The question was:

Which of the words below completes the following sequence?

unicorn, compass, Rocket Richard or Gordie Howe,...

A. a baker's dozen

B. a pound of butter

C. a box of donuts

D. a liter of juice

The following numbers are associated with the given words:

unicorn....number of horns = 1 = 1^{2}

compass...# of principal directions = 4 = 2^{2}

Rocket Richard.wore the # 9 = 3^{2}

The next member of the series must be associated with 4^{2} = 16

So the answer is a pound of butter = 16 ounces

The question was:

Estimate the average speed of ketchup that is flowing from the mouth of an upended bottle. Express your answer in miles per year.

(*inches/60sec)(3600s/h)(24h/day)(365.25 days/y)(ft/12 in)(mile/5280 ft)

* using estimates that range from 1 to 3 inches per minute, we obtain an average speed in the range of 8 to 25 miles per year.

.

The question was:

Prove: 0^{0} is undefined.

0^{0}= 0^{(n-n)} where n =/= 0

= 0^{n}/0^{n}

But 0^{n} = 0, and division by zero is undefined.

Here's a classic. The following seems to prove that 1 = 2. Every step seems legitimate, but where does the logic go astray ?

Let a = b.

a + a = a + b

a + a - 2b = b + a - 2b

2a - 2b = a - b

2(a-b) = a - b

2(a-b)/(a-b) = (a - b)/(a-b)

2 = 1.

Since a = b. a-b = 0. So division by zero in the second laststep is not permitted.

Solve for x .

3^{x }+ 3^{-x} = 3.

Let u = 3^{x}

u + 1/u = 3

u^{2} - 3u + 1 = 0.

u = 2.62 or 0.38

x = 0.88 or -0.88

The difference between a yard and a meter is about 3.37 inches.But if you are getting a cubic metre of cement as opposed to a cubic yard, how much more cement are you getting? Express your answer as a percent.

A cubic metre is about 39.37^3 = 61 023 cubic inches. A cubicyard is 36^3 = 46 656 cubic inches, a difference of 14 367 or about 31%.Those 3 inches make the cubic metre 31 % bigger than a cubic yard. Many amateur and some professional construction workers have learned this the hard way.

Your friend tells you that after a 14% tax on the original cost and after a 15% tip, also based on the original tab, he paid $20 for a meal. What was the menu price?

$20 is 129% of the original price, x. Thus x = 20/1.29 = $15.50

Given 19 hockey players , of which only 2 can play in nets, only 5 on defense and the rest only as forwards, how many possible lineups does a coach have to choose from? ( A lineup consists of a goalie, two defenceman, and three forwards; each forward is adaptable to either wingor center, and each defenceman can play either defensive wing)

12 X 11 X 10 X 5 X 4 X 2 = 52 800 lineups, enough to outlast their playing careers.

An elephant outlives a mouse by 73.5 years. But if life was measured in heartbeats, we'd have to say that a mouse lives as long as an elephant. This is because a mouse's heart beats 50 times faster than an elephant's. How long, then, does a mouse live?

The mouse lives 1.5 years.

- 50rx =r(x + 73.5) where r = mouse's heart rate.
- and x = mouse's lifespan.
- 50x = x + 73.5
- x = 1.5

If log x is the average of log Y and log Z, and Y >Z, how are Y and Z related to x?

log x = (log Y + log Z)/2

2 log x = log Y + log Z

log x^{2} = log Y + log Z

log x^{2} = log YZ

x^{2} = YZ,

so x^{2} = (ax)(x/a)

Y is some multiple of x

And Z is x divided by that same multiple.

(Think of 100, 1000 and 10 000.)

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