3You can use the formula A = C G to find

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1 Using Formulas ORDER OF OPERATIONS In When Zombies Attack! on page 4, you learned how to solve problems using formulas. When solving an equation, you need to use the order of operations. Round all money answers to the nearest cent. Round all years and temperatures to the nearest whole number. Order of Operations: 1. Simplify terms in parentheses or brackets. 2. Simplify terms that include exponents. 3. Complete any multiplication and division. Do this from left to right (whichever comes first). 4. Complete any addition and subtraction. Do this from left to right (whichever comes first). EXAMPLE: A soup company uses the formula for surface area of a cylinder (SA = 2πr 2 + 2πrh) to find out how much metal is needed to make each soup can. The soup cans have a radius of 1.5 inches and a height of 3 inches. To solve this equation, replace the variables with their given values: SA = 2 5 π π Now you can solve the equation using order of operations. 1. There are no parentheses or brackets in the equation, so skip this step. 2. Simplify the term that includes an exponent: = 2.25 SA = 2 5 π π Complete multiplication and division from left to right: 2 5 π = and 2 5 π = SA = Complete addition and subtraction from left to right: = So, each soup can uses about square inches of metal. 1The total cost (including tax) of dinner at a pizza place is: C = (2.5p d), where p is the number of slices of pizza and d is the number of drinks. A family buys 6 slices of pizza and 4 drinks. A. Find 2.5p. B. Find 1.89d. C. Find (2.5p d). D. Find (2.5p d). E. Another family buys 7 pieces of pizza and 3 drinks. How much does their meal cost? 2A. Convert 86 Fahrenheit to degrees Celsius using the formula: C = 5(F 32) 9. B. Convert 24 Celsius to degrees Fahrenheit using the formula F = 9C You can use the formula A = C G to find the approximate age of a tree. C is the tree s circumference in inches and G is the tree s growth factor. A. A white oak has a growth factor of 5 and a circumference of 56 inches. About how old is the white oak? B. A green ash tree has a growth factor of 4 and a circumference of 22 inches. About how old is the green ash?

2 Using Formulas A ZOMBIE BOOM In When Zombies Attack! on page 4, you read about how to use formulas to solve word problems. Use the formulas below to answer five more questions about a (make-believe!) zombie invasion. N = uninfected human population Z = number of zombies R = transmission rate per hour b = number of people a zombie infects in an hour t = number of hours Number of people a single zombie can infect in 1 hour: N 5 R Number of new infections that zombies cause in 1 hour: N 5 Z 5 R Number of people turned into zombies over time: b t 1A. There are 200 people trapped in a room with a single zombie whose transmission rate is Which formula would you use to determine the number of people who will be infected after an hour? B. Solve the formula using the information above. 2A. If there were 3 zombies, all with a transmission rate of 0.01, in a room with 200 people, which formula would you use to find the number of people infected after an hour? B. Solve the formula using the information above. 3A zombie can infect 5 humans in one hour. Which formula would you use to determine how many people it can infect in 3 hours? 4Zombie A, who has a transmission rate of 0.001, enters a small town with a population of 15,000 people. At the same time, Zombie B, who has a transmission rate of 0.01, enters a neighboring town with a population of 10,000. Which zombie will infect more people in 1 hour? 5One powerful zombie can infect 8 humans in an hour. How many new people will be infected if it goes prowling between midnight and 6 a.m.?

3 Ratios SOLVING WITH RATE TABLES In Dyelicious Candy on page 6, you learned how to solve problems involving ratios. You can also use a type of chart called a rate table to solve ratio problems. EXAMPLE: A costume store sold 4 princess costumes yesterday and made $140 in revenue. How much revenue would the store make if it sold 5 princess costumes? First, find the unit rate of revenue for each costume sold. To do this, divide both the number of costumes sold and the revenue by the number of costumes sold (4). Next, scale the unit rate up. Multiply both the 1 costume sold and the $35 revenue by 5, to find out how much revenue the sale of 5 costumes would generate. Costumes Sold Revenue (in dollars) Costumes Sold Revenue (in dollars) So, the store would make $175 if it sold 5 princess costumes. Use the rate table method to answer the following ratio problems. 1 3 One costume store makes $184 in revenue by selling A. The rate tables below show how much revenue a 4 vampire costumes. Fill in the rate table below to find costume store makes from two different types of out how much revenue the store would make if it sold costumes. Complete the rate tables. 1 costume, 2 costumes, 6 costumes, or 8 costumes. Costumes Sold Revenue (in dollars) Pirate Costumes Sold Revenue (in dollars) One factory needs 6 buttons to make 1 witch costume. Fill in the rate table to determine how many witch costumes the factory can make with 18, 42, 66, or 84 buttons. Costumes Made Buttons Used Zombie Costumes Sold 3 Revenue (in dollars) B. Which costume costs more? How do you know?

4 Ratios TECHNICOLOR TREATS In Dye-licious Candy on page 6, you read that brightly colored foods sometimes contain chemical dyes that can affect behavior. You can use ratios to express the amounts of dye in one or more servings of these foods. Use what you learned about solving word problems with ratios to answer the questions below. 1A. One single-serving packet of candy-coated chocolates contains about 30 mg of artificial dyes. What is the ratio of dyes to serving size? 4Each 1-cup serving of berry-flavored cereal contains 41 mg of artificial dye. If you have cups of the cereal for breakfast, how much dye will you have consumed? B. If you eat 1 2 consumed? of a packet, how much dye will you have 2A. A cherry-flavored drink contains about 52 mg of dye in each 6.7 oz bottle. How much artificial dye does it have per ounce? Round your answer to the nearest tenth. B. A package of the drink includes 6 bottles. How much dye does the package contain in total? 3A. An orange sports drink contains 150 mg of sodium and about 22 mg of dyes in a 12 oz serving. What is the ratio of sodium to dye in a single serving? B. A serving of the orange sports drink also has 21 grams of sugar. What is the ratio of sugar to dye in a single serving? 5A. There are 31 milligrams of dye in a 3 4 -cup serving of frosted cereal. If you have 1 cup of the cereal, how many milligrams of dye will you have consumed? B. Which cereal contains more dye per cup: the berryflavored cereal from question 4 or the frosted cereal?

5 Cross Sections IDENTIFYING 3-D SOLIDS In Building Big Heroes on page 8, you learned how to find 2-D cross sections of 3-D solids by slicing the solids with a plane. The slices can be parallel to the base (horizontal), perpendicular to the base (vertical), or at an angle. It is important to understand the 3-D solids before finding their cross sections. A pyramid is a solid with a polygonal base and multiple triangular faces. The pyramid is named after the shape of the base. 3-D SOLIDS A prism is a solid with two parallel, identical, polygonal bases and multiple rectangular faces. The prism is named after the shape of the bases. hexagonal base faces hexagonal bases faces hexagonal pyramid hexagonal prism A cone is a solid with a circular base and only one vertex. A cylinder is a solid with two circular bases that are connected by a curved side. vertex base When you slice into 3-D figures to create cross sections, a slice that is parallel to the base of a solid will result in a 2-D cross section that is the same shape as the base. A slice that is perpendicular to the base of a prism or a cylinder will always result in a 2-D cross section that is a rectangle. A slice that is perpendicular to the base of a cone or a pyramid and goes through the top vertex will always result in a 2-D cross section that is a triangle. Use this information to answer the questions on the next page. (Hint: If you get stuck, try drawing a cross section on the figure to help find your answer!) cone page 1 of 2 cylinder base base

6 Cross Sections IDENTIFYING 3-D SOLIDS 1A. the shape of the solid below. 4A. the shape of the solid below. B. What shape will result from a cross section that is parallel to the solid s base? B. What shape will result from a cross section that is perpendicular to the solid s base? 2 A. the shape of the solid below. 5A. the shape of the solid below. B. What shape will result from a cross section that is parallel to the solid s base? 3 A. the shape of the solid below. B. What shape will result from a cross section that is perpendicular to the solid s base? page 2 of 2 B. What shape will result from a cross section that is parallel to the solid s base?

7 3-D Cross Sections SPOTTING HIDDEN SHAPES In Building Big Heroes on page 8, you learned how to identify the 2-D shapes hidden inside of 3-D figures by using an imaginary 2-D plane to create a cross section. Use this information to name the type of cross section (horizontal, vertical, or angled) that would create a certain 2-D shape in each of the figures below. 1A. What type (or types) of cross section(s) would create a circle in this cone? 4A. What type (or types) of cross section(s) would create a hexagon in this hexagonal prism? B. What type of cross section would create a triangle? B. What 2-D shape would a vertical cross section create? 2A. What type (or types) of cross section(s) would create a square in this cube? B. What type of cross section would create a triangle? 3A. What type (or types) of cross section(s) would create a circle in this cylinder? B. What type of cross section would create an ellipse? 5A. What type (or types) of cross section(s) would create a triangle in this square pyramid? B. What 2-D shape(s) would an angled cross section create?

8 Data Analysis using dot plots In That Gorilla on page 14, you read about how to find the mean, median, mode, and range of a data set. You can also use a type of graph called a dot plot to find these measures. Each dot on a dot plot represents a single data value. The dot plot below shows the number of pieces of candy that 13 trick-or-treaters collected on Halloween. The data values are: 74, 54, 106, 68, 74, 109, 106, 87, 68, 106, 102, 90, and 74. modes median range = 55 MODE: The mode is the most frequent data value. On a dot plot, this is the tallest set of dots. Above, the modes are 74 and 106. MEAN: The mean is the sum of all the items in a data set divided by the number of items. To find the mean using a dot plot, add all the original data values, and then divide by the total number of dots. The total number of pieces of candy collected is: = 1,118 The total number of dots on the plot is 13. To find the mean, divide 1,118 by 13: 1, = 86 So the mean is What is the median of the data? 3What is the range of the data? MEDIAN: The median is the middle number of a data set when the values are ordered from least to greatest. On a dot plot, this is the dot that has the same number of dots to its left and to its right. On this plot, the median is 87. RANGE: The range is the difference between the maximum value and the minimum value. On the dot plot, the minimum value is the dot farthest left, and the maximum value is the dot farthest right. To find the range, subtract the minimum value from the maximum value. On this plot, the maximum value is 109 and the minimum value is 54, so the range is: = 55 1Create a dot plot using these values of number of pieces of candy collected by trick-or-treaters: 107, 73, 62, 88, 73, 107, 111, 91, 107 4What is the mode of the data? 5What is the mean of the data?

9 Mean, Median, Mode, Range gorilla intervention In That Gorilla on page 14, you read about how conservationists are helping to restore mountain gorilla populations. Use what you learned about mean, median, mode, and range in the article to answer the following questions about Gorilla Doctors, a team of veterinarians who have been working to save sick and injured gorillas in their natural habitats since Year Number of Interventions by Gorilla Doctors What was the mean of interventions from 2004 to 2013? Round your answer to the nearest whole number. 2What is the median of this data set? 3What is the mode of this data set? 4What is the range of this data set? 5If you had to choose one number the mean, median, mode, or range to represent this data set, which would you choose? Explain your answer.

10 Practice Test ISSUE SKILLS REVIEW The percent chance of one person surviving a zombie 1 outbreak can be represented as the percent chance of killing one zombie (k), written as a decimal, raised to the power of the total number of zombies (z). Express this as a formula using the variables k and z. Using your formula from question 1, calculate your 2 percent chance of survival if there are 3 zombies in your vicinity and your percent chance of killing one is 20%, or 0.2. (Remember to convert your answer into a percent by multiplying by 100.) 6If you made a vertical slice through the shape shown above, how many sides would the resulting cross section have? 7If you made a horizontal cut through the shape shown above, how many sides would the resulting cross section have? A serving of fruit-flavored cereal contains 31 mg of 3 artificial dye and 135 mg of sodium. What is the ratio of dye to sodium in one serving? 8Gorillas live in small social groups. In one group, the four female members weigh 197 pounds, 225 pounds, 198 pounds, and 180 pounds. What is the mean weight of these gorillas? 4An 8-ounce serving of a berry-flavored drink contains 18.8 mg of artificial dye. If you drink 12 oz. of this drink, how much dye will you have consumed? 5What is the greatest common factor of 15 and 35? The median of the number of baby gorillas named at 9 Kwita Izina in the past three years is 18. Which of the following sets of values could represent the number of gorillas named during this time period? A 14, 12, 16 C 18, 20, 22 B 20, 12, 18 D 17, 17, 20 What is the greatest common factor of 1028, 42, and 63?