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What shapes (positive or negative) go into creating the track around the football field? What are their dimensions?
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(Right end is slightly distorted in the satellite picture.)
Initial questions:
What shapes (positive or negative) go into making the green part inside the track?
Calculations:
If the green is FieldTurf? at $5/ft˛ and the red is TopTrax? at $2/ft˛, how much money does the Booster Club have to convince the town to put on the ballot?
Everything outside of the track is natural grass.
The preparation cost is $2.25/ft˛ for the track and the field.
The two gray rectangles on the sidelines are protective felt laid over the track to protect it from football cleats. The light grey on the left is also a protective felt. They should be ignored because there's track under them.
The two sandy pits at the end of the straightaway are the long jump pits. The narrow stripe in the left end-zone is the pole vault run and the large rectangle in the right end-zone is the high jump run.
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How many different math concepts can you use this church as an example for?
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What kind of approach might give us the thickness of the atmosphere in the video?
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What's a good problem you can make based on this video?
https://pbs.twimg.com/tweet_video/B0Qu4GjIgAACdCD.mp4
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Where should we start this shape substitution puzzle?
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Your teacher (me) is thinking about buying a new car. Presently, the cost of gas is $3.60 per gallon and he knows that he is going to commute to work each day and drive errands on the weekend ... about 300 miles per week.
He wonders whether or not to buy a Corolla or a Prius. Currently, he drives a Ford Ranger pickup truck, which is paid off but is starting to have some expensive repair bills. If he averages those costs, it's about $200 per month.
Option 1: The Corolla costs $16,800 (about $400/month) and gets roughly 36 mpg.
Option 2: The Prius costs $24,200 (about $570/month) and gets roughly 49 mpg.
Option 3: The Ranger is paid off but has repairs (about $200/month) and gets 21 mpg.
What should he do?
Prius:
Corolla:
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R1
Below are are four lists:
Best Actor, Best Actress, Best Director, Best Supporting Actress.
Do you expect to see any significant differences in their ages?
Do you expect to see any changes over the years?
Why are there different numbers of entries?
Best Actor, Age when receiving the Oscar
1, Emil Jannings, 44 years,
2, Warner Baxter, 41 years,
3, George Arliss, 62 years,
4, Lionel Barrymore, 53 years,
5, Wallace Beery, 47 years,
6, Fredric March, 35 years,
7, Charles Laughton, 34 years,
8, Clark Gable, 34 years,
9, Victor McLaglen, 49 years,
10, Paul Muni, 41 years,
11, Spencer Tracy, 37 years,
12, Spencer Tracy, 38 years,
13, Robert Donat, 34 years,
14, James Stewart, 32 years,
15, Gary Cooper, 40 years,
16, James Cagney, 43 years,
17, Paul Lukas, 48 years,
18, Bing Crosby, 41 years,
19, Ray Milland, 39 years,
20, Fredric March, 49 years,
21, Ronald Colman, 57 years,
22, Laurence Olivier, 41 years,
23, Broderick Crawford, 38 years,
24, José Ferrer, 39 years,
25, Humphrey Bogart, 52 years,
26, Gary Cooper, 51 years,
27, William Holden, 35 years,
28, Marlon Brando, 30 years,
29, Ernest Borgnine, 39 years,
30, Yul Brynner, 36 years,
31, Alec Guinness, 43 years,
32, David Niven, 49 years,
33, Charlton Heston, 36 years,
34, Burt Lancaster, 47 years,
35, Maximilian Schell, 31 years,
36, Gregory Peck, 47 years,
37, Sidney Poitier, 37 years,
38, Rex Harrison, 57 years,
39, Lee Marvin, 42 years,
40, Paul Scofield, 45 years,
41, Rod Steiger, 42 years,
42, Cliff Robertson, 45 years,
43, John Wayne, 62 years,
44, George C. Scott, 43 years,
45, Gene Hackman, 42 years,
46, Marlon Brando, 48 years,
47, Jack Lemmon, 49 years,
48, Art Carney, 56 years,
49, Jack Nicholson, 38 years,
50, Peter Finch, 60 years,
51, Richard Dreyfuss, 30 years,
52, Jon Voight, 40 years,
53, Dustin Hoffman, 42 years,
54, Robert De Niro, 37 years,
55, Henry Fonda, 76 years,
56, Ben Kingsley, 39 years,
57, Robert Duvall, 53 years,
58, F. Murray Abraham, 45 years,
59, William Hurt, 36 years,
60, Paul Newman, 62 years,
61, Michael Douglas, 43 years,
62, Dustin Hoffman, 51 years,
63, Daniel Day-Lewis, 32 years,
64, Jeremy Irons, 42 years,
65, Anthony Hopkins, 54 years,
66, Al Pacino, 52 years,
67, Tom Hanks, 37 years,
68, Tom Hanks, 38 years,
69, Nicolas Cage, 32 years,
70, Geoffrey Rush, 45 years,
71, Jack Nicholson, 60 years,
72, Roberto Benigni, 46 years,
73, Kevin Spacey, 40 years,
74, Russell Crowe, 36 years,
75, Denzel Washington, 47 years,
76, Adrien Brody, 29 years,
77, Sean Penn, 43 years,
78, Jamie Foxx, 37 years,
79, Philip Seymour Hoffman, 38 years,
80, Forest Whitaker, 45 years,
81, Daniel Day-Lewis, 50 years,
82, Sean Penn, 48 years,
83, Jeff Bridges, 60 years,
84, Colin Firth, 50 years,
85, Jean Dujardin, 39 years,
86, Daniel Day-Lewis, 55 years,
87, Matthew McConaughey, 44 years,
Best Actress, Age when receiving Oscar.
1, Janet Gaynor, 22 years, 222 days
2, Mary Pickford, 37 years, 360 days
3, Norma Shearer, 28 years, 87 days
4, Marie Dressler, 63 years, 1 day
5, Helen Hayes, 32 years, 39 days
6, Katharine Hepburn, 26 years, 308 days
7, Claudette Colbert, 31 years, 167 days
8, Bette Davis, 27 years, 335 days
9, Luise Rainer, 27 years, 51 days
10, Luise Rainer, 28 years, 57 days
11, Bette Davis, 30 years, 324 days
12, Vivien Leigh, 26 years, 116 days
13, Ginger Rogers, 29 years, 226 days
14, Joan Fontaine, 24 years, 127 days
15, Greer Garson, 38 years, 156 days
16, Jennifer Jones, 25 years, 0 days
17, Ingrid Bergman, 29 years, 198 days
18, Joan Crawford, 41 years, 349 days
19, Olivia de Havilland, 30 years, 255 days
20, Loretta Young, 35 years, 74 days
21, Jane Wyman, 32 years, 78 days
22, Olivia de Havilland, 33 years, 265 days
23, Judy Holliday, 29 years, 281 days
24, Vivien Leigh, 38 years, 136 days
25, Shirley Booth, 54 years, 201 days
26, Audrey Hepburn, 24 years, 325 days
27, Grace Kelly, 25 years, 138 days
28, Anna Magnani, 48 years, 14 days
29, Ingrid Bergman, 41 years, 210 days
30, Joanne Woodward, 28 years, 27 days
31, Susan Hayward, 41 years, 280 days
32, Simone Signoret, 39 years, 10 days
33, Elizabeth Taylor, 29 years, 49 days
34, Sophia Loren, 27 years, 201 days
35, Anne Bancroft, 31 years, 203 days
36, Patricia Neal, 38 years, 84 days
37, Julie Andrews, 29 years, 186 days
38, Julie Christie, 25 years, 4 days
39, Elizabeth Taylor, 35 years, 42 days
40, Katharine Hepburn, 60 years, 334 days
41, Katharine Hepburn, 61 years, 337 days
42, Barbra Streisand, 26 years, 355 days
43, Maggie Smith, 35 years, 100 days
44, Glenda Jackson, 34 years, 341 days
45, Jane Fonda, 34 years, 111 days
46, Liza Minnelli, 27 years, 15 days
47, Glenda Jackson, 37 years, 328 days
48, Ellen Burstyn, 42 years, 122 days
49, Louise Fletcher, 41 years, 251 days
50, Faye Dunaway, 36 years, 73 days
51, Diane Keaton, 32 years, 88 days
52, Jane Fonda, 41 years, 109 days
53, Sally Field, 33 years, 160 days
54, Sissy Spacek, 31 years, 96 days
55, Katharine Hepburn, 74 years, 321 days
56, Meryl Streep, 33 years, 293 days
57, Shirley MacLaine, 49 years, 351 days
58, Sally Field, 38 years, 139 days
59, Geraldine Page, 61 years, 122 days
60, Marlee Matlin, 21 years, 218 days
61, Cher, 41 years, 327 days
62, Jodie Foster, 26 years, 128 days
63, Jessica Tandy, 80 years, 292 days
64, Kathy Bates, 42 years, 270 days
65, Jodie Foster, 29 years, 132 days
66, Emma Thompson, 33 years, 348 days
67, Holly Hunter, 36 years, 1 day
68, Jessica Lange, 45 years, 341 days
69, Susan Sarandon, 49 years, 173 days
70, Frances McDormand, 39 years, 274 days
71, Helen Hunt, 34 years, 281 days
72, Gwyneth Paltrow, 26 years, 175 days
73, Hilary Swank, 25 years, 240 days
74, Julia Roberts, 33 years, 148 days
75, Halle Berry, 35 years, 222 days
76, Nicole Kidman, 35 years, 276 days
77, Charlize Theron, 28 years, 206 days
78, Hilary Swank, 30 years, 212 days
79, Reese Witherspoon, 29 years, 348 days
80, Helen Mirren, 61 years, 214 days
81, Marion Cotillard, 32 years, 147 days
82, Kate Winslet, 33 years, 140 days
83, Sandra Bullock, 45 years, 224 days
84, Natalie Portman, 29 years, 263 days
85, Meryl Streep, 62 years, 249 days
86, Jennifer Lawrence, 22 years, 193 days
87, Cate Blanchett, 44 years, 292 days
Best Director, Age when receiving Oscar
1, Frank Borzage, 35 years, 23 days
2, Lewis Milestone, 33 years, 228 days
3, Frank Lloyd, 44 years,60 days
4, Lewis Milestone, 35 years,36 days
5, Norman Taurog, 32 years,260 days
6, Frank Borzage, 38 years, 209 days
7, Frank Lloyd, 48 years, 42 days
8, Frank Capra, 37 years, 285 days
9, John Ford, 42 years, 33 days
10, Frank Capra, 39 years, 290 days
11, Leo McCarey, 39 years, 158 days
12, Frank Capra, 41 years, 281 days
13, Victor Fleming, 51 years, 6 days
14, John Ford, 47 years, 26 days
15, John Ford, 48 years, 25 days
16, William Wyler, 40 years, 246 days
17, Michael Curtiz, 57 years, 69 days
18, Leo McCarey, 46 years, 163 days
19, Billy Wilder, 39 years, 258 days
20, William Wyler, 44 years, 255 days
21, Elia Kazan, 38 years, 195 days
22, John Huston, 42 years, 231 days
23, Joseph L. Mankiewicz, 41 years, 40 days
24, Joseph L. Mankiewicz, 42 years, 46 days
25, George Stevens, 47 years, 103 days
26, John Ford, 59 years, 46 days
27, Fred Zinnemann, 46 years, 330 days
28, Elia Kazan, 45 years, 204 days
29, Delbert Mann, 36 years, 51 days
30, George Stevens, 52 years, 99 days
31, David Lean, 50 years, 1 day
32, Vincente Minnelli, 56 years, 37 days
33, William Wyler, 57 years, 278 days
34, Billy Wilder, 54 years, 299 days
35, Jerome Robbins, 43 years, 180 days
36, Robert Wise, 47 years, 211 days
37, David Lean, 55 years, 14 days
38, Tony Richardson, 35 years, 313 days
39, George Cukor, 65 years, 272 days
40, Robert Wise, 51 years, 220 days
41, Fred Zinnemann, 59 years,346 days
42, Mike Nichols, 36 years,156 days
43, Carol Reed, 62 years,105 days
44, John Schlesinger, 44 years,50 days
45, Franklin J. Schaffner, 50 years,320 days
46, William Friedkin, 36 years,225 days
47, Bob Fosse, 45 years, 277 days
48, George Roy Hill, 52 years,103 days
49, Francis Ford Coppola, 36 years,1 day
50, Milo Forman, 44 years,40 days
51, John G. Avildsen, 41 years,97 days
52, Woody Allen, 42 years,123 days
53, Michael Cimino, 40 years,65 days
54, Robert Benton, 47 years,198 days
55, Robert Redford, 44 years,225 days
56, Warren Beatty, 44 years,364 days
57, Richard Attenborough, 59 years,225 days
58, James L. Brooks, 43 years,336 days
59, Milo Forman, 53 years,35 days
60, Sydney Pollack, 51 years,266 days
61, Oliver Stone, 40 years,196 days
62, Bernardo Bertolucci, 48 years,26 days
63, Barry Levinson, 46 years,355 days
64, Oliver Stone, 43 years,192 days
65, Kevin Costner, 36 years,66 days
66, Jonathan Demme, 48 years,37 days
67, Clint Eastwood, 62 years,302 days
68, Steven Spielberg, 47 years,93 days
69, Robert Zemeckis, 43 years,317 days
70, Mel Gibson, 40 years,82 days
71, Anthony Minghella, 43 years,77 days
72, James Cameron, 43 years,219 days
73, Steven Spielberg, 52 years,93 days
74, Sam Mendes, 34 years,238 days
75, Steven Soderbergh, 38 years,70 days
76, Ron Howard, 48 years,23 days
77, Roman Polanski, 69 years,217 days
78, Peter Jackson, 42 years,121 days
79, Clint Eastwood, 74 years,272 days
80, Ang Lee, 51 years, 133 days
81, Martin Scorsese, 64 years,100 days
82, Ethan Coen, 50 years,156 days
83, Joel Coen, 53 years, 87 days
84, Danny Boyle, 52 years,125 days
85, Kathryn Bigelow, 58 years,100 days
86, Tom Hooper, 38 years,149 days
87, Michel Hazanavicius, 44 years,334 days
88, Ang Lee, 58 years, 124 days
89, Alfonso Cuaron, 52 years,94 days
Best Supporting Actress, Age when receiving Oscar.
1, Gale Sondergaard, 38 years,17 days
2, Alice Brady, 45 years,128 days
3, Fay Bainter, 45 years,78 days
4, Hattie McDaniel, 44 years,264 days
5, Jane Darwell, 61 years,135 days
6, Mary Astor, 35 years, 299 days
7, Teresa Wright, 24 years,128 days
8, Katina Paxinou, 43 years,76 days
9, Ethel Barrymore, 65 years,212 days
10, Anne Revere, 42 years,255 days
11, Anne Baxter, 23 years,310 days
12, Celeste Holm, 30 years,326 days
13, Claire Trevor, 39 years,16 days
14, Mercedes McCambridge, 34 years,7 days
15, Josephine Hull, 74 years,85 days
16, Kim Hunter, 29 years,139 days
17, Gloria Grahame, 29 years,111 days
18, Donna Reed, 33 years,57 days
19, Eva Marie Saint, 30 years,269 days
20, Jo Van Fleet, 41 years,82 days
21, Dorothy Malone, 32 years,56 days
22, Miyoshi Umeki, 28 years,322 days
23, Wendy Hiller, 46 years,234 days
24, Shelley Winters, 39 years,230 days
25, Shirley Jones, 27 years,17 days
26, Rita Moreno, 30 years,119 days
27, Patty Duke, 16 years,115 days
28, Margaret Rutherford, 71 years,338 days
29, Lila Kedrova, 46 years,178 days
30, Shelley Winters, 45 years,243 days
31, Sandy Dennis, 29 years,348 days
32, Estelle Parsons, 40 years,142 days
33, Ruth Gordon, 72 years,166 days
34, Goldie Hawn, 24 years,137 days
35, Helen Hayes, 70 years,187 days
36, Cloris Leachman, 45 years,346 days
37, Eileen Heckart, 53 years,363 days
38, Tatum O'Neal, 10 years,148 days
39, Ingrid Bergman, 59 years,222 days
40, Lee Grant, 48 years, 150 days
41, Beatrice Straight, 62 years,238 days
42, Vanessa Redgrave, 41 years,63 days
43, Maggie Smith, 44 years,102 days
44, Meryl Streep, 30 years,297 days
45, Mary Steenburgen, 28 years,51 days
46, Maureen Stapleton, 56 years,281 days
47, Jessica Lange, 33 years,356 days
48, Linda Hunt, 39 years,7 days
49, Peggy Ashcroft, 77 years,93 days
50, Anjelica Huston, 34 years,259 days
51, Dianne Wiest, 39 years,2 days
52, Olympia Dukakis, 56 years,296 days
53, Geena Davis, 33 years,65 days
54, Brenda Fricker, 45 years,37 days
55, Whoopi Goldberg, 35 years,132 days
56, Mercedes Ruehl, 44 years,31 days
57, Marisa Tomei, 28 years,115 days
58, Anna Paquin, 11 years,240 days
59, Dianne Wiest, 46 years,364 days
60, Mira Sorvino, 28 years,179 days
61, Juliette Binoche, 33 years,15 days
62, Kim Basinger, 44 years,105 days
63, Judi Dench, 64 years,102 days
64, Angelina Jolie, 24 years,296 days
65, Marcia Gay Harden, 41 years,223 days
66, Jennifer Connelly, 31 years,102 days
67, Catherine Zeta-Jones, 33 years,179 days
68, Renée Zellweger, 34 years,310 days
69, Cate Blanchett, 35 years,289 days
70, Rachel Weisz, 35 years,363 days
71, Jennifer Hudson, 25 years,166 days
72, Tilda Swinton, 47 years,111 days
73, Penélope Cruz, 34 years,300 days
74, Monique Imes, 42 years,86 days
75, Melissa Leo, 50 years,166 days
76, Octavia Spencer, 39 years,277 days
77, Anne Hathaway, 30 years,104 days
78, Lupita Nyong'o, 31 years,1 day
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100 students were surveyed about their preferences for bell peppers (capsicum), carrots and spinach, with the following results:
- 72 students said they like bell peppers, and 36 students said they like only bell peppers.
- 41 students said they like carrots, and 9 students said they like only carrots.
- 31 students said they like spinach, and 3 students said they like only spinach.
- 9 students said they like neither bell peppers, nor carrots, nor spinach.
What is the best way to model/analyze this survey data?
Graphically (and what type of graph)?
Tables? How?
Algebra?
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Find the visual fractions.
Discuss the geometrical constructions the builder would have employed if he were limited to the following tools: a straight iron rod of 16.5 feet, string and a piece of chalk.