## Monday, April 26, 2010

### Homework Probability Day 6

Day 6 homework:

1. In the instant lottery, 20% of the tickets purchased are winning tickets. If Joe purchases 8 lottery tickets, what is the probability that 2 of his tickets are winning tickets (4 decimal places)?

2. Leghorn chickens are raised for lying eggs. 0.5 is the probability of a female chick hatching. Assuming independence, find the probability that there are exactly 6 females out of 10 newly hatched chicks (4 decimal places).

3. Suppose that we are in those rare times when 65% of the American public approve of the way the President of The United States is handling his job. Find the probability that 6 out of 8 Americans do not approve of the President (4 decimal places).

4. At a certain intersection, the light for eastbound traffic is red for 15 seconds, yellow for 5 seconds, and green for 30 seconds. Find, to the nearest tenth, the probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red light (4 decimal places).

5. The Coolidge family's favorite television channels are 3, 6, 7, 10, 11, and 13. If the Coolidge family selects a favorite channel at random to view each night, what is the probability that they choose exactly three even-numbered channels in five nights? Express your answer as a fraction or as a decimal rounded to four decimal places.

6. During a recent survey, students at Franconia College were asked if they drink coffee in the morning. The results showed that two-thirds of the students drink coffee in the morning and the remainder do not. What is the probability that of six students selected at random, exactly two of them drink coffee in the morning? Express your answer as a fraction or as a decimal rounded to four decimal places.

## Saturday, April 24, 2010

### Colin and Catherine

This Is OUR SCATTER plot. we used exponential regression!!!!!!

y=.56*1.1^x

1.1 is multiplied by the number in the previous month to get the next months number of people

.56 would be the number of people (in millions) starting

x=number of months passed

and y=number of FACEBOOK users

Right now there are 644.68 million users! starting in February 2004, you can plug in 75 for x (because 75 is the number of months since February 2004

in six more months there will be 1.124 BILLION users!

Everyone will have a facebook in 1yr, 6month and 22 days!

## Friday, April 16, 2010

### Harry and Matt's Facebook World Domination

**Facebook World Domination:**

**Table:**

1 | 0 |

5.5 | 12 |

12 | 24 |

20 | 28 |

50 | 34 |

100 | 44 |

150 | 49 |

175 | 50 |

200 | 51 |

250 | 52 |

300 | 55 |

350 | 57 |

**Regression Equation (Picture Below): Y=1.252(1.1051^X)**

**Follow Up Questions:**

## Wednesday, April 14, 2010

### ...And We're Walking!

y=.054447x -7.392687

A is miles per minute, yet it takes more than one minute to walk half a mile.

B is the distance that you go when you drive nowhere. (the graph is not perfect)

LOCATIONS Miles Hours

Ryans house 2.8 .83

School 3.3 .99

Library .7 .23

Church .1 .02

Wegmans 3.2 1.1

Papa Gallos 1.2 .45

Fox Rd 12 3.96

Erie Boulivard 6.4 2.18

------

Manhattan 222 74

Ithica 54.2 18

Inlet 92.4 30

Honeoye 87.5 29

Utica 30.8 13.5

Whiteface 192 62

Niagara Falls 166 54

Plattsburg 215 71

---------

Outer Banks Nc 636 209

Wickford Ri 290 96

Middletown De 284 95

Wakeforest Nc 581 192

Las Vegas Nv 2452 777

Fairbanks Ak 3998 1282

Florida 1410 462

Milwakee Wi 749 244

### Facebook World Domination

**L1 L2**

12 1

24 5.5

36 12

40 20

46 50

56 100

61 150

62 175

64 200

67 250

69 300

72 350

exponential regression equation: y=(.45)(1.o99^x)

x= the number of months

y= the millions of users

1. The amount of users on Facebook during this month would be 556 Million People.

1.252(1.1051^61) --> 1.252(444.115)= 556 (Million)

X=61, as it has been 61 months since December 2004.

2. Six months from now, will be November 2010, and 67 (61+6) months since Facebook's start.

1.252(1.1051^67) --> 1.252(808.9203) = 1,012,000000 People (around 1 Billion People will have Facebook pages.)

3. The UN states that the World's population is now around 6,692,030,277.

--- To find out when all of them have facebooks, plug that number into the equation.

(In millions) 6692.030277=1.252(1.1051^X)

5345.072106=1.1051^X

Log(5345.072106)=X Log(1.1051)

85.89=X

86-61=25

25 Months from now is May 2012.

The world will be Facebook's then.

## Tuesday, April 13, 2010

## Sunday, April 11, 2010

### Tevy Nuon and Megan Cross... I Get a Shiver in My Bones

SYRACUSE:

Equation: Sine Regression y= (a)(sin(bx+c)) +d

y=(12.78984)(sin(.5643x- 2.66123) + 60.4501

amplitude: 12.78984

wrap line: 60.4501

x= the month

y= the approximate temperature

JEFFERSON CITY, MISSOURI

Equation: Sine Regression y=(a)(sin(bx+c))+d

y= (25.2057)(sin(.48599x - 1. 87728) +51.69428

amplitude: 25.2057

wrap line: 51.69428

x= the month

y= the approximate temperature

BARCELONA, SPAIN

Equation: Sine Regression y= (a)(sin(bx+c))+d

y= (12.798)(sin(.56433x - 2.66124)) + 60.45

amplitude: 12.798

wrap line: 60.45

x=the month

y= the approximate temperature

- The wrap line represents the point in the graph where the y-intercept starts. It is also the line that cuts the graph in half horizontally. If the wrap line is greater than zero the whole graph shifts upwards based in the number given. If the wrap line is less than zero the whole graph shifts downwards based on the number given.

- The amplitude represents how high the graph goes representing the maximum and minimum points. In the situation it represents the highest and lowest average temperatures.

- The three locations seem to have similar temperature in each month. The highest value of Syracuse is in August at 70. For Jefferson City, Missouri, it is 77.4 in July. In addition, for Barcelona, Spain, it is 74. So Syracuse and Barcelona have their highest temperatures in August while Jefferson City has it is highest in July. Therefore, they all have their highest temperatures in the summer time. Syracuse’s lowest temperature is 24 in January. Jefferson City is 27.4 in January, and for Barcelona, its lowest temperature is 48 in January. They all have their lowest temperatures in January, though Spain’s is a lot more than Syracuse and Jefferson City’s temperatures. Another different thing is that Spain’s averages are higher than the others for winter, while Syracuse has the lowest. But for summer, Jefferson City has the highest averages. In addition, for spring, Barcelona has the highest averages while Syracuse has the lowest. Some of Barcelona’s averages are equal to Syracuse ‘s averages by a month later. For example, Syracuse is 70 in August when Barcelona is 70 in September, and it goes for September to October.

- My favorite temperature is early to mid 70’s. Warm, sunny, and breezy. Warm enough to wear shorts and sandals but cool enough to wear jeans, or denim jackets. I do not think 70 is hot I think its more mild to me. According to the data and graph, the best time to go Jefferson Missouri and Barcelona Spain would be from July to September. For Jefferson City, it would be from June to September.

### Chris and Sherry Regressions

Chris Marchitelli and Sherry Pohar

**Blink**

Date | Transistor Count |

1971 | 2300 |

1972 | 3500 |

1974 | 4500 |

1979 | 29000 |

1982 | 134000 |

1985 | 275000 |

1989 | 1180000 |

1993 | 3100000 |

1996 | 4300000 |

1997 | 7500000 |

1997 | 8800000 |

1999 | 9500000 |

1999 | 21300000 |

1999 | 2200000 |

2000 | 42000000 |

2008 | 47000000 |

2003 | 54300000 |

2003 | 105900000 |

2003 | 220000000 |

2006 | 241000000 |

2006 | 291000000 |

2007 | 463000000 |

2004 | 592000000 |

2008 | 731000000 |

2007 | 789000000 |

2009 | 904000000 |

2006 | 1700000000 |

2008 | 1900000000 |

2010 | 2000000000 |

2010 | 2300000000 |

Y=(3.8970)1.413^x

In the table, X represents the date and Y represents the transistor count. In the equation, both A and B together are the slope.

In 2029, the quad-core Itanium will be released with 2 billion transistors. We found our answer by solving the equation as a log and adding 58 to our starting year, 1971.

In 2036, the 8-core xeon, with 2.3 billion transistors, will be released. We found this answer by solving the equation as a log and adding 65 to our starting year, 1971.

This equation does not support Moore’s law initially because the number of transistors does not double every two years. However, the graph eventually shows Moore’s law after a set period of time.

**Will The Ball Hit The Can?**

Picture 1: Quad. Regression

Y= -.0067x^2+-.0449x+26.5714

Picture 2: Cubic Regression

Y= -2.3435x^3+-.0090x^2+.0100x+36.7063

Picture: 3 Quartic Regression

Y= -6.9578^4+-5.30804x^3+-.01907x^2+.0144x+75.3053

The X in the equation is the distance the tennis ball traveled and the Y is the height of the ball. A represents how wide or narrow the graph is, based lying in Quadrant II, B moves the graph left to right and C is where the graph crosses the y axis. Coordinates of the can were 58.3 for the x and 0 for the y.

None of the tennis balls will hit the trash can because none were thrown from ground level, which will skew the throw to be higher than required to hit the trash can, located roughly at 60.

### Odelia Ryan and Heather Cooper

**Facebook World Domination**

table:

**L1 L2**

12 1

24 5.5

36 12

40 20

46 50

56 100

61 150

62 175

64 200

67 250

69 300

72 350

74 400

exponential regression equation: y=(.45)(1.o99^x)

x= the number of months

y= the millions of users

this month is the 76th month. there are 591 million people

plug in 76 for x and solve for y.

In six months it is 82 months total, there will be 1.o35 billion people. plug in 82 for x and solve for y.

In 14 years every one in the world would have a facebook. Now there is 6,814,169,763 people in the world. plug that in for y.

**A piece of Cake**

L1 L2

1 2

2 4

3 7

4 11

5 16

6 22

7 28

8 35

quadratic regression equation: y= .5x^2+.5x+1

y- is the number of pieces

x-is the number of cuts

.5x^2- is the width of the func.

.5x- location of vertex

domain-(1,2,3,4,5,6,7,8)

range-(2,4,7,11,16,22,28,35)

**Harder, Faster, Stronger**

mens 100m backstroke

start 1956- 1st year

linear regression equation: y=ax=b

y=-.0018x+.6058

womens 100m backstrokey= -.0018x+.6839

a=the slope

b=y intercept

x=year

y=time

men tend to have faster times than women. An amazing time would be be under 50 seconds. this might happen by 2015

## Saturday, April 10, 2010

### Tevy Nuon and Megan Cross- Harder, Faster, Stronger

-Table of the year and gold medal time for each year- women.

L1 L2

1920 274

1924 362

1928 343

1932 329

1936 326

1948 318

1952 312

1956 295

1960 291

1964 283

1968 271

1972 259

1976 250

Liner Regression Graph for Women (y=ax+b)

Equation: y= -1.07488740554156x + 2389.4

-Table of the year and gold medal time for each year men

L1 L2

1896 493

1904 376

1906 383

1908 337

1912 324

1920 326

1924 304

1928 301

1932 288

1936 284

1948 281

Linear Regression Graph for Men (y=ax+b)

Equation: -1.646595713201x +3497.8121

X= symbolizes the slope of the graph (-1.646596x)

B= symbolizes the y-intercept of the graph (3497.8121)

r^2= helps us predict the regression and shows us how x and y are related. (.7927268076)

r= the percent of the variation of this regression (89%)women's gold medal results are faster than the men’s gold medal results.

• This model makes sense because as the years go one the time for the gold medal will decrease according to the slope and the trend of the graph.

• The results of both the men’s and women’s events is that the women’s gold medal times seemed to have decreaY= symbolizes the approximate gold medal time

• Predictions that I can make about the future of these events is the in time both the men and women’s times would be very similar.

• An amazing time would be a time that would be under 0 minutes and this can expect to happen in the year 2019.