs nd Benefits of Tretment nd Rehbilittion, Report No. 33, District of Columbi Deprtment of Corrections, October Bsed on Bronx District Attorney Burton Robert's estimte tht bout four tenths of the persons in detention re ddicts. 8. New York Stte "Report of the Nrcotic Addiction Control Commission for the First Twenty One Month Period." The Commission did not relese comprble figures in its second nnul report. In the week of Jnury 2531, 1970, only 48 percent were known to be ginfully occupied. 10. The progrm voids constrints on the vilbility of professionl mnpower by using ex ddicts. However, retining ex ddicts in the progrm delys the time they will hve to re enter the community. The djustment process my be mde more difficult in the future if lrge numbers of persons must be bsorbed into the community in reltively short period of time. If the rtio of the number of ddicts to ex ddict employees is R, the rte of growth per two yer tretment period needed to retin S percent of persons treted s employees is S R. If the growth of the progrm were suddenly hlted, R of those in the progrm would be R ending tretment nd hve to find jobs. 11. At older ges the slopes re smller nd *'s higher. 9. John C. Krmer nd Richrd A. Bss, "Civil Commitment for Addicts: The Cliforni Progrm," Report of the Committee on Problems of Drug Dependency of the Ntionl Acdemy of Sciences nd the Ntionl Reserch Council,
Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )
Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +
More informationReasoning to Solve Equations and Inequalities
Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing
More informationTreatment Spring Late Summer Fall 0.10 5.56 3.85 0.61 6.97 3.01 1.91 3.01 2.13 2.99 5.33 2.50 1.06 3.53 6.10 Mean = 1.33 Mean = 4.88 Mean = 3.
The nlysis of vrince (ANOVA) Although the ttest is one of the most commonly used sttisticl hypothesis tests, it hs limittions. The mjor limittion is tht the ttest cn be used to compre the mens of only
More informationDlNBVRGH + Sickness Absence Monitoring Report. Executive of the Council. Purpose of report
DlNBVRGH + + THE CITY OF EDINBURGH COUNCIL Sickness Absence Monitoring Report Executive of the Council 8fh My 4 I.I...3 Purpose of report This report quntifies the mount of working time lost s result of
More informationUtilization of Smoking Cessation Benefits in Medicaid Managed Care, 20092013
Utiliztion of Smoking Cesstion Benefits in Medicid Mnged Cre, 20092013 Office of Qulity nd Ptient Sfety New York Stte Deprtment of Helth Jnury 2015 Introduction According to the New York Stte Tocco Control
More informationHelicopter Theme and Variations
Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the
More informationHealth insurance exchanges What to expect in 2014
Helth insurnce exchnges Wht to expect in 2014 33096CAEENABC 02/13 The bsics of exchnges As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum mount
More informationHumana Critical Illness/Cancer
Humn Criticl Illness/Cncer Criticl illness/cncer voluntry coverges py benefits however you wnt With our criticl illness nd cncer plns, you'll receive benefit fter serious illness or condition such s hert
More informationFactoring Polynomials
Fctoring Polynomils Some definitions (not necessrily ll for secondry school mthemtics): A polynomil is the sum of one or more terms, in which ech term consists of product of constnt nd one or more vribles
More informationLumpSum Distributions at Job Change, p. 2
Jnury 2009 Vol. 30, No. 1 LumpSum Distributions t Job Chnge, p. 2 E X E C U T I V E S U M M A R Y LumpSum Distributions t Job Chnge GROWING NUMBER OF WORKERS FACED WITH ASSET DECISIONS AT JOB CHANGE:
More informationHealth insurance marketplace What to expect in 2014
Helth insurnce mrketplce Wht to expect in 2014 33096VAEENBVA 06/13 The bsics of the mrketplce As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationEcon 4721 Money and Banking Problem Set 2 Answer Key
Econ 472 Money nd Bnking Problem Set 2 Answer Key Problem (35 points) Consider n overlpping genertions model in which consumers live for two periods. The number of people born in ech genertion grows in
More informationAll pay auctions with certain and uncertain prizes a comment
CENTER FOR RESEARC IN ECONOMICS AND MANAGEMENT CREAM Publiction No. 12015 All py uctions with certin nd uncertin prizes comment Christin Riis All py uctions with certin nd uncertin prizes comment Christin
More informationSmall Businesses Decisions to Offer Health Insurance to Employees
Smll Businesses Decisions to Offer Helth Insurnce to Employees Ctherine McLughlin nd Adm Swinurn, June 2014 Employersponsored helth insurnce (ESI) is the dominnt source of coverge for nonelderly dults
More informationEnterprise Risk Management Software Buyer s Guide
Enterprise Risk Mngement Softwre Buyer s Guide 1. Wht is Enterprise Risk Mngement? 2. Gols of n ERM Progrm 3. Why Implement ERM 4. Steps to Implementing Successful ERM Progrm 5. Key Performnce Indictors
More informationAppendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered:
Appendi D: Completing the Squre nd the Qudrtic Formul Fctoring qudrtic epressions such s: + 6 + 8 ws one of the topics introduced in Appendi C. Fctoring qudrtic epressions is useful skill tht cn help you
More informationActive & Retiree Plan: Trustees of the Milwaukee Roofers Health Fund Coverage Period: 06/01/201505/31/2016 Summary of Benefits and Coverage:
Summry of Benefits nd Coverge: Wht this Pln Covers & Wht it Costs Coverge for: Single & Fmily Pln Type: NPOS This is only summry. If you wnt more detil bout your coverge nd costs, you cn get the complete
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationExperiment 6: Friction
Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht
More informationAnthem Blue Cross Life and Health Insurance Company University of Southern California Custom Premier PPO 800/20%/20%
Anthem Blue Cross Life nd Helth Insurnce Compny University of Southern Cliforni Custom Premier 800/20%/20% Summry of Benefits nd Coverge: Wht this Pln Covers & Wht it Costs Coverge Period: 01/01/201512/31/2015
More informationBasic Analysis of Autarky and Free Trade Models
Bsic Anlysis of Autrky nd Free Trde Models AUTARKY Autrky condition in prticulr commodity mrket refers to sitution in which country does not engge in ny trde in tht commodity with other countries. Consequently
More informationCOMPARISON OF SOME METHODS TO FIT A MULTIPLICATIVE TARIFF STRUCTURE TO OBSERVED RISK DATA BY B. AJNE. Skandza, Stockholm ABSTRACT
COMPARISON OF SOME METHODS TO FIT A MULTIPLICATIVE TARIFF STRUCTURE TO OBSERVED RISK DATA BY B. AJNE Skndz, Stockholm ABSTRACT Three methods for fitting multiplictive models to observed, crossclssified
More informationHealth insurance exchanges What to expect in 2014
Helth insurnce exchnges Wht to expect in 2014 33096CAEENABC 11/12 The bsics of exchnges As prt of the Affordble Cre Act (ACA or helth cre reform lw), strting in 2014 ALL Americns must hve minimum mount
More informationRational Functions. Rational functions are the ratio of two polynomial functions. Qx bx b x bx b. x x x. ( x) ( ) ( ) ( ) and
Rtionl Functions Rtionl unctions re the rtio o two polynomil unctions. They cn be written in expnded orm s ( ( P x x + x + + x+ Qx bx b x bx b n n 1 n n 1 1 0 m m 1 m + m 1 + + m + 0 Exmples o rtionl unctions
More informationAn Undergraduate Curriculum Evaluation with the Analytic Hierarchy Process
An Undergrdute Curriculum Evlution with the Anlytic Hierrchy Process Les Frir Jessic O. Mtson Jck E. Mtson Deprtment of Industril Engineering P.O. Box 870288 University of Albm Tuscloos, AL. 35487 Abstrct
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationPROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY
MAT 0630 INTERNET RESOURCES, REVIEW OF CONCEPTS AND COMMON MISTAKES PROF. BOYAN KOSTADINOV NEW YORK CITY COLLEGE OF TECHNOLOGY, CUNY Contents 1. ACT Compss Prctice Tests 1 2. Common Mistkes 2 3. Distributive
More information2. Transaction Cost Economics
3 2. Trnsction Cost Economics Trnsctions Trnsctions Cn Cn Be Be Internl Internl or or Externl Externl n n Orgniztion Orgniztion Trnsctions Trnsctions occur occur whenever whenever good good or or service
More informationPlotting and Graphing
Plotting nd Grphing Much of the dt nd informtion used by engineers is presented in the form of grphs. The vlues to be plotted cn come from theoreticl or empiricl (observed) reltionships, or from mesured
More information9 CONTINUOUS DISTRIBUTIONS
9 CONTINUOUS DISTIBUTIONS A rndom vrible whose vlue my fll nywhere in rnge of vlues is continuous rndom vrible nd will be ssocited with some continuous distribution. Continuous distributions re to discrete
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationEconomics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999
Economics Letters 65 (1999) 9 15 Estimting dynmic pnel dt models: guide for q mcroeconomists b, * Ruth A. Judson, Ann L. Owen Federl Reserve Bord of Governors, 0th & C Sts., N.W. Wshington, D.C. 0551,
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply
More information2001 Attachment Sequence No. 118
Form Deprtment of the Tresury Internl Revenue Service Importnt: Return of U.S. Persons With Respect to Certin Foreign Prtnerships Attch to your tx return. See seprte instructions. Informtion furnished
More informationMAX. As an increasingly larger share of Medicaid enrollees MEDICAID POLICY BRIEF
MAX CENTERS FOR MEDICARE & MEDICAID SERVICES MEDICAID POLICY BRIEF Brief 14 December 2012 The Avilbility nd Usbility of Behviorl Helth Orgniztion Encounter Dt in MAX 2009 Jessic Nysenbum, Ellen Bouchery,
More informationOr more simply put, when adding or subtracting quantities, their uncertainties add.
Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re
More informationHomework #4: Answers. 1. Draw the array of world outputs that free trade allows by making use of each country s transformation schedule.
Text questions, Chpter 5, problems 15: Homework #4: Answers 1. Drw the rry of world outputs tht free trde llows by mking use of ech country s trnsformtion schedule.. Drw it. This digrm is constructed
More informationSection 54 Trigonometric Functions
5 Trigonometric Functions Section 5 Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form
More informationa GAO03568 GAO COLLEGE COMPLETION Additional Efforts Could Help Education with Its Completion Goals Report to Congressional Requesters
GAO United Sttes Generl Accounting Office Report to Congressionl Requesters My 2003 COLLEGE COMPLETION Additionl Efforts Could Help Eduction with Its Completion Gols GAO03568 My 2003 COLLEGE COMPLETION
More informationClearPeaks Customer Care Guide. Business as Usual (BaU) Services Peace of mind for your BI Investment
ClerPeks Customer Cre Guide Business s Usul (BU) Services Pece of mind for your BI Investment ClerPeks Customer Cre Business s Usul Services Tble of Contents 1. Overview...3 Benefits of Choosing ClerPeks
More informationGraphs on Logarithmic and Semilogarithmic Paper
0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl
More informationLowWage Workers and Health Insurance Coverage: Can Policymakers Target Them through Their Employers?
Stephen H. Long M. Susn Mrquis LowWge Workers nd Helth Insurnce Coverge: Cn Policymkers Trget Them through Their Employers? Mny policy inititives to increse helth insurnce coverge would subsidize employers
More informationExponentiation: Theorems, Proofs, Problems Pre/Calculus 11, Veritas Prep.
Exponentition: Theorems, Proofs, Problems Pre/Clculus, Verits Prep. Our Exponentition Theorems Theorem A: n+m = n m Theorem B: ( n ) m = nm Theorem C: (b) n = n b n ( ) n n Theorem D: = b b n Theorem E:
More informationFDIC Study of Bank Overdraft Programs
FDIC Study of Bnk Overdrft Progrms Federl Deposit Insurnce Corportion November 2008 Executive Summry In 2006, the Federl Deposit Insurnce Corportion (FDIC) initited twoprt study to gther empiricl dt on
More informationSmall Business Networking
Why Network is n Essentil Productivity Tool for Any Smll Business TechAdvisory.org SME Reports sponsored by Effective technology is essentil for smll businesses looking to increse their productivity. Computer
More informationCcrcs Cognitive  Counselling Research & Conference Services (eissn: 23012358)
Ccrcs Cognitive  Counselling Reserch & Conference Services (eissn: 23012358) Volume I Effects of Music Composition Intervention on Elementry School Children b M. Hogenes, B. Vn Oers, R. F. W. Diekstr,
More informationChapter 8  Practice Problems 1
Chpter 8  Prctice Problems 1 MULTIPLE CHOICE. Choose the one lterntive tht best completes the sttement or nswers the question. A hypothesis test is to be performed. Determine the null nd lterntive hypotheses.
More information2 DIODE CLIPPING and CLAMPING CIRCUITS
2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of
More informationWhy is the NSW prison population falling?
NSW Bureu of Crime Sttistics nd Reserch Bureu Brief Issue pper no. 80 September 2012 Why is the NSW prison popultion flling? Jcqueline Fitzgerld & Simon Corben 1 Aim: After stedily incresing for more thn
More informationMath Review 1. , where α (alpha) is a constant between 0 and 1, is one specific functional form for the general production function.
Mth Review Vribles, Constnts nd Functions A vrible is mthemticl bbrevition for concept For emple in economics, the vrible Y usully represents the level of output of firm or the GDP of n economy, while
More informationMathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100
hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by
More informationJaERM SoftwareasaSolution Package
JERM SoftwresSolution Pckge Enterprise Risk Mngement ( ERM ) Public listed compnies nd orgnistions providing finncil services re required by Monetry Authority of Singpore ( MAS ) nd/or Singpore Stock
More information1 Numerical Solution to Quadratic Equations
cs42: introduction to numericl nlysis 09/4/0 Lecture 2: Introduction Prt II nd Solving Equtions Instructor: Professor Amos Ron Scribes: Yunpeng Li, Mrk Cowlishw Numericl Solution to Qudrtic Equtions Recll
More informationUse Geometry Expressions to create a more complex locus of points. Find evidence for equivalence using Geometry Expressions.
Lerning Objectives Loci nd Conics Lesson 3: The Ellipse Level: Preclculus Time required: 120 minutes In this lesson, students will generlize their knowledge of the circle to the ellipse. The prmetric nd
More informationSection A4 Rational Expressions: Basic Operations
A Appendi A A BASIC ALGEBRA REVIEW 7. Construction. A rectngulr opentopped bo is to be constructed out of 9 by 6inch sheets of thin crdbord by cutting inch squres out of ech corner nd bending the
More informationAccording to Webster s, the
dt modeling Universl Dt Models nd P tterns By Len Silversn According Webster s, term universl cn be defined s generlly pplicble s well s pplying whole. There re some very common ptterns tht cn be generlly
More informationGAO IRS AUDIT RATES. Rate for Individual Taxpayers Has Declined But Effect on Compliance Is Unknown
GAO United Sttes Generl Accounting Office Report to the Chirmn, Subcommittee on Oversight, Committee on Wys nd Mens, House of Representtives April 2001 IRS AUDIT RATES Rte for Individul Txpyers Hs Declined
More informationExample 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers.
2 Rtionl Numbers Integers such s 5 were importnt when solving the eqution x+5 = 0. In similr wy, frctions re importnt for solving equtions like 2x = 1. Wht bout equtions like 2x + 1 = 0? Equtions of this
More informationSTATUS OF LANDBASED WIND ENERGY DEVELOPMENT IN GERMANY
Yer STATUS OF LANDBASED WIND ENERGY Deutsche WindGurd GmbH  Oldenburger Strße 6526316 Vrel  Germny +49 (4451)/9515  info@windgurd.de  www.windgurd.com Annul Added Cpcity [MW] Cumultive Cpcity [MW]
More informationFUNDING OF GROUP LIFE INSURANCE
TRANSACTIONS OF SOCIETY OF ACTUARIES 1955 VOL. 7 NO. 18 FUNDING OF GROUP LIFE INSURANCE CHARLES L. TROWBRIDGE INTRODUCTION T RADITIONALLY the group life insurnce benefit hs been finnced on yerly renewble
More information** Dpt. Chemical Engineering, Kasetsart University, Bangkok 10900, Thailand
Modelling nd Simultion of hemicl Processes in Multi Pulse TP Experiment P. Phnwdee* S.O. Shekhtmn +. Jrungmnorom** J.T. Gleves ++ * Dpt. hemicl Engineering, Ksetsrt University, Bngkok 10900, Thilnd + Dpt.hemicl
More informationSPECIAL PRODUCTS AND FACTORIZATION
MODULE  Specil Products nd Fctoriztion 4 SPECIAL PRODUCTS AND FACTORIZATION In n erlier lesson you hve lernt multipliction of lgebric epressions, prticulrly polynomils. In the study of lgebr, we come
More informationLecture 3 Gaussian Probability Distribution
Lecture 3 Gussin Probbility Distribution Introduction l Gussin probbility distribution is perhps the most used distribution in ll of science. u lso clled bell shped curve or norml distribution l Unlike
More informationJuly 2005, NCJ 209588 Substance Dependence, Abuse, and Treatment of Jail Inmates, 2002. Highlights. No dependence or abuse 53 47 32.
U.S. Deprtment of Justice Office of Justice Progrms Bureu of Justice Sttistics Specil Report By Jennifer C. Krerg nd Doris J. Jmes BJS Sttisticins In 2002 more thn twothirds of jil inmtes were found to
More informationUNIVERSITY OF NOTTINGHAM. Discussion Papers in Economics STRATEGIC SECOND SOURCING IN A VERTICAL STRUCTURE
UNVERSTY OF NOTTNGHAM Discussion Ppers in Economics Discussion Pper No. 04/15 STRATEGC SECOND SOURCNG N A VERTCAL STRUCTURE By Arijit Mukherjee September 004 DP 04/15 SSN 10438 UNVERSTY OF NOTTNGHAM Discussion
More informationCOMPONENTS: COMBINED LOADING
LECTURE COMPONENTS: COMBINED LOADING Third Edition A. J. Clrk School of Engineering Deprtment of Civil nd Environmentl Engineering 24 Chpter 8.4 by Dr. Ibrhim A. Asskkf SPRING 2003 ENES 220 Mechnics of
More information2015 EDITION. AVMA Report on Veterinary Compensation
2015 EDITION AVMA Report on Veterinry Compenstion AVMA Report on Veterinry Compenstion 2015 EDITION Copyright 2015 by the All rights reserved. ISBN13: 9781882691319 AVMA Report on Veterinry Compenstion
More informationCurve Sketching. 96 Chapter 5 Curve Sketching
96 Chpter 5 Curve Sketching 5 Curve Sketching A B A B A Figure 51 Some locl mximum points (A) nd minimum points (B) If (x, f(x)) is point where f(x) reches locl mximum or minimum, nd if the derivtive of
More informationRidgewood South Natural Areas Priority Evaluation. Background Report
Ridgewood South Nturl Ares Priority Evlution Bckground Report September 2013 Ridgewood South Nturl Ares Priority Evlution Bckground Report Ridgewood South Nturl Ares Priority Evlution Bckground Report
More informationDistributions. (corresponding to the cumulative distribution function for the discrete case).
Distributions Recll tht n integrble function f : R [,] such tht R f()d = is clled probbility density function (pdf). The distribution function for the pdf is given by F() = (corresponding to the cumultive
More informationJuly 22, 2009. The Honorable Henry A. Waxman Chairman Committee on Energy and Commerce House of Representatives
United Sttes Government Accountbility Office Wshington, DC 20548 July 22, 2009 The Honorble Henry A. Wxmn Chirmn Committee on Energy nd Commerce House of Representtives The Honorble John D. Dingell Chirmn
More informationSTATE OF MONTANA Developomental Disabilities Program Comprehensive Evaluation HiLine Home Programs, Inc Adult Services
Dtes of Review: FY '09 Evluttor(s): S. Crpenter DESK REVIEW: Accredittion: Acredittion is no longer required by the stte contrct. Significnt Events from the Agency: Developomentl Disbilities Progrm Comprehensive
More informationUNITED STATES DEPARTMENT OF AGRICULTURE Washington, D.C. 20250. ACTION BY: All Divisions and Offices. FGIS Directive 2510.
UNITED STATES DEPARTMENT OF AGRICULTURE Wshington, D.C. 20250 ACTION BY: All Divisions nd Offices FGIS Directive 2510.1 121173 FEDERAL TORT CLAIMS I PURPOSE This Instruction: A Sets forth the bsic provisions
More informationSTATEMENT OF ALICE M. RIVLIN, DIRECTOR CONGRESSIONAL BUDGET OFFICE. Before the
STATEMENT OF ALICE M. RIVLIN, DIRECTOR CONGRESSIONAL BUDGET OFFICE Before the SUBCOMMITTEE ON ECONOMIC STABILIZATION COMMITTEE ON BANKING, HOUSING, AND URBAN AFFAIRS UNITED STATES SENATE MARCH 13, 1980
More informationSection 74 Translation of Axes
62 7 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY Section 74 Trnsltion of Aes Trnsltion of Aes Stndrd Equtions of Trnslted Conics Grphing Equtions of the Form A 2 C 2 D E F 0 Finding Equtions of Conics In the
More informationPortfolio approach to information technology security resource allocation decisions
Portfolio pproch to informtion technology security resource lloction decisions Shivrj Knungo Deprtment of Decision Sciences The George Wshington University Wshington DC 20052 knungo@gwu.edu Abstrct This
More informationThreshold Population Levels for Rural Retail Businesses in North Dakota, 2000
Agribusiness & Applied Economics Miscellneous Report No. 191 July 2002 Threshold Popultion Levels for Rurl Retil Businesses in North Dkot, 2000 Rndl C. Coon nd F. Lrry Leistritz Deprtment of Agribusiness
More informationP.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn
33337_0P03.qp 2/27/06 24 9:3 AM Chpter P Pge 24 Prerequisites P.3 Polynomils nd Fctoring Wht you should lern Polynomils An lgeric epression is collection of vriles nd rel numers. The most common type of
More informationBinary Representation of Numbers Autar Kaw
Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse rel number to its binry representtion,. convert binry number to n equivlent bse number. In everydy
More informationPolicy Brief. Receipt of Public Benefits and Private Support among Lowincome Households with Children after the Great Recession.
Policy Brief #31, April 2012 The Ntionl Poverty Center s Policy Brief series summrizes key cdemic reserch findings, highlighting implictions for policy. The NPC encourges the dissemintion of this publiction
More informationEQUATIONS OF LINES AND PLANES
EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in pointdirection nd twopoint
More information2013 Flax Weed Control Trial
2013 Flx Weed Control Tril Dr. Hether Drby, UVM Extension Agronomist Susn Monhn, Conner Burke, Eric Cummings, nd Hnnh Hrwood UVM Extension Crops nd Soils Technicins 8025246501 Visit us on the web: http://www.uvm.edu/extension/cropsoil
More informationExample A rectangular box without lid is to be made from a square cardboard of sides 18 cm by cutting equal squares from each corner and then folding
1 Exmple A rectngulr box without lid is to be mde from squre crdbord of sides 18 cm by cutting equl squres from ech corner nd then folding up the sides. 1 Exmple A rectngulr box without lid is to be mde
More informationEstimating Exchange Rate Exposures:
Estimting Exchnge Rte Exposures: Issues in Model Structure * Gordon M. Bodnr ** Pul H. Nitze School of Advnced Interntionl Studies, The Johns Hopkins University 1740 Msschusetts Avenue NW Wshington, DC
More informationIn addition, the following elements form an integral part of the Agency strike prevention plan:
UNITED STTES DEPRTMENT OF GRICULTURE Wshington, DC 20250 Federl Grin Inspection Service FGIS Directive 4711.2 6/16/80 STRIKE PREVENTION ND STRIKE CONTINGENCY PLNS I PURPOSE This Instruction: Estlishes
More informationCredit Ratings, Collateral, and Loan Characteristics: Implications for Yield*
Kose John New York University Anthony W. Lynch New York University nd Ntionl Bureu of Economic Reserch Mnju Puri Stnford University nd Ntionl Bureu of Economic Reserch Credit Rtings, Collterl, nd Lon Chrcteristics:
More informationNewton s Three Laws. d dt F = If the mass is constant, this relationship becomes the familiar form of Newton s Second Law: dv dt
Newton s Three Lws For couple centuries before Einstein, Newton s Lws were the bsic principles of Physics. These lws re still vlid nd they re the bsis for much engineering nlysis tody. Forml sttements
More informationReversing Medications That Cause Bleeding
Reversing Medictions Tht Cuse Bleeding Dine M. Birnbumer, M.D., FACEP Professor of Medicine University of Cliforni, Los Angeles Senior Fculty Deprtment of Emergency Medicine HrborUCLA Medicl Center The
More informationVectors 2. 1. Recap of vectors
Vectors 2. Recp of vectors Vectors re directed line segments  they cn be represented in component form or by direction nd mgnitude. We cn use trigonometry nd Pythgors theorem to switch between the forms
More informationTechniques for Requirements Gathering and Definition. Kristian Persson Principal Product Specialist
Techniques for Requirements Gthering nd Definition Kristin Persson Principl Product Specilist Requirements Lifecycle Mngement Elicit nd define business/user requirements Vlidte requirements Anlyze requirements
More informationPortability of Social Benefits: The Economics of a Critical Topic in Globalisation
Portbility of Socil Benefits: The Economics of Criticl Topic in Globlistion Orgniser: Robert Holzmnn nd Mrtin Werding Interntionl Portbility of HelthCost Cover: Mobility, Insurnce, nd Redistribution Mrtin
More informationContextualizing NSSE Effect Sizes: Empirical Analysis and Interpretation of Benchmark Comparisons
Contextulizing NSSE Effect Sizes: Empiricl Anlysis nd Interprettion of Benchmrk Comprisons NSSE stff re frequently sked to help interpret effect sizes. Is.3 smll effect size? Is.5 relly lrge effect size?
More informationPhysics 43 Homework Set 9 Chapter 40 Key
Physics 43 Homework Set 9 Chpter 4 Key. The wve function for n electron tht is confined to x nm is. Find the normliztion constnt. b. Wht is the probbility of finding the electron in. nmwide region t x
More informationAN ANALYTICAL HIERARCHY PROCESS METHODOLOGY TO EVALUATE IT SOLUTIONS FOR ORGANIZATIONS
AN ANALYTICAL HIERARCHY PROCESS METHODOLOGY TO EVALUATE IT SOLUTIONS FOR ORGANIZATIONS Spiros Vsilkos (), Chrysostomos D. Stylios (),(b), John Groflkis (c) () Dept. of Telemtics Center, Computer Technology
More informationPROPERTY AND CASUALTY INSURANCE. Effects of the Nonadmitted and Reinsurance Reform Act of 2010
United Sttes Government Accountbility Office Report to Congressionl Committees Jnury 2014 PROPERTY AND CASUALTY INSURANCE Effects of the Nondmitted nd Reinsurnce Reform Act of 2010 GAO14136 Jnury 2014
More information6.2 Volumes of Revolution: The Disk Method
mth ppliction: volumes of revolution, prt ii Volumes of Revolution: The Disk Method One of the simplest pplictions of integrtion (Theorem ) nd the ccumultion process is to determine soclled volumes of
More informationWeek 7  Perfect Competition and Monopoly
Week 7  Perfect Competition nd Monopoly Our im here is to compre the industrywide response to chnges in demnd nd costs by monopolized industry nd by perfectly competitive one. We distinguish between
More informationVoluntary Prekindergarten Parent Handbook
Voluntry Prekindergrten Prent Hndbook Wht is Voluntry Prekindergrten (VPK)? Voluntry Prekindergrten (VPK) is legisltively mndted progrm designed to prepre every fouryerold in Florid for kindergrten nd
More information