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The first part contains 60 multiple-choice questions. Each question has four answer choices. The questions are loosely grouped into 10 sets of 6 items; each set corresponds to a different chemistry topic.
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6. Is the data machine-readable? (15 marks)This question addresses whether the data is in a form that can be easily processed by the computer.
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b. If you were in charge of awarding the prizes, would you have awarded the same amounts for the places. Why or why not? c. Suppose you are a judge. What would you use as criteria for judging the essay?
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There are four events in the TMSCA at both the middle and high school level: Number Sense, General Mathematics, Calculator Applications, and General Science. Number Sense is an 80-question exam that students are given only 10 minutes to solve. Additionally, no scratch work or paper calculations are allowed. These questions range from simple calculations such as 99+98 to more complicated operations such as 1001ร1938.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "102149"}
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Since many students who apply to graduate programs in biology do so during the first half of their fourth year, the scope of most questions is largely that of the first three years of a standard American undergraduate biology curriculum. A sampling of test item content is given below:
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The test had 50 multiple choice questions that were to be answered in one hour. All questions had five answer choices. Students received 1 point for every correct answer, lost ยผ of a point for each incorrect answer, and received 0 points for questions left blank. The questions covered a broad range of topics. Approximately 10-14% of questions focused on Numbers and Operations, 38-42% focused on Algebra and functions, 38-42% focused on Geometry (including Euclidean, coordinate, three-dimensional, and trigonometry), and 6-10% focused on Data analysis, Statistics, and probability.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "110538"}
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The test had 75 multiple choice questions that were to be answered in one hour. All questions had five answer choices. Students received 1 point for every correct answer, lost ยผ of a point for each incorrect answer, and received 0 points for questions left blank.
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These problems are usually more challenging than questions on the Number Sense test, and the General Mathematics word problems take more thinking to figure out. Every problem correct is worth 5 points, and for every problem incorrect, 2 points are deducted. Tiebreakers are determined by the person that misses the first problem and by percent accuracy.
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It contains 5 questions where the answer is a certain number and 2 open questions. There are a few optional training days and then the third round takes place at the Eindhoven University of Technology. It contains 5 open questions.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "44369"}
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It consists of 24 up to 30 problems. The sections for 3 point-, 4 point-, and 5 point-problems are equally divided. There is a penalty for an incorrect answer and no penalty for skipping a question.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "45877"}
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A radical equation is one that includes a radical sign, which includes square roots, x , {\displaystyle {\sqrt {x}},} cube roots, x 3 {\displaystyle {\sqrt{x}}} , and nth roots, x n {\displaystyle {\sqrt{x}}} . Recall that an nth root can be rewritten in exponential format, so that x n {\displaystyle {\sqrt{x}}} is equivalent to x 1 n {\displaystyle x^{\frac {1}{n}}} . Combined with regular exponents (powers), then x 3 2 {\displaystyle {\sqrt{x^{3}}}} (the square root of x cubed), can be rewritten as x 3 2 {\displaystyle x^{\frac {3}{2}}} . So a common form of a radical equation is x m n = a {\displaystyle {\sqrt{x^{m}}}=a} (equivalent to x m n = a {\displaystyle x^{\frac {m}{n}}=a} ) where m and n are integers. It has real solution(s): For example, if: ( x + 5 ) 2 / 3 = 4 {\displaystyle (x+5)^{2/3}=4} then x + 5 = ยฑ ( 4 ) 3 , x + 5 = ยฑ 8 , x = โ 5 ยฑ 8 , {\displaystyle {\begin{aligned}x+5&=\pm ({\sqrt {4}})^{3},\\x+5&=\pm 8,\\x&=-5\pm 8,\end{aligned}}} and thus x = 3 or x = โ 13 {\displaystyle x=3\quad {\text{or}}\quad x=-13}
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"The answer to this question is... Can you find a way to work it out?" "You've used substitution to solve all of these systems of equations. Can you use elimination now to solve them?
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Row 6. Number of HT - H298 equations required. Row 7.
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The College Board stated that a calculator "may be useful or necessary" for about 40-50% of the questions on the test. The College Board also encouraged the use of a graphing calculator over a scientific calculator. It also said that this test was "developed with the expectation that most students are using graphing calculators.
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Problem: 3 bundles of high-quality rice straws, 2 bundles of mid-quality rice straws and 1 bundle of low-quality rice straw produce 39 units of rice 2 bundles of high-quality rice straws, 3 bundles of mid-quality rice straws and 1 bundle of low-quality rice straw produce 34 units of rice 1 bundles of high-quality rice straw, 2 bundles of mid-quality rice straws and 3 bundle of low-quality rice straws produce 26 units of rice Question: how many units of rice can high, mid and low quality rice straw produce respectively? Solution: High-quality rice straw each produces 9 + 1/4 units of rice Mid-quality rice straw each produces 4 + 1/4 units of rice Low-quality rice straw each produces 2 + 3/4 units of riceThe presentation of Problem 1 contains a description (not a crisp indication) of the procedure for obtaining the solution. The procedure has been referred to as fangcheng shu, which means "fangcheng procedure." The remaining problems all give the instruction "follow the fangcheng" procedure sometimes followed by the instruction to use the "procedure for positive and negative numbers".
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Problems involving lateral forces are covered on the second day. Each day's morning session features multiple-choice questions, while the afternoon sessions are devoted to essay questions. == References ==
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maximal 1. For "maximal compact subgroup", see #compact. 2. For "maximal torus", see #torus.
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By visualizing these two parts, students would simply solve the above word problem by adding both parts together to build a whole bar of 100. Conversely, a student could use whole-part model to solve a subtraction problem such as 100 - 70, by having the longer part be 70 and the whole bar be 100. They would then solve the problem by inferring the shorter part to be 30.
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{\displaystyle y=\pm {\sqrt {1-x^{2}}}\,.} But even without specifying this explicit solution, it is possible to refer to the implicit solution of the unit circle equation as y = f(x), where f is the multi-valued implicit function. While explicit solutions can be found for equations that are quadratic, cubic, and quartic in y, the same is not in general true for quintic and higher degree equations, such as y 5 + 2 y 4 โ 7 y 3 + 3 y 2 โ 6 y โ x = 0 . {\displaystyle y^{5}+2y^{4}-7y^{3}+3y^{2}-6y-x=0\,.} Nevertheless, one can still refer to the implicit solution y = f(x) involving the multi-valued implicit function f.
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Lastly, type IV is also known as Waardenburg-Shah syndrome, and afflicted individuals display both Waardenburg's syndrome and Hirschsprung's disease. Types I and III are inherited in an autosomal dominant fashion, while II and IV exhibit an autosomal recessive pattern of inheritance. Overall, Waardenburg's syndrome is rare, with an incidence of ~ 2/100,000 people in the United States. All races and sexes are equally affected. There is no current cure or treatment for Waardenburg's syndrome.
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The second part contains 8 free response questions. Complete written explanations and calculations are required for full credit on a question, and partial credit is awarded. More thorough knowledge of basic theories is required, and often there are questions on less-emphasized portions of normal high school chemistry curricula, such as organic chemistry and coordination chemistry. One hour and 45 minutes (105 minutes) are allowed for this section.
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This test had 80 multiple-choice questions that were to be answered in one hour. All questions had five answer choices. Students received one point for each correct answer, lost ยผ of a point for each incorrect answer, and received 0 points for questions left blank.
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The student's score was based entirely on his or her performance in answering the multiple-choice questions. The questions covered a broad range of topics in general biology. There were more specific questions related respectively on ecological concepts (such as population studies and general Ecology) on the E test and molecular concepts such as DNA structure, translation, and biochemistry on the M test.
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The GRE subject test in chemistry is a standardized test in the United States created by the Educational Testing Service, and is designed to assess a candidate's potential for graduate or post-graduate study in the field of chemistry. It contains questions from many fields of chemistry. 15% of the questions will come from analytical chemistry, 25% will come from inorganic chemistry, 30% will come from organic chemistry and 30% will come from physical chemistry.This exam, like all the GRE subject tests, is paper-based, as opposed to the GRE general test which is usually computer-based. It contains 130 questions, which are to be answered within 2 hours and 50 minutes.
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Notes(a) As quoted in the text: "the scale is calculated using the average discretionary addition (adjusted to spread winter fuel costs throughout the year) for retirement pensioners. It does not include any allowance for rent. The price index used for the single pensioner is that in the Employment and Productivity Gazette." (b) As quoted in the text: "it is assumed that the children are aged four, six, and eleven."
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The examination will consist of totally 65 questions, segregated as One-mark and Two-mark questions. Out of 65 questions, 10 questions will be from General Aptitude (Verbal and Numerical ability) and 55 questions will be Technical, based on the Paper chosen. The General Aptitude section will have 5 One-mark questions and 5 Two-mark questions, accounting for about 15% of total marks. The Technical section and Engineering Mathematics section will combinedly have 25 One-mark questions and 30 Two-mark questions, accounting for about 85% of total marks.
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The mathematical definition is: Input: A strongly connected, mixed graph G = ( V , E , A ) {\displaystyle G=(V,E,A)} with cost c ( e ) โฅ 0 {\displaystyle c(e)\geq 0} for every edge e โ E โช A {\displaystyle e\subset E\cup A} and a maximum cost c m a x {\displaystyle c_{max}} . Question: is there a (directed) tour that traverses every edge in E {\displaystyle E} and every arc in A {\displaystyle A} at least once and has cost at most c m a x {\displaystyle c_{max}} ?
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One of the simplest possible relationships between x {\displaystyle x} and y {\displaystyle y} is a line y = ฮฒ 1 + ฮฒ 2 x {\displaystyle y=\beta _{1}+\beta _{2}x} . The intercept ฮฒ 1 {\displaystyle \beta _{1}} and the slope ฮฒ 2 {\displaystyle \beta _{2}} are initially unknown. The researcher would like to find values of ฮฒ 1 {\displaystyle \beta _{1}} and ฮฒ 2 {\displaystyle \beta _{2}} that cause the line to pass through the four data points. In other words, the researcher would like to solve the system of linear equations With four equations in two unknowns, this system is overdetermined.
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This means the alleles (variants) inherited from both parents are expressed equally: Each person carries 2 alleles of each of the 3 class-I genes, (HLA-A, HLA-B and HLA-C), and so can express six different types of MHC-I (see figure). In the class-II locus, each person inherits a pair of HLA-DP genes (DPA1 and DPB1, which encode ฮฑ and ฮฒ chains), a couple of genes HLA-DQ (DQA1 and DQB1, for ฮฑ and ฮฒ chains), one gene HLA-DRฮฑ (DRA1), and one or more genes HLA-DRฮฒ (DRB1 and DRB3, -4 or -5). That means that one heterozygous individual can inherit six or eight functioning class-II alleles, three or more from each parent.
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After calculating scores, question difficulty was used as a tie-breaker to determine ranks for students with same scores.
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Calculator Applications is an 80-question exam that students are given only 30 minutes to solve. This test requires practice on the calculator, knowledge of a few crucial formulas, and much speed and intensity. Memorizing formulas, tips, and tricks will not be enough.
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3. Between two groups, may mean that the first one is a proper subgroup of the second one. > 1.
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All quadratic equations will have two solutions in the complex number system, but need not have any in the real number system. For example, x 2 + 1 = 0 {\displaystyle x^{2}+1=0} has no real number solution since no real number squared equals โ1. Sometimes a quadratic equation has a root of multiplicity 2, such as: ( x + 1 ) 2 = 0.
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The values of the variables which make the equation true are the solutions of the equation and can be found through equation solving. Another type of equation is inequality. Inequalities are used to show that one side of the equation is greater, or less, than the other. The symbols used for this are: a > b {\displaystyle a>b} where > {\displaystyle >} represents 'greater than', and a < b {\displaystyle a
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A system of equations is a set of simultaneous equations, usually in several unknowns for which the common solutions are sought. Thus, a solution to the system is a set of values for each of the unknowns, which together form a solution to each equation in the system. For example, the system 3 x + 5 y = 2 5 x + 8 y = 3 {\displaystyle {\begin{aligned}3x+5y&=2\\5x+8y&=3\end{aligned}}} has the unique solution x = โ1, y = 1.
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In a survey of 53 Psychology freshmen taking an introductory probability course, 35 incorrectly responded 1/2; only 3 students correctly responded 2/3.
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The whole-part model can also be used to solve problems involving multiplication or division. A multiplication problem could be presented as follows: How much money would Jane have if she saved $30 each week for 4 weeks in a row?The student could solve this multiplication problem by drawing one bar to represent the unknown answer, and subdivide that bar into four equal parts, with each part representing $30. Based on the drawn model, the student could then visualize this problem as providing a solution of $120.
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Zemmer. However, the proof is quite difficult, and it is more convenient to include this in the axioms so that progress with establishing the properties of near-fields can start more rapidly. Sometimes a list of axioms is given in which A4 and A5 are replaced by the following single statement: A4*: The non-zero elements form a group under multiplication.
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The standard deviation between test scores in 2006 was 102.Less than one percent of the 2006 College-Bound Seniors taking the test received a perfect score of 800. None got a score lower than 260. The mean score was 593.
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Polynomial equations of degree 8 are octic equations. These have the form a x 8 + b x 7 + c x 6 + d x 5 + e x 4 + f x 3 + g x 2 + h x + k = 0. {\displaystyle ax^{8}+bx^{7}+cx^{6}+dx^{5}+ex^{4}+fx^{3}+gx^{2}+hx+k=0.\,} The smallest known eighth power that can be written as a sum of eight eighth powers is 1409 8 = 1324 8 + 1190 8 + 1088 8 + 748 8 + 524 8 + 478 8 + 223 8 + 90 8 . {\displaystyle 1409^{8}=1324^{8}+1190^{8}+1088^{8}+748^{8}+524^{8}+478^{8}+223^{8}+90^{8}.}
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Find k {\displaystyle k} . (1989 AIME #7)Answer: 925Complex numbers a {\displaystyle a} , b {\displaystyle b} and c {\displaystyle c} are the zeros of a polynomial P ( z ) = z 3 + q z + r {\displaystyle P(z)=z^{3}+qz+r} , and | a | 2 + | b | 2 + | c | 2 = 250 {\displaystyle |a|^{2}+|b|^{2}+|c|^{2}=250} . The points corresponding to a {\displaystyle a} , b {\displaystyle b} , and c {\displaystyle c} in the complex plane are the vertices of a right triangle with hypotenuse h {\displaystyle h} . Find h 2 {\displaystyle h^{2}} . (2012 AIME I #14)Answer: 375
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Approximately the top 400 students from the F=ma exam are invited to take a free-response, calculus-based exam covering all topics in introductory physics, including mechanics, electricity and magnetism, thermodynamics, fluids, relativity, waves, and nuclear and atomic physics. There are two parts in the exam, each allotted 90 minutes, and 6 problems in total. Prior to 2017, the exam could be taken at any time during a two-week window in March.
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The reverse process of expressing a proper rational fraction as the sum of two or more fractions is called resolving it into partial fractions. For example, 2 x x 2 โ 1 = 1 x โ 1 + 1 x + 1 . {\displaystyle {\frac {2x}{x^{2}-1}}={\frac {1}{x-1}}+{\frac {1}{x+1}}.} Here, the two terms on the right are called partial fractions.
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{\displaystyle 9=3^{2}=(2+{\sqrt {-5}})(2-{\sqrt {-5}}).} This equation shows that 3 divides the product (2 + โ-5)(2 - โ-5) = 9.
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Historically, and in current teaching, the study of algebra starts with the solving of equations, such as the quadratic equation above. Then more general questions, such as "does an equation have a solution? ", "how many solutions does an equation have?
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There are also systems which have infinitely many solutions, in contrast to a system with a unique solution (meaning, a unique pair of values for x and y) For example: { 4 x + 2 y = 12 โ 2 x โ y = โ 6 {\displaystyle {\begin{cases}{\begin{aligned}4x+2y&=12\\-2x-y&=-6\end{aligned}}\end{cases}}} Isolating y in the second equation: y = โ 2 x + 6 {\displaystyle y=-2x+6} And using this value in the first equation in the system: 4 x + 2 ( โ 2 x + 6 ) = 12 4 x โ 4 x + 12 = 12 12 = 12 {\displaystyle {\begin{aligned}4x+2(-2x+6)=12\\4x-4x+12=12\\12=12\end{aligned}}} The equality is true, but it does not provide a value for x. Indeed, one can easily verify (by just filling in some values of x) that for any x there is a solution as long as y = โ 2 x + 6 {\displaystyle y=-2x+6} . There is an infinite number of solutions for this system.
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GATE, for long, has been known to test the Engineering basics in a smart way. Complaints of "lengthy" problems have been rare. But the task of mastering an entire course of Engineering (around 30 undergraduate subjects) for a three-hour test, itself gives the test a certain level of toughness.
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GRE Subject Biochemistry, Cell and Molecular Biology was a standardized exam provided by ETS (Educational Testing Service) that was discontinued in December 2016. It is a paper-based exam and there are no computer-based versions of it. ETS places this exam three times per year: once in April, once in October and once in November.
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The GRE subject test in biology was a standardized test in the United States created by the Educational Testing Service, and is designed to assess a candidate's potential for graduate or post-graduate study in the field of biology. The test is comprehensive and coversโin equal proportionsโmolecular biology, organismal biology, and ecology and evolution.This exam, like all the GRE subject tests, is paper-based, as opposed to the GRE general test which is usually computer-based. It contains 194 questions, which are to be answered within 2 hours and 50 minutes. Scores on this exam are required for entrance to some biology Ph.D.
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Students are encouraged to participate in Mathematic activities which host up to 20 questions related to a certain topic. Once a student answers a question, the website recognises its completion and then adapts to the "student's progress in understanding", leading to questions that may be more complex in difficulty. At the completion of each topic, students are offered the opportunity to take a 'Topic Test' which summates the hardest questions in the past activities.
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In other occurrences, the same disease, for instance, some forms of carcinoma or melanoma, may stem from an inbred condition in some people, from new changes in other people, and from non-genetic causes in still other individuals.There are more than six thousand known single-gene disorders (monogenic), which occur in about 1 out of every 200 births. As their term suggests, these diseases are caused by a mutation in one gene. By contrast, polygenic disorders are caused by several genes, regularly in combination with environmental factors. Examples of genetic phenotypes include Alzheimer's disease, breast cancer, leukemia, Down syndrome, heart defects, and deafness; therefore, cataloguing to sort out all the diseases related to genes is needed.
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Genetic Broadly speaking, genetic diseases are caused by aberrations in genes or chromosomes. Many genetic diseases are developed from before birth. Genetic disorders account for a significant number of the health care problems in our society.
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If n is between 50 and 500, what are n and x?' This is a bivariate problem with multiple solutions. Ramanujan thought about it and gave the answer with a twist: He gave a continued fraction.
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then the object's velocity is x ห ( t ) = x โฒ ( t ) = โ 32 t + 16 , {\displaystyle {\dot {x}}(t)=x'(t)=-32t+16,\,\!} and the object's acceleration is x ยจ ( t ) = x โณ ( t ) = โ 32 , {\displaystyle {\ddot {x}}(t)=x''(t)=-32,\,\!} which is constant.
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The College Board suggested a year-long course in biology at the college preparatory level, as well as a one-year course in algebra, and lab experience as preparation for the test. The test required understanding of biological data and concepts, science-related terms, and the ability to effectively synthesize and interpret data from charts, maps, and other visual media. However, most questions from this test were derived from, or are similar to, the pre-2012 AP Biology multiple choice questions. By taking an AP class or a class with similar rigor, one's chances at doing well on this test should have improved.
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The ordinary range of chemical shifts ranges from about ฮด250 to โฮด250, which is much wider than typical for 1H NMR. Unlike 1H NMR spectroscopy, 31P NMR shifts are primarily not determined by the magnitude of the diamagnetic shielding, but are dominated by the so-called paramagnetic shielding tensor (unrelated to paramagnetism). The paramagnetic shielding tensor, ฯp, includes terms that describe the radial expansion (related to charge), energies of excited states, and bond overlap. Illustrative of the effects lead to big changes in chemical shifts, the chemical shifts of the two phosphate esters (MeO)3PO (ฮด2.1) and (t-BuO)3PO (ฮด-13.3). More dramatic are the shifts for phosphine derivatives H3P (ฮด-240), (CH3)3P (ฮด-62), (i-Pr)3P (ฮด20), and (t-Bu)3P (ฮด61.9).
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Student materials included in the 2002 Grade 5 package for TERC Investigations: 4 rolls of adding machine tape; 36 blank 5/8" cubes; 1,000 stickers for blank cubes; 200 1-cm cubes; 16 transparent blank spinners; 4 450-piece sets of power polygons; 4 buckets of square color tiles (400 per bucket); 1,000 Snap(TM) cubes; 1 set of elementary bar mass set-Ohaus; 4 graduated measuring prisms (2-cm x 5-cm x 21-cm); 4-liter measuring pitcher (calibrated 100 ml - 1,000 ml); 4 spectrum school balance (includes 7-piece mass set); 4 sets standard measuring pitchers (3 pitchers: quart, pint, cup per set); 10 measuring tapes; 12 meter/yard sticks. The total package for Grade 5 is listed at $1,388.42, and within that total the cost of the just mentioned student materials, for a class of 32, is $817.00 Many mathematics classrooms where active learning occurs already own many of these materials, so it is not necessary to purchase all of these items from the publisher. In the original edition, there was no multiplication table presented.
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The test had 50 multiple choice questions that were to be answered in one hour. All questions had five answer choices. Students received 1 point for every correct answer, lost ยผ of a point for each incorrect answer, and received 0 points for questions left blank.
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Typically, the topics are, in order, descriptive chemistry/laboratory techniques, stoichiometry, gases/liquids/solids, thermodynamics, kinetics, equilibrium, electrochemistry, electronic structure/periodic trends, bonding theories, and organic chemistry. There is no penalty for guessing; a student's score is equal to the number of questions answered correctly. One and a half hours (90 minutes) are allotted for this first part.
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In this event, plenty of practice is necessary in order to master the locations of the keys and develop the speed necessary. All correct questions are worth 5 points and all incorrect questions or skipped questions that are before the last answered questions will lose 4 points; answers are to be given with three significant figures. Science is a 50-question exam that is solved in 40 minutes at the middle school level or a 60-question exam that is solved in a 2-hour time limit at the high school level. Tiebreakers are determined by the person that misses the first problem and by percent accuracy. As the name suggests, the test focuses on the science subjects learned in the middle school or high school level depending on the student's grade and the version of the test being taken.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "7080"}
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The requirement that a solution circle must exactly touch each of the three given circles can be expressed as three coupled quadratic equations for xs, ys and rs: ( x s โ x 1 ) 2 + ( y s โ y 1 ) 2 = ( r s โ s 1 r 1 ) 2 {\displaystyle \left(x_{s}-x_{1}\right)^{2}+\left(y_{s}-y_{1}\right)^{2}=\left(r_{s}-s_{1}r_{1}\right)^{2}} ( x s โ x 2 ) 2 + ( y s โ y 2 ) 2 = ( r s โ s 2 r 2 ) 2 {\displaystyle \left(x_{s}-x_{2}\right)^{2}+\left(y_{s}-y_{2}\right)^{2}=\left(r_{s}-s_{2}r_{2}\right)^{2}} ( x s โ x 3 ) 2 + ( y s โ y 3 ) 2 = ( r s โ s 3 r 3 ) 2 . {\displaystyle \left(x_{s}-x_{3}\right)^{2}+\left(y_{s}-y_{3}\right)^{2}=\left(r_{s}-s_{3}r_{3}\right)^{2}.} The three numbers s1, s2 and s3 on the right-hand side, called signs, may equal ยฑ1, and specify whether the desired solution circle should touch the corresponding given circle internally (s = 1) or externally (s = โ1).
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{"source": "wikipedia", "start_index": 0, "docstore_id": "43917"}
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To check that the graph does represent the equations given, go to node x1. Look at the arrows incoming to this node (colored green for emphasis) and the weights attached to them. The equation for x1 is satisfied by equating it to the sum of the nodes attached to the incoming arrows multiplied by the weights attached to these arrows.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "136095"}
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1H-NMR (400 MHz, CD3OD): /ฯ = 8.07 (dd,3J = 2.5 Hz,4J = 1.1 Hz, 1H, C-6), 7.98 (dd,3J = 4.0 Hz,3J = 2.0 Hz, 1H, C-3), 7.23 (dd,3J = 2.5 Hz,3J = 2.0 Hz, 1H, C-5), 7.21 (dd,3J = 4.0 Hz,4J = 1.0 Hz, 1H, C-4).
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{"source": "wikipedia", "start_index": 0, "docstore_id": "142871"}
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Tables of values of n3 + n2 were used to solve certain cubic equations. For example, consider the equation: a x 3 + b x 2 = c . {\displaystyle \ ax^{3}+bx^{2}=c.}
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{"source": "wikipedia", "start_index": 0, "docstore_id": "85906"}
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After the on-line questions, students will take a test about what they have learned while solving the on-line questions. First grade students in high school take this test. The questions are based on basic chemistry. The test can determine how much the students understand basic chemistry.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "6054"}
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{\displaystyle {\begin{cases}{\begin{aligned}x+y&=1\\0x+0y&=2\,.\end{aligned}}\end{cases}}} As 0โ 2, the second equation in the system has no solution. Therefore, the system has no solution. However, not all inconsistent systems are recognized at first sight. As an example, consider the system { 4 x + 2 y = 12 โ 2 x โ y = โ 4 . {\displaystyle {\begin{cases}{\begin{aligned}4x+2y&=12\\-2x-y&=-4\,.\end{aligned}}\end{cases}}} Multiplying by 2 both sides of the second equation, and adding it to the first one results in 0 x + 0 y = 4 , {\displaystyle 0x+0y=4\,,} which clearly has no solution.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "33902"}
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However, this trend has diverged recently, and questions that are in both the AMC 10 and 12 are in increasingly similar positions. Problem 18 on the 2022 AMC 10A was the same as problem 18 on the 2022 AMC 12A.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "27918"}
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While receiving ART some patients with undetectable viral load measurements may experience an increase in viral load, to a low level (usually below 400 copies/mL blood), and then returned to an undetectable level. These transient blips do not indicate that the virus is developing resistance to drug therapy. Blips appear to be more common in the winter, suggesting a connection with illness such as colds and influenza. Viral load blips are partially explained by various patient related factors, and thought to be relatively common. High level and sustained increases in viral load are frequently related to the development of drug resistance and/or viral mutations, and often dictate changes in ART.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "20910"}
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The questions are divided into four categories: arithmetic, algebra, geometry and problem solving, and the number of questions that the student answered correctly for each category is listed along with the regional mean. Every school receives a more comprehensive analysis, with a complete record of answers given by all students, as well as the percentage of students choosing any given answer for a given question, and a comparison to the percentage of students choosing any given answer for a given question in the whole region. Schools also receive an analysis of their students by mathematical topic, compared to the entire region.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "108144"}
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On-line Questions are uploaded again after the Winter School. The leftovers of the Winter School and other people who didn't join the Winter School have to take this test to join the Summer School 2. Second grade students in the high school take this test. In this test, almost half of these questions will be related to Organic Chemistry. 20 well-ranked students can join the Winter School 2.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "36099"}
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The learning process consists of estimating model parameters S and associating signals with concepts by maximizing the similarity L. Note that all possible combinations of signals and models are accounted for in expression (2) for L. This can be seen by expanding a sum and multiplying all the terms resulting in MN items, a huge number. This is the number of combinations between all signals (N) and all models (M). This is the source of Combinatorial Complexity, which is solved in NMF by utilizing the idea of dynamic logic,. An important aspect of dynamic logic is matching vagueness or fuzziness of similarity measures to the uncertainty of models.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "6693"}
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Students generally spend several weeks preparing for the TMUA exam. There are various different preparation materials available for students wanting to get ready for the exam such as textbooks, courses and online materials. However, past papers are the most valuable resource as they are directly from the exam administrators themselves. The past papers are freely available from the exam administrator, and various other sources. Answer keys are also released alongside TMUA past papers.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "106509"}
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Suppose we wished to find an element x {\displaystyle x\ } of a group G {\displaystyle G\ } satisfying the conditions (equations and inequations): x 2 = 1 {\displaystyle x^{2}=1\ } x 3 = 1 {\displaystyle x^{3}=1\ } x โ 1 {\displaystyle x\neq 1\ } Then it is easy to see that this is impossible because the first two equations imply x = 1 {\displaystyle x=1\ } . In this case we say the set of conditions are inconsistent with G {\displaystyle G\ } . (In fact this set of conditions are inconsistent with any group whatsoever.)
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{"source": "wikipedia", "start_index": 0, "docstore_id": "90333"}
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The two preceding examples define the same polynomial function. Two important and related problems in algebra are the factorization of polynomials, that is, expressing a given polynomial as a product of other polynomials that cannot be factored any further, and the computation of polynomial greatest common divisors. The example polynomial above can be factored as (x โ 1)(x + 3). A related class of problems is finding algebraic expressions for the roots of a polynomial in a single variable.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "132152"}
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A linear function is a polynomial function in which the variable x has degree at most one: f ( x ) = a x + b {\displaystyle f(x)=ax+b} .Such a function is called linear because its graph, the set of all points ( x , f ( x ) ) {\displaystyle (x,f(x))} in the Cartesian plane, is a line. The coefficient a is called the slope of the function and of the line (see below). If the slope is a = 0 {\displaystyle a=0} , this is a constant function f ( x ) = b {\displaystyle f(x)=b} defining a horizontal line, which some authors exclude from the class of linear functions. With this definition, the degree of a linear polynomial would be exactly one, and its graph would be a line that is neither vertical nor horizontal.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "118047"}
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For a student to get two questions fully correct is considered "very good". All people taking part in this challenge will get a certificate (participation for the bottom 50%, merit for the next 25% and distinction for the top 25%). The mark boundaries for these certificates change every year, but normally around 30 marks will gain a Distinction. Those scoring highly (the top 50) will gain a book prize; again, this changes every year, with 44 marks required in the Maclaurin paper in 2006. Also, the top 100 candidates will receive a medal; bronze for Cayley, silver for Hamilton and gold for Maclaurin.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "71364"}
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The actual square root of 15 is 3.872983... One thing to note is that, no matter what the original guess was, the estimated answer will always be larger than the actual answer due to the inequality of arithmetic and geometric means. Thus, one should try rounding the estimated answer down. Note that if n2 is the closest perfect square to the desired square x and d = x - n2 is their difference, it is more convenient to express this approximation in the form of mixed fraction as n d 2 n {\displaystyle n{\tfrac {d}{2n}}} .
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{"source": "wikipedia", "start_index": 0, "docstore_id": "16888"}
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(5) X1 = (7*103*Y*A*SIN ALPHA)3 / (B POW D+C POW E) . (6) WRITE AND EDIT A Y D E X1 SERVO 6 . (7) JUMP TO SENTENCE 2A .
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{"source": "wikipedia", "start_index": 0, "docstore_id": "49642"}
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If the curve is required to be in a particular sub-category of n-th degree polynomial equations, then fewer than n(n + 3) / 2 points may be necessary and sufficient to determine a unique curve. For example, three (non-collinear) points determine a circle: the generic circle is given by the equation ( x โ a ) 2 + ( y โ b ) 2 = r 2 {\displaystyle (x-a)^{2}+(y-b)^{2}=r^{2}} where the center is located at (a, b) and the radius is r. Equivalently, by expanding the squared terms, the generic equation is x 2 โ 2 a x + y 2 โ 2 b y = k , {\displaystyle x^{2}-2ax+y^{2}-2by=k,} where k = r 2 โ a 2 โ b 2 . {\displaystyle k=r^{2}-a^{2}-b^{2}.} Two restrictions have been imposed here compared to the general conic case of n = 2: the coefficient of the term in xy is restricted to equal 0, and the coefficient of y2 is restricted to equal the coefficient of x2. Thus instead of five points being needed, only 5 โ 2 = 3 are needed, coinciding with the 3 parameters a, b, k (equivalently a, b, r) that need to be identified.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "59470"}
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The first question of Part B was a chemical equation question in which 3 scenarios were presented and the student was required to work all 3 scenarios, authoring a balanced net ionic chemical equation for each scenario and answering questions about the equations and scenarios. If time permitted, students may have edited their responses from Part A during the time allotted for responding to Part B, though without the use of a calculator. The student needed to have completed all six questions.While the use of calculators was prohibited during Section I and Section II Part B, a periodic table, a list of selected standard reduction potentials, and two pages of equations and conventions are available for use during the entirety of Section II.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "119463"}
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Human females are born with all the primary oocytes they will ever have. Starting at puberty the process of meiosis can complete resulting in the secondary oocyte and the first polar body. The secondary oocyte can later be fertilized with the male sperm.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "90238"}
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x โ 1 3 x 3 + 2 15 x 5 โ 17 315 x 7 {\displaystyle x-{\frac {1}{3}}\,x^{3}+{\frac {2}{15}}\,x^{5}-{\frac {17}{315}}\,x^{7}} + 62 2835 x 9 โ 1382 155925 x 11 + 21844 6081075 x 13 + O ( x 15 ) {\displaystyle {}+{\frac {62}{2835}}\,x^{9}-{\frac {1382}{155925}}\,x^{11}+{\frac {21844}{6081075}}\,x^{13}+{\mathcal {O}}\left(x^{15}\right)}
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{"source": "wikipedia", "start_index": 0, "docstore_id": "67217"}
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Column legend Cpt: Is this group G compact? (Yes or No) ฯ 0 {\displaystyle \pi _{0}}: Gives the group of components of G. The order of the component group gives the number of connected components. The group is connected if and only if the component group is trivial (denoted by 0). ฯ 1 {\displaystyle \pi _{1}}: Gives the fundamental group of G whenever G is connected. The group is simply connected if and only if the fundamental group is trivial (denoted by 0). UC: If G is not simply connected, gives the universal cover of G.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "10796"}
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The respondent is required to click on the circle, which corresponds to the desired answer. A dot in the middle will appear once an answer is chosen. Only one answer can be chosen. Recommended when the choice of answers are mutually exclusive.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "84044"}
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For example, HIV infects a limited range of human leucocytes. This is because its surface protein, gp120, specifically interacts with the CD4 moleculeโa chemokine receptorโwhich is most commonly found on the surface of CD4+ T-Cells. This mechanism has evolved to favour those viruses that infect only cells in which they are capable of replication.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "96453"}
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The third chapter contains examples of quadratic irrationalities as solutions and coefficients. The fourth chapter shows how these irrationalities are used to solve problems involving polygons.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "89852"}
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All quadratic equations have exactly two solutions in complex numbers (but they may be equal to each other), a category that includes real numbers, imaginary numbers, and sums of real and imaginary numbers. Complex numbers first arise in the teaching of quadratic equations and the quadratic formula. For example, the quadratic equation x 2 + x + 1 = 0 {\displaystyle x^{2}+x+1=0} has solutions x = โ 1 + โ 3 2 and x = โ 1 โ โ 3 2 . {\displaystyle x={\frac {-1+{\sqrt {-3}}}{2}}\quad \quad {\text{and}}\quad \quad x={\frac {-1-{\sqrt {-3}}}{2}}.} Since โ 3 {\displaystyle {\sqrt {-3}}} is not any real number, both of these solutions for x are complex numbers.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "113427"}
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Equations can be classified according to the types of operations and quantities involved. Important types include: An algebraic equation or polynomial equation is an equation in which both sides are polynomials (see also system of polynomial equations). These are further classified by degree: linear equation for degree one quadratic equation for degree two cubic equation for degree three quartic equation for degree four quintic equation for degree five sextic equation for degree six septic equation for degree seven octic equation for degree eight A Diophantine equation is an equation where the unknowns are required to be integers A transcendental equation is an equation involving a transcendental function of its unknowns A parametric equation is an equation in which the solutions for the variables are expressed as functions of some other variables, called parameters appearing in the equations A functional equation is an equation in which the unknowns are functions rather than simple quantities Equations involving derivatives, integrals and finite differences: A differential equation is a functional equation involving derivatives of the unknown functions, where the function and its derivatives are evaluated at the same point, such as f โฒ ( x ) = x 2 {\displaystyle f'(x)=x^{2}} . Differential equations are subdivided into ordinary differential equations for functions of a single variable and partial differential equations for functions of multiple variables An integral equation is a functional equation involving the antiderivatives of the unknown functions.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "71015"}
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In two variables the non-zero quadratic forms are classified as: x 2 + y 2 {\displaystyle x^{2}+y^{2}} โ positive-definite (the negative is also included), corresponding to ellipses, x 2 {\displaystyle x^{2}} โ degenerate, corresponding to parabolas, and x 2 โ y 2 {\displaystyle x^{2}-y^{2}} โ indefinite, corresponding to hyperbolas. In two variables quadratic forms are classified by discriminant, analogously to conics, but in higher dimensions the more useful classification is as definite, (all positive or all negative), degenerate, (some zeros), or indefinite (mix of positive and negative but no zeros). This classification underlies many that follow.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "38439"}
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This potential energy guides ATP synthesis via complex V (ATP synthase), which conflates ADP with another P to create ATP by pushing protons (H+) back into the matrix (this process is known as oxidative phosphorylation). Finally, the outer mitochondrial membrane (OMM) houses a voltage-dependent anion channel called the VDAC. This site is important for converting energy signals into electro-chemical outputs for ATP transfer.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "10041"}
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This problem's result is used in problem 50, where the scribe finds the area of a round field of diameter 9 khet. Hemisphere: Problem 10 in the MMP finds the area of a hemisphere. Volumes: Cylindrical (cylinder): Several problems compute the volume of cylindrical granaries (RMP 41โ43), while problem 60 RMP seems to concern a pillar or a cone instead of a pyramid.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "128006"}
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The NSEC contains only multiple choice questions. The questions include physical chemistry, organic chemistry, and inorganic chemistry. The stress on biochemistry is more in the NSEC than in the typical school syllabi.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "135586"}
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In infinite groups, such an n {\displaystyle n} may not exist, in which case the order of a {\displaystyle a} is said to be infinity. The order of an element equals the order of the cyclic subgroup generated by this element. More sophisticated counting techniques, for example, counting cosets, yield more precise statements about finite groups: Lagrange's Theorem states that for a finite group G {\displaystyle G} the order of any finite subgroup H {\displaystyle H} divides the order of G {\displaystyle G} .
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{"source": "wikipedia", "start_index": 0, "docstore_id": "65455"}
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One important factor for sibling detection, especially relevant for older siblings, is that if an infant and one's mother are seen to care for the infant, then the infant and oneself are assumed to be related. Another factor, especially important for younger siblings who cannot use the first method, is that persons who grew up together see one another as related. Yet another may be genetic detection based on the major histocompatibility complex (See Major Histocompatibility Complex and Sexual Selection).
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{"source": "wikipedia", "start_index": 0, "docstore_id": "50173"}
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For instance problem 19 asks one to calculate a quantity taken 1+1/2 times and added to 4 to make 10. In other words, in modern mathematical notation we are asked to solve the linear equation: 3 2 ร x + 4 = 10.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "145299"}
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Mendelian laws (Dominance and Uniformity, segregation of genes, and Independent Assortment) HardyโWeinberg principle
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{"source": "wikipedia", "start_index": 0, "docstore_id": "101530"}
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For example, consider a line running through points (2,8) and (3,20). This line has a slope, m, of ( 20 โ 8 ) ( 3 โ 2 ) = 12. {\displaystyle {\frac {(20-8)}{(3-2)}}=12.} One can then write the line's equation, in point-slope form: y โ 8 = 12 ( x โ 2 ) = 12 x โ 24.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "104420"}
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If B = 0 {\displaystyle B=0} in the original equation, the resulting line x = C A {\displaystyle x={\tfrac {C}{A}}} is vertical, and cannot be written as y = f ( x ) {\displaystyle y=f(x)} . The features of the graph y = f ( x ) = a x + b {\displaystyle y=f(x)=ax+b} can be interpreted in terms of the variables x and y. The y-intercept is the initial value y = f ( 0 ) = b {\displaystyle y=f(0)=b} at x = 0 {\displaystyle x=0} . The slope a measures the rate of change of the output y per unit change in the input x. In the graph, moving one unit to the right (increasing x by 1) moves the y-value up by a: that is, f ( x + 1 ) = f ( x ) + a {\displaystyle f(x{+}1)=f(x)+a} . Negative slope a indicates a decrease in y for each increase in x. For example, the linear function y = โ 2 x + 4 {\displaystyle y=-2x+4} has slope a = โ 2 {\displaystyle a=-2} , y-intercept point ( 0 , b ) = ( 0 , 4 ) {\displaystyle (0,b)=(0,4)} , and x-intercept point ( 2 , 0 ) {\displaystyle (2,0)} .
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{"source": "wikipedia", "start_index": 0, "docstore_id": "54402"}
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A rational function is the same, with divisions also allowed, such as f ( x ) = x โ 1 x + 1 , {\displaystyle f(x)={\frac {x-1}{x+1}},} and f ( x ) = 1 x + 1 + 3 x โ 2 x โ 1 . {\displaystyle f(x)={\frac {1}{x+1}}+{\frac {3}{x}}-{\frac {2}{x-1}}.} An algebraic function is the same, with nth roots and roots of polynomials also allowed. An elementary function is the same, with logarithms and exponential functions allowed.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "113506"}
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As an example of the usefulness of the first approach, suppose we wish to calculate the distance a cannonball travels when fired with a vertical velocity component V y {\displaystyle V_{\mathrm {y} }} and a horizontal velocity component V x {\displaystyle V_{\mathrm {x} }} , assuming it is fired on a flat surface. Assuming no use of directed lengths, the quantities of interest are then R, the distance travelled, with dimension L, V x {\displaystyle V_{\mathrm {x} }} , V y {\displaystyle V_{\mathrm {y} }} , both dimensioned as Tโ1L, and g the downward acceleration of gravity, with dimension Tโ2L. With these four quantities, we may conclude that the equation for the range R may be written: R โ V x a V y b g c . {\displaystyle R\propto V_{\text{x}}^{a}\,V_{\text{y}}^{b}\,g^{c}.\,} Or dimensionally L = ( L T ) a + b ( L T 2 ) c {\displaystyle {\mathsf {L}}=\left({\frac {\mathsf {L}}{\mathsf {T}}}\right)^{a+b}\left({\frac {\mathsf {L}}{{\mathsf {T}}^{2}}}\right)^{c}\,} from which we may deduce that a + b + c = 1 {\displaystyle a+b+c=1} and a + b + 2 c = 0 {\displaystyle a+b+2c=0} , which leaves one exponent undetermined.
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{"source": "wikipedia", "start_index": 0, "docstore_id": "28516"}
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