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BEARINGS - MATHSTEACHER.COM.AU A directional compass is shown below. It is used to find a direction or bearing.. The four main directions of a compass are known as cardinal points.They are north (N), east (E), south (S) and west (W). Sometimes, the half-cardinal points of north-east (NE), north-west (NW), south-east (SE) and south-west (SW) are shown on the compass. GROUPING 'THREE AND ONE' Grouping 'Three and One'. If an expression consists of four terms and part of it is a perfect square , then the expression can be factorised by grouping 'Three and One'. INTERACTIVE MATHS SERIES SOFTWARE (INTERACTIVE MATHEMATICSTRIAL MATHS SOFTWARETUTORYEAR 8 MATHS SOFTWAREORDER MATHS SOFTWARE Interactive maths software for just $19.95 per year level by the proven Australian author, G S Rehill. The maths software is used by students in over 40 countries. The maths software is produced by mathsteacher.com Pty Ltd. Interactive mathematics software for just $19.95 per year level by the proven Australian author, G S Rehill. The mathematics software is used by students in over 40 countries. POLYGONS - MATHSTEACHER.COM.AU A polygon is a closed plane figure with three or more sides that are all straight.. Some examples of polygons are shown below. The following figure is not a polygon as it is not a closed figure.. A circle is not a polygon as it does not have straight sides.. Polygons are named according to the number of sides. The names of the most common polygons are given below: GEOMETRY - MATHSTEACHER.COM.AU Geometry revision including the sum of adjacent angles forming a straight line, supplementary angles and complementary angles and applying these geometrical facts to solve problems. INCREASING OR DECREASING A QUANTITY IN A GIVEN RATIO If the ratio of a new quantity to an old quantity can be expressed as an improper fraction, then the new quantity is greater than the old quantity.Applying this ratio to the old quantity is known as increasing the old quantity in a given ratio.. If the ratio of a new quantity to an old quantity can be expressed as a proper fraction, then the new quantity is less than the old quantity. RATIOS - MATHSTEACHER.COM.AU Ratios for Year 8. This chapter covers comparing quantities, finding the ratio of two quantities, increasing or decreasing a quantity in a given ratio, using a ratio to solve problems, dividing a quantity in a given ratio and scale drawings. INDICES - MATHSTEACHER.COM.AU Indices for Year 10. This chapter covers indices, index form, index law for multiplication, index law for division, index law for powers, index law for powers of products, index law for powers of quotients, zero index, negative indices and standard form (scientific notation). PROBLEM SOLVING UNIT Problem 15.1 Coins: You are given one coin with a diameter of 7 cm and a large supply of coins each with a diameter of 3 cm. b. FACTORS BY GROUPING 'TWO AND TWO' Now, consider the expression 7x + 14y + bx + 2by.Clearly, there is no factor common to every term. However, it is clear that 7 is a common factor of the first two terms and b is a common factor of the last two terms. So, the expression can be grouped into two pairs of two termsas shown.
BEARINGS - MATHSTEACHER.COM.AU A directional compass is shown below. It is used to find a direction or bearing.. The four main directions of a compass are known as cardinal points.They are north (N), east (E), south (S) and west (W). Sometimes, the half-cardinal points of north-east (NE), north-west (NW), south-east (SE) and south-west (SW) are shown on the compass. GROUPING 'THREE AND ONE' Grouping 'Three and One'. If an expression consists of four terms and part of it is a perfect square , then the expression can be factorised by grouping 'Three and One'. POLYGONS - MATHSTEACHER.COM.AU A polygon is a closed plane figure with three or more sides that are all straight.. Some examples of polygons are shown below. The following figure is not a polygon as it is not a closed figure.. A circle is not a polygon as it does not have straight sides.. Polygons are named according to the number of sides. The names of the most common polygons are given below: FORMULAS - MATHSTEACHER.COM.AU A formula is a rule (or equation) that describes the relationship between variables occurring in some practical situation.. E.g. A = lw is a formula for the area of a rectangle, A, having length l and width w.: Substitution. If a formula is given and the values of all but one of the variables in the formula are known, the value of the remaining variable can be evaluated by substituting the MEAN, MEDIAN AND MODE We use statistics such as the mean, median and mode to obtain information about a population from our sample set of observed values. Mean. The mean (or average) of a set of data values is the sum of all of the data values divided by the number of data values. That is: Example 1. The marks of seven students in a mathematics test with a maximum possible mark of 20 are given below: TRANSPOSITION OF FORMULAS A formula is an algebraic relationship between two or more variable quantities.. For example, A = lw is a formula for the area, A, of a rectangle of length l and width w.In the formula, A is expressed in terms of l and w.We say that A is the subject of the formula.. If we know the values of l and w, the corresponding value of A is determined by substituting l and w into the formula. EQUATIONS CONTAINING BRACKETS To solve an equation containing brackets, we may proceed as follows: . Remove the brackets by expanding according to the Distributive Law.Collect the pronumeral terms on the left-hand side of the equation and the numerical terms on the right-hand side of the equation by doing the same operations(s) to both sides of the equation. REARRANGEMENT OF FORMULAS Consider the formula A = lw. for the area, A, of a rectangle of length l and width w. The formula describes A in terms of other variables (i.e. pronumerals) and we can find the value of A simply by substituting the values of l and w.We say that A is the subject of the formula.. To obtain the subject of the formula, we use the followingrules:
DIRECTIONS AND BEARINGS The direction to a point is stated as the number of degrees east or west of north or south.. For example, the direction of A from O is N30ºE. B is N60ºW from O. C is S70ºE from O. D is S80ºW from O.. Note: N30ºE means the direction is 30º east of north. The bearing to a point is the angle measured in a clockwise direction from the northline.
BEARINGS - MATHSTEACHER.COM.AU A directional compass is shown below. It is used to find a direction or bearing.. The four main directions of a compass are known as cardinal points.They are north (N), east (E), south (S) and west (W). Sometimes, the half-cardinal points of north-east (NE), north-west (NW), south-east (SE) and south-west (SW) are shown on the compass. LOWEST COMMON MULTIPLE (LCM) OF EXPRESSIONS The LCM of given expression is the smallest expression that is divisible by each of the given expressions.. To find the LCM of given expressions, we proceed as follows: Express each of the expressions as the product of its factors including prime factors where applicable. TRANSPOSITIONS INVOLVING FRACTIONS This topic covers transposition of formulas involving fractions. Year 10 Interactive Maths - Second Edition INTERACTIVE MATHS SERIES SOFTWARE (INTERACTIVE MATHEMATICSTRIAL MATHS SOFTWARETUTORYEAR 8 MATHS SOFTWAREORDER MATHS SOFTWARE Interactive maths software for just $19.95 per year level by the proven Australian author, G S Rehill. The maths software is used by students in over 40 countries. The maths software is produced by mathsteacher.com Pty Ltd. Interactive mathematics software for just $19.95 per year level by the proven Australian author, G S Rehill. The mathematics software is used by students in over 40 countries. POLYGONS - MATHSTEACHER.COM.AU A polygon is a closed plane figure with three or more sides that are all straight.. Some examples of polygons are shown below. The following figure is not a polygon as it is not a closed figure.. A circle is not a polygon as it does not have straight sides.. Polygons are named according to the number of sides. The names of the most common polygons are given below: FORMULAS - MATHSTEACHER.COM.AU A formula is a rule (or equation) that describes the relationship between variables occurring in some practical situation.. E.g. A = lw is a formula for the area of a rectangle, A, having length l and width w.: Substitution. If a formula is given and the values of all but one of the variables in the formula are known, the value of the remaining variable can be evaluated by substituting the RATIOS - MATHSTEACHER.COM.AU Ratios for Year 8. This chapter covers comparing quantities, finding the ratio of two quantities, increasing or decreasing a quantity in a given ratio, using a ratio to solve problems, dividing a quantity in a given ratio and scale drawings. INCREASING OR DECREASING A QUANTITY IN A GIVEN RATIO If the ratio of a new quantity to an old quantity can be expressed as an improper fraction, then the new quantity is greater than the old quantity.Applying this ratio to the old quantity is known as increasing the old quantity in a given ratio.. If the ratio of a new quantity to an old quantity can be expressed as a proper fraction, then the new quantity is less than the old quantity. INDICES - MATHSTEACHER.COM.AU Indices for Year 10. This chapter covers indices, index form, index law for multiplication, index law for division, index law for powers, index law for powers of products, index law for powers of quotients, zero index, negative indices and standard form (scientific notation). PROBLEM SOLVING UNIT Problem 15.1 Coins: You are given one coin with a diameter of 7 cm and a large supply of coins each with a diameter of 3 cm. b. MEAN, MEDIAN AND MODE We use statistics such as the mean, median and mode to obtain information about a population from our sample set of observed values. Mean. The mean (or average) of a set of data values is the sum of all of the data values divided by the number of data values. That is: Example 1. The marks of seven students in a mathematics test with a maximum possible mark of 20 are given below: BEARINGS - MATHSTEACHER.COM.AU A directional compass is shown below. It is used to find a direction or bearing.. The four main directions of a compass are known as cardinal points.They are north (N), east (E), south (S) and west (W). Sometimes, the half-cardinal points of north-east (NE), north-west (NW), south-east (SE) and south-west (SW) are shown on the compass. GROUPING 'THREE AND ONE' Grouping 'Three and One'. If an expression consists of four terms and part of it is a perfect square , then the expression can be factorised by grouping 'Three and One'. INTERACTIVE MATHS SERIES SOFTWARE (INTERACTIVE MATHEMATICSTRIAL MATHS SOFTWARETUTORYEAR 8 MATHS SOFTWAREORDER MATHS SOFTWARE Interactive maths software for just $19.95 per year level by the proven Australian author, G S Rehill. The maths software is used by students in over 40 countries. The maths software is produced by mathsteacher.com Pty Ltd. Interactive mathematics software for just $19.95 per year level by the proven Australian author, G S Rehill. The mathematics software is used by students in over 40 countries. POLYGONS - MATHSTEACHER.COM.AU A polygon is a closed plane figure with three or more sides that are all straight.. Some examples of polygons are shown below. The following figure is not a polygon as it is not a closed figure.. A circle is not a polygon as it does not have straight sides.. Polygons are named according to the number of sides. The names of the most common polygons are given below: FORMULAS - MATHSTEACHER.COM.AU A formula is a rule (or equation) that describes the relationship between variables occurring in some practical situation.. E.g. A = lw is a formula for the area of a rectangle, A, having length l and width w.: Substitution. If a formula is given and the values of all but one of the variables in the formula are known, the value of the remaining variable can be evaluated by substituting the RATIOS - MATHSTEACHER.COM.AU Ratios for Year 8. This chapter covers comparing quantities, finding the ratio of two quantities, increasing or decreasing a quantity in a given ratio, using a ratio to solve problems, dividing a quantity in a given ratio and scale drawings. INCREASING OR DECREASING A QUANTITY IN A GIVEN RATIO If the ratio of a new quantity to an old quantity can be expressed as an improper fraction, then the new quantity is greater than the old quantity.Applying this ratio to the old quantity is known as increasing the old quantity in a given ratio.. If the ratio of a new quantity to an old quantity can be expressed as a proper fraction, then the new quantity is less than the old quantity. INDICES - MATHSTEACHER.COM.AU Indices for Year 10. This chapter covers indices, index form, index law for multiplication, index law for division, index law for powers, index law for powers of products, index law for powers of quotients, zero index, negative indices and standard form (scientific notation). PROBLEM SOLVING UNIT Problem 15.1 Coins: You are given one coin with a diameter of 7 cm and a large supply of coins each with a diameter of 3 cm. b. MEAN, MEDIAN AND MODE We use statistics such as the mean, median and mode to obtain information about a population from our sample set of observed values. Mean. The mean (or average) of a set of data values is the sum of all of the data values divided by the number of data values. That is: Example 1. The marks of seven students in a mathematics test with a maximum possible mark of 20 are given below: BEARINGS - MATHSTEACHER.COM.AU A directional compass is shown below. It is used to find a direction or bearing.. The four main directions of a compass are known as cardinal points.They are north (N), east (E), south (S) and west (W). Sometimes, the half-cardinal points of north-east (NE), north-west (NW), south-east (SE) and south-west (SW) are shown on the compass. GROUPING 'THREE AND ONE' Grouping 'Three and One'. If an expression consists of four terms and part of it is a perfect square , then the expression can be factorised by grouping 'Three and One'. MEAN, MEDIAN AND MODE We use statistics such as the mean, median and mode to obtain information about a population from our sample set of observed values. Mean. The mean (or average) of a set of data values is the sum of all of the data values divided by the number of data values. That is: Example 1. The marks of seven students in a mathematics test with a maximum possible mark of 20 are given below: FORMULAS - MATHSTEACHER.COM.AU A formula is a rule (or equation) that describes the relationship between variables occurring in some practical situation.. E.g. A = lw is a formula for the area of a rectangle, A, having length l and width w.: Substitution. If a formula is given and the values of all but one of the variables in the formula are known, the value of the remaining variable can be evaluated by substituting the INDICES - MATHSTEACHER.COM.AU Indices for Year 9. This chapter covers indices, index form, index law for multiplication, index law for division, index law for powers, index law for powers of products, index law for powers of quotients, powers of 10, zero index and standard form (scientific notation). TRANSPOSITION OF FORMULAS A formula is an algebraic relationship between two or more variable quantities.. For example, A = lw is a formula for the area, A, of a rectangle of length l and width w.In the formula, A is expressed in terms of l and w.We say that A is the subject of the formula.. If we know the values of l and w, the corresponding value of A is determined by substituting l and w into the formula.AREA OF A CIRCLE
Activity 12.1. Equipment: You will need a compass, pair of scissors, ruler and protractor for this activity. Purpose: To discover a formula for the area of a circle. Step 1: Using the compass, draw a circle of radius 7 cm.Then mark the circle's centre and draw its radius. Step 2: Place the centre of the protractor at the centre of the circle and the zero line along the radius. BEARINGS - MATHSTEACHER.COM.AU A directional compass is shown below. It is used to find a direction or bearing.. The four main directions of a compass are known as cardinal points.They are north (N), east (E), south (S) and west (W). Sometimes, the half-cardinal points of north-east (NE), north-west (NW), south-east (SE) and south-west (SW) are shown on the compass. FRACTIONS AND DECIMALS Fractions and decimals for Year 8. This chapter revises fractions, mixed numbers, addition and subtraction of fractions, multiplication of fractions, addition and subtraction of decimals, multiplication of decimals, division of decimals, rounding off and recurring decimals. DIRECTIONS AND BEARINGS The direction to a point is stated as the number of degrees east or west of north or south.. For example, the direction of A from O is N30ºE. B is N60ºW from O. C is S70ºE from O. D is S80ºW from O.. Note: N30ºE means the direction is 30º east of north. The bearing to a point is the angle measured in a clockwise direction from the northline.
PERCENTAGES
A percentage is a fraction that is written out of 100.. For example, 15 per cent means 15 parts out of 100. The term per cent means per one hundred. The symbol used for per cent is %. Note: From the preceding discussion, we notice that: LOWEST COMMON MULTIPLE (LCM) OF EXPRESSIONS The LCM of given expression is the smallest expression that is divisible by each of the given expressions.. To find the LCM of given expressions, we proceed as follows: Express each of the expressions as the product of its factors including prime factors where applicable. INTERACTIVE MATHS SERIES SOFTWARE (INTERACTIVE MATHEMATICSTRIAL MATHS SOFTWARETUTORYEAR 8 MATHS SOFTWAREORDER MATHS SOFTWARE Interactive maths software for just $19.95 per year level by the proven Australian author, G S Rehill. The maths software is used by students in over 40 countries. The maths software is produced by mathsteacher.com Pty Ltd. Interactive mathematics software for just $19.95 per year level by the proven Australian author, G S Rehill. The mathematics software is used by students in over 40 countries. POLYGONS - MATHSTEACHER.COM.AU A polygon is a closed plane figure with three or more sides that are all straight.. Some examples of polygons are shown below. The following figure is not a polygon as it is not a closed figure.. A circle is not a polygon as it does not have straight sides.. Polygons are named according to the number of sides. The names of the most common polygons are given below: MEAN, MEDIAN AND MODE We use statistics such as the mean, median and mode to obtain information about a population from our sample set of observed values. Mean. The mean (or average) of a set of data values is the sum of all of the data values divided by the number of data values. That is: Example 1. The marks of seven students in a mathematics test with a maximum possible mark of 20 are given below: INCREASING OR DECREASING A QUANTITY IN A GIVEN RATIO If the ratio of a new quantity to an old quantity can be expressed as an improper fraction, then the new quantity is greater than the old quantity.Applying this ratio to the old quantity is known as increasing the old quantity in a given ratio.. If the ratio of a new quantity to an old quantity can be expressed as a proper fraction, then the new quantity is less than the old quantity. BEARINGS - MATHSTEACHER.COM.AU A directional compass is shown below. It is used to find a direction or bearing.. The four main directions of a compass are known as cardinal points.They are north (N), east (E), south (S) and west (W). Sometimes, the half-cardinal points of north-east (NE), north-west (NW), south-east (SE) and south-west (SW) are shown on the compass. RATIOS - MATHSTEACHER.COM.AU Ratios for Year 8. This chapter covers comparing quantities, finding the ratio of two quantities, increasing or decreasing a quantity in a given ratio, using a ratio to solve problems, dividing a quantity in a given ratio and scale drawings. ADDITION AND SUBTRACTION OF ALGEBRAIC FRACTIONS Addition and subtraction involving algebraic fractions. Knowledge of adding and subtracting algebraic fractions is as important as knowledge of factorisation. DIRECTIONS AND BEARINGS The direction to a point is stated as the number of degrees east or west of north or south.. For example, the direction of A from O is N30ºE. B is N60ºW from O. C is S70ºE from O. D is S80ºW from O.. Note: N30ºE means the direction is 30º east of north. The bearing to a point is the angle measured in a clockwise direction from the northline.
MULTIPLICATION OF ALGEBRAIC FRACTIONS Multiplication of Algebraic Fractions. To multiply algebraic fractions, factorise the numerators and denominators. Then cancel the factors common to the numerator and denominator before applying multiplication to obtain the answer. GROUPING 'THREE AND ONE' Grouping 'Three and One'. If an expression consists of four terms and part of it is a perfect square , then the expression can be factorised by grouping 'Three and One'. INTERACTIVE MATHS SERIES SOFTWARE (INTERACTIVE MATHEMATICSTRIAL MATHS SOFTWARETUTORYEAR 8 MATHS SOFTWAREORDER MATHS SOFTWARE Interactive maths software for just $19.95 per year level by the proven Australian author, G S Rehill. The maths software is used by students in over 40 countries. The maths software is produced by mathsteacher.com Pty Ltd. Interactive mathematics software for just $19.95 per year level by the proven Australian author, G S Rehill. The mathematics software is used by students in over 40 countries. POLYGONS - MATHSTEACHER.COM.AU A polygon is a closed plane figure with three or more sides that are all straight.. Some examples of polygons are shown below. The following figure is not a polygon as it is not a closed figure.. A circle is not a polygon as it does not have straight sides.. Polygons are named according to the number of sides. The names of the most common polygons are given below: MEAN, MEDIAN AND MODE We use statistics such as the mean, median and mode to obtain information about a population from our sample set of observed values. Mean. The mean (or average) of a set of data values is the sum of all of the data values divided by the number of data values. That is: Example 1. The marks of seven students in a mathematics test with a maximum possible mark of 20 are given below: INCREASING OR DECREASING A QUANTITY IN A GIVEN RATIO If the ratio of a new quantity to an old quantity can be expressed as an improper fraction, then the new quantity is greater than the old quantity.Applying this ratio to the old quantity is known as increasing the old quantity in a given ratio.. If the ratio of a new quantity to an old quantity can be expressed as a proper fraction, then the new quantity is less than the old quantity. BEARINGS - MATHSTEACHER.COM.AU A directional compass is shown below. It is used to find a direction or bearing.. The four main directions of a compass are known as cardinal points.They are north (N), east (E), south (S) and west (W). Sometimes, the half-cardinal points of north-east (NE), north-west (NW), south-east (SE) and south-west (SW) are shown on the compass. RATIOS - MATHSTEACHER.COM.AU Ratios for Year 8. This chapter covers comparing quantities, finding the ratio of two quantities, increasing or decreasing a quantity in a given ratio, using a ratio to solve problems, dividing a quantity in a given ratio and scale drawings. ADDITION AND SUBTRACTION OF ALGEBRAIC FRACTIONS Addition and subtraction involving algebraic fractions. Knowledge of adding and subtracting algebraic fractions is as important as knowledge of factorisation. DIRECTIONS AND BEARINGS The direction to a point is stated as the number of degrees east or west of north or south.. For example, the direction of A from O is N30ºE. B is N60ºW from O. C is S70ºE from O. D is S80ºW from O.. Note: N30ºE means the direction is 30º east of north. The bearing to a point is the angle measured in a clockwise direction from the northline.
MULTIPLICATION OF ALGEBRAIC FRACTIONS Multiplication of Algebraic Fractions. To multiply algebraic fractions, factorise the numerators and denominators. Then cancel the factors common to the numerator and denominator before applying multiplication to obtain the answer. GROUPING 'THREE AND ONE' Grouping 'Three and One'. If an expression consists of four terms and part of it is a perfect square , then the expression can be factorised by grouping 'Three and One'. GEOMETRY - MATHSTEACHER.COM.AU Geometry revision including the sum of adjacent angles forming a straight line, supplementary angles and complementary angles and applying these geometrical facts to solve problems. YEAR 7 INTERACTIVE MATHS SOFTWARE, MATHEMATICS SOFTWARE Year 7 Interactive Maths Software (Mathematics Software or Math Software) that is just $19.95 to accelerate maths learning. It is written by the experienced Australian mathematics author and teacher, G S Rehill. The software has 208 interactive exercises spanning 16 chapters that cover Whole Numbers, Powers and Roots, Multiples and Factors, Fractions, Algebra, Decimals, Equations, Angles MULTIPLICATION OF ALGEBRAIC FRACTIONS Multiplication of Algebraic Fractions. To multiply algebraic fractions, factorise the numerators and denominators. Then cancel the factors common to the numerator and denominator before applying multiplication to obtain the answer.AREA OF A CIRCLE
Activity 12.1. Equipment: You will need a compass, pair of scissors, ruler and protractor for this activity. Purpose: To discover a formula for the area of a circle. Step 1: Using the compass, draw a circle of radius 7 cm.Then mark the circle's centre and draw its radius. Step 2: Place the centre of the protractor at the centre of the circle and the zero line along the radius. LOWEST COMMON MULTIPLE (LCM) OF EXPRESSIONS The LCM of given expression is the smallest expression that is divisible by each of the given expressions.. To find the LCM of given expressions, we proceed as follows: Express each of the expressions as the product of its factors including prime factors where applicable. HORIZONTAL AND VERTICAL LINES The graph of a relation of the form y = 5 is a line parallel to the x-axis because the y value never changes.. Note: A line parallel to the x-axis is called a horizontal line.. The graph of a relation of the form x = 5 is a line parallel to the y-axis because the x value never changes.. Note: A line parallel to the y-axis is called a vertical line.. Example 8. Plot the graph of each of the RATIOS - MATHSTEACHER.COM.AU Ratios for Year 8. This chapter covers comparing quantities, finding the ratio of two quantities, increasing or decreasing a quantity in a given ratio, using a ratio to solve problems, dividing a quantity in a given ratio and scale drawings. TABLES - MATHSTEACHER.COM.AU A table helps us to organise and analyse a set of data values. In this section we will consider frequency tables and stemplots (i.e. stem-and-leaf plots). Frequency Tables. A frequency table is a tabular representation of a data set in an ascending order of magnitude with their corresponding frequencies. CONSTRUCTING ANGLES OF 60º, 120º, 30º AND 90º Constructing a 60 degree angle, constructing a 30 degree angle, constructing a 120 degree angle and constructing a 90 degree angle using a compass. An activity involving a compass and a ruler.PERCENTAGE INCREASE
Example 10. The price of a printer increases from $400 to $550. Express this increase as a percentage of the original price. mathsteacher.com.au (a mathsteacher.com Pty Ltd Website) offers maths software licences for the Interactive Maths Series (Second Edition) software for Year 7 to 10 students, that has been used by students in 52 countries. The software is written by the experienced and well-respected Australian author G S REHILL . As Homework Licences are available from just $19.95 (AUD) per year level, this maths software series offers tremendous value for students. Our Homework and Tutor mathematics software are delivered by Internet download and can be ordered using MasterCard, VISA or PayPal. To find out more about the Interactive Maths Series software which is both Microsoft® Windows® and Apple® Mac® OS X compatible, click here. ------------------------- | Home Page | Order Maths Software| About the Series
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