Reteaching Investigating Exponential Growth and Decay

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1 Name Date Class Investigating Eponential Growth and Deca INV 11 An eponential function that has an increasing graph is an eponential growth function. The function f() kb where k 0 and b 1 models eponential growth. The value of b is the percent the quantit increases each time period. A bacteria sample starts with 5 cells and doubles ever hour. The function f() 5( ) represents the number of cells after hours. Graph the function. Then use the graph to estimate the number of cells after.5 hours. Make a table of values. Then plot the points and connect them with a smooth curve. Hours Number of Cells 0 5( 0 ) 5 1 5( 1 ) 50 5( ) ( 3 ) 00 5( ) = Using the graph, it appears there are about 10 cells after.5 hours. Complete the steps to graph the eponential growth function. 1. Antwan bus an antique lamp for $100. Ever 5 ears, the lamp s value increases b 50%. The function f() 100( 1.5 ) represents its value after intervals of 5 ears. How long does it take for the value of the lamp to reach $5? Time Value 0 100( ) $ ( ) $ ( 1.5 ) $ ( ) $ ( 1.5 ) $50.5 The value equals $5 when. The time to reach $5 is (5) 10 ears. Use the function f() 10(.5 ), which represents the number of cells in a bacteria sample after hours. Round to the nearest tenth.. How man cells does the sample start with? 10 cells 3. How man cells are in the sample after hours?.5 cells. How man cells are in the sample after 5 hours? 97. cells Saon. All rights reserved. 1 Saon Algebra

2 continued INV 11 The function f () kb where k 0 and 0 b 1 models eponential deca. In an eponential deca function, the quantit decreases b the same percent ever time period. A common application of eponential deca is half-lives. A half-life is the amount of time it takes for one half of the quantit of a substance to deca. For eample, the half-life of Carbon-1 is 5730 ears. If a sample contains grams of Carbon-1, then in 5730 ears there will be grams remaining. When the original amount of a substance is k, the function f () k 1 represents the amount remaining after half-lives. The half-life of Uranium-9 is 3 minutes. A sample contains 51 mg. How much of the sample is left after 15 minutes? Find the number of half-lives in 15 minutes. 15 min 1 half-life 5 half-lives 3 min f() k 1 Write the eponential deca formula Substitute 51 for k and 5 for Evaluate the power. 1 Simplif. There are 1 mg of Uranium-9 left after 15 minutes. Complete the steps to find the amount of the substance remaining. 5. Iodine-18 has a half-life of 8 minutes. How much of a 3 mg sample remains after 11 minutes? 11 min 1 half-life half-lives 8 min f () 3 1 mg Find the amount of the substance remaining.. Radium- has a half-life of 100 ears. How much of a 5 mg sample remains after 800 ears? 3 mg 7. Aspirin has a half-life of about 15 minutes. The function gives the percent of aspirin remaining after half-lives. Moll takes an aspirin at noon for a headache. What percent of the aspirin remains in her sstem at 1:30 PM? (Hint: Use 90 min 1 half-life 15 min to find the number of half-lives.) 1.55% Saon. All rights reserved. Saon Algebra 1

3 Name Date Class To find the total number of possible outcomes for a situation, ou can use the Fundamental Counting Principle, which sas that if there m was to choose the first outcome and n was to choose the second, then total number of outcomes m n Abb s school is selling long sleeve and short sleeve T-shirts. The shirts come in sizes small, medium, large, and -large. Find all of the possible combinations of shirts. Then use the Fundamental Counting Principle to find the total number of combinations. You can use a tree diagram to show the possible combinations. Tpe Size utcomes Solving Problems Involving Permutations 111 Tpe Size utcomes Small Long Sleeve Small Small Short Sleeve Small Medium Long Sleeve Medium Medium Short Sleeve Medium Long Sleeve Short Sleeve Large Long Sleeve Large Large Short Sleeve Large X-large Long Sleeve X-large Use the Fundamental Counting Principle to find the number of combinations. (number of choices of tpe)(number of size choices) = ()() = 8 possible combinations. Make a tree diagram of the possible outcomes. Then find the total number of possible outcomes. 1. A deli has a soup and sandwich lunch special. The soup choices are vegetable and chicken noodle. The have 3 choices of sandwiches: turke, ham, and tuna. Soup Sandwich X-large utcomes Soup Sandwich utcomes Short Sleeve X-large Turke Vegetable with Turke Turke Chicken Noodle with Turke Vegetable Ham Vegetable with Ham Chicken Noodle Ham Chicken Noodle with Ham Tuna Vegetable with Tuna (number of soup choices)(number of sandwich choices) ( )(3 ) Find the number of possible outcomes.. Colt can participate in a sport and one other activit. His choices for a sport are soccer, football, and track. The other activities are drama, band, and student council Dean rolls a si-sided number cube and tosses a coin times Tuna Chicken Noodle with Tuna Saon. All rights reserved. 3 Saon Algebra 1

4 continued 111 An ordered arrangement is called a permutation. Finding the number of permutations is similar to using the Fundamental Counting Principle. After choosing the item in one position, there is one less choice for the net. For eample, the number of was 3 winners can be ordered 1st, nd, and 3rd is 3 1. n! is the product of all positive integers up to and including n. When arranging all items in a group, ou can use a factorial to find the number of permutations. If onl part of a group is being arranged, the number of was to order r objects out of a group of n is n P r n! (n r)!. Si students are running for class office. How man was can a president, vice president, secretar, and treasurer be chosen from the si? There are offices to fill. Find the number of permutations of students from the group of. n P r n! Write the formula. (n r)!! Substitute for n and for r. ( )!! Simplif.! Write the factorials as products There are 30 was to choose a president, vice president, secretar, and treasurer. Complete the steps to find the number of permutations.. How man was can 8 people sit in 3 seats? 8! (8 3 )! 8! 5! Find the number of permutations. 5. How man was can people stand in a row?! 3 1. Bruce has 5 books. How man was can he arrange them all on a shelf? Mark has 7 posters to put on his wall. How man was can he arrange the first 3? 10 Saon. All rights reserved. Saon Algebra 1

5 Name Date Class Graphing and Solving Sstems of Linear and Quadratic Equations 11 Now ou will graph and solve a sstem consisting of a linear equation and a quadratic equation. Solve the sstem of equations b graphing. Check our solution. 8 Step 1 Graph the parabola. Use the verte (0, 0) and the points where, 1, 1, and. Step Graph 8. Plot the point where = 0 (0, 8) and where = 0 (, 0). Draw a line through those points. Step 3 The two graphs intersect at (, ) and (, 1). So, the solution to this sstem of equations is (, ) and (, 1). Step Check our solution. ( ) 8 ( ) Complete the steps to solve the sstem of equations b graphing Step 1 Graph the parabola. Use the verte (0, 0) and two other points on either side of the verte Step Graph. The slope of this equation is 0, so its graph is a horizontal line that intersects the -ais at (0, 9). Step 3 The graphs intersect at ( 3, 9) and (3, 9). This means the solution to the sstem is ( 3, 9) and (3, 9). Solve each sstem of equations b graphing ( 1, 1) and (1, 1) no solution Saon. All rights reserved. 5 Saon Algebra 1

6 Solve the sstem of equations b substitution continued 11 Substitute quadratic equation into linear equation. Add 3 9 to both sides. 0 Factor the left side. 0 and 0 Write each factor as a separate equation 0. Solve both equations. To find the -values, substitute each -value into one of the equations The solutions are the ordered pairs (, 3) and (, 3). Solve each problem.. A ski resort is making snow with a machine and spraing it on one of its ski slopes. The path of the snow is modeled b the equation. The shape of the ski slope is represented 100 b the equation. At what height will the snow from the 10 machine fall onto the ski slope? (All dimensions are in feet.) Substitute quadratic equation into linear equation. 100 Multipl both sides b 100 to clear the fractions. Use the Distributive Propert Subtract 0 from both sides. Factor the binomial Rewrite as two equations and solve for Substitute the nonzero -value into one of the original equations and solve for. The snow will fall onto the ski slope at a height of 1 feet. 5. Solve the sstem of equations b substitution ( 3, 7); (, 13) Saon. All rights reserved. Saon Algebra 1

7 Name Date Class You have solved quadratic equations using the quadratic formula. Now ou will use part of the quadratic formula to find the number of solutions. The discriminant is the epression under the radical sign in the quadratic formula. For the quadratic equation a b c 0 where a 0, the discriminant is b ac. You can use the discriminant to determine the number of real solutions and the number of -intercepts. Using the Discriminant If b ac 0, then there are no real solutions and no -intercepts. If b ac 0, then there is one real solution and one -intercept. If b ac 0, then there are two real solutions and two -intercepts. Interpreting the Discriminant 113 Use the discriminant to find the number of real solutions for Step 1: Identif a, b, and c. a = 1, b = 8, c = 18 Step : Substitute values into discriminant. b ac Step 3: Simplif Step : Find number of real solutions. Since the discriminant is less than 0, there are no real solutions. Use the discriminant to find the number of real solutions for 1 0. Step 1: Identif a, b, and c. a = 1, b =, c = 1 Step : Substitute values into discriminant. b ac 1 1 Step 3: Simplif Step : Find number of real solutions. Since the discriminant is greater than 0, there are two real solutions. Complete the steps to find the number of real solutions a 1, b 1, c 3 a, b 1, c 19 b ac b ac Since the discriminant equals 0, there is one real solution. 8 Since the discriminant is less than 0, there are no real solution. Saon. All rights reserved. 7 Saon Algebra 1

8 continued 113 A ball is tossed up from a height of 3 feet with an initial velocit of feet per second. Use the equation 1 3 to model the situation. Use the discriminant to determine if the ball can reach a height of 15 feet. Step 1: Set the equation equal to Step : Solve for zero Step 3: Find the discriminant Step : Find number of real solutions. Since the discriminant is negative, the ball will not reach a height of 15 feet. Determine if each solution is possible. 3. A ball is tossed up from a height of 3 feet with an initial velocit of 10 feet per second. Use the equation to model the situation. Use the discriminant to determine if the ball can reach a height of feet b ac The ball will not reach a height of feet.. A ball is thrown from a height of 3 feet with an initial velocit of 0 feet per second. Use the equation to model the situation. Use the discriminant to determine if the ball can reach a height of 10 feet b ac 0 ( 1) The ball will reach a height of 10 feet. 5. A ball is kicked from a height of feet with an initial velocit of 50 feet per second. Use the equation 1 50 to model the situation. Use the discriminant to determine if the ball can reach a height of 5 feet. The ball will reach a height of 5 ft.. A ball is tossed up from a height of feet with an initial velocit of 10 feet per second. Use the equation 1 10 to model the situation. Use the discriminant to determine if the ball can reach a height of 0 feet. The ball will not reach a height of 0 ft. Saon. All rights reserved. 8 Saon Algebra 1

9 Name Date Class To graph a square-root function, ou can make a table of values and plot points, recall the number under the square root smbol cannot be negative, so use numbers that will make the value greater than or equal to 0. Graph the function 1. Make a table. The value of 1 must be positive, so the domain is 1. Choose numbers that will make the number under the square-root smbol a perfect square. Plot the points and draw a smooth curve Graphing Square-Root Functions Graph each function Saon. All rights reserved. 9 Saon Algebra 1

10 is the most basic square-root function. The graph of the function can be transformed in man was. You can sometimes identif the tpes of transformations applied to b looking at the function. continued 11 Transformation Vertical Translation Horizontal Translation Reflection across the -ais Reflection across the -ais Equation c ; If c > 0, the graph of is shifted c units up. If c < 0, the graph of is shifted c units down. c ; If c > 0, the graph of is shifted c units right. If c < 0, the graph of is shifted c units left. Describe the transformation applied to to form. The equation can be written as. This has the form of c, with c =. The graph is a vertical translation, units down, from the graph of. - = 8 = Describe the transformation applied to.. The epression tells that the graph is translated units left. Adding tells that the graph is translated units up reflected across the -ais translated 9 units right translated 1 unit right and reflected across the -ais and units down translated 5 units up 9. The function t 0.5 gives the time in seconds it takes an object dropped from a height of meters to reach the ground. Anita drops a ball from a height of 11 meters. Estimate the time it takes for the ball to hit the ground. (Hint: Make a graph.) about 1.5 seconds Saon. All rights reserved. 50 Saon Algebra 1

11 Name Date Class Graphing Cubic Functions 115 Now ou will graph and solve cubic functions. Graph 3 1. To make an accurate graph, ou should plot several points, both positive and negative. Evaluate the function for when, 1, 0, 1 and. Place the values in a table Plot the points and sketch the curve to graph the function Graph each function Make a table of values Plot the points and sketch the curve to graph the function Saon. All rights reserved. 51 Saon Algebra 1

12 continued 115 nce ou have graphed a function, ou can use the graph to find its approimate solution. Solve 3 b graphing. Step 1: Rewrite the equation so that one side equals Step : Make a table of values and graph the related function 3. Step 3: To solve, find the point on the graph where it crosses the -ais. This is where 0. This point is called the -intercept. The -intercept is the solution. For this function, the solution is Complete the steps to solve the problem using a graphing calculator.. The volume of a prism is represented b the formula V 3 9. Use a graphing calculator to estimate the value of when the volume of the prism is about 800 cubic units. To graph this equation on a graphing calculator, let represent V. Step 1 Enter the function as 3 9. Step In the WINDW screen, adjust the window size so that a -value of 800 will be included in the graph. Set the -ma value to be greater than 800. You can set the -min and -min values at 0, and the -ma value at 15. Step 3 Press the TRACE function ke and scroll up until 800. Read the -value at this point. When 800, Solve 3 b graphing The volume of a cube can be represented b the formula, where V s 3 Where V is the volume and s is the length of a side. Use a graphing calculator to estimate the length of a side of a cube that has a volume of 89 cubic centimeters.(hint: Solve 89 3.) about.5 cm Saon. All rights reserved. 5 Saon Algebra 1

13 Name Date Class Solving Simple and Compound Interest Problems 11 The principal is the initial amount of mone ou borrow or invest. Interest is the amount of mone paid for using the principal. Simple interest is interest paid onl on the original amount borrowed or invested. You calculate simple interest using the formula I = Prt, where I is the interest, P is the principal, r is the interest rate per ear epressed as a decimal, and t is the time in ears. Use the simple interest formula to solve the following problem. Ale deposits $1000 in a savings account earning 3% simple interest. How much mone will be in the account after 1 months? l Prt Convert 1 months to a decimal portion of a ear. 3% 0.03 Epress 3% as a decimal. l 1000(0.03)(1.75) Substitute the information given in the problem. l 5.5 Evaluate the epression To find the total in the account, add the interest to the principal. There will be $ in Ale s account after 1 months. Use the simple interest formula to solve each problem. 1. Mrs. Kim borrowed $3500 at a simple interest rate of 9.5%. She paid a total of $1995 in interest. For how long did she borrow the mone? l Prt 1995 (3500) (0.095) t 9.5% epressed as a decimal is (0.095) t Evaluate the epression. t Solve for t. Mrs. Kim borrowed the mone for ears. A club invested $00. After.5 ears, the club earned $805 interest. What was the interest rate? Solve the simple interest formula for r. 7% 3. A small business owner took out a loan for 5 ears. She paid a total of $315 interest at an interest rate of.5%. How much mone did she borrow? Hint: Solve the simple interest formula for P. $10,000 Saon. All rights reserved. 53 Saon Algebra 1

14 Compound interest is interest that is added to the principal and interest at regular timeintervals. You calculate compound interest using the formula A P 1 n r nt, where A is the final amount, P is the principal, r is the interest rate per ear epressed as a decimal, n is the number of interest periods, and t is the time in ears. Use the compound interest formula to solve the following problem. Lero invested $500 at an interest rate of 5.5% compounded quarterl. What is the value of his investment after 8 ears? A P 1 r n nt n A (8) A 500 ( ) (8) A 500 ( ) continued 11 The interest compounded quartel, or times per ear. Substitute the information given in the problem. Evaluate the epression inside the parentheses first. Use a calculator to calculate the epression inside parentheses to the correct power. Do not round. A Multipl and round the product to the nearest cent. After 8 ears, Lero will have an investment of $ Use the compound interest formula to solve each problem.. The Walters famil invested $8000 at an interest rate of 7% compounded annuall. After 5 ears, what is the value of their investment? A P 1 n r nt n 1 A A 8000 (1.07) 5 A 8000 ( ) 5 The interest compounded annuall, or 1 time per ear. In this case, nt 5. Do not round the epression inside the parentheses. A 11,0.0 Round the product to the nearest cent. After 5 ears, the Walters will have an investment of $11, Lana invested $1000 at an interest rate of % compounded annuall. After 7 ears,what is the value of her investment? $ Saon. All rights reserved. 5 Saon Algebra 1

15 Name Date Class Using Trigonometric Ratios 117 Now ou will solve problems using other special relationships of right triangles. Trigonometric ratios are ratios of two sides of a right triangle. There are si trigonometric ratios that can be formed b the lengths of the sides. For acute A in the right triangle shown, the si ratios are: sin A opposite side hpotenuse cos A adjacent side hpotenuse tan A opposite side adjacent side adjacent to A C A hpotenuse opposite A B csc A hpotenuse opposite side hpotenuse sec A adjacent side cot A adjacent side opposite side If ou know one acute angle and the length of one side of a right triangle, ou can use the sin, cos, or tan ratios to find the lengths of one or both of the other sides. Find the value of in the right triangle shown. You are given the length of the side adjacent to the angle given. You want to find the opposite side. The tan ratio shows the relationship between the opposite and adjacent sides. tan tan 70 Solve for. Use our calculator to find tan 70. Multipl tan 70 and 3. Round to the nearest hundredth Find the value of in the right triangle Round to the nearest hundredth. You are given an acute angle measure and the length of the side opposite the angle. You want to find the length of the hpotenuse. 50 sin Use the sin ratio sin Use our calculator to solve for. Solve each problem. Round to the nearest hundredth.. Find the value of in the right triangle Use the cosine ratio Find the value of in the right triangle Use the tangent ratio Saon. All rights reserved. 55 Saon Algebra 1

16 If ou know the length of two sides of a right triangle, ou can use the inverse sine, cosine, and tangent ratios to find one or both of the acute angles. The inverse sine ratio is sin 1, the inverse cosine ratio is cos 1, and the inverse tangent ratio is tan 1. It is important to remember that is sin 1 NT equal to the reciprocal of sin. So, sin 1 1. This is true for sin all inverse ratios. continued 117 Find the measure of B in the right triangle shown. opposite side sin B hpotenuse B sin B You are given the length of the hpotenuse and the side opposite B. 10 sin 1 (sin B) sin Use sin 1 to fine B. m B 30 Use our calculator to find sin 1 (70/10). C 70 A Complete the steps using trigonometric ratios.. The top of a tree makes a 0 angle with a point on the ground 30 meters from the base of the tree. What is the height of the tree? Round our answer to the nearest meter. You are given the measure of one acute angle and the length of its adjacent side. You want to find the length of the side opposite the angle given. Use the tangent ratio. tan 0 h 30 Use the tan ratio. h 30 tan 0 Use our calculator to find tan 0. h 30 m 0 h 5 m Multipl tan 0 and 30. Round to the nearest meter. Solve each problem. Round to the nearest tenth. 5. If A 0 and the length of side b is 5 meters, find the length of a. Use the tangent ratio. a 3.3 m. If the length of the hpotenuse c is 75 meters and the length of side a is meters, find the measure of B. Use the secant ratio. m B.8 A c b B a C Saon. All rights reserved. 5 Saon Algebra 1

17 Name Date Class Now ou will solve problems using combinations, or arrangements in which order does not matter. n C r n! r! n r! Solving Problems Involving Combinations 118 To calculate the number of combinations, use the combination formula, where C is the number of combinations, n is total number of items, and r is the number of items to be chosen. A teacher must choose a committee of 5 students from a group of 10 students. How man combinations of students can she choose? n C r n! Use the combination formula. r! n r! 10 C 5 10 C 5 10! 5! 10 5! 10! 5! 5! 10 C 5 3,58, Substitute 10 for n and 5 for r. Subtract inside the parentheses. Use our calculator to calculate the factorials. 10 C 5 5 Simplif. There are 5 was to choose 5 students from a group of 10 students. 1. B the end of the semester, students in an English class must read books out of a list of 0. How man combinations of books can the students choose? n C r n! r! n r! 0 0 C!! 0! 0 C 0!! 1! 0 0 C !! 1! Use combination formula. Substitute 0 for n and for r. Subtract inside the parentheses. Rewrite 0! as ! 0 0 C Cancel 1!.! 0 C 85 There are 85 was to choose books out of 0. Saon. All rights reserved. 57 Saon Algebra 1

18 continued 118 You can use the combination formula to calculate probabilities. Lesle has different colored beads. She wants to choose 5 of them to make a bracelet. What is the probabilit that she will choose a red bead, an orange bead, a ellow bead, a green bead, and a blue bead? n C r n! Use the combination formula. r! n r! C 5! 5! 5! C 5 5,100,80 10 Substitute for n and 5 for r. Evaluate the factorial epressions. C 5,50 Simplif. There are,50 was Lesle can choose 5 different colored beads. There is onl one wa she can choose a red, orange, ellow, green, and blue one. The probabilit of choosing the 5 colors is 1,50.. Mrs. Colbert wants to bu kinds of vegetable seeds to plant in her garden. She has a choice of 1 different kinds of vegetables. What is the probabilit she will bu pumpkin, carrot, pea, bean, cucumber, and tomato seeds? n C r 1 C n! r! n r! 1!! 1! Substitute 1 for n and for r. 1 1 C !! 10! 1 1 C ! Rewrite 1! as !. Cancel 10! 1 C 8008 Evaluate the factorial epression and simplif. There are 8008 combinations of different seeds that Mrs. Colbert can bu from a selection of 1 different seeds. There is onl one wa that she can bu onl pumpkin, carrot, pea, bean, cucumber, and tomato seeds. 1 The probabilit of her buing that particular combination is Steve is making chili. He has 7 seasonings he can use. His recipe calls for onl 3 of them. What is the probabilit that Steve will use pepper, salt, 1 and chili powder? 35 Saon. All rights reserved. 58 Saon Algebra 1

19 Name Date Class You have graphed linear, quadratic, and eponential functions. Now ou will identif tpes of functions b graphs and tables. A function famil is a set of functions whose graphs are similar to a basic function called a parent function. The graphs within a function famil ma var in size and position, but the have the same characteristics of the parent function. Function Famil Graphing and Comparing Linear, Quadratic, and Eponential Functions 119 Parent Function Shape of Graph Maimum or Minimum Rate of Change Linear f() = line none constant Quadratic f() = parabola at its verte not constant Eponential f() = b curve none not constant Identif the function famil the graph belongs to. The graph is similar to the graph of f(). It is a parabola. It has minimum value of 1 at its verte (0, 1). Its rate of change is not constant. The graph belongs to the quadratic function famil. - - Identif the function famil each graph belongs to. 1. The graph is similar to the graph of f(). It is a line. It has no maimum or minimum value. - Its rate of change is constant. - The graph belongs to the linear function famil eponential quadratic. If a graph is alwas increasing and has a constant rate of change, it belongs to the linear famil. Saon. All rights reserved. 59 Saon Algebra 1

20 continued 119 If ou have a table of values, ou can make a graph to help identif the famil the function belongs to. Identif the function famil using the table of values f() Plot the points from the table on a graph and connect them using a smooth curve. The graph is a curve that does not have a maimum or minimum value. It also gets steeper as the -values increase. - - The function belongs to the eponential function famil. Use the table of values to graph the function. Then identif the function famil f() Plot the points ( 3, ), (, 1 ), ( 1, ), ( 0, 3), - - ( 1, ), (, 1 ), and ( 3, ). The function belongs to the quadratic function famil f() linear - 7. Renée is ordering fabric for a craft project. The compan charges $.50 per ard for the fabric. The also charge a shipping fee of $5. Which tpe of function could model the total cost of the fabric? linear The number of cells of a certain tpe of bacteria triples ever two das. Which tpe of function could model the total number of bacteria cells after a given number of das? eponential Saon. All rights reserved. 0 Saon Algebra 1

21 Name Date Class You have found probabilities b comparing the number of favorable outcomes to the total number of possible outcomes. Now ou will find probabilities involving geometric figures. Geometric probabilit is similar to theoretical probabilit. Instead of finding the number of favorable outcomes, ou find the area of the region ou are looking for. You then compare this to the total area of the figure. area of favorable region geometric probabilit area of total region An enclosed rectangular pool area measures 30 feet b 0 feet. The pool is 0 feet long and 10 feet wide. A ball is tossed over the fence. What is the probabilit that it lands in the pool? probabilit area of favorable region area of total region area of small rectangle area of large rectangle Using Geometric Formulas to Find the Probabilit of an Event The probabilit that the ball lands in the pool is ft 0 ft Pool 10 ft 30 ft Complete the steps to find the probabilit of landing in the shaded circle. 1. area of circle area of square ( 1 ) ( 10 ) m m 5 m 1 m 3 m 3.1 % 10 m Use the diagram in Problem 1 to find each probabilit.. landing in the shaded triangle 3. landing in the shaded rectangle Saon. All rights reserved. 1 Saon Algebra 1

22 continued 10 To find the probabilit that an event does not happen, ou can subtract the probabilit that the event will happen from 1. Mand drops a piece of paper over a trash can that has the circular opening shown. What is the probabilit that the paper does not land in the can? First, find the probabilit that the paper lands in the can. area of circle area of square (15 ) 0 5(3.1) or % Subtract the probabilit from 1. 1 % = 5% The probabilit that the paper does not land in the can is about 5%. 0 cm 15 cm 0 cm Complete the steps to find the probabilit of not landing in the shaded square.. 1 area of square area of large triangle 1 ( ) 1 (1)( ) 1 3 in. in. in. 5 in. 1 in. in Use the diagram in Problem to find each probabilit. 5. not landing in the shaded triangle. not landing in the shaded rectangle Use the target. 7. Mart shoots an arrow. What is the probabilit that it hits the inner circle? 8. What is the probabilit that the arrow does not hit the inner circle? ft 1 ft Saon. All rights reserved. Saon Algebra 1