Wednesday, December 17, 2014

345: Fair or Foul?

Sullivan bought a die at the magic shop. He rolls it 155 times and gets the following results:
  • ONE: twenty-eight times
  • TWO: twenty times
  • THREE: fifteen times
  • FOUR: thirty-one times
  • FIVE: thirty-two times
  • SIX: twenty-nine times.
Is this die loaded?
What is the probability he will get a 6 on the next roll?

Tuesday, December 16, 2014

344: Monty Hall

Once upon a time, the world's smartest person (Marilyn vos Savant, IQ: 228) received a question for her newspaper column …
 Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He says to you, "Do you want to pick door number 2?" Is it to your advantage to switch your choice of doors? Craig. F. Whitaker, Columbia, MD

Marilyn's answer was surprising to many people. What do you think?

Wednesday, December 10, 2014

343: Forces and Friction

Your teenage son has a fast car.

He knows that friction is determined by the weight of the car over the wheels, the "normal" force. He also knows that additional weight means that the car can't accelerate as fast, but he's also having problems with the rear tires spinning out.  He's convinced that having Fat Eddie sit in the back will help his quarter-mile time.

 Will the extra weight help him or hurt him?

Tuesday, December 9, 2014

Monday, December 8, 2014

341: Sensible or Not? Study Types

Defend your answer! Here's your claim ... what's your warrant?
Give an example or a situation to bolster your position  
  1. The Department of Education conducted an observational study to determine the average salary of high school teachers in each of the United States 
  2. A paint company conducted a double-blind experiment to determine which of two types of exterior paint was more resistant to rain. 
  3. The lab conducted an experiment to determine whether the throat culture was positive for strep. 
  4. In a study of medications designed to slow the rate of balding in men, a placebo group had better results than the control group. 
  5. A meta-analysis was conducted to determine the population of New Zealand. 
  6. A case-control experiment was used to determine the average family size in Utah.

340: Giving Raises

A small company wants to give raises to their 5 employees. They have $10,000 available to distribute. Imagine that you are in charge of deciding how the raises should be determined.
  1. What are some variables you should consider?
  2. Describe mathematically as many different methods you can think of to distribute the raises. (We came up with nine; can you beat that?)
  3. What information will you need to compute those raises according to your various methods?
  4. Which of your methods do you feel is the most fair?

Use an atbash cipher decoder:
  1. zm vjfzo znlfmg, gdl gslfhzmw vzxs.
  2. vjfzo kvixvmgztv yzhvw lm hzozib.
  3. mvklgrhn: 1p, 1p, 1p, 1p, Ldmvi'h hlm: 6p.
  4. R'n lmv lu gsv vnkolbvvh: 0p, 0p, 0p, 0p, nv: 10p
  5. kilwfxgrergb tlzoh: 1p, 1p, 2p, 2p, 4p
  6. olggvib, zoo li mlgsrmt.
  7. olggvib, 0p, 1p, 2p, 3p, 4p.
  8. zokszyvgrxzo liwvi, 0p, 1p, 2p, 3p, 4p.
  9. vnkolbvv'h xsrow'h gvhg hxlivh rm gsv olxzo hxsllo ... ru gsviv'h ml rnkilevnvmg, ml ylmfh.

Sunday, December 7, 2014

334: Which values of x do we choose? Absolutes

For the following functions, think about "How to graph like a math teacher." Math teachers want to sketch graphs quickly and efficiently and choose values of x that work "nicely" in the equation and  generate integer values of y, thus making it easier to graph.
  • Which points are best found by inspection?
  • Which points are best found by substitution?
  • Which points are best found by symmetry?

$y = \lvert x \rvert$

$y = \lvert x \rvert - x$

$y = 2\lvert x+2 \rvert$

$y = \dfrac{1}{2}\lvert x-3 \rvert$

What are your favorite examples of this?