{"id":1132,"date":"2021-08-19T15:23:28","date_gmt":"2021-08-19T15:23:28","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&p=1132"},"modified":"2022-01-26T23:05:06","modified_gmt":"2022-01-26T23:05:06","slug":"summary-review-4","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/summary-review-4\/","title":{"raw":"Summary: Review","rendered":"Summary: Review"},"content":{"raw":"

Key Concepts<\/h2>\r\n

Translating Word Problems Into Expressions<\/h3>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Addition<\/td>\r\n[latex]+[\/latex]<\/td>\r\nsum,\u00a0 total, together,\u00a0 more than, increased by, ...<\/td>\r\n<\/tr>\r\n
Subtraction<\/td>\r\n[latex]-[\/latex]<\/td>\r\ndifference, less than, decreased by, ...<\/td>\r\n<\/tr>\r\n
Multiplication<\/td>\r\n[latex]\\times[\/latex]<\/td>\r\nproduct, double, half, percent of, ...<\/td>\r\n<\/tr>\r\n
Equality<\/td>\r\n[latex]=[\/latex]<\/td>\r\nis, is the same as, is not different from, ...<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Inequality Symbols<\/h3>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
\r\n

Symbol<\/h4>\r\n<\/td>\r\n

\r\n

In Words<\/h4>\r\n<\/td>\r\n

\r\n

Example<\/h4>\r\n<\/td>\r\n<\/tr>\r\n

[latex]\\neq[\/latex]<\/td>\r\nNot equal to<\/td>\r\n[latex]3 \\neq 5[\/latex]<\/td>\r\n<\/tr>\r\n
[latex]>[\/latex]<\/td>\r\nGreater than<\/td>\r\n[latex]5>3[\/latex]<\/td>\r\n<\/tr>\r\n
[latex]<[\/latex]<\/td>\r\nLess than<\/td>\r\n[latex]2<7[\/latex]<\/td>\r\n<\/tr>\r\n
[latex]\\geq[\/latex]<\/td>\r\nGreater than or equal to<\/td>\r\n[latex]5 \\geq 5[\/latex]<\/td>\r\n<\/tr>\r\n
[latex]\\leq[\/latex]<\/td>\r\nLess than or equal to<\/td>\r\n[latex]4 \\leq 7[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe inequality [latex]a<b[\/latex] can also be written [latex]b>a[\/latex].\r\n

Graphing an Inequality<\/h3>\r\n
    \r\n \t
  1. Locate the endpoint of the inequality on the number line. Draw a closed (shaded) circle if the inequality includes the endpoint [latex](\\geq \\mathrm{or} \\leq)[\/latex]. Draw an open circle for a strict inequality ([latex]< \\mathrm{or} >[\/latex]).<\/li>\r\n \t
  2. Shade the portion of the number line which satisfies the stated inequality.<\/li>\r\n<\/ol>\r\n

    Translating Verbal Statements Involving Inequalities<\/h3>\r\n
    \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    \r\n

    Verbal Statement:\u00a0x<\/em> is...<\/h4>\r\n<\/td>\r\n

    		\r\n

    Mathematical Statement<\/h4>\r\n<\/td>\r\n<\/tr>\r\n

    greater than or equal to [latex]k[\/latex]\r\nat least [latex]k[\/latex]\r\nnot more than [latex]k[\/latex]<\/td>\r\n\u00a0[latex]x \\geq k[\/latex]<\/td>\r\n<\/tr>\r\n
    less than or equal to [latex]k[\/latex]\r\nat most [latex]k[\/latex]\r\nnot more than [latex]k[\/latex]<\/td>\r\n\u00a0[latex]x \\leq k[\/latex]<\/td>\r\n<\/tr>\r\n
    less than [latex]k[\/latex]\r\nbelow [latex]k[\/latex]\r\nfewer than [latex]k[\/latex]<\/td>\r\n\u00a0[latex]x<k[\/latex]<\/td>\r\n<\/tr>\r\n
    greater than [latex]k[\/latex]\r\nmore than [latex]k[\/latex]\r\nabove [latex]k[\/latex]<\/td>\r\n[latex]x>k[\/latex]<\/td>\r\n<\/tr>\r\n
    equal to [latex]k[\/latex]\r\nis [latex]k[\/latex]\r\nexactly [latex]k[\/latex]\r\nthe same as [latex]k[\/latex]<\/td>\r\n[latex]x=k[\/latex]<\/td>\r\n<\/tr>\r\n
    not equal to [latex]k[\/latex]\r\nnot\u00a0[latex]k[\/latex]\r\ndifferent from\u00a0[latex]k[\/latex]<\/td>\r\n[latex]x \\neq k[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nTo convert a number in scientific notation<\/strong> to standard notation, move the decimal point [latex]n[\/latex] places to the write if [latex]n[\/latex] is positive, or [latex]|n|[\/latex] places to the left if [latex]n[\/latex] is negative. Add zeros as needed.\r\n\r\nTo write a number in scientific notation, move the decimal point to the right of the first nonzero digit in the number. Write the digits as a decimal number between 1 and 10. Count the number of places [latex]n[\/latex] that you moved the decimal point. Multiply the decimal number by 10 raised to a power of [latex]n[\/latex]. If you moved the decimal left as in a very large number, [latex]n[\/latex] is positive. If you moved the decimal right as in a small large number, [latex]n[\/latex] is negative.\r\n

    Glossary<\/h2>\r\nconstant:<\/strong> number whose value does not change\r\n\r\ninequality:<\/strong> compares two expressions, identifying one as more, less, or simply different than the other\r\n\r\ninference:\u00a0<\/strong>drawing reliable conclusions about the population on the basis of what we\u2019ve discovered in our sample\r\n\r\nprobability:\u00a0<\/strong>a number between zero and one, inclusive, that gives the likelihood that a specific event will occur; also described as long-term relative frequency. Probabilities are between 0 and 1, inclusive.\r\n\r\nreal number line:<\/strong> a horizontal line used to represent the real numbers. An arbitrary fixed point is chosen to represent 0; positive numbers lie to the right of 0 and negative numbers to the left.\r\n\r\nscientific notation:<\/strong> number is written in the form [latex]a \\times 10^{n}[\/latex] where [latex]1 \\leq |a| < 10[\/latex]\r\n\r\nsolution set:<\/strong> values of a variable which make a statement true\r\n\r\nvariable:<\/strong> a quantity that may change value, or whose value we don\u2019t know\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"

    Key Concepts<\/h2>\n

    Translating Word Problems Into Expressions<\/h3>\n
    \n\n\n\n\n\n\n
    Addition<\/td>\n[latex]+[\/latex]<\/td>\nsum,\u00a0 total, together,\u00a0 more than, increased by, …<\/td>\n<\/tr>\n
    Subtraction<\/td>\n[latex]-[\/latex]<\/td>\ndifference, less than, decreased by, …<\/td>\n<\/tr>\n
    Multiplication<\/td>\n[latex]\\times[\/latex]<\/td>\nproduct, double, half, percent of, …<\/td>\n<\/tr>\n
    Equality<\/td>\n[latex]=[\/latex]<\/td>\nis, is the same as, is not different from, …<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Inequality Symbols<\/h3>\n
    \n\n\n\n\n\n\n\n\n
    \n

    Symbol<\/h4>\n<\/td>\n

    		\n

    In Words<\/h4>\n<\/td>\n

    		\n

    Example<\/h4>\n<\/td>\n<\/tr>\n

    [latex]\\neq[\/latex]<\/td>\nNot equal to<\/td>\n[latex]3 \\neq 5[\/latex]<\/td>\n<\/tr>\n
    [latex]>[\/latex]<\/td>\nGreater than<\/td>\n[latex]5>3[\/latex]<\/td>\n<\/tr>\n
    [latex]<[\/latex]<\/td>\nLess than<\/td>\n[latex]2<7[\/latex]<\/td>\n<\/tr>\n
    [latex]\\geq[\/latex]<\/td>\nGreater than or equal to<\/td>\n[latex]5 \\geq 5[\/latex]<\/td>\n<\/tr>\n
    [latex]\\leq[\/latex]<\/td>\nLess than or equal to<\/td>\n[latex]4 \\leq 7[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    The inequality [latex]aa[\/latex].<\/p>\n

    Graphing an Inequality<\/h3>\n
      \n
    1. Locate the endpoint of the inequality on the number line. Draw a closed (shaded) circle if the inequality includes the endpoint [latex](\\geq \\mathrm{or} \\leq)[\/latex]. Draw an open circle for a strict inequality ([latex]< \\mathrm{or} >[\/latex]).<\/li>\n
    2. Shade the portion of the number line which satisfies the stated inequality.<\/li>\n<\/ol>\n

      Translating Verbal Statements Involving Inequalities<\/h3>\n
      \n\n\n\n\n\n\n\n\n\n
      \n

      Verbal Statement:\u00a0x<\/em> is…<\/h4>\n<\/td>\n

      		\n

      Mathematical Statement<\/h4>\n<\/td>\n<\/tr>\n

      greater than or equal to [latex]k[\/latex]
      \nat least [latex]k[\/latex]
      \nnot more than [latex]k[\/latex]<\/td>\n      		\u00a0[latex]x \\geq k[\/latex]<\/td>\n<\/tr>\n
      less than or equal to [latex]k[\/latex]
      \nat most [latex]k[\/latex]
      \nnot more than [latex]k[\/latex]<\/td>\n      		\u00a0[latex]x \\leq k[\/latex]<\/td>\n<\/tr>\n
      less than [latex]k[\/latex]
      \nbelow [latex]k[\/latex]
      \nfewer than [latex]k[\/latex]<\/td>\n      		\u00a0[latex]x\n<\/tr>\n
      greater than [latex]k[\/latex]
      \nmore than [latex]k[\/latex]
      \nabove [latex]k[\/latex]<\/td>\n      		[latex]x>k[\/latex]<\/td>\n<\/tr>\n
      equal to [latex]k[\/latex]
      \nis [latex]k[\/latex]
      \nexactly [latex]k[\/latex]
      \nthe same as [latex]k[\/latex]<\/td>\n      		[latex]x=k[\/latex]<\/td>\n<\/tr>\n
      not equal to [latex]k[\/latex]
      \nnot\u00a0[latex]k[\/latex]
      \ndifferent from\u00a0[latex]k[\/latex]<\/td>\n      		[latex]x \\neq k[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      To convert a number in scientific notation<\/strong> to standard notation, move the decimal point [latex]n[\/latex] places to the write if [latex]n[\/latex] is positive, or [latex]|n|[\/latex] places to the left if [latex]n[\/latex] is negative. Add zeros as needed.<\/p>\n

      To write a number in scientific notation, move the decimal point to the right of the first nonzero digit in the number. Write the digits as a decimal number between 1 and 10. Count the number of places [latex]n[\/latex] that you moved the decimal point. Multiply the decimal number by 10 raised to a power of [latex]n[\/latex]. If you moved the decimal left as in a very large number, [latex]n[\/latex] is positive. If you moved the decimal right as in a small large number, [latex]n[\/latex] is negative.<\/p>\n

      Glossary<\/h2>\n

      constant:<\/strong> number whose value does not change<\/p>\n

      inequality:<\/strong> compares two expressions, identifying one as more, less, or simply different than the other<\/p>\n

      inference:\u00a0<\/strong>drawing reliable conclusions about the population on the basis of what we\u2019ve discovered in our sample<\/p>\n

      probability:\u00a0<\/strong>a number between zero and one, inclusive, that gives the likelihood that a specific event will occur; also described as long-term relative frequency. Probabilities are between 0 and 1, inclusive.<\/p>\n

      real number line:<\/strong> a horizontal line used to represent the real numbers. An arbitrary fixed point is chosen to represent 0; positive numbers lie to the right of 0 and negative numbers to the left.<\/p>\n

      scientific notation:<\/strong> number is written in the form [latex]a \\times 10^{n}[\/latex] where [latex]1 \\leq |a| < 10[\/latex]\n\nsolution set:<\/strong> values of a variable which make a statement true<\/p>\n

      variable:<\/strong> a quantity that may change value, or whose value we don\u2019t know<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\t\t\t

      \n\t\t\t

      Candela Citations<\/h3>\n\t\t\t\t\t
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      CC licensed content, Original<\/div>