Chapter 9 Section 4 – 6 Chapter 10 and Test

Name: ______Date: ______

Type your name and date at the top of this document. Copy the Step-by-step Template for Assignments at the

bottom of the document. Show all your work in the Your Solution column. Place your Final Answer in the final

answer column. Remember to use the equation editor to create any special mathematical symbols. Use Microsoft

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

black 6.

2. Given that , 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. 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.

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

DH.

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

measures of angles ∠ABE, ∠FCD, and ∠BCD.

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

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. 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

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, 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

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

B → A → E → B → C → A → D → E → C → D

14

It is the same as ∠IJN, by alternate exterior 54°

angles. 15

∠ABE: = 180-64 = 116, because straight lines ∠ABE= 116°

add to 180 degrees ∠FCD = 116°

∠FCD: equal to ∠ABE, by alternate exterior ∠BCD = 64°

angles

∠BCD: using alternate interior angles from the

given angle

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

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 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