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Chapter 9 Section 4 – 6 Chapter 10 and Test

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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 black 6.

2. Given that [pic] , what are the odds against A occurring?

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 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:

HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT

THHH THHT THTH THTT TTHH TTHT TTTH TTTT

Let X denote the total number of tails obtained in the four tosses. Find the probability distribution of the random variable X. Leave your probabilities in fraction form.

5. Find the z-score for the given raw score, mean, and standard deviation. Assume a normal probability 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 beer poured by this filling machine follows a normal distribution with a mean of and a standard deviation of 0.04 ounce. Find the probability that a randomly selected bottle contains between 12.31 and 12.37 ounces.

7. A musician plans to perform 4 selections. In how many ways can she arrange the musical selections?

8. There are 10 members on a board of directors. If they must elect a chairperson, a secretary, and a 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 different subcommittees are possible?

10. License plates are made using 3 letters followed by 3 digits. How many plates can be made if repetition of letters and digits is allowed?

11. F24 = 75,025 and F25 = 121,393 where Fn is the nth term in the Fibonacci sequence. Find F27.

12. Find the area of △ABC.

[pic]

13. Find a traversable path that begins at vertex B.

[pic]

14. Refer to this figure to answer the question. Line DH is parallel to line IM. Line BO is perpendicular to line DH.

[pic]

If m∠IJN = 54°, what is the measure of ∠AEF?

15. Use the properties of parallel lines to solve the problem. Given [pic] and m∠ABC = 64°, find the measures of angles ∠ABE, ∠FCD, and ∠BCD.

[pic]

16. Find the measure of the exterior angle x where ∠x = ( 197 - 5n)°, ∠y = ( 5n + 21)°, ∠z = (n + 11)°

[pic]

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 of the ladder is 14 ft from the house. How high is the wall?

? 18 ft

14 ft

19. Find d in simplest radical form.

30(

d 8

60(

20. Determine whether the triple of numbers can be the sides of a right triangle: 9, 12, and 16.

 

|Section |Problem |Your Solution |Final Answer |

| | | | |

| | | | |

|  | 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. |  |

| | |0 tails: 1 way |x |

| | |1 tail: 4 ways |P(x) |

| | |2 tails: 6 ways | |

| | |3 tails: 4 ways |0 |

| | |4 tails: 1 way |1/16 |

| | | | |

| | | |1 |

| | | |1/4 |

| | | | |

| | | |2 |

| | | |3/8 |

| | | | |

| | | |3 |

| | | |1/4 |

| | | | |

| | | |4 |

| | | |1/16 |

| | | | |

|  | 5 | z = (raw-μ)/σ |about 1.529 |

| | |= (124-98)/17 | |

| | |= about 1.529 | |

|  | 6 | We need Z for 12.31 and 12.37 |  0.1524 |

| | |Z(12.31) = (12.31-12.41)/0.04 = -2.5 | |

| | |Z(12.37) = (12.37-12.41)/0.04 = -1 | |

| | |Prob(-2.5 < z < -1) from a table is: | |

| | |0.1524 | |

|  | 7 | 4 ways to pick the first one, then 3 ways, 2 ways, and 1 way: | 24 |

| | |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 | A traversable path means you go on every line segment. | B → A → E → B → C → A → D → E → C → D |

| | |B → A → E → B → C → A → D → E → C → D | |

|  | 14 | It is the same as ∠IJN, by alternate exterior angles. | 54° |

|  | 15 |  ∠ABE: = 180-64 = 116, because straight lines add to 180 degrees | ∠ABE= 116° |

| | |∠FCD: equal to ∠ABE, by alternate exterior angles |∠FCD = 116° |

| | |∠BCD: using alternate interior angles from the given angle |∠BCD = 64° |

|  | 16 | The angle inside the triangle near “x” plus y and z must be 180 | 122° |

| | |degrees. The angle inside the triangle near x plus x must be 180 | |

| | |degrees, because it’s a straight line. Therefore, x is equal to | |

| | |y+z: | |

| | |x=y+z | |

| | |197 - 5n = 5n + 21 + n + 11 | |

| | |197 = 11n + 32 | |

| | |11n = 165 | |

| | |N = 15 | |

| | |Get x: | |

| | |197 – 5*15 = 122 degrees | |

|  | 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 long side, so | 4√3 |

| | |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 | |

 

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