conversations.from: human
conversations.value: What could be a title for a book about Teachers, Nightingale-Bamford, School with the genre: Science & Math, Mathematics?
conversations.from: assistant
conversations.value: A title for this book could be 'Practice Makes Perfect Algebra'
conversations.from: human
conversations.value: What is the first five paragraphs for this book? Start with the sentence 'Practice Makes Perfect Algebra
  Some basic rules of working with irrational expressions are perfect powers larger than 1 cannot be kept within the radical; radicands should not contain fractions; and it is common practice to rationalize the denominators of fractions'.
conversations.from: assistant
conversations.value: Practice Makes Perfect Algebra
  Some basic rules of working with irrational expressions are perfect powers larger than 1 cannot be kept within the radical; radicands should not contain fractions; and it is common practice to rationalize the denominators of fractions.
  The basic format for solving irrational equations is to isolate the radical expression on one side of the equation, and then raise both sides of the resulting equation to an appropriate power to remove the radical.
  Compound interest, population growth, radioactive decay, the pH of a solution, and the Richter scale are examples of exponential and logarithmic functions.
  There are two important consequences to these rules, which, although they might not seem intuitive, do follow from the rules of exponents.
  The second consequence has to do with fraction exponents. In earlier math courses you learned about roots of numbers, that is, square roots, cube roots, fourth roots, etc.
conversations.from: human
conversations.value: What is five more paragraphs?
conversations.from: assistant
conversations.value: The **Central Limit Theorem** states that as the sample size gets larger, the sampling distribution of the mean can be approximated by the normal distribution. This is true whether or not the original distribution is normal. That is to say, if we take repeated samples from a population, compute the mean of the sample, and analyze the distribution of the means, this distribution will be approximately normally distributed, provided the size of each sample is sufficiently large.
  We can then apply the normal distribution to compute probabilities for the mean of the selected sample. This is the basis for the work on inferential statistics involving the parameters mean and proportions and large samples. (There is a great deal more to the topic of inferential statistics that is well beyond the scope of this course. The intent at this level is to give the student a feel for how decisions are made based on the use of statistics.)
  The height of the students at Niskayuna High School has a mean of 67.2 inches with a standard deviation of 3.4 inches. A random sample of 50 students is selected and their heights measured.
  Ninety-eight percent of all the batteries made at the Fort Mill factory meet the manufacturer's specifications. A random sample of 500 batteries is selected for testing.
  Mrs. Stockwell is teaching three sections of Algebra II. She gives different versions of an exam on statistics to the three sections. John, Alice, and Julio, three friends who are each in different sections, meet after the exams are returned and are surprised to see that they each scored 90% on the test. John commented that he was really pleased with his result because the average grade on the exam in his class was 84. Alice also expressed her pleasure at her score because the average grade in her class was 86. Julio seemed a little bummed by this conversation. He explained that the average score in his class was 92. (Mrs. Stockwell confirmed that all three versions were comparable in their level of difficulty and that the scores on all three exams had a standard deviation of 4 points.) As people will often do, the three friends discuss which of them did better. John argued that he did the best because his score was 1.5 standard deviations higher than the mean, whereas Alice scored 1 standard deviation above the mean and Julio scored a half a standard deviation below the mean.
conversations.from: human
conversations.value: Reverse the sentences.
conversations.from: assistant
conversations.value: 5 standard deviations higher than the mean, whereas Alice scored 1 standard deviation above the mean and Julio scored a half a standard deviation below the mean.. John argued that he did the best because his score was 1.) As people will often do, the three friends discuss which of them did better. Stockwell confirmed that all three versions were comparable in their level of difficulty and that the scores on all three exams had a standard deviation of 4 points. (Mrs. He explained that the average score in his class was 92. Julio seemed a little bummed by this conversation. Alice also expressed her pleasure at her score because the average grade in her class was 86. John commented that he was really pleased with his result because the average grade on the exam in his class was 84. John, Alice, and Julio, three friends who are each in different sections, meet after the exams are returned and are surprised to see that they each scored 90% on the test. She gives different versions of an exam on statistics to the three sections. Stockwell is teaching three sections of Algebra II.
  Mrs. A random sample of 500 batteries is selected for testing.
  Ninety-eight percent of all the batteries made at the Fort Mill factory meet the manufacturer's specifications. A random sample of 50 students is selected and their heights measured.4 inches.2 inches with a standard deviation of 3.)
  The height of the students at Niskayuna High School has a mean of 67. The intent at this level is to give the student a feel for how decisions are made based on the use of statistics. (There is a great deal more to the topic of inferential statistics that is well beyond the scope of this course. This is the basis for the work on inferential statistics involving the parameters mean and proportions and large samples.
  We can then apply the normal distribution to compute probabilities for the mean of the selected sample. That is to say, if we take repeated samples from a population, compute the mean of the sample, and analyze the distribution of the means, this distribution will be approximately normally distributed, provided the size of each sample is sufficiently large. This is true whether or not the original distribution is normal.The **Central Limit Theorem** states that as the sample size gets larger, the sampling distribution of the mean can be approximated by the normal distribution
conversations.from: human
conversations.value: What is the last two paragraphs?
conversations.from: assistant
conversations.value: Interpretation: The data supports management's claim that the number of overtime hours worked each week is increasing.
  Interpretation: The evidence supports Jack's claim that less than 50% of the rock-and-roll songs played on the radio are "love" songs.
conversations.from: human
conversations.value: What is the first four paragraphs for this book?
conversations.from: assistant
conversations.value: Practice Makes Perfect Algebra
  Many problems can be solved by linear equations, but there are certain types of problems that follow a clear pattern. Knowing that routine setup for each type of problem makes it easier to translate the problem into an equation. Here are a few of the common types.
  Problems that involve adding tax or a tip to a bill, or applying a discount to a purchase often require you to use percentages. Remember that a percent is just another way of expressing a part or a fraction of a whole. The whole is 100%. A percent greater than 100% indicates more than the whole.
  When you calculate, you convert percents to decimals (or fractions): 100% = 1.00, 40% = 0.40, and 3% = 0.03. If you add a tax of 6% to a bill, you'll have 100% of the bill plus another 6% of the bill, or 106% of the bill. If you receive a 15% discount on your bill, you pay 100% of the bill minus 15% of the bill, or 85% of the bill.
  Jeff sees an advertisement for a television at an attractive price. Because Jeff has a loyalty card for the vendor, he receives a 10% discount. When he purchases the TV, the discount is ­applied, but after that, a 7% tax is added. If Jeff pays $383.27, what was the advertised price to the nearest dollar?
conversations.from: human
conversations.value: What is three more paragraphs?
conversations.from: assistant
conversations.value: The longer leg of a right triangle is 14 inches longer than the shorter leg, and 2 inches shorter than the hypotenuse. Find the lengths of the three sides.
  It is not reasonable to have a negative side length, so the shorter leg is 10 inches, the longer leg is 10 + 14 = 24 inches, and the hypotenuse is 24 + 2 = 26 inches.
  Area problems often give rise to quadratic equations because they require that you multiply length times width or base times height. If both quantities involve the variable, the multiplication results in a variable squared.
conversations.from: human
conversations.value: What is the last five paragraphs?
conversations.from: assistant
conversations.value: The part of the job done in one hour, times the number of hours, will always equal one. Your equation comes not from adding the hours, but from adding the part of the job done in an hour.
  At a fixed temperature, the volume of a certain quantity of gas varies inversely with the pressure. If the volume is 16 in3 when the pressure is 18 psi, find the pressure that produces a volume of 20 in3.
  Write the general form of the inverse variation equation. Substitute known values to find the constant of variation.
  In theory, you could do that with any problem with two unknowns with one variable if you know how the unknowns are related, but that's easy when you know they add to 10. It's not so easy when you know that 17 of these and 32 of those cost $107.32. There are times when it's just easier to use two variables.
  Suppose a group of friends go out to get some fast food, and split into two groups in two different lines while waiting to order. The first group bought 8 slices of pizza and 6 soft drinks for $41.14. The second group bought 5 slices of pizza and 6 soft drinks for $30.10. How much does one slice of pizza cost?