<p> Chapter 9 Section 4 – 6 Chapter 10 and Test</p><p>Name: ______Date: ______</p><p>Type your name and date at the top of this document. Copy the Step-by-step Template for Assignments at the </p><p> bottom of the document. Show all your work in the Your Solution column. Place your Final Answer in the final </p><p> answer column. Remember to use the equation editor to create any special mathematical symbols. Use Microsoft </p><p>Excel to create charts and graphs. 1. When a single card is drawn from an ordinary 52-card deck, find the odds in favor of getting a red 10 or a </p><p> black 6. </p><p>2. Given that , what are the odds against A occurring?</p><p>3. Suppose you pay $2.00 to roll a fair die with the understanding that you will get back $4.00 for rolling a 3 </p><p> or a 6, nothing otherwise. What is your expected value? 4. When a coin is tossed four times, sixteen equally likely outcomes are possible as shown below: </p><p>HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT</p><p>THHH THHT THTH THTT TTHH TTHT TTTH TTTT</p><p>Let X denote the total number of tails obtained in the four tosses. Find the probability distribution of the </p><p> random variable X. Leave your probabilities in fraction form. </p><p>5. Find the z-score for the given raw score, mean, and standard deviation. Assume a normal probability </p><p> distribution. Raw score = 124, μ = 98, and σ = 17. 6. Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of </p><p> beer poured by this filling machine follows a normal distribution with a mean of and a standard deviation </p><p> of 0.04 ounce. Find the probability that a randomly selected bottle contains between 12.31 and 12.37 </p><p> ounces.</p><p>7. A musician plans to perform 4 selections. In how many ways can she arrange the musical selections?</p><p>8. There are 10 members on a board of directors. If they must elect a chairperson, a secretary, and a </p><p> treasurer, how many different slates of candidates are possible? 9. There are 8 members on a board of directors. If they must form a subcommittee of 3 members, how many </p><p> different subcommittees are possible?</p><p>10. License plates are made using 3 letters followed by 3 digits. How many plates can be made if repetition of </p><p> letters and digits is allowed?</p><p>11. F = 75,025 and F = 121,393 where F is the nth term in the Fibonacci sequence. Find F27. 24 25 n 12. Find the area of △ABC.</p><p>13. Find a traversable path that begins at vertex B. 14. Refer to this figure to answer the question. Line DH is parallel to line IM. Line BO is perpendicular to line </p><p>DH.</p><p>If m∠IJN = 54°, what is the measure of ∠AEF? 15. Use the properties of parallel lines to solve the problem. Given and m∠ABC = 64°, find the </p><p> measures of angles ∠ABE, ∠FCD, and ∠BCD.</p><p>16. Find the measure of the exterior angle x where ∠x = ( 197 - 5n)°, ∠y = ( 5n + 21)°, ∠z = (n + 11)°</p><p>17. If each angle of a regular polygon measures 140°, how many sides does it have? 18. A painter leans a ladder against one wall of a house (as depicted below). The ladder is 18 ft long. The base </p><p> of the ladder is 14 ft from the house. How high is the wall?</p><p>? 18 ft</p><p>14 ft 19. Find d in simplest radical form.</p><p>30</p><p> d 8</p><p>60 20. Determine whether the triple of numbers can be the sides of a right triangle: 9, 12, and 16.</p><p>Section Problem Your Solution Final Answer</p><p>1 There are two red 10’s and two black 6’s. 1/12 That’s a total of 4 valid cards out of 52. Prob = 4/52 = 2/26 = 1/13 Odds in favor = p/(1-p) = 1/13 / (1-1/13) = 1/12 2 Odds against = (1-p)/p 35 = (1-1/36)/(1/36) (35 to 1) = 35 3 EV = -payment + p(winning)*winnings -$0.67 = -2 + 1/3 * 4 = -2/3 = -$0.67 (rounded) 4 Count the number of tails for each, and divide by 16. x P(x) 0 tails: 1 way 0 1/16 1 tail: 4 ways 1 1/4 2 tails: 6 ways 2 3/8 3 tails: 4 ways 3 1/4 4 tails: 1 way 4 1/16 5 z = (raw-μ)/σ about 1.529 = (124-98)/17 = about 1.529 6</p><p>We need Z for 12.31 and 12.37 0.1524</p><p>Z(12.31) = (12.31-12.41)/0.04 = -2.5</p><p>Z(12.37) = (12.37-12.41)/0.04 = -1</p><p>Prob(-2.5 < z < -1) from a table is:</p><p>0.1524</p><p>7 4 ways to pick the first one, then 3 ways, 2 ways, 24 and 1 way: 4! = 4*3*2*1 = 24 ways 8 10 ways for the chair 720 9 ways for the sec 8 ways for the treas 10*9*8 = 720 9 8 choose 3 56 = 8! / (3! * (8-3)!) = 8*7*6 / (3*2*1) = 56 10 26 letters 17576000 10 digits 26*26*26*10*10*10 = 17576000 11 F26 = F24 + F25 317811 = 75025 + 121393 = 196418 F27 = F25 + F26 = 121393 + 196418 = 317811 12 Area for a triangle = ½ b h 35 square units = ½ * 10* 7 = 35 13</p><p>A traversable path means you go on every line B → A → E → B → C → A → D → E → C → D segment.</p><p>B → A → E → B → C → A → D → E → C → D</p><p>14</p><p>It is the same as ∠IJN, by alternate exterior 54°</p><p> angles. 15</p><p>∠ABE: = 180-64 = 116, because straight lines ∠ABE= 116°</p><p> add to 180 degrees ∠FCD = 116°</p><p>∠FCD: equal to ∠ABE, by alternate exterior ∠BCD = 64°</p><p> angles</p><p>∠BCD: using alternate interior angles from the </p><p> given angle</p><p>16 The angle inside the triangle near “x” plus y and z must be 180 degrees. The angle inside the triangle near x plus x must be 180 degrees, 122° because it’s a straight line. Therefore, x is equal to y+z: x=y+z</p><p>197 - 5n = 5n + 21 + n + 11 197 = 11n + 32</p><p>11n = 165</p><p>N = 15</p><p>Get x:</p><p>197 – 5*15 = 122 degrees</p><p>17 180(n-2)/n = 140 9 sides Multiply by n: 180(n-2) = 140n 180n – 360 = 140n 40n = 360 N = 360/40 N = 9 18 Pythagorean Theorem: 8 √2 feet = approx 11.3137 feet a^2 + b^2 = c^2 14^2 + b^2 = 18^2 196 + b^2 = 324 b^2 = 128 b = sqrt(128) b = 8 sqrt(2) = approx 11.3137 feet 19 In a 30-60-90 triangle, the short side is half the 4√3 long side, so 4. The longer leg is √3 times the short side: 4√3 20 Use the Pythagorean Theorem: NO a^2 + b^2 = c^2 9^2 + 12^2 = c^2 c^2 = 81 + 144 c^2 = 225 c = 15, not 16 </p>