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#1 Help Me ! » Dots and toothpicks » Yesterday 15:22:01

mathgogocart
Replies: 2

We connect dots with toothpicks in a grid as shown below. For example, the grid below has 7 horizontal toothpicks in each row and 5 vertical toothpicks in each column.
3e647e404aae07454e84e5e36b2f00ba2f4ba047.png
(a) Suppose we instead have a grid of dots that requires 10 horizontal toothpicks in each row and 20 vertical ones in each column. Then, how many total toothpicks will we need? Also, how many total dots are there?
Me: What I tried to do was find a pattern:
a 2 x 2 square has 12 toothpicks. 4 of the "sides" are shared and 8 are not shared. A 1 vert x 2 horiz  has 1 shared side and 6 n.s sides(7). A 3 x 3 square has 8 shared sides and 12 unshared sides. 20. I gave up after this
(b) Can you generalize your answer? Suppose we have a grid that requires $h$ horizontal toothpicks in each row and $v$ vertical toothpicks in each column. Then, how many total toothpicks will we need? Also, how many total dots are there?
???? I have no clue on how to start this?

#2 Re: Exercises » Quickies #4, Mathematics. » 2016-06-12 22:34:40

clarification: Slime guy starts the fight.

#3 Re: Help Me ! » Probability and Geometry Unit HW help » 2016-06-12 04:08:44

bobbym wrote:

Hi;

Bobbym, can you explain why it is 9/9

There are 9 total balls and you can pick anyone of the 9 first so 9 / 9. Once you have picked anyone of them there are only 2 left of that color.

Hey bobbym, how did you find the 3 exponents that add up to 400? Guess and check?

A simple program would have been fastest but I used generating functions instead. This will seem like overkill but it is more in keeping with the Teakettle Principle.

Bobbym, my teacher said not to use a computer on the powers problem. Is there a reasonably easy and simple way?

#4 Re: Help Me ! » Probability and Geometry Unit HW help » 2016-06-11 00:33:25

Bobbym, can you explain why it is 9/9 for the first question?

bobbym wrote:

Hi;

Hey bobbym, how did you find the 3 exponents that add up to 400? Guess and check?

#5 Help Me ! » Probability and Geometry Unit HW help » 2016-06-10 10:44:04

mathgogocart
Replies: 8

1. A bag contains 3 red marbles, 3 blue marbles, and 3 yellow marbles. 2 marbles are chosen randomly WITHOUT replacement. Find the probablity that both marbles chosen ARE the SAME color.

Reasoning: 3/9 * 2/8 = 6/72 = 1/12.

2. What is the area of a isosceles right triangle with a hypotenuse of 20 inches?

Reasoning: 1:1:√2
so
20/√2 * 20/√2 = 400/2 = 200/2 = 100/2 = 50
^ 1/2BH

3. If 400 were to be expressed as a sum of AT LEAST 2 distinct powers of two, what would be the least possible sum of the powers? i.e, 2^2 + 2^3 = 12, 2+3 =5.
Reasoning: Have no idea on how to approach effectively. tried for 20 mins and found nothing.

4. How many positive 5 digit numbers have 123 AS A BLOCK. 2 such numbers are 12399 and 91239
I said 300

5. If (4^5)(5^13) is written as a integer, how many digits are in it?
Reasoning: 12?

#6 Re: Exercises » Quickies #4, Mathematics. » 2016-06-09 22:51:59

bobbym wrote:

Hi;

We are almost ready to solve this:

5. Agnishom is stuck in a stone dungeon in where he fights a slime. Agnishom has 10 health points. He has a 40% chance to deal 1 damage, a 20% chance to deal 2 damage, and 20% chance to do nothing. The slime deals 2 damage when Agnishom does nothing. What is the chance that Agnishom kills the slime without getting killed?

40% + 20%+ 20% = 80%

What happens the remaining 20% ?

Perhaps you would like to change the percentages to 40%, 30% and 30%.

Change it to what you say.

#7 Re: Help Me ! » Line + Geometry probability » 2016-06-09 07:56:03

Hi, can anyone find a anwser to my next one?
In a scale drawing, 1 inch represents 100  feet.  How many square inches on the diagram represent 1 square foot?

#8 Re: Help Me ! » Line + Geometry probability » 2016-06-08 22:29:42

thickhead wrote:

It is 2 even in 3D. If the line M has direction only one. smile

big_smile cool. I am also interested in 4 dimensions

#10 Help Me ! » Line + Geometry probability » 2016-06-08 11:49:59

mathgogocart
Replies: 6

1) P is a point that is not on line m. How many lines can be drawn through P that makes a 30 degree angle with m?
I said 2 because you can draw two ..
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#11 Help Me ! » Simple question » 2016-06-07 13:39:47

mathgogocart
Replies: 3

1) Just a little nagging problem in the back of my head.
To turn the equation y=2x+1 into y=-2x+1, what would you do?
I said flip it over the y axis? true?

#12 Re: Exercises » Quickies #4, Mathematics. » 2016-06-07 12:00:33

sorry for misunderstandings bobbym

#13 Re: Exercises » Quickies #4, Mathematics. » 2016-06-07 08:01:10

bobbym wrote:

however h h h h h would be 2 pairs.

2 pairs? How do you get that?

because there are only two COMPLETE pairs of h.

#14 Re: Puzzles and Games » Card Game Recommendation » 2016-06-06 22:12:04

Well bobbym there are fish that rest using 3 fins. Not legs but interesting.
Tripod_fish1.jpg

#15 Re: Help Me ! » Probability problems(review!) » 2016-06-06 22:07:43

bobbym wrote:

I am a bumpkin, I  am from Bumpkinland.  I now live in Florida.

I thought it was in Vegas. Anyhow I live in Michigan.

#16 Re: Exercises » Quickies #4, Mathematics. » 2016-06-06 22:02:50

bobbym wrote:

You are adding increasing large powers of 2 with some small numbers. There can be no convergence because the terms of this series do not get smaller.

I also will need a bit more to solve #3. I can make assumptions but they may not be what you want.

For instance, supposing we get this for 10 coin flips:

H, T, T, H, H, H, H, T, H, T

That H, H, H, H, do you call it 3 groups of H, H and add 30?

Yes and I knew it would not converge.
however h h h h h would be 2 pairs.

#17 Re: Help Me ! » Probability problems(review!) » 2016-06-06 14:03:01

bobbym wrote:

How far north of me do you live?

since you live in bumpkinland obviously ∞ miles.

#18 Re: Help Me ! » Geometry Proof » 2016-06-06 14:01:58

I haven't had time to work on this, but..
5e95ff0f346c35f3a6cc9ae53d6ce2dc585bb21e.png is the photo.

#19 Re: Exercises » Quickies #3 Assorted Math » 2016-06-06 13:29:49

bobbym wrote:

Hi;

May I ask whom is giving you these problems?

I make them, bobbym.

#21 Exercises » Quickies #4, Mathematics. » 2016-06-06 09:24:07

mathgogocart
Replies: 21

1. If x and y are real numbers,and x^2 = (y^2-x^2), find all possible values of x and y.

2. What is 2^2 + 2^-3 + 2^4 + 2^-5........
3. Bobbym is stranded on a desert island. To cure his boredom, he plays the game of Bobbymcoin. He flips a fair coin 10 times.
He gets 2 points for every head and -2 points for every tail. However, he gets +10 points for 1 PAIR of heads. What is bobbym's average score?
4. 1/2 + 1/3 + 1/4 + 1/5..... =
5. Agnishom is stuck in a stone dungeon in where he fights a slime. Agnishom has 10 health points. He has a 40% chance to deal 1 damage, a 20% chance to deal 2 damage, and 20% chance to do nothing. The slime deals 2 damage when Agnishom does nothing. What is the chance that Agnishom kills the slime without getting killed?
6. f(x) = 2x^2-log(2x^2). What is f(1)-f(2)+f(3)-f(4)..... If it diverges, r\write DIVE as your answer.

#23 Re: Help Me ! » Probability problems(review!) » 2016-06-05 22:30:54

bobbym wrote:

Hi;

1.A bag contains 3 red marbles, 3 blues, and 3 yellows. 2 marbles are going to be drawn WITHOUT replacement. What is the chance the both marbles drawn are the same color?

thanks.

#24 Re: Exercises » Quickies #3 Assorted Math » 2016-06-05 12:24:51

bobbym wrote:

Hi;

Is there something you left out for 1)?

Is it incomplete?

#25 Exercises » Quickies #3 Assorted Math » 2016-06-05 08:02:27

mathgogocart
Replies: 32

1) if x-(yz)=100, find the maximum value of x^3-y^2+z^2.

2) Find the product of ALL the numbers in this grid.
061d7fd7208adb35149f52ef57990e317d73f23f.png

3) if ab = 100 and a^2 + b^2 = 200, find (a+b)^2.

4) How many computer pixels are required to cover a 9 meter radius sphere?

5) A man is driving his car at a constant speed of 36 km/hour. He gets shocked by seeing a boy standing on the road in front of his way and in order to save him starts applying brakes. The car decelerates at the rate of 5/6 m/s^2 and he stops right in front of the boy after 14 seconds. what was his reaction time (in seconds)?

6) The escape velocity of Earth and Bobbymland are 11. 2 km/h and 20 km/h, respectively.  The mass of bobbymland is 20000 kg.  What is the ratio of Earth's radius  to Bobbymland's radius?

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